%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:01:10 PM UTC 2026
% Result : Theorem 237.80s 238.09s
% Output : Proof 238.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 6 01:07:09 UTC 2026
% 0.13/0.36 % CPUTime :
% 237.80/238.09 % SZS status Theorem
% 237.80/238.09 % SZS output start Proof
% 237.80/238.09 tff(tptp_fun_X17_0_type, type, (
% 237.80/238.09 tptp_fun_X17_0: $i)).
% 237.80/238.09 tff(tptp_fun_______type, type, (
% 237.80/238.09 tptp_fun______: ( $i * $i ) > $i)).
% 237.80/238.09 tff(tptp_fun__1__type, type, (
% 237.80/238.09 tptp_fun__1_: $i)).
% 237.80/238.09 tff(tptp_fun______type, type, (
% 237.80/238.09 tptp_fun_____: ( $i * $i ) > $o)).
% 237.80/238.09 tff(tptp_fun_____type, type, (
% 237.80/238.09 tptp_fun____: ( $i * $i ) > $i)).
% 237.80/238.09 tff(tptp_fun__0__type, type, (
% 237.80/238.09 tptp_fun__0_: $i)).
% 237.80/238.09 tff(1,plain,
% 237.80/238.09 (^[A: $i] : refl((tptp_fun____(A, |'0'|) = A) <=> (tptp_fun____(A, |'0'|) = A))),
% 237.80/238.09 inference(bind,[status(th)],[])).
% 237.80/238.09 tff(2,plain,
% 237.80/238.09 (![A: $i] : (tptp_fun____(A, |'0'|) = A) <=> ![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 237.80/238.09 inference(quant_intro,[status(thm)],[1])).
% 237.80/238.09 tff(3,plain,
% 237.80/238.09 (![A: $i] : (tptp_fun____(A, |'0'|) = A) <=> ![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 237.80/238.09 inference(rewrite,[status(thm)],[])).
% 237.80/238.09 tff(4,axiom,(![A: $i] : (tptp_fun____(A, |'0'|) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_03')).
% 237.80/238.09 tff(5,plain,
% 237.80/238.09 (![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[4, 3])).
% 237.80/238.09 tff(6,plain,(
% 237.80/238.09 ![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 237.80/238.09 inference(skolemize,[status(sab)],[5])).
% 237.80/238.09 tff(7,plain,
% 237.80/238.09 (![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[6, 2])).
% 237.80/238.09 tff(8,plain,
% 237.80/238.09 ((~![A: $i] : (tptp_fun____(A, |'0'|) = A)) | (tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|) = tptp_fun______(X17!0, |'1'|))),
% 237.80/238.09 inference(quant_inst,[status(thm)],[])).
% 237.80/238.09 tff(9,plain,
% 237.80/238.09 (tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|) = tptp_fun______(X17!0, |'1'|)),
% 237.80/238.09 inference(unit_resolution,[status(thm)],[8, 7])).
% 237.80/238.09 tff(10,plain,
% 237.80/238.09 (tptp_fun______(tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|), X17!0) = tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)),
% 237.80/238.09 inference(monotonicity,[status(thm)],[9])).
% 237.80/238.09 tff(11,plain,
% 237.80/238.09 (^[A: $i, B: $i] : refl((tptp_fun____(A, B) = tptp_fun____(B, A)) <=> (tptp_fun____(A, B) = tptp_fun____(B, A)))),
% 237.80/238.09 inference(bind,[status(th)],[])).
% 237.80/238.09 tff(12,plain,
% 237.80/238.09 (![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A)) <=> ![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 237.80/238.09 inference(quant_intro,[status(thm)],[11])).
% 237.80/238.09 tff(13,plain,
% 237.80/238.09 (![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A)) <=> ![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 237.80/238.09 inference(rewrite,[status(thm)],[])).
% 237.80/238.09 tff(14,axiom,(![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_02')).
% 237.80/238.09 tff(15,plain,
% 237.80/238.09 (![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[14, 13])).
% 237.80/238.09 tff(16,plain,(
% 237.80/238.09 ![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 237.80/238.09 inference(skolemize,[status(sab)],[15])).
% 237.80/238.09 tff(17,plain,
% 237.80/238.09 (![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[16, 12])).
% 237.80/238.09 tff(18,plain,
% 237.80/238.09 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.09 inference(quant_inst,[status(thm)],[])).
% 237.80/238.09 tff(19,plain,
% 237.80/238.09 (tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))),
% 237.80/238.09 inference(unit_resolution,[status(thm)],[18, 17])).
% 237.80/238.09 tff(20,plain,
% 237.80/238.09 (tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|)),
% 237.80/238.09 inference(symmetry,[status(thm)],[19])).
% 237.80/238.09 tff(21,plain,
% 237.80/238.09 (tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)) = tptp_fun______(X17!0, |'1'|)),
% 237.80/238.09 inference(transitivity,[status(thm)],[20, 9])).
% 237.80/238.09 tff(22,plain,
% 237.80/238.09 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) <=> tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.80/238.09 inference(monotonicity,[status(thm)],[21])).
% 237.80/238.09 tff(23,plain,
% 237.80/238.09 (tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) <=> tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.80/238.09 inference(symmetry,[status(thm)],[22])).
% 237.80/238.09 tff(24,plain,
% 237.80/238.09 (^[X5: $i, X6: $i, X7: $i] : refl((tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7))) <=> (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7))))),
% 237.80/238.09 inference(bind,[status(th)],[])).
% 237.80/238.09 tff(25,plain,
% 237.80/238.09 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7))) <=> ![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 237.80/238.09 inference(quant_intro,[status(thm)],[24])).
% 237.80/238.09 tff(26,plain,
% 237.80/238.09 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7))) <=> ![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 237.80/238.09 inference(rewrite,[status(thm)],[])).
% 237.80/238.09 tff(27,axiom,(![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_07')).
% 237.80/238.09 tff(28,plain,
% 237.80/238.09 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[27, 26])).
% 237.80/238.09 tff(29,plain,(
% 237.80/238.09 ![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 237.80/238.09 inference(skolemize,[status(sab)],[28])).
% 237.80/238.09 tff(30,plain,
% 237.80/238.09 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[29, 25])).
% 237.80/238.09 tff(31,plain,
% 237.80/238.09 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))))),
% 237.80/238.09 inference(quant_inst,[status(thm)],[])).
% 237.80/238.09 tff(32,plain,
% 237.80/238.09 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.80/238.09 inference(unit_resolution,[status(thm)],[31, 30])).
% 237.80/238.09 tff(33,plain,
% 237.80/238.09 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.80/238.09 inference(quant_inst,[status(thm)],[])).
% 237.80/238.09 tff(34,plain,
% 237.80/238.09 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.80/238.09 inference(unit_resolution,[status(thm)],[33, 17])).
% 237.80/238.09 tff(35,plain,
% 237.80/238.09 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.80/238.09 inference(monotonicity,[status(thm)],[34])).
% 237.80/238.09 tff(36,plain,
% 237.80/238.09 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.80/238.09 inference(symmetry,[status(thm)],[35])).
% 237.80/238.09 tff(37,assumption,(~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))), introduced(assumption)).
% 237.80/238.09 tff(38,plain,
% 237.80/238.09 (^[A: $i] : refl(tptp_fun_____(A, A) <=> tptp_fun_____(A, A))),
% 237.80/238.09 inference(bind,[status(th)],[])).
% 237.80/238.09 tff(39,plain,
% 237.80/238.09 (![A: $i] : tptp_fun_____(A, A) <=> ![A: $i] : tptp_fun_____(A, A)),
% 237.80/238.09 inference(quant_intro,[status(thm)],[38])).
% 237.80/238.09 tff(40,plain,
% 237.80/238.09 (![A: $i] : tptp_fun_____(A, A) <=> ![A: $i] : tptp_fun_____(A, A)),
% 237.80/238.09 inference(rewrite,[status(thm)],[])).
% 237.80/238.09 tff(41,axiom,(![A: $i] : tptp_fun_____(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_04')).
% 237.80/238.09 tff(42,plain,
% 237.80/238.09 (![A: $i] : tptp_fun_____(A, A)),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[41, 40])).
% 237.80/238.09 tff(43,plain,(
% 237.80/238.09 ![A: $i] : tptp_fun_____(A, A)),
% 237.80/238.09 inference(skolemize,[status(sab)],[42])).
% 237.80/238.09 tff(44,plain,
% 237.80/238.09 (![A: $i] : tptp_fun_____(A, A)),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[43, 39])).
% 237.80/238.09 tff(45,plain,
% 237.80/238.09 ((~![A: $i] : tptp_fun_____(A, A)) | tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))),
% 237.80/238.09 inference(quant_inst,[status(thm)],[])).
% 237.80/238.09 tff(46,plain,
% 237.80/238.09 ($false),
% 237.80/238.09 inference(unit_resolution,[status(thm)],[45, 44, 37])).
% 237.80/238.09 tff(47,plain,(tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))), inference(lemma,lemma(discharge,[]))).
% 237.80/238.09 tff(48,plain,
% 237.80/238.09 (^[X8: $i, X9: $i, X10: $i] : refl(((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10))) <=> ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10))))),
% 237.80/238.09 inference(bind,[status(th)],[])).
% 237.80/238.09 tff(49,plain,
% 237.80/238.09 (![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10))) <=> ![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 237.80/238.09 inference(quant_intro,[status(thm)],[48])).
% 237.80/238.09 tff(50,plain,
% 237.80/238.09 (![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10))) <=> ![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 237.80/238.09 inference(rewrite,[status(thm)],[])).
% 237.80/238.09 tff(51,plain,
% 237.80/238.09 (^[X8: $i, X9: $i, X10: $i] : rewrite((tptp_fun_____(X8, X9) => tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10))) <=> ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10))))),
% 237.80/238.09 inference(bind,[status(th)],[])).
% 237.80/238.09 tff(52,plain,
% 237.80/238.09 (![X8: $i, X9: $i, X10: $i] : (tptp_fun_____(X8, X9) => tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10))) <=> ![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 237.80/238.09 inference(quant_intro,[status(thm)],[51])).
% 237.80/238.09 tff(53,axiom,(![X8: $i, X9: $i, X10: $i] : (tptp_fun_____(X8, X9) => tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_09')).
% 237.80/238.09 tff(54,plain,
% 237.80/238.09 (![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[53, 52])).
% 237.80/238.09 tff(55,plain,
% 237.80/238.09 (![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[54, 50])).
% 237.80/238.09 tff(56,plain,(
% 237.80/238.09 ![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 237.80/238.09 inference(skolemize,[status(sab)],[55])).
% 237.80/238.09 tff(57,plain,
% 237.80/238.09 (![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[56, 49])).
% 237.80/238.09 tff(58,plain,
% 237.80/238.09 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) <=> ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.80/238.09 inference(rewrite,[status(thm)],[])).
% 237.80/238.09 tff(59,plain,
% 237.80/238.09 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.80/238.09 inference(quant_inst,[status(thm)],[])).
% 237.80/238.09 tff(60,plain,
% 237.80/238.09 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[59, 58])).
% 237.80/238.09 tff(61,plain,
% 237.80/238.09 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.80/238.09 inference(unit_resolution,[status(thm)],[60, 57, 47])).
% 237.80/238.09 tff(62,plain,
% 237.80/238.09 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.80/238.09 inference(modus_ponens,[status(thm)],[61, 36])).
% 237.80/238.09 tff(63,plain,
% 237.80/238.09 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.80/238.09 inference(tautology,[status(thm)],[])).
% 237.80/238.09 tff(64,plain,
% 237.80/238.09 (tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.80/238.09 inference(unit_resolution,[status(thm)],[63, 62, 32])).
% 237.80/238.10 tff(65,plain,
% 237.80/238.10 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[64, 23])).
% 237.80/238.10 tff(66,plain,
% 237.80/238.10 (tptp_fun______(X17!0, |'1'|) = tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|)),
% 237.80/238.10 inference(symmetry,[status(thm)],[9])).
% 237.80/238.10 tff(67,plain,
% 237.80/238.10 (tptp_fun______(X17!0, |'1'|) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))),
% 237.80/238.10 inference(transitivity,[status(thm)],[66, 19])).
% 237.80/238.10 tff(68,plain,
% 237.80/238.10 (tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))),
% 237.80/238.10 inference(symmetry,[status(thm)],[34])).
% 237.80/238.10 tff(69,plain,
% 237.80/238.10 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.10 inference(monotonicity,[status(thm)],[68, 67])).
% 237.80/238.10 tff(70,plain,
% 237.80/238.10 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))) <=> tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(X17!0, |'1'|))),
% 237.80/238.10 inference(symmetry,[status(thm)],[69])).
% 237.80/238.10 tff(71,plain,
% 237.80/238.10 (^[A: $i] : refl(tptp_fun_____(A, |'0'|) <=> tptp_fun_____(A, |'0'|))),
% 237.80/238.10 inference(bind,[status(th)],[])).
% 237.80/238.10 tff(72,plain,
% 237.80/238.10 (![A: $i] : tptp_fun_____(A, |'0'|) <=> ![A: $i] : tptp_fun_____(A, |'0'|)),
% 237.80/238.10 inference(quant_intro,[status(thm)],[71])).
% 237.80/238.10 tff(73,plain,
% 237.80/238.10 (![A: $i] : tptp_fun_____(A, |'0'|) <=> ![A: $i] : tptp_fun_____(A, |'0'|)),
% 237.80/238.10 inference(rewrite,[status(thm)],[])).
% 237.80/238.10 tff(74,axiom,(![A: $i] : tptp_fun_____(A, |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_08')).
% 237.80/238.10 tff(75,plain,
% 237.80/238.10 (![A: $i] : tptp_fun_____(A, |'0'|)),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[74, 73])).
% 237.80/238.10 tff(76,plain,(
% 237.80/238.10 ![A: $i] : tptp_fun_____(A, |'0'|)),
% 237.80/238.10 inference(skolemize,[status(sab)],[75])).
% 237.80/238.10 tff(77,plain,
% 237.80/238.10 (![A: $i] : tptp_fun_____(A, |'0'|)),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[76, 72])).
% 237.80/238.10 tff(78,plain,
% 237.80/238.10 ((~![A: $i] : tptp_fun_____(A, |'0'|)) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)),
% 237.80/238.10 inference(quant_inst,[status(thm)],[])).
% 237.80/238.10 tff(79,plain,
% 237.80/238.10 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)),
% 237.80/238.10 inference(unit_resolution,[status(thm)],[78, 77])).
% 237.80/238.10 tff(80,plain,
% 237.80/238.10 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))))) <=> ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.10 inference(rewrite,[status(thm)],[])).
% 237.80/238.10 tff(81,plain,
% 237.80/238.10 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.10 inference(quant_inst,[status(thm)],[])).
% 237.80/238.10 tff(82,plain,
% 237.80/238.10 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[81, 80])).
% 237.80/238.10 tff(83,plain,
% 237.80/238.10 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.10 inference(unit_resolution,[status(thm)],[82, 57, 79])).
% 237.80/238.10 tff(84,plain,
% 237.80/238.10 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(X17!0, |'1'|))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[83, 70])).
% 237.80/238.10 tff(85,plain,
% 237.80/238.10 (^[X14: $i, X15: $i, X16: $i] : refl(((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15))) <=> ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15))))),
% 237.80/238.10 inference(bind,[status(th)],[])).
% 237.80/238.10 tff(86,plain,
% 237.80/238.10 (![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15))) <=> ![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 237.80/238.10 inference(quant_intro,[status(thm)],[85])).
% 237.80/238.10 tff(87,plain,
% 237.80/238.10 (![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15))) <=> ![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 237.80/238.10 inference(rewrite,[status(thm)],[])).
% 237.80/238.10 tff(88,plain,
% 237.80/238.10 (^[X14: $i, X15: $i, X16: $i] : rewrite((tptp_fun_____(X14, X15) => tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15))) <=> ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15))))),
% 237.80/238.10 inference(bind,[status(th)],[])).
% 237.80/238.10 tff(89,plain,
% 237.80/238.10 (![X14: $i, X15: $i, X16: $i] : (tptp_fun_____(X14, X15) => tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15))) <=> ![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 237.80/238.10 inference(quant_intro,[status(thm)],[88])).
% 237.80/238.10 tff(90,axiom,(![X14: $i, X15: $i, X16: $i] : (tptp_fun_____(X14, X15) => tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_11')).
% 237.80/238.10 tff(91,plain,
% 237.80/238.10 (![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[90, 89])).
% 237.80/238.10 tff(92,plain,
% 237.80/238.10 (![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[91, 87])).
% 237.80/238.10 tff(93,plain,(
% 237.80/238.10 ![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 237.80/238.10 inference(skolemize,[status(sab)],[92])).
% 237.80/238.10 tff(94,plain,
% 237.80/238.10 (![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[93, 86])).
% 237.80/238.10 tff(95,plain,
% 237.80/238.10 (((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) <=> ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.10 inference(rewrite,[status(thm)],[])).
% 237.80/238.10 tff(96,plain,
% 237.80/238.10 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.10 inference(quant_inst,[status(thm)],[])).
% 237.80/238.10 tff(97,plain,
% 237.80/238.10 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[96, 95])).
% 237.80/238.10 tff(98,plain,
% 237.80/238.10 ((~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.10 inference(unit_resolution,[status(thm)],[97, 94])).
% 237.80/238.10 tff(99,plain,
% 237.80/238.10 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.10 inference(unit_resolution,[status(thm)],[98, 84])).
% 237.80/238.10 tff(100,plain,
% 237.80/238.10 (![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2))) <=> ![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))),
% 237.80/238.10 inference(rewrite,[status(thm)],[])).
% 237.80/238.10 tff(101,plain,
% 237.80/238.10 (^[X0: $i, X1: $i, X2: $i] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2)) <=> (~((~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2))))), ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) <=> (~(~((~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2))))))), rewrite((~(~((~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2))))) <=> ((~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))), ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) <=> ((~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2))))), (((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2)) <=> (((~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2)))), rewrite((((~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2)) <=> (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))), (((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2)) <=> (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))))),
% 237.80/238.10 inference(bind,[status(th)],[])).
% 237.80/238.10 tff(102,plain,
% 237.80/238.10 (![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2)) <=> ![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))),
% 237.80/238.10 inference(quant_intro,[status(thm)],[101])).
% 237.80/238.10 tff(103,plain,
% 237.80/238.10 (![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2)) <=> ![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2))),
% 237.80/238.10 inference(rewrite,[status(thm)],[])).
% 237.80/238.10 tff(104,plain,
% 237.80/238.10 (^[X0: $i, X1: $i, X2: $i] : rewrite(((tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2)) => tptp_fun_____(X0, X2)) <=> ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2)))),
% 237.80/238.10 inference(bind,[status(th)],[])).
% 237.80/238.10 tff(105,plain,
% 237.80/238.10 (![X0: $i, X1: $i, X2: $i] : ((tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2)) => tptp_fun_____(X0, X2)) <=> ![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2))),
% 237.80/238.10 inference(quant_intro,[status(thm)],[104])).
% 237.80/238.10 tff(106,axiom,(![X0: $i, X1: $i, X2: $i] : ((tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2)) => tptp_fun_____(X0, X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_05')).
% 237.80/238.10 tff(107,plain,
% 237.80/238.10 (![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[106, 105])).
% 237.80/238.10 tff(108,plain,
% 237.80/238.10 (![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[107, 103])).
% 237.80/238.10 tff(109,plain,(
% 237.80/238.10 ![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2))),
% 237.80/238.10 inference(skolemize,[status(sab)],[108])).
% 237.80/238.10 tff(110,plain,
% 237.80/238.10 (![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[109, 102])).
% 237.80/238.10 tff(111,plain,
% 237.80/238.10 (![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))),
% 237.80/238.10 inference(modus_ponens,[status(thm)],[110, 100])).
% 237.80/238.10 tff(112,plain,
% 237.80/238.10 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.80/238.10 inference(rewrite,[status(thm)],[])).
% 237.80/238.10 tff(113,plain,
% 237.80/238.10 ((tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) <=> ((~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.80/238.11 inference(rewrite,[status(thm)],[])).
% 237.80/238.11 tff(114,plain,
% 237.80/238.11 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))))),
% 237.80/238.11 inference(monotonicity,[status(thm)],[113])).
% 237.80/238.11 tff(115,plain,
% 237.80/238.11 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.80/238.11 inference(transitivity,[status(thm)],[114, 112])).
% 237.80/238.11 tff(116,plain,
% 237.80/238.11 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.80/238.11 inference(quant_inst,[status(thm)],[])).
% 237.80/238.11 tff(117,plain,
% 237.80/238.11 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.11 inference(modus_ponens,[status(thm)],[116, 115])).
% 237.80/238.11 tff(118,plain,
% 237.80/238.11 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.11 inference(unit_resolution,[status(thm)],[117, 111, 99, 65])).
% 237.80/238.11 tff(119,plain,
% 237.80/238.11 ((~![A: $i] : (tptp_fun____(A, |'0'|) = A)) | (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|) = tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.11 inference(quant_inst,[status(thm)],[])).
% 237.80/238.11 tff(120,plain,
% 237.80/238.11 (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|) = tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))),
% 237.80/238.11 inference(unit_resolution,[status(thm)],[119, 7])).
% 237.80/238.11 tff(121,plain,
% 237.80/238.11 (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)),
% 237.80/238.11 inference(symmetry,[status(thm)],[120])).
% 237.80/238.11 tff(122,plain,
% 237.80/238.11 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|))),
% 237.80/238.11 inference(monotonicity,[status(thm)],[121, 20])).
% 237.80/238.11 tff(123,plain,
% 237.80/238.11 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.11 inference(symmetry,[status(thm)],[122])).
% 237.80/238.11 tff(124,plain,
% 237.80/238.11 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(X17!0, |'1'|))),
% 237.80/238.11 inference(monotonicity,[status(thm)],[121])).
% 237.80/238.11 tff(125,plain,
% 237.80/238.11 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))),
% 237.80/238.11 inference(symmetry,[status(thm)],[124])).
% 237.80/238.11 tff(126,plain,
% 237.80/238.11 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.11 inference(quant_inst,[status(thm)],[])).
% 237.80/238.11 tff(127,plain,
% 237.80/238.11 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.11 inference(unit_resolution,[status(thm)],[126, 30])).
% 237.80/238.11 tff(128,plain,
% 237.80/238.11 (^[A: $i] : refl((tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|) <=> (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|))),
% 237.80/238.11 inference(bind,[status(th)],[])).
% 237.80/238.11 tff(129,plain,
% 237.80/238.11 (![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|) <=> ![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|)),
% 237.80/238.11 inference(quant_intro,[status(thm)],[128])).
% 237.80/238.11 tff(130,plain,
% 237.80/238.11 (![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|) <=> ![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|)),
% 237.80/238.11 inference(rewrite,[status(thm)],[])).
% 237.80/238.11 tff(131,axiom,(![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_13')).
% 237.80/238.11 tff(132,plain,
% 237.80/238.11 (![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|)),
% 237.80/238.11 inference(modus_ponens,[status(thm)],[131, 130])).
% 237.80/238.11 tff(133,plain,(
% 237.80/238.11 ![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|)),
% 237.80/238.11 inference(skolemize,[status(sab)],[132])).
% 237.80/238.11 tff(134,plain,
% 237.80/238.11 (![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|)),
% 237.80/238.11 inference(modus_ponens,[status(thm)],[133, 129])).
% 237.80/238.11 tff(135,plain,
% 237.80/238.11 ((~![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|)) | (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0) = |'0'|)),
% 237.80/238.11 inference(quant_inst,[status(thm)],[])).
% 237.80/238.11 tff(136,plain,
% 237.80/238.11 (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0) = |'0'|),
% 237.80/238.11 inference(unit_resolution,[status(thm)],[135, 134])).
% 237.80/238.11 tff(137,plain,
% 237.80/238.11 (|'0'| = tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)),
% 237.80/238.11 inference(symmetry,[status(thm)],[136])).
% 237.80/238.11 tff(138,plain,
% 237.80/238.11 ((~![A: $i] : (tptp_fun______(tptp_fun______(tptp_fun______(A, |'1'|), A), A) = |'0'|)) | (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|)) = |'0'|)),
% 237.80/238.11 inference(quant_inst,[status(thm)],[])).
% 237.80/238.11 tff(139,plain,
% 237.80/238.11 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|)) = |'0'|),
% 237.80/238.11 inference(unit_resolution,[status(thm)],[138, 134])).
% 237.80/238.11 tff(140,plain,
% 237.80/238.11 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|)) = tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)),
% 237.80/238.11 inference(transitivity,[status(thm)],[139, 137])).
% 237.80/238.11 tff(141,plain,
% 237.80/238.11 (tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) <=> tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))),
% 237.80/238.11 inference(monotonicity,[status(thm)],[137, 140])).
% 237.80/238.11 tff(142,plain,
% 237.80/238.11 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.11 inference(symmetry,[status(thm)],[141])).
% 237.80/238.11 tff(143,plain,
% 237.80/238.11 (^[X11: $i, X12: $i, X13: $i] : refl(((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13))) <=> ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13))))),
% 237.80/238.11 inference(bind,[status(th)],[])).
% 237.80/238.11 tff(144,plain,
% 237.80/238.11 (![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13))) <=> ![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 237.80/238.11 inference(quant_intro,[status(thm)],[143])).
% 237.80/238.11 tff(145,plain,
% 237.80/238.11 (![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13))) <=> ![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 237.80/238.11 inference(rewrite,[status(thm)],[])).
% 237.80/238.11 tff(146,plain,
% 237.80/238.11 (^[X11: $i, X12: $i, X13: $i] : rewrite((tptp_fun_____(X11, X12) => tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13))) <=> ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13))))),
% 237.80/238.11 inference(bind,[status(th)],[])).
% 237.80/238.11 tff(147,plain,
% 237.80/238.11 (![X11: $i, X12: $i, X13: $i] : (tptp_fun_____(X11, X12) => tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13))) <=> ![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 237.80/238.11 inference(quant_intro,[status(thm)],[146])).
% 237.80/238.11 tff(148,axiom,(![X11: $i, X12: $i, X13: $i] : (tptp_fun_____(X11, X12) => tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_10')).
% 237.80/238.11 tff(149,plain,
% 237.80/238.11 (![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 237.80/238.11 inference(modus_ponens,[status(thm)],[148, 147])).
% 237.80/238.11 tff(150,plain,
% 237.80/238.11 (![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 237.80/238.11 inference(modus_ponens,[status(thm)],[149, 145])).
% 237.80/238.11 tff(151,plain,(
% 237.80/238.11 ![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 237.80/238.11 inference(skolemize,[status(sab)],[150])).
% 237.80/238.11 tff(152,plain,
% 237.80/238.11 (![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 237.80/238.11 inference(modus_ponens,[status(thm)],[151, 144])).
% 237.80/238.11 tff(153,plain,
% 237.80/238.11 (((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) <=> ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.80/238.12 inference(rewrite,[status(thm)],[])).
% 237.80/238.12 tff(154,plain,
% 237.80/238.12 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.80/238.12 inference(quant_inst,[status(thm)],[])).
% 237.80/238.12 tff(155,plain,
% 237.80/238.12 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[154, 153])).
% 237.80/238.12 tff(156,plain,
% 237.80/238.12 ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.80/238.12 inference(unit_resolution,[status(thm)],[155, 152])).
% 237.80/238.12 tff(157,plain,
% 237.80/238.12 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.80/238.12 inference(unit_resolution,[status(thm)],[156, 47])).
% 237.80/238.12 tff(158,plain,
% 237.80/238.12 (((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))) <=> ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))),
% 237.80/238.12 inference(rewrite,[status(thm)],[])).
% 237.80/238.12 tff(159,plain,
% 237.80/238.12 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))),
% 237.80/238.12 inference(quant_inst,[status(thm)],[])).
% 237.80/238.12 tff(160,plain,
% 237.80/238.12 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[159, 158])).
% 237.80/238.12 tff(161,plain,
% 237.80/238.12 ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))),
% 237.80/238.12 inference(unit_resolution,[status(thm)],[160, 152])).
% 237.80/238.12 tff(162,plain,
% 237.80/238.12 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))),
% 237.80/238.12 inference(unit_resolution,[status(thm)],[161, 157])).
% 237.80/238.12 tff(163,plain,
% 237.80/238.12 (tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[162, 142])).
% 237.80/238.12 tff(164,plain,
% 237.80/238.12 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(X17!0, |'1'|)) | (~tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.12 inference(tautology,[status(thm)],[])).
% 237.80/238.12 tff(165,plain,
% 237.80/238.12 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(X17!0, |'1'|))),
% 237.80/238.12 inference(unit_resolution,[status(thm)],[164, 163, 127])).
% 237.80/238.12 tff(166,plain,
% 237.80/238.12 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[165, 125])).
% 237.80/238.12 tff(167,plain,
% 237.80/238.12 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|)))) <=> ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|)))),
% 237.80/238.12 inference(rewrite,[status(thm)],[])).
% 237.80/238.12 tff(168,plain,
% 237.80/238.12 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|)))),
% 237.80/238.12 inference(quant_inst,[status(thm)],[])).
% 237.80/238.12 tff(169,plain,
% 237.80/238.12 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[168, 167])).
% 237.80/238.12 tff(170,plain,
% 237.80/238.12 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|))),
% 237.80/238.12 inference(unit_resolution,[status(thm)],[169, 57, 166])).
% 237.80/238.12 tff(171,plain,
% 237.80/238.12 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[170, 123])).
% 237.80/238.12 tff(172,plain,
% 237.80/238.12 (![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))) <=> ![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 237.80/238.12 inference(rewrite,[status(thm)],[])).
% 237.80/238.12 tff(173,plain,
% 237.80/238.12 (^[X3: $i, X4: $i] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3)) <=> (~((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))))), ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) <=> (~(~((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))))))), rewrite((~(~((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))))) <=> ((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))), ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) <=> ((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))))), (((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)) <=> (((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))) | (X3 = X4)))), rewrite((((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))) | (X3 = X4)) <=> ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))), (((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)) <=> ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))))),
% 237.80/238.12 inference(bind,[status(th)],[])).
% 237.80/238.12 tff(174,plain,
% 237.80/238.12 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)) <=> ![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 237.80/238.12 inference(quant_intro,[status(thm)],[173])).
% 237.80/238.12 tff(175,plain,
% 237.80/238.12 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)) <=> ![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 237.80/238.12 inference(rewrite,[status(thm)],[])).
% 237.80/238.12 tff(176,plain,
% 237.80/238.12 (^[X3: $i, X4: $i] : rewrite(((tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3)) => (X3 = X4)) <=> ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)))),
% 237.80/238.12 inference(bind,[status(th)],[])).
% 237.80/238.12 tff(177,plain,
% 237.80/238.12 (![X3: $i, X4: $i] : ((tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3)) => (X3 = X4)) <=> ![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 237.80/238.12 inference(quant_intro,[status(thm)],[176])).
% 237.80/238.12 tff(178,axiom,(![X3: $i, X4: $i] : ((tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3)) => (X3 = X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_06')).
% 237.80/238.12 tff(179,plain,
% 237.80/238.12 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[178, 177])).
% 237.80/238.12 tff(180,plain,
% 237.80/238.12 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[179, 175])).
% 237.80/238.12 tff(181,plain,(
% 237.80/238.12 ![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 237.80/238.12 inference(skolemize,[status(sab)],[180])).
% 237.80/238.12 tff(182,plain,
% 237.80/238.12 (![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[181, 174])).
% 237.80/238.12 tff(183,plain,
% 237.80/238.12 (![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 237.80/238.12 inference(modus_ponens,[status(thm)],[182, 172])).
% 237.80/238.12 tff(184,plain,
% 237.80/238.12 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.12 inference(rewrite,[status(thm)],[])).
% 237.80/238.12 tff(185,plain,
% 237.80/238.12 (((tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) <=> ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.12 inference(rewrite,[status(thm)],[])).
% 237.80/238.12 tff(186,plain,
% 237.80/238.12 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))))),
% 237.80/238.12 inference(monotonicity,[status(thm)],[185])).
% 237.80/238.12 tff(187,plain,
% 237.80/238.12 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.12 inference(transitivity,[status(thm)],[186, 184])).
% 237.80/238.12 tff(188,plain,
% 237.80/238.12 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.80/238.13 inference(quant_inst,[status(thm)],[])).
% 237.80/238.13 tff(189,plain,
% 237.80/238.13 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.13 inference(modus_ponens,[status(thm)],[188, 187])).
% 237.80/238.13 tff(190,plain,
% 237.80/238.13 (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[189, 183, 171, 118])).
% 237.80/238.13 tff(191,plain,
% 237.80/238.13 (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|)),
% 237.80/238.13 inference(transitivity,[status(thm)],[190, 20])).
% 237.80/238.13 tff(192,plain,
% 237.80/238.13 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0) = tptp_fun______(tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|), X17!0)),
% 237.80/238.13 inference(monotonicity,[status(thm)],[191])).
% 237.80/238.13 tff(193,plain,
% 237.80/238.13 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0) = tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)),
% 237.80/238.13 inference(transitivity,[status(thm)],[192, 10])).
% 237.80/238.13 tff(194,plain,
% 237.80/238.13 (tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0)) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.80/238.13 inference(monotonicity,[status(thm)],[193])).
% 237.80/238.13 tff(195,plain,
% 237.80/238.13 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0)))),
% 237.80/238.13 inference(quant_inst,[status(thm)],[])).
% 237.80/238.13 tff(196,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0))),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[195, 30])).
% 237.80/238.13 tff(197,plain,
% 237.80/238.13 (tptp_fun____(X17!0, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|))),
% 237.80/238.13 inference(monotonicity,[status(thm)],[121])).
% 237.80/238.13 tff(198,plain,
% 237.80/238.13 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0) = tptp_fun____(X17!0, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.80/238.13 inference(quant_inst,[status(thm)],[])).
% 237.80/238.13 tff(199,plain,
% 237.80/238.13 (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0) = tptp_fun____(X17!0, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[198, 17])).
% 237.80/238.13 tff(200,plain,
% 237.80/238.13 (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0) = tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|))),
% 237.80/238.13 inference(transitivity,[status(thm)],[199, 197])).
% 237.80/238.13 tff(201,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)), X17!0)),
% 237.80/238.13 inference(monotonicity,[status(thm)],[200])).
% 237.80/238.13 tff(202,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)), X17!0) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), X17!0)),
% 237.80/238.13 inference(symmetry,[status(thm)],[201])).
% 237.80/238.13 tff(203,plain,
% 237.80/238.13 ((~![A: $i] : (tptp_fun____(A, |'0'|) = A)) | (tptp_fun____(X17!0, |'0'|) = X17!0)),
% 237.80/238.13 inference(quant_inst,[status(thm)],[])).
% 237.80/238.13 tff(204,plain,
% 237.80/238.13 (tptp_fun____(X17!0, |'0'|) = X17!0),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[203, 7])).
% 237.80/238.13 tff(205,plain,
% 237.80/238.13 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(|'0'|, X17!0) = tptp_fun____(X17!0, |'0'|))),
% 237.80/238.13 inference(quant_inst,[status(thm)],[])).
% 237.80/238.13 tff(206,plain,
% 237.80/238.13 (tptp_fun____(|'0'|, X17!0) = tptp_fun____(X17!0, |'0'|)),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[205, 17])).
% 237.80/238.13 tff(207,plain,
% 237.80/238.13 (tptp_fun____(|'0'|, X17!0) = X17!0),
% 237.80/238.13 inference(transitivity,[status(thm)],[206, 204])).
% 237.80/238.13 tff(208,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), tptp_fun____(|'0'|, X17!0)) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)), X17!0)),
% 237.80/238.13 inference(monotonicity,[status(thm)],[200, 207])).
% 237.80/238.13 tff(209,plain,
% 237.80/238.13 ((~![A: $i] : tptp_fun_____(A, |'0'|)) | tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)),
% 237.80/238.13 inference(quant_inst,[status(thm)],[])).
% 237.80/238.13 tff(210,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[209, 77])).
% 237.80/238.13 tff(211,plain,
% 237.80/238.13 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|))),
% 237.80/238.13 inference(rewrite,[status(thm)],[])).
% 237.80/238.13 tff(212,plain,
% 237.80/238.13 ((tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|))) <=> ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|))),
% 237.80/238.13 inference(rewrite,[status(thm)],[])).
% 237.80/238.13 tff(213,plain,
% 237.80/238.13 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)))),
% 237.80/238.13 inference(monotonicity,[status(thm)],[212])).
% 237.80/238.13 tff(214,plain,
% 237.80/238.13 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|))),
% 237.80/238.13 inference(transitivity,[status(thm)],[213, 211])).
% 237.80/238.13 tff(215,plain,
% 237.80/238.13 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)))),
% 237.80/238.13 inference(quant_inst,[status(thm)],[])).
% 237.80/238.13 tff(216,plain,
% 237.80/238.13 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)),
% 237.80/238.13 inference(modus_ponens,[status(thm)],[215, 214])).
% 237.80/238.13 tff(217,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[216, 111, 210, 166])).
% 237.80/238.13 tff(218,plain,
% 237.80/238.13 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), tptp_fun____(|'0'|, X17!0)))) <=> ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), tptp_fun____(|'0'|, X17!0)))),
% 237.80/238.13 inference(rewrite,[status(thm)],[])).
% 237.80/238.13 tff(219,plain,
% 237.80/238.13 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), tptp_fun____(|'0'|, X17!0)))),
% 237.80/238.13 inference(quant_inst,[status(thm)],[])).
% 237.80/238.13 tff(220,plain,
% 237.80/238.13 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), tptp_fun____(|'0'|, X17!0))),
% 237.80/238.13 inference(modus_ponens,[status(thm)],[219, 218])).
% 237.80/238.13 tff(221,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), tptp_fun____(|'0'|, X17!0))),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[220, 57, 217])).
% 237.80/238.13 tff(222,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|)), X17!0)),
% 237.80/238.13 inference(modus_ponens,[status(thm)],[221, 208])).
% 237.80/238.13 tff(223,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), X17!0)),
% 237.80/238.13 inference(modus_ponens,[status(thm)],[222, 202])).
% 237.80/238.13 tff(224,plain,
% 237.80/238.13 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0), X17!0)) | tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0))),
% 237.80/238.13 inference(tautology,[status(thm)],[])).
% 237.80/238.13 tff(225,plain,
% 237.80/238.13 (tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), X17!0))),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[224, 223, 196])).
% 237.80/238.13 tff(226,plain,
% 237.80/238.13 (tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.80/238.13 inference(modus_ponens,[status(thm)],[225, 194])).
% 237.80/238.13 tff(227,plain,
% 237.80/238.13 ((~![A: $i] : (tptp_fun____(A, |'0'|) = A)) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|) = tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.80/238.13 inference(quant_inst,[status(thm)],[])).
% 237.80/238.13 tff(228,plain,
% 237.80/238.13 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|) = tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)),
% 237.80/238.13 inference(unit_resolution,[status(thm)],[227, 7])).
% 237.80/238.13 tff(229,plain,
% 237.80/238.13 (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|)),
% 237.80/238.13 inference(symmetry,[status(thm)],[228])).
% 237.80/238.13 tff(230,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), X17!0)),
% 237.80/238.13 inference(monotonicity,[status(thm)],[229])).
% 237.80/238.13 tff(231,plain,
% 237.80/238.13 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)),
% 237.80/238.13 inference(symmetry,[status(thm)],[230])).
% 237.80/238.13 tff(232,plain,
% 237.80/238.13 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))),
% 237.80/238.14 inference(quant_inst,[status(thm)],[])).
% 237.80/238.14 tff(233,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))),
% 237.80/238.14 inference(unit_resolution,[status(thm)],[232, 30])).
% 237.80/238.14 tff(234,plain,
% 237.80/238.14 (tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))),
% 237.80/238.14 inference(monotonicity,[status(thm)],[137])).
% 237.80/238.14 tff(235,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))),
% 237.80/238.14 inference(symmetry,[status(thm)],[234])).
% 237.80/238.14 tff(236,plain,
% 237.80/238.14 (tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))),
% 237.80/238.14 inference(modus_ponens,[status(thm)],[162, 235])).
% 237.80/238.14 tff(237,plain,
% 237.80/238.14 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), X17!0) | (~tptp_fun_____(|'0'|, tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))),
% 237.80/238.14 inference(tautology,[status(thm)],[])).
% 237.80/238.14 tff(238,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), X17!0)),
% 237.80/238.14 inference(unit_resolution,[status(thm)],[237, 236, 233])).
% 237.80/238.14 tff(239,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)),
% 237.80/238.14 inference(modus_ponens,[status(thm)],[238, 231])).
% 237.80/238.14 tff(240,plain,
% 237.80/238.14 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0))),
% 237.80/238.14 inference(rewrite,[status(thm)],[])).
% 237.80/238.14 tff(241,plain,
% 237.80/238.14 (((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) <=> ((~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0))),
% 237.80/238.14 inference(rewrite,[status(thm)],[])).
% 237.80/238.14 tff(242,plain,
% 237.80/238.14 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0)))),
% 237.80/238.14 inference(monotonicity,[status(thm)],[241])).
% 237.80/238.14 tff(243,plain,
% 237.80/238.14 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0))),
% 237.80/238.14 inference(transitivity,[status(thm)],[242, 240])).
% 237.80/238.14 tff(244,plain,
% 237.80/238.14 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.80/238.14 inference(quant_inst,[status(thm)],[])).
% 237.80/238.14 tff(245,plain,
% 237.80/238.14 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0)),
% 237.80/238.14 inference(modus_ponens,[status(thm)],[244, 243])).
% 237.80/238.14 tff(246,plain,
% 237.80/238.14 ((~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0)),
% 237.80/238.14 inference(unit_resolution,[status(thm)],[245, 183, 239])).
% 237.80/238.14 tff(247,plain,
% 237.80/238.14 (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = X17!0),
% 237.80/238.14 inference(unit_resolution,[status(thm)],[246, 226])).
% 237.80/238.14 tff(248,plain,
% 237.80/238.14 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.80/238.14 inference(quant_inst,[status(thm)],[])).
% 237.80/238.14 tff(249,plain,
% 237.80/238.14 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.80/238.14 inference(unit_resolution,[status(thm)],[248, 17])).
% 237.80/238.14 tff(250,plain,
% 237.80/238.14 (tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)),
% 237.80/238.14 inference(symmetry,[status(thm)],[249])).
% 237.80/238.14 tff(251,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|))),
% 237.80/238.14 inference(monotonicity,[status(thm)],[250, 229])).
% 237.80/238.14 tff(252,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|)) <=> tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.80/238.14 inference(symmetry,[status(thm)],[251])).
% 237.80/238.14 tff(253,plain,
% 237.80/238.14 (tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0) = tptp_fun______(tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|), X17!0)),
% 237.80/238.14 inference(monotonicity,[status(thm)],[20])).
% 237.80/238.14 tff(254,plain,
% 237.80/238.14 (tptp_fun______(tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0)),
% 237.80/238.14 inference(symmetry,[status(thm)],[253])).
% 237.80/238.14 tff(255,plain,
% 237.80/238.14 (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(tptp_fun______(X17!0, |'1'|), |'0'|), X17!0)),
% 237.80/238.14 inference(symmetry,[status(thm)],[10])).
% 237.80/238.14 tff(256,plain,
% 237.80/238.14 (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0)),
% 237.80/238.14 inference(transitivity,[status(thm)],[255, 254])).
% 237.80/238.14 tff(257,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) <=> tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0))),
% 237.80/238.14 inference(monotonicity,[status(thm)],[256])).
% 237.80/238.14 tff(258,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0)) <=> tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.80/238.14 inference(symmetry,[status(thm)],[257])).
% 237.80/238.14 tff(259,plain,
% 237.80/238.14 (((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0)))) <=> ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0)))),
% 237.80/238.14 inference(rewrite,[status(thm)],[])).
% 237.80/238.14 tff(260,plain,
% 237.80/238.14 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0)))),
% 237.80/238.14 inference(quant_inst,[status(thm)],[])).
% 237.80/238.14 tff(261,plain,
% 237.80/238.14 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0))),
% 237.80/238.14 inference(modus_ponens,[status(thm)],[260, 259])).
% 237.80/238.14 tff(262,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), X17!0))),
% 237.80/238.14 inference(unit_resolution,[status(thm)],[261, 94, 239])).
% 237.80/238.14 tff(263,plain,
% 237.80/238.14 (tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.80/238.14 inference(modus_ponens,[status(thm)],[262, 258])).
% 237.80/238.14 tff(264,plain,
% 237.80/238.14 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.80/238.14 inference(quant_inst,[status(thm)],[])).
% 237.90/238.14 tff(265,plain,
% 237.90/238.14 (tptp_fun_____(tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.14 inference(unit_resolution,[status(thm)],[264, 30])).
% 237.90/238.14 tff(266,plain,
% 237.90/238.14 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|))),
% 237.90/238.14 inference(quant_inst,[status(thm)],[])).
% 237.90/238.14 tff(267,plain,
% 237.90/238.14 (tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|)),
% 237.90/238.14 inference(unit_resolution,[status(thm)],[266, 17])).
% 237.90/238.14 tff(268,plain,
% 237.90/238.14 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.14 inference(symmetry,[status(thm)],[267])).
% 237.90/238.14 tff(269,plain,
% 237.90/238.14 (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.14 inference(transitivity,[status(thm)],[229, 268])).
% 237.90/238.14 tff(270,plain,
% 237.90/238.14 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.14 inference(quant_inst,[status(thm)],[])).
% 237.90/238.14 tff(271,plain,
% 237.90/238.14 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.14 inference(unit_resolution,[status(thm)],[270, 17])).
% 237.90/238.14 tff(272,plain,
% 237.90/238.14 (tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(X17!0, |'1'|))),
% 237.90/238.14 inference(monotonicity,[status(thm)],[228])).
% 237.90/238.14 tff(273,plain,
% 237.90/238.14 (^[A: $i, B: $i, C: $i] : refl((tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C))) <=> (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C))))),
% 237.90/238.14 inference(bind,[status(th)],[])).
% 237.90/238.14 tff(274,plain,
% 237.90/238.14 (![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C))) <=> ![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))),
% 237.90/238.14 inference(quant_intro,[status(thm)],[273])).
% 237.90/238.14 tff(275,plain,
% 237.90/238.14 (![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C))) <=> ![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))),
% 237.90/238.14 inference(rewrite,[status(thm)],[])).
% 237.90/238.14 tff(276,axiom,(![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_01')).
% 237.90/238.14 tff(277,plain,
% 237.90/238.14 (![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))),
% 237.90/238.14 inference(modus_ponens,[status(thm)],[276, 275])).
% 237.90/238.14 tff(278,plain,(
% 237.90/238.14 ![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))),
% 237.90/238.14 inference(skolemize,[status(sab)],[277])).
% 237.90/238.14 tff(279,plain,
% 237.90/238.14 (![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))),
% 237.90/238.14 inference(modus_ponens,[status(thm)],[278, 274])).
% 237.90/238.14 tff(280,plain,
% 237.90/238.14 ((~![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))) | (tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.14 inference(quant_inst,[status(thm)],[])).
% 237.90/238.14 tff(281,plain,
% 237.90/238.14 (tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))),
% 237.90/238.14 inference(unit_resolution,[status(thm)],[280, 279])).
% 237.90/238.14 tff(282,plain,
% 237.90/238.14 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))) = tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun______(X17!0, |'1'|))),
% 237.90/238.14 inference(symmetry,[status(thm)],[281])).
% 237.90/238.14 tff(283,plain,
% 237.90/238.14 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.14 inference(quant_inst,[status(thm)],[])).
% 237.90/238.14 tff(284,plain,
% 237.90/238.14 (tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)))),
% 237.90/238.14 inference(unit_resolution,[status(thm)],[283, 17])).
% 237.90/238.14 tff(285,plain,
% 237.90/238.14 (tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) = tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.14 inference(transitivity,[status(thm)],[284, 282, 272, 271])).
% 237.90/238.14 tff(286,plain,
% 237.90/238.14 (tptp_fun_____(tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) <=> tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.14 inference(monotonicity,[status(thm)],[285, 269])).
% 237.90/238.14 tff(287,plain,
% 237.90/238.14 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) <=> tptp_fun_____(tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.14 inference(symmetry,[status(thm)],[286])).
% 237.90/238.14 tff(288,plain,
% 237.90/238.14 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.90/238.14 inference(rewrite,[status(thm)],[])).
% 237.90/238.14 tff(289,plain,
% 237.90/238.14 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.90/238.14 inference(quant_inst,[status(thm)],[])).
% 237.90/238.14 tff(290,plain,
% 237.90/238.14 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.15 inference(modus_ponens,[status(thm)],[289, 288])).
% 237.90/238.15 tff(291,plain,
% 237.90/238.15 ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.15 inference(unit_resolution,[status(thm)],[290, 57])).
% 237.90/238.15 tff(292,plain,
% 237.90/238.15 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.15 inference(unit_resolution,[status(thm)],[291, 210])).
% 237.90/238.15 tff(293,plain,
% 237.90/238.15 (tptp_fun_____(tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.15 inference(modus_ponens,[status(thm)],[292, 287])).
% 237.90/238.15 tff(294,plain,
% 237.90/238.15 ((~(tptp_fun_____(tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) | (~tptp_fun_____(tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.15 inference(tautology,[status(thm)],[])).
% 237.90/238.15 tff(295,plain,
% 237.90/238.15 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.15 inference(unit_resolution,[status(thm)],[294, 293, 265])).
% 237.90/238.15 tff(296,plain,
% 237.90/238.15 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.90/238.15 inference(rewrite,[status(thm)],[])).
% 237.90/238.15 tff(297,plain,
% 237.90/238.15 (((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) <=> ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.90/238.15 inference(rewrite,[status(thm)],[])).
% 237.90/238.15 tff(298,plain,
% 237.90/238.15 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))))),
% 237.90/238.15 inference(monotonicity,[status(thm)],[297])).
% 237.90/238.15 tff(299,plain,
% 237.90/238.15 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.90/238.15 inference(transitivity,[status(thm)],[298, 296])).
% 237.90/238.15 tff(300,plain,
% 237.90/238.15 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.90/238.15 inference(quant_inst,[status(thm)],[])).
% 237.90/238.15 tff(301,plain,
% 237.90/238.15 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.15 inference(modus_ponens,[status(thm)],[300, 299])).
% 237.90/238.15 tff(302,plain,
% 237.90/238.15 ((~tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.15 inference(unit_resolution,[status(thm)],[301, 183, 295])).
% 237.90/238.15 tff(303,plain,
% 237.90/238.15 (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.15 inference(unit_resolution,[status(thm)],[302, 263])).
% 237.90/238.15 tff(304,plain,
% 237.90/238.15 (tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) = tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)),
% 237.90/238.15 inference(symmetry,[status(thm)],[303])).
% 237.90/238.15 tff(305,plain,
% 237.90/238.15 (tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|)),
% 237.90/238.15 inference(transitivity,[status(thm)],[304, 229])).
% 237.90/238.15 tff(306,plain,
% 237.90/238.15 ((~![A: $i] : (tptp_fun____(A, |'0'|) = A)) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|) = tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.15 inference(quant_inst,[status(thm)],[])).
% 237.90/238.15 tff(307,plain,
% 237.90/238.15 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|) = tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)),
% 237.90/238.15 inference(unit_resolution,[status(thm)],[306, 7])).
% 237.90/238.15 tff(308,plain,
% 237.90/238.15 (tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)),
% 237.90/238.15 inference(symmetry,[status(thm)],[307])).
% 237.90/238.15 tff(309,plain,
% 237.90/238.15 (tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), |'1'|) = tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)),
% 237.90/238.15 inference(monotonicity,[status(thm)],[21])).
% 237.90/238.15 tff(310,plain,
% 237.90/238.15 (tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), |'1'|) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)),
% 237.90/238.15 inference(transitivity,[status(thm)],[309, 308])).
% 237.90/238.15 tff(311,plain,
% 237.90/238.15 (tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|))),
% 237.90/238.15 inference(monotonicity,[status(thm)],[310, 305])).
% 237.90/238.15 tff(312,plain,
% 237.90/238.15 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.15 inference(monotonicity,[status(thm)],[190])).
% 237.90/238.15 tff(313,plain,
% 237.90/238.15 (tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), |'1'|)),
% 237.90/238.15 inference(symmetry,[status(thm)],[309])).
% 237.90/238.15 tff(314,plain,
% 237.90/238.15 (tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)),
% 237.90/238.15 inference(transitivity,[status(thm)],[250, 307])).
% 237.90/238.15 tff(315,plain,
% 237.90/238.15 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.15 inference(monotonicity,[status(thm)],[314])).
% 237.90/238.15 tff(316,plain,
% 237.90/238.15 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(symmetry,[status(thm)],[315])).
% 237.90/238.16 tff(317,plain,
% 237.90/238.16 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(quant_inst,[status(thm)],[])).
% 237.90/238.16 tff(318,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[317, 30])).
% 237.90/238.16 tff(319,plain,
% 237.90/238.16 (((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) <=> ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(rewrite,[status(thm)],[])).
% 237.90/238.16 tff(320,plain,
% 237.90/238.16 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(quant_inst,[status(thm)],[])).
% 237.90/238.16 tff(321,plain,
% 237.90/238.16 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.16 inference(modus_ponens,[status(thm)],[320, 319])).
% 237.90/238.16 tff(322,plain,
% 237.90/238.16 ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[321, 152])).
% 237.90/238.16 tff(323,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[322, 47])).
% 237.90/238.16 tff(324,plain,
% 237.90/238.16 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(tautology,[status(thm)],[])).
% 237.90/238.16 tff(325,plain,
% 237.90/238.16 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[324, 323])).
% 237.90/238.16 tff(326,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[325, 318])).
% 237.90/238.16 tff(327,plain,
% 237.90/238.16 (((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) <=> ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(rewrite,[status(thm)],[])).
% 237.90/238.16 tff(328,plain,
% 237.90/238.16 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(quant_inst,[status(thm)],[])).
% 237.90/238.16 tff(329,plain,
% 237.90/238.16 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.16 inference(modus_ponens,[status(thm)],[328, 327])).
% 237.90/238.16 tff(330,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[329, 94, 326])).
% 237.90/238.16 tff(331,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(modus_ponens,[status(thm)],[330, 316])).
% 237.90/238.16 tff(332,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.16 inference(monotonicity,[status(thm)],[314])).
% 237.90/238.16 tff(333,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) <=> tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.16 inference(symmetry,[status(thm)],[332])).
% 237.90/238.16 tff(334,plain,
% 237.90/238.16 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))))),
% 237.90/238.16 inference(quant_inst,[status(thm)],[])).
% 237.90/238.16 tff(335,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[334, 30])).
% 237.90/238.16 tff(336,plain,
% 237.90/238.16 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.16 inference(tautology,[status(thm)],[])).
% 237.90/238.16 tff(337,plain,
% 237.90/238.16 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[336, 61])).
% 237.90/238.16 tff(338,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[337, 335])).
% 237.90/238.16 tff(339,plain,
% 237.90/238.16 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.16 inference(modus_ponens,[status(thm)],[338, 333])).
% 237.90/238.16 tff(340,plain,
% 237.90/238.16 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))))),
% 237.90/238.16 inference(rewrite,[status(thm)],[])).
% 237.90/238.16 tff(341,plain,
% 237.90/238.16 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))))),
% 237.90/238.16 inference(quant_inst,[status(thm)],[])).
% 237.90/238.16 tff(342,plain,
% 237.90/238.16 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.16 inference(modus_ponens,[status(thm)],[341, 340])).
% 237.90/238.16 tff(343,plain,
% 237.90/238.16 ((tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[342, 183])).
% 237.90/238.16 tff(344,plain,
% 237.90/238.16 (tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(unit_resolution,[status(thm)],[343, 339, 331])).
% 237.90/238.16 tff(345,plain,
% 237.90/238.16 (tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.16 inference(symmetry,[status(thm)],[344])).
% 237.90/238.16 tff(346,plain,
% 237.90/238.16 (tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)) = tptp_fun______(X17!0, |'1'|)),
% 237.90/238.16 inference(transitivity,[status(thm)],[190, 20, 9])).
% 237.90/238.16 tff(347,plain,
% 237.90/238.16 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) = tptp_fun______(tptp_fun______(X17!0, |'1'|), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.16 inference(monotonicity,[status(thm)],[346])).
% 237.90/238.16 tff(348,plain,
% 237.90/238.16 (tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.16 inference(transitivity,[status(thm)],[308, 249])).
% 237.90/238.16 tff(349,plain,
% 237.90/238.16 (tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)) = tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))),
% 237.90/238.16 inference(symmetry,[status(thm)],[190])).
% 237.90/238.16 tff(350,plain,
% 237.90/238.16 (tptp_fun______(X17!0, |'1'|) = tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))),
% 237.90/238.16 inference(transitivity,[status(thm)],[66, 19, 349])).
% 237.90/238.16 tff(351,plain,
% 237.90/238.16 (tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.17 inference(monotonicity,[status(thm)],[350, 348])).
% 237.90/238.17 tff(352,plain,
% 237.90/238.17 (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) = tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.17 inference(symmetry,[status(thm)],[351])).
% 237.90/238.17 tff(353,plain,
% 237.90/238.17 ((~![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))) | (tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.17 inference(quant_inst,[status(thm)],[])).
% 237.90/238.17 tff(354,plain,
% 237.90/238.17 (tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.17 inference(unit_resolution,[status(thm)],[353, 279])).
% 237.90/238.17 tff(355,plain,
% 237.90/238.17 (tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.17 inference(monotonicity,[status(thm)],[120])).
% 237.90/238.17 tff(356,plain,
% 237.90/238.17 (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.17 inference(symmetry,[status(thm)],[355])).
% 237.90/238.17 tff(357,plain,
% 237.90/238.17 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.17 inference(quant_inst,[status(thm)],[])).
% 237.90/238.17 tff(358,plain,
% 237.90/238.17 (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.90/238.17 inference(unit_resolution,[status(thm)],[357, 17])).
% 237.90/238.17 tff(359,plain,
% 237.90/238.17 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.17 inference(symmetry,[status(thm)],[358])).
% 237.90/238.17 tff(360,plain,
% 237.90/238.17 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.17 inference(transitivity,[status(thm)],[359, 356, 354, 352])).
% 237.90/238.17 tff(361,plain,
% 237.90/238.17 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) = tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.17 inference(monotonicity,[status(thm)],[360])).
% 237.90/238.17 tff(362,plain,
% 237.90/238.17 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) = tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), |'1'|)),
% 237.90/238.17 inference(transitivity,[status(thm)],[361, 347, 345, 250, 307, 313])).
% 237.90/238.17 tff(363,plain,
% 237.90/238.17 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) <=> tptp_fun_____(tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun______(tptp_fun____(|'0'|, tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.17 inference(monotonicity,[status(thm)],[362, 312])).
% 237.90/238.17 tff(364,plain,
% 237.90/238.17 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) <=> tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.17 inference(transitivity,[status(thm)],[363, 311, 252])).
% 237.90/238.17 tff(365,plain,
% 237.90/238.17 (X17!0 = tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)),
% 237.90/238.17 inference(symmetry,[status(thm)],[247])).
% 237.90/238.17 tff(366,plain,
% 237.90/238.17 (tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.17 inference(monotonicity,[status(thm)],[365])).
% 237.90/238.17 tff(367,plain,
% 237.90/238.17 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) = tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.17 inference(symmetry,[status(thm)],[366])).
% 237.90/238.17 tff(368,plain,
% 237.90/238.17 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.17 inference(monotonicity,[status(thm)],[359])).
% 237.90/238.17 tff(369,plain,
% 237.90/238.17 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.17 inference(symmetry,[status(thm)],[368])).
% 237.90/238.17 tff(370,plain,
% 237.90/238.17 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) <=> ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.17 inference(rewrite,[status(thm)],[])).
% 237.90/238.17 tff(371,plain,
% 237.90/238.17 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.90/238.17 inference(quant_inst,[status(thm)],[])).
% 237.90/238.17 tff(372,plain,
% 237.90/238.17 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.17 inference(modus_ponens,[status(thm)],[371, 370])).
% 237.90/238.17 tff(373,plain,
% 237.90/238.17 ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.17 inference(unit_resolution,[status(thm)],[372, 57])).
% 237.90/238.17 tff(374,plain,
% 237.90/238.17 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.17 inference(unit_resolution,[status(thm)],[373, 166])).
% 237.90/238.17 tff(375,plain,
% 237.90/238.17 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.17 inference(modus_ponens,[status(thm)],[374, 369])).
% 237.90/238.17 tff(376,plain,
% 237.90/238.17 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|))),
% 237.90/238.17 inference(rewrite,[status(thm)],[])).
% 237.90/238.17 tff(377,plain,
% 237.90/238.17 ((tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|))) <=> ((~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|))),
% 237.90/238.18 inference(rewrite,[status(thm)],[])).
% 237.90/238.18 tff(378,plain,
% 237.90/238.18 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)))),
% 237.90/238.18 inference(monotonicity,[status(thm)],[377])).
% 237.90/238.18 tff(379,plain,
% 237.90/238.18 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|))),
% 237.90/238.18 inference(transitivity,[status(thm)],[378, 376])).
% 237.90/238.18 tff(380,plain,
% 237.90/238.18 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)))),
% 237.90/238.18 inference(quant_inst,[status(thm)],[])).
% 237.90/238.18 tff(381,plain,
% 237.90/238.18 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), |'1'|)) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun____(tptp_fun______(X17!0, |'1'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)),
% 237.90/238.18 inference(modus_ponens,[status(thm)],[380, 379])).
% 237.90/238.18 tff(382,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)),
% 237.90/238.18 inference(unit_resolution,[status(thm)],[381, 111, 326, 375])).
% 237.90/238.18 tff(383,plain,
% 237.90/238.18 (^[A: $i] : refl((tptp_fun____(A, |'1'|) = |'1'|) <=> (tptp_fun____(A, |'1'|) = |'1'|))),
% 237.90/238.18 inference(bind,[status(th)],[])).
% 237.90/238.18 tff(384,plain,
% 237.90/238.18 (![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|) <=> ![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|)),
% 237.90/238.18 inference(quant_intro,[status(thm)],[383])).
% 237.90/238.18 tff(385,plain,
% 237.90/238.18 (![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|) <=> ![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|)),
% 237.90/238.18 inference(rewrite,[status(thm)],[])).
% 237.90/238.18 tff(386,axiom,(![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_12')).
% 237.90/238.18 tff(387,plain,
% 237.90/238.18 (![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|)),
% 237.90/238.18 inference(modus_ponens,[status(thm)],[386, 385])).
% 237.90/238.18 tff(388,plain,(
% 237.90/238.18 ![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|)),
% 237.90/238.18 inference(skolemize,[status(sab)],[387])).
% 237.90/238.18 tff(389,plain,
% 237.90/238.18 (![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|)),
% 237.90/238.18 inference(modus_ponens,[status(thm)],[388, 384])).
% 237.90/238.18 tff(390,plain,
% 237.90/238.18 ((~![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|)) | (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|) = |'1'|)),
% 237.90/238.18 inference(quant_inst,[status(thm)],[])).
% 237.90/238.18 tff(391,plain,
% 237.90/238.18 (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|) = |'1'|),
% 237.90/238.18 inference(unit_resolution,[status(thm)],[390, 389])).
% 237.90/238.18 tff(392,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) <=> tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.18 inference(monotonicity,[status(thm)],[391])).
% 237.90/238.18 tff(393,plain,
% 237.90/238.18 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))))),
% 237.90/238.18 inference(quant_inst,[status(thm)],[])).
% 237.90/238.18 tff(394,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.90/238.18 inference(unit_resolution,[status(thm)],[393, 30])).
% 237.90/238.18 tff(395,plain,
% 237.90/238.18 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.18 inference(transitivity,[status(thm)],[361, 347, 345])).
% 237.90/238.18 tff(396,plain,
% 237.90/238.18 (tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) <=> tptp_fun_____(|'1'|, tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.18 inference(monotonicity,[status(thm)],[395])).
% 237.90/238.18 tff(397,plain,
% 237.90/238.18 (tptp_fun_____(|'1'|, tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.90/238.18 inference(symmetry,[status(thm)],[396])).
% 237.90/238.18 tff(398,plain,
% 237.90/238.18 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|) = tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)),
% 237.90/238.18 inference(monotonicity,[status(thm)],[346])).
% 237.90/238.18 tff(399,plain,
% 237.90/238.18 (tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.90/238.18 inference(transitivity,[status(thm)],[398, 308, 249])).
% 237.90/238.18 tff(400,plain,
% 237.90/238.18 (tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)) <=> tptp_fun_____(|'1'|, tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.90/238.18 inference(monotonicity,[status(thm)],[399])).
% 237.90/238.18 tff(401,plain,
% 237.90/238.18 (tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.90/238.18 inference(transitivity,[status(thm)],[400, 397])).
% 237.90/238.18 tff(402,plain,
% 237.90/238.18 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), |'1'|) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)))),
% 237.90/238.18 inference(quant_inst,[status(thm)],[])).
% 237.90/238.18 tff(403,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), |'1'|) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|))),
% 237.90/238.18 inference(unit_resolution,[status(thm)],[402, 30])).
% 237.90/238.18 tff(404,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), |'1'|) <=> tptp_fun_____(|'1'|, |'1'|)),
% 237.90/238.18 inference(monotonicity,[status(thm)],[391])).
% 237.90/238.18 tff(405,plain,
% 237.90/238.18 (tptp_fun_____(|'1'|, |'1'|) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), |'1'|)),
% 237.90/238.18 inference(symmetry,[status(thm)],[404])).
% 237.90/238.18 tff(406,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)) <=> tptp_fun_____(|'1'|, |'1'|)),
% 237.90/238.18 inference(monotonicity,[status(thm)],[391, 391])).
% 237.90/238.18 tff(407,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), |'1'|)),
% 237.90/238.18 inference(transitivity,[status(thm)],[406, 405])).
% 237.90/238.18 tff(408,plain,
% 237.90/238.18 (((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) <=> ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.18 inference(rewrite,[status(thm)],[])).
% 237.90/238.18 tff(409,plain,
% 237.90/238.18 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.18 inference(quant_inst,[status(thm)],[])).
% 237.90/238.18 tff(410,plain,
% 237.90/238.18 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.90/238.18 inference(modus_ponens,[status(thm)],[409, 408])).
% 237.90/238.18 tff(411,plain,
% 237.90/238.18 ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.90/238.18 inference(unit_resolution,[status(thm)],[410, 94])).
% 237.90/238.18 tff(412,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.90/238.18 inference(unit_resolution,[status(thm)],[411, 47])).
% 237.90/238.18 tff(413,plain,
% 237.90/238.18 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)))) <=> ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)))),
% 237.90/238.18 inference(rewrite,[status(thm)],[])).
% 237.90/238.18 tff(414,plain,
% 237.90/238.18 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)))),
% 237.90/238.18 inference(quant_inst,[status(thm)],[])).
% 237.90/238.18 tff(415,plain,
% 237.90/238.18 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|))),
% 237.90/238.18 inference(modus_ponens,[status(thm)],[414, 413])).
% 237.90/238.18 tff(416,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|))),
% 237.90/238.18 inference(unit_resolution,[status(thm)],[415, 57, 412])).
% 237.90/238.18 tff(417,plain,
% 237.90/238.18 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), |'1'|)),
% 237.90/238.18 inference(modus_ponens,[status(thm)],[416, 407])).
% 237.90/238.18 tff(418,plain,
% 237.90/238.18 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), |'1'|) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), |'1'|)) | tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|))),
% 237.90/238.18 inference(tautology,[status(thm)],[])).
% 237.90/238.18 tff(419,plain,
% 237.90/238.18 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), |'1'|) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|)))) | tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|))),
% 237.90/238.19 inference(unit_resolution,[status(thm)],[418, 417])).
% 237.90/238.19 tff(420,plain,
% 237.90/238.19 (tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|))),
% 237.90/238.19 inference(unit_resolution,[status(thm)],[419, 403])).
% 237.90/238.19 tff(421,plain,
% 237.90/238.19 (tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.90/238.19 inference(modus_ponens,[status(thm)],[420, 401])).
% 237.90/238.19 tff(422,plain,
% 237.90/238.19 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) | (~tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))))),
% 237.90/238.19 inference(tautology,[status(thm)],[])).
% 237.90/238.19 tff(423,plain,
% 237.90/238.19 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) <=> tptp_fun_____(|'1'|, tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.19 inference(unit_resolution,[status(thm)],[422, 421])).
% 237.90/238.19 tff(424,plain,
% 237.90/238.19 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'1'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.19 inference(unit_resolution,[status(thm)],[423, 394])).
% 237.90/238.19 tff(425,plain,
% 237.90/238.19 (tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.19 inference(modus_ponens,[status(thm)],[424, 392])).
% 237.90/238.19 tff(426,plain,
% 237.90/238.19 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|))),
% 237.90/238.19 inference(rewrite,[status(thm)],[])).
% 237.90/238.19 tff(427,plain,
% 237.90/238.19 (((tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))) <=> ((~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|))),
% 237.90/238.19 inference(rewrite,[status(thm)],[])).
% 237.90/238.19 tff(428,plain,
% 237.90/238.19 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|)))),
% 237.90/238.19 inference(monotonicity,[status(thm)],[427])).
% 237.90/238.19 tff(429,plain,
% 237.90/238.19 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|))),
% 237.90/238.19 inference(transitivity,[status(thm)],[428, 426])).
% 237.90/238.19 tff(430,plain,
% 237.90/238.19 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))))),
% 237.90/238.19 inference(quant_inst,[status(thm)],[])).
% 237.90/238.19 tff(431,plain,
% 237.90/238.19 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(|'1'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'1'|)) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|)),
% 237.90/238.19 inference(modus_ponens,[status(thm)],[430, 429])).
% 237.90/238.19 tff(432,plain,
% 237.90/238.19 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = |'1'|),
% 237.90/238.19 inference(unit_resolution,[status(thm)],[431, 183, 425, 382])).
% 237.90/238.19 tff(433,plain,
% 237.90/238.19 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|)),
% 237.90/238.19 inference(monotonicity,[status(thm)],[432])).
% 237.90/238.19 tff(434,plain,
% 237.90/238.19 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.19 inference(symmetry,[status(thm)],[433])).
% 237.90/238.19 tff(435,plain,
% 237.90/238.19 ((~![A: $i] : (tptp_fun____(A, |'1'|) = |'1'|)) | (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|) = |'1'|)),
% 237.90/238.19 inference(quant_inst,[status(thm)],[])).
% 237.90/238.19 tff(436,plain,
% 237.90/238.19 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|) = |'1'|),
% 237.90/238.19 inference(unit_resolution,[status(thm)],[435, 389])).
% 237.90/238.19 tff(437,plain,
% 237.90/238.19 (|'1'| = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|)),
% 237.90/238.19 inference(symmetry,[status(thm)],[436])).
% 237.90/238.19 tff(438,plain,
% 237.90/238.19 (tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.90/238.19 inference(transitivity,[status(thm)],[432, 437, 434, 367])).
% 237.90/238.19 tff(439,plain,
% 237.90/238.19 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.19 inference(monotonicity,[status(thm)],[438])).
% 237.90/238.19 tff(440,plain,
% 237.90/238.19 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.19 inference(symmetry,[status(thm)],[439])).
% 237.90/238.19 tff(441,plain,
% 237.90/238.19 (((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) <=> ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.19 inference(rewrite,[status(thm)],[])).
% 237.90/238.19 tff(442,plain,
% 237.90/238.19 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.90/238.19 inference(quant_inst,[status(thm)],[])).
% 237.90/238.19 tff(443,plain,
% 237.90/238.19 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.19 inference(modus_ponens,[status(thm)],[442, 441])).
% 237.90/238.19 tff(444,plain,
% 237.90/238.19 (tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.90/238.19 inference(unit_resolution,[status(thm)],[443, 152, 210])).
% 237.90/238.19 tff(445,plain,
% 237.90/238.19 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0)))),
% 237.90/238.19 inference(quant_inst,[status(thm)],[])).
% 237.90/238.19 tff(446,plain,
% 237.90/238.19 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))),
% 237.90/238.19 inference(unit_resolution,[status(thm)],[445, 30])).
% 237.90/238.19 tff(447,plain,
% 237.90/238.19 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), X17!0) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), X17!0)),
% 237.90/238.19 inference(monotonicity,[status(thm)],[267])).
% 237.90/238.19 tff(448,plain,
% 237.90/238.19 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), X17!0) <=> tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), X17!0)),
% 237.95/238.20 inference(symmetry,[status(thm)],[447])).
% 237.95/238.20 tff(449,plain,
% 237.95/238.20 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), X17!0)),
% 237.95/238.20 inference(modus_ponens,[status(thm)],[238, 448])).
% 237.95/238.20 tff(450,plain,
% 237.95/238.20 ((~(tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))),
% 237.95/238.20 inference(tautology,[status(thm)],[])).
% 237.95/238.20 tff(451,plain,
% 237.95/238.20 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))),
% 237.95/238.20 inference(unit_resolution,[status(thm)],[450, 449, 446])).
% 237.95/238.20 tff(452,plain,
% 237.95/238.20 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0)))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0)))),
% 237.95/238.20 inference(rewrite,[status(thm)],[])).
% 237.95/238.20 tff(453,plain,
% 237.95/238.20 (((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) <=> ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0)))),
% 237.95/238.20 inference(rewrite,[status(thm)],[])).
% 237.95/238.20 tff(454,plain,
% 237.95/238.20 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0))))),
% 237.95/238.20 inference(monotonicity,[status(thm)],[453])).
% 237.95/238.20 tff(455,plain,
% 237.95/238.20 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0)))),
% 237.95/238.20 inference(transitivity,[status(thm)],[454, 452])).
% 237.95/238.20 tff(456,plain,
% 237.95/238.20 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.95/238.20 inference(quant_inst,[status(thm)],[])).
% 237.95/238.20 tff(457,plain,
% 237.95/238.20 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(|'0'|, X17!0))) | (~tptp_fun_____(tptp_fun______(|'0'|, X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0))),
% 237.95/238.20 inference(modus_ponens,[status(thm)],[456, 455])).
% 237.95/238.20 tff(458,plain,
% 237.95/238.20 (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun______(|'0'|, X17!0)),
% 237.95/238.20 inference(unit_resolution,[status(thm)],[457, 183, 451, 444])).
% 237.95/238.20 tff(459,plain,
% 237.95/238.20 (tptp_fun______(|'0'|, X17!0) = tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)),
% 237.95/238.20 inference(symmetry,[status(thm)],[458])).
% 237.95/238.20 tff(460,plain,
% 237.95/238.20 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(|'0'|, X17!0)) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.95/238.20 inference(monotonicity,[status(thm)],[459])).
% 237.95/238.20 tff(461,plain,
% 237.95/238.20 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(|'0'|, X17!0)))),
% 237.95/238.20 inference(quant_inst,[status(thm)],[])).
% 237.95/238.20 tff(462,plain,
% 237.95/238.20 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(|'0'|, X17!0))),
% 237.95/238.20 inference(unit_resolution,[status(thm)],[461, 30])).
% 237.95/238.20 tff(463,plain,
% 237.95/238.20 (tptp_fun____(X17!0, |'0'|) = tptp_fun____(|'0'|, X17!0)),
% 237.95/238.20 inference(symmetry,[status(thm)],[206])).
% 237.95/238.20 tff(464,plain,
% 237.95/238.20 (X17!0 = tptp_fun____(X17!0, |'0'|)),
% 237.95/238.20 inference(symmetry,[status(thm)],[204])).
% 237.95/238.20 tff(465,plain,
% 237.95/238.20 (X17!0 = tptp_fun____(|'0'|, X17!0)),
% 237.95/238.20 inference(transitivity,[status(thm)],[464, 463])).
% 237.95/238.20 tff(466,plain,
% 237.95/238.20 (tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) = tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), |'0'|), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.95/238.20 inference(symmetry,[status(thm)],[354])).
% 237.95/238.20 tff(467,plain,
% 237.95/238.20 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.95/238.20 inference(quant_inst,[status(thm)],[])).
% 237.95/238.20 tff(468,plain,
% 237.95/238.20 (tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = tptp_fun____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.95/238.20 inference(unit_resolution,[status(thm)],[467, 17])).
% 237.95/238.20 tff(469,plain,
% 237.95/238.20 ((~![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))) | (tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = tptp_fun____(|'0'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.95/238.20 inference(quant_inst,[status(thm)],[])).
% 237.95/238.20 tff(470,plain,
% 237.95/238.20 (tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))) = tptp_fun____(|'0'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.95/238.20 inference(unit_resolution,[status(thm)],[469, 279])).
% 237.95/238.20 tff(471,plain,
% 237.95/238.20 (tptp_fun____(|'0'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) = tptp_fun____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.95/238.20 inference(symmetry,[status(thm)],[470])).
% 237.95/238.20 tff(472,plain,
% 237.95/238.20 (tptp_fun____(|'0'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) = tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.95/238.20 inference(transitivity,[status(thm)],[471, 468, 466, 355, 358])).
% 237.95/238.20 tff(473,plain,
% 237.95/238.20 (tptp_fun____(tptp_fun____(|'0'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), X17!0) = tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0)),
% 237.95/238.20 inference(monotonicity,[status(thm)],[472])).
% 237.95/238.20 tff(474,plain,
% 237.95/238.20 ((~![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))) | (tptp_fun____(tptp_fun____(|'0'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), X17!0) = tptp_fun____(|'0'|, tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0)))),
% 237.95/238.20 inference(quant_inst,[status(thm)],[])).
% 237.95/238.20 tff(475,plain,
% 237.95/238.20 (tptp_fun____(tptp_fun____(|'0'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), X17!0) = tptp_fun____(|'0'|, tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0))),
% 237.95/238.20 inference(unit_resolution,[status(thm)],[474, 279])).
% 237.95/238.20 tff(476,plain,
% 237.95/238.20 (tptp_fun____(|'0'|, tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0)) = tptp_fun____(tptp_fun____(|'0'|, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), X17!0)),
% 237.95/238.20 inference(symmetry,[status(thm)],[475])).
% 237.95/238.20 tff(477,plain,
% 237.95/238.20 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0) = tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))))),
% 237.95/238.20 inference(quant_inst,[status(thm)],[])).
% 237.95/238.20 tff(478,plain,
% 237.95/238.20 (tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0) = tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.95/238.20 inference(unit_resolution,[status(thm)],[477, 17])).
% 237.95/238.20 tff(479,plain,
% 237.95/238.20 (tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))) = tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0)),
% 237.95/238.20 inference(symmetry,[status(thm)],[478])).
% 237.95/238.20 tff(480,plain,
% 237.95/238.20 (tptp_fun____(|'0'|, tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) = tptp_fun____(|'0'|, tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0))),
% 237.95/238.20 inference(monotonicity,[status(thm)],[479])).
% 237.95/238.20 tff(481,plain,
% 237.95/238.20 (tptp_fun____(|'0'|, tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) = tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0)),
% 237.95/238.20 inference(transitivity,[status(thm)],[480, 476, 473])).
% 237.95/238.20 tff(482,plain,
% 237.95/238.20 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))), X17!0) <=> tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0), tptp_fun____(|'0'|, X17!0))),
% 237.95/238.20 inference(monotonicity,[status(thm)],[481, 465])).
% 237.95/238.20 tff(483,plain,
% 237.95/238.20 (tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0), tptp_fun____(|'0'|, X17!0)) <=> tptp_fun_____(tptp_fun____(|'0'|, tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))), X17!0)),
% 237.95/238.20 inference(symmetry,[status(thm)],[482])).
% 237.95/238.20 tff(484,plain,
% 237.95/238.20 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.95/238.21 inference(quant_inst,[status(thm)],[])).
% 237.95/238.21 tff(485,plain,
% 237.95/238.21 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.95/238.21 inference(unit_resolution,[status(thm)],[484, 30])).
% 237.95/238.21 tff(486,plain,
% 237.95/238.21 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))),
% 237.95/238.21 inference(tautology,[status(thm)],[])).
% 237.95/238.21 tff(487,plain,
% 237.95/238.21 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))),
% 237.95/238.21 inference(unit_resolution,[status(thm)],[486, 412])).
% 237.95/238.21 tff(488,plain,
% 237.95/238.21 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))),
% 237.95/238.21 inference(unit_resolution,[status(thm)],[487, 485])).
% 237.95/238.21 tff(489,plain,
% 237.95/238.21 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|))),
% 237.95/238.21 inference(rewrite,[status(thm)],[])).
% 237.95/238.21 tff(490,plain,
% 237.95/238.21 ((tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|))) <=> ((~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|))),
% 237.95/238.21 inference(rewrite,[status(thm)],[])).
% 237.95/238.21 tff(491,plain,
% 237.95/238.21 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|)))),
% 237.95/238.21 inference(monotonicity,[status(thm)],[490])).
% 237.95/238.21 tff(492,plain,
% 237.95/238.21 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|))),
% 237.95/238.21 inference(transitivity,[status(thm)],[491, 489])).
% 237.95/238.21 tff(493,plain,
% 237.95/238.21 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)))),
% 237.95/238.21 inference(quant_inst,[status(thm)],[])).
% 237.95/238.21 tff(494,plain,
% 237.95/238.21 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(X17!0, |'1'|))) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|)),
% 237.95/238.21 inference(modus_ponens,[status(thm)],[493, 492])).
% 237.95/238.21 tff(495,plain,
% 237.95/238.21 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|)),
% 237.95/238.21 inference(unit_resolution,[status(thm)],[494, 111, 488, 210])).
% 237.95/238.21 tff(496,plain,
% 237.95/238.21 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0), tptp_fun____(|'0'|, X17!0)))) <=> ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0), tptp_fun____(|'0'|, X17!0)))),
% 237.95/238.21 inference(rewrite,[status(thm)],[])).
% 237.95/238.21 tff(497,plain,
% 237.95/238.21 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0), tptp_fun____(|'0'|, X17!0)))),
% 237.95/238.21 inference(quant_inst,[status(thm)],[])).
% 237.95/238.21 tff(498,plain,
% 237.95/238.21 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), |'0'|)) | tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0), tptp_fun____(|'0'|, X17!0))),
% 237.95/238.21 inference(modus_ponens,[status(thm)],[497, 496])).
% 237.95/238.21 tff(499,plain,
% 237.95/238.21 (tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), X17!0), tptp_fun____(|'0'|, X17!0))),
% 237.95/238.21 inference(unit_resolution,[status(thm)],[498, 57, 495])).
% 237.95/238.21 tff(500,plain,
% 237.95/238.21 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))), X17!0)),
% 237.95/238.21 inference(modus_ponens,[status(thm)],[499, 483])).
% 237.95/238.21 tff(501,plain,
% 237.95/238.21 ((~(tptp_fun_____(tptp_fun____(|'0'|, tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(|'0'|, X17!0)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))))), X17!0)) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(|'0'|, X17!0))),
% 237.95/238.21 inference(tautology,[status(thm)],[])).
% 237.95/238.21 tff(502,plain,
% 237.95/238.21 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(|'0'|, X17!0))),
% 237.95/238.21 inference(unit_resolution,[status(thm)],[501, 500, 462])).
% 237.95/238.21 tff(503,plain,
% 237.95/238.21 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.95/238.21 inference(modus_ponens,[status(thm)],[502, 460])).
% 237.95/238.21 tff(504,plain,
% 237.95/238.21 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.95/238.21 inference(modus_ponens,[status(thm)],[503, 440])).
% 237.95/238.21 tff(505,assumption,(~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))), introduced(assumption)).
% 237.95/238.21 tff(506,plain,
% 237.95/238.21 ($false),
% 237.95/238.21 inference(unit_resolution,[status(thm)],[505, 504])).
% 237.95/238.21 tff(507,plain,(tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))), inference(lemma,lemma(discharge,[]))).
% 237.95/238.21 tff(508,plain,
% 237.95/238.21 (((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.95/238.22 inference(rewrite,[status(thm)],[])).
% 237.95/238.22 tff(509,plain,
% 237.95/238.22 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.95/238.22 inference(quant_inst,[status(thm)],[])).
% 237.95/238.22 tff(510,plain,
% 237.95/238.22 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.95/238.22 inference(modus_ponens,[status(thm)],[509, 508])).
% 237.95/238.22 tff(511,plain,
% 237.95/238.22 ((~tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|))), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[510, 94])).
% 237.95/238.22 tff(512,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)))), tptp_fun______(tptp_fun______(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), tptp_fun______(X17!0, |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[511, 507])).
% 237.95/238.22 tff(513,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))),
% 237.95/238.22 inference(modus_ponens,[status(thm)],[512, 364])).
% 237.95/238.22 tff(514,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) <=> tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|))),
% 237.95/238.22 inference(monotonicity,[status(thm)],[229, 250])).
% 237.95/238.22 tff(515,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)) <=> tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.95/238.22 inference(symmetry,[status(thm)],[514])).
% 237.95/238.22 tff(516,plain,
% 237.95/238.22 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.95/238.22 inference(quant_inst,[status(thm)],[])).
% 237.95/238.22 tff(517,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[516, 30])).
% 237.95/238.22 tff(518,plain,
% 237.95/238.22 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)))),
% 237.95/238.22 inference(quant_inst,[status(thm)],[])).
% 237.95/238.22 tff(519,plain,
% 237.95/238.22 (tptp_fun____(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[518, 17])).
% 237.95/238.22 tff(520,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)), |'1'|)),
% 237.95/238.22 inference(monotonicity,[status(thm)],[519])).
% 237.95/238.22 tff(521,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)), |'1'|) <=> tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|)),
% 237.95/238.22 inference(symmetry,[status(thm)],[520])).
% 237.95/238.22 tff(522,plain,
% 237.95/238.22 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)), |'1'|) <=> tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.95/238.22 inference(quant_inst,[status(thm)],[])).
% 237.95/238.22 tff(523,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)), |'1'|) <=> tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[522, 30])).
% 237.95/238.22 tff(524,plain,
% 237.95/238.22 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)), |'1'|) <=> tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|)))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)), |'1'|) | (~tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|)))),
% 237.95/238.22 inference(tautology,[status(thm)],[])).
% 237.95/238.22 tff(525,plain,
% 237.95/238.22 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)), |'1'|) <=> tptp_fun_____(tptp_fun______(X17!0, |'1'|), tptp_fun______(X17!0, |'1'|)))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)), |'1'|)),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[524, 47])).
% 237.95/238.22 tff(526,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'1'|)), |'1'|)),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[525, 523])).
% 237.95/238.22 tff(527,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|)),
% 237.95/238.22 inference(modus_ponens,[status(thm)],[526, 521])).
% 237.95/238.22 tff(528,plain,
% 237.95/238.22 ((~(tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(tptp_fun______(X17!0, |'1'|), X17!0), |'1'|)) | tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.95/238.22 inference(tautology,[status(thm)],[])).
% 237.95/238.22 tff(529,plain,
% 237.95/238.22 (tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[528, 527, 517])).
% 237.95/238.22 tff(530,plain,
% 237.95/238.22 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))),
% 237.95/238.22 inference(rewrite,[status(thm)],[])).
% 237.95/238.22 tff(531,plain,
% 237.95/238.22 ((tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) <=> (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))),
% 237.95/238.22 inference(rewrite,[status(thm)],[])).
% 237.95/238.22 tff(532,plain,
% 237.95/238.22 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))))),
% 237.95/238.22 inference(monotonicity,[status(thm)],[531])).
% 237.95/238.22 tff(533,plain,
% 237.95/238.22 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)))),
% 237.95/238.22 inference(transitivity,[status(thm)],[532, 530])).
% 237.95/238.22 tff(534,plain,
% 237.95/238.22 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.95/238.22 inference(quant_inst,[status(thm)],[])).
% 237.95/238.22 tff(535,plain,
% 237.95/238.22 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), X17!0))),
% 237.95/238.22 inference(modus_ponens,[status(thm)],[534, 533])).
% 237.95/238.22 tff(536,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[535, 111, 239])).
% 237.95/238.22 tff(537,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[536, 529])).
% 237.95/238.22 tff(538,plain,
% 237.95/238.22 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)))) <=> ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)))),
% 237.95/238.22 inference(rewrite,[status(thm)],[])).
% 237.95/238.22 tff(539,plain,
% 237.95/238.22 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|)))),
% 237.95/238.22 inference(quant_inst,[status(thm)],[])).
% 237.95/238.22 tff(540,plain,
% 237.95/238.22 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|))),
% 237.95/238.22 inference(modus_ponens,[status(thm)],[539, 538])).
% 237.95/238.22 tff(541,plain,
% 237.95/238.22 ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[540, 57])).
% 237.95/238.22 tff(542,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), |'0'|), tptp_fun____(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|), |'0'|))),
% 237.95/238.22 inference(unit_resolution,[status(thm)],[541, 537])).
% 237.95/238.22 tff(543,plain,
% 237.95/238.22 (tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.95/238.22 inference(modus_ponens,[status(thm)],[542, 515])).
% 237.95/238.22 tff(544,plain,
% 237.95/238.22 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.95/238.22 inference(rewrite,[status(thm)],[])).
% 237.95/238.22 tff(545,plain,
% 237.95/238.22 (((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)))) <=> ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.95/238.23 inference(rewrite,[status(thm)],[])).
% 237.95/238.23 tff(546,plain,
% 237.95/238.23 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))))),
% 237.95/238.23 inference(monotonicity,[status(thm)],[545])).
% 237.95/238.23 tff(547,plain,
% 237.95/238.23 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))))),
% 237.95/238.23 inference(transitivity,[status(thm)],[546, 544])).
% 237.95/238.23 tff(548,plain,
% 237.95/238.23 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))))),
% 237.95/238.23 inference(quant_inst,[status(thm)],[])).
% 237.95/238.23 tff(549,plain,
% 237.95/238.23 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0), tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))) | (~tptp_fun_____(tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)), tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0))) | (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)))),
% 237.95/238.23 inference(modus_ponens,[status(thm)],[548, 547])).
% 237.95/238.23 tff(550,plain,
% 237.95/238.23 (tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0) = tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|))),
% 238.25/238.51 inference(unit_resolution,[status(thm)],[549, 183, 543, 513])).
% 238.25/238.51 tff(551,plain,
% 238.25/238.51 (tptp_fun____(|'0'|, tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|)) = tptp_fun______(tptp_fun______(X17!0, |'1'|), X17!0)),
% 238.25/238.51 inference(symmetry,[status(thm)],[550])).
% 238.25/238.51 tff(552,plain,
% 238.25/238.51 (tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|) = X17!0),
% 238.25/238.51 inference(transitivity,[status(thm)],[308, 249, 551, 247])).
% 238.25/238.51 tff(553,plain,
% 238.25/238.51 ((~![X17: $i] : (tptp_fun______(tptp_fun______(X17, |'1'|), |'1'|) = X17)) <=> (~![X17: $i] : (tptp_fun______(tptp_fun______(X17, |'1'|), |'1'|) = X17))),
% 238.25/238.51 inference(rewrite,[status(thm)],[])).
% 238.25/238.51 tff(554,axiom,(~![X17: $i] : (tptp_fun______(tptp_fun______(X17, |'1'|), |'1'|) = X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals_14')).
% 238.25/238.51 tff(555,plain,
% 238.25/238.51 (~![X17: $i] : (tptp_fun______(tptp_fun______(X17, |'1'|), |'1'|) = X17)),
% 238.25/238.51 inference(modus_ponens,[status(thm)],[554, 553])).
% 238.25/238.51 tff(556,plain,
% 238.25/238.51 (~![X17: $i] : (tptp_fun______(tptp_fun______(X17, |'1'|), |'1'|) = X17)),
% 238.25/238.51 inference(modus_ponens,[status(thm)],[555, 553])).
% 238.25/238.51 tff(557,plain,
% 238.25/238.51 (~![X17: $i] : (tptp_fun______(tptp_fun______(X17, |'1'|), |'1'|) = X17)),
% 238.25/238.51 inference(modus_ponens,[status(thm)],[556, 553])).
% 238.25/238.51 tff(558,plain,
% 238.25/238.51 (~![X17: $i] : (tptp_fun______(tptp_fun______(X17, |'1'|), |'1'|) = X17)),
% 238.25/238.51 inference(modus_ponens,[status(thm)],[557, 553])).
% 238.25/238.51 tff(559,plain,(
% 238.25/238.51 ~(tptp_fun______(tptp_fun______(X17!0, |'1'|), |'1'|) = X17!0)),
% 238.25/238.51 inference(skolemize,[status(sab)],[558])).
% 238.25/238.51 tff(560,plain,
% 238.25/238.51 ($false),
% 238.25/238.51 inference(unit_resolution,[status(thm)],[559, 552])).
% 238.25/238.51 % SZS output end Proof
% 0.15/239.02 % E exiting
%------------------------------------------------------------------------------