%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL893+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 03:01:09 PM UTC 2026
% Result : Theorem 3.97s 4.27s
% Output : Proof 4.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL893+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_E %s %d THM
% 0.15/0.41 % Computer : n019.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 6 00:27:10 UTC 2026
% 0.15/0.41 % CPUTime :
% 3.97/4.27 % SZS status Theorem
% 3.97/4.27 % SZS output start Proof
% 3.97/4.27 tff(tptp_fun__0__type, type, (
% 3.97/4.27 tptp_fun__0_: $i)).
% 3.97/4.27 tff(tptp_fun_X17_0_type, type, (
% 3.97/4.27 tptp_fun_X17_0: $i)).
% 3.97/4.27 tff(tptp_fun_____type, type, (
% 3.97/4.27 tptp_fun____: ( $i * $i ) > $i)).
% 3.97/4.27 tff(tptp_fun_______type, type, (
% 3.97/4.27 tptp_fun______: ( $i * $i ) > $i)).
% 3.97/4.27 tff(tptp_fun______type, type, (
% 3.97/4.27 tptp_fun_____: ( $i * $i ) > $o)).
% 3.97/4.27 tff(h_type, type, (
% 3.97/4.27 h: $i > $i)).
% 3.97/4.27 tff(1,plain,
% 3.97/4.27 (^[A: $i, B: $i] : refl((tptp_fun____(A, B) = tptp_fun____(B, A)) <=> (tptp_fun____(A, B) = tptp_fun____(B, A)))),
% 3.97/4.27 inference(bind,[status(th)],[])).
% 3.97/4.27 tff(2,plain,
% 3.97/4.27 (![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A)) <=> ![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 3.97/4.27 inference(quant_intro,[status(thm)],[1])).
% 3.97/4.27 tff(3,plain,
% 3.97/4.27 (![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A)) <=> ![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 3.97/4.27 inference(rewrite,[status(thm)],[])).
% 3.97/4.27 tff(4,axiom,(![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_02')).
% 3.97/4.27 tff(5,plain,
% 3.97/4.27 (![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.97/4.27 tff(6,plain,(
% 3.97/4.27 ![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 3.97/4.27 inference(skolemize,[status(sab)],[5])).
% 3.97/4.27 tff(7,plain,
% 3.97/4.27 (![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.97/4.27 tff(8,plain,
% 3.97/4.27 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|) = tptp_fun____(|'0'|, tptp_fun______(|'0'|, X17!0)))),
% 3.97/4.27 inference(quant_inst,[status(thm)],[])).
% 3.97/4.27 tff(9,plain,
% 3.97/4.27 (tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|) = tptp_fun____(|'0'|, tptp_fun______(|'0'|, X17!0))),
% 3.97/4.27 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.97/4.27 tff(10,plain,
% 3.97/4.27 (tptp_fun____(|'0'|, tptp_fun______(|'0'|, X17!0)) = tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|)),
% 3.97/4.27 inference(symmetry,[status(thm)],[9])).
% 3.97/4.27 tff(11,plain,
% 3.97/4.27 (^[A: $i, B: $i] : refl((tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A))) <=> (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A))))),
% 3.97/4.27 inference(bind,[status(th)],[])).
% 3.97/4.27 tff(12,plain,
% 3.97/4.27 (![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A))) <=> ![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A)))),
% 3.97/4.27 inference(quant_intro,[status(thm)],[11])).
% 3.97/4.27 tff(13,plain,
% 3.97/4.27 (![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A))) <=> ![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A)))),
% 3.97/4.27 inference(rewrite,[status(thm)],[])).
% 3.97/4.27 tff(14,axiom,(![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_13')).
% 3.97/4.27 tff(15,plain,
% 3.97/4.27 (![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A)))),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[14, 13])).
% 3.97/4.27 tff(16,plain,(
% 3.97/4.27 ![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A)))),
% 3.97/4.27 inference(skolemize,[status(sab)],[15])).
% 3.97/4.27 tff(17,plain,
% 3.97/4.27 (![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A)))),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[16, 12])).
% 3.97/4.27 tff(18,plain,
% 3.97/4.27 ((~![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A)))) | (tptp_fun____(|'0'|, tptp_fun______(|'0'|, X17!0)) = tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))),
% 3.97/4.27 inference(quant_inst,[status(thm)],[])).
% 3.97/4.27 tff(19,plain,
% 3.97/4.27 (tptp_fun____(|'0'|, tptp_fun______(|'0'|, X17!0)) = tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))),
% 3.97/4.27 inference(unit_resolution,[status(thm)],[18, 17])).
% 3.97/4.27 tff(20,plain,
% 3.97/4.27 (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = tptp_fun____(|'0'|, tptp_fun______(|'0'|, X17!0))),
% 3.97/4.27 inference(symmetry,[status(thm)],[19])).
% 3.97/4.27 tff(21,plain,
% 3.97/4.27 (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|)),
% 3.97/4.27 inference(transitivity,[status(thm)],[20, 10])).
% 3.97/4.27 tff(22,plain,
% 3.97/4.27 (^[A: $i] : refl((tptp_fun____(A, |'0'|) = A) <=> (tptp_fun____(A, |'0'|) = A))),
% 3.97/4.27 inference(bind,[status(th)],[])).
% 3.97/4.27 tff(23,plain,
% 3.97/4.27 (![A: $i] : (tptp_fun____(A, |'0'|) = A) <=> ![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 3.97/4.27 inference(quant_intro,[status(thm)],[22])).
% 3.97/4.27 tff(24,plain,
% 3.97/4.27 (![A: $i] : (tptp_fun____(A, |'0'|) = A) <=> ![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 3.97/4.27 inference(rewrite,[status(thm)],[])).
% 3.97/4.27 tff(25,axiom,(![A: $i] : (tptp_fun____(A, |'0'|) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_03')).
% 3.97/4.27 tff(26,plain,
% 3.97/4.27 (![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[25, 24])).
% 3.97/4.27 tff(27,plain,(
% 3.97/4.27 ![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 3.97/4.27 inference(skolemize,[status(sab)],[26])).
% 3.97/4.27 tff(28,plain,
% 3.97/4.27 (![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[27, 23])).
% 3.97/4.27 tff(29,plain,
% 3.97/4.27 ((~![A: $i] : (tptp_fun____(A, |'0'|) = A)) | (tptp_fun____(X17!0, |'0'|) = X17!0)),
% 3.97/4.27 inference(quant_inst,[status(thm)],[])).
% 3.97/4.27 tff(30,plain,
% 3.97/4.27 (tptp_fun____(X17!0, |'0'|) = X17!0),
% 3.97/4.27 inference(unit_resolution,[status(thm)],[29, 28])).
% 3.97/4.27 tff(31,plain,
% 3.97/4.27 (X17!0 = tptp_fun____(X17!0, |'0'|)),
% 3.97/4.27 inference(symmetry,[status(thm)],[30])).
% 3.97/4.27 tff(32,plain,
% 3.97/4.27 (tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))) <=> tptp_fun_____(tptp_fun____(X17!0, |'0'|), tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|))),
% 3.97/4.27 inference(monotonicity,[status(thm)],[31, 21])).
% 3.97/4.27 tff(33,plain,
% 3.97/4.27 (tptp_fun_____(tptp_fun____(X17!0, |'0'|), tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|)) <=> tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))),
% 3.97/4.27 inference(symmetry,[status(thm)],[32])).
% 3.97/4.27 tff(34,plain,
% 3.97/4.27 ((~![A: $i] : (tptp_fun____(A, |'0'|) = A)) | (tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|) = tptp_fun______(|'0'|, X17!0))),
% 3.97/4.27 inference(quant_inst,[status(thm)],[])).
% 3.97/4.27 tff(35,plain,
% 3.97/4.27 (tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|) = tptp_fun______(|'0'|, X17!0)),
% 3.97/4.27 inference(unit_resolution,[status(thm)],[34, 28])).
% 3.97/4.27 tff(36,plain,
% 3.97/4.27 ((~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))) <=> (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|)))),
% 3.97/4.27 inference(rewrite,[status(thm)],[])).
% 3.97/4.27 tff(37,plain,
% 3.97/4.27 ((~![X17: $i] : ((h(X17) = X17) => (X17 = |'0'|))) <=> (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|)))),
% 3.97/4.27 inference(rewrite,[status(thm)],[])).
% 3.97/4.27 tff(38,axiom,(~![X17: $i] : ((h(X17) = X17) => (X17 = |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals_15')).
% 3.97/4.27 tff(39,plain,
% 3.97/4.27 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[38, 37])).
% 3.97/4.27 tff(40,plain,
% 3.97/4.27 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[39, 36])).
% 3.97/4.27 tff(41,plain,
% 3.97/4.27 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[40, 36])).
% 3.97/4.27 tff(42,plain,
% 3.97/4.27 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 3.97/4.27 inference(modus_ponens,[status(thm)],[41, 36])).
% 3.97/4.27 tff(43,plain,(
% 3.97/4.27 ~((~(h(X17!0) = X17!0)) | (X17!0 = |'0'|))),
% 3.97/4.27 inference(skolemize,[status(sab)],[42])).
% 3.97/4.27 tff(44,plain,
% 3.97/4.27 (h(X17!0) = X17!0),
% 3.97/4.27 inference(or_elim,[status(thm)],[43])).
% 3.97/4.27 tff(45,plain,
% 3.97/4.27 (X17!0 = h(X17!0)),
% 3.97/4.27 inference(symmetry,[status(thm)],[44])).
% 3.97/4.27 tff(46,plain,
% 3.97/4.27 (tptp_fun______(X17!0, X17!0) = tptp_fun______(h(X17!0), X17!0)),
% 3.97/4.27 inference(monotonicity,[status(thm)],[45])).
% 3.97/4.27 tff(47,plain,
% 3.97/4.27 (tptp_fun______(h(X17!0), X17!0) = tptp_fun______(X17!0, X17!0)),
% 3.97/4.27 inference(symmetry,[status(thm)],[46])).
% 3.97/4.27 tff(48,plain,
% 3.97/4.27 (^[A: $i] : refl((h(A) = tptp_fun______(h(A), A)) <=> (h(A) = tptp_fun______(h(A), A)))),
% 3.97/4.27 inference(bind,[status(th)],[])).
% 3.97/4.27 tff(49,plain,
% 3.97/4.27 (![A: $i] : (h(A) = tptp_fun______(h(A), A)) <=> ![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 3.97/4.27 inference(quant_intro,[status(thm)],[48])).
% 3.97/4.28 tff(50,plain,
% 3.97/4.28 (![A: $i] : (h(A) = tptp_fun______(h(A), A)) <=> ![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 3.97/4.28 inference(rewrite,[status(thm)],[])).
% 3.97/4.28 tff(51,axiom,(![A: $i] : (h(A) = tptp_fun______(h(A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_14')).
% 3.97/4.28 tff(52,plain,
% 3.97/4.28 (![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 3.97/4.28 inference(modus_ponens,[status(thm)],[51, 50])).
% 3.97/4.28 tff(53,plain,(
% 3.97/4.28 ![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 3.97/4.28 inference(skolemize,[status(sab)],[52])).
% 3.97/4.28 tff(54,plain,
% 3.97/4.28 (![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 3.97/4.28 inference(modus_ponens,[status(thm)],[53, 49])).
% 3.97/4.28 tff(55,plain,
% 3.97/4.28 ((~![A: $i] : (h(A) = tptp_fun______(h(A), A))) | (h(X17!0) = tptp_fun______(h(X17!0), X17!0))),
% 3.97/4.28 inference(quant_inst,[status(thm)],[])).
% 3.97/4.28 tff(56,plain,
% 3.97/4.28 (h(X17!0) = tptp_fun______(h(X17!0), X17!0)),
% 3.97/4.28 inference(unit_resolution,[status(thm)],[55, 54])).
% 3.97/4.28 tff(57,plain,
% 3.97/4.28 (tptp_fun____(X17!0, |'0'|) = tptp_fun______(X17!0, X17!0)),
% 3.97/4.28 inference(transitivity,[status(thm)],[30, 45, 56, 47])).
% 3.97/4.28 tff(58,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun____(X17!0, |'0'|), tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|)) <=> tptp_fun_____(tptp_fun______(X17!0, X17!0), tptp_fun______(|'0'|, X17!0))),
% 3.97/4.28 inference(monotonicity,[status(thm)],[57, 35])).
% 3.97/4.28 tff(59,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun______(X17!0, X17!0), tptp_fun______(|'0'|, X17!0)) <=> tptp_fun_____(tptp_fun____(X17!0, |'0'|), tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|))),
% 3.97/4.28 inference(symmetry,[status(thm)],[58])).
% 3.97/4.28 tff(60,plain,
% 3.97/4.28 (X17!0 = tptp_fun______(X17!0, X17!0)),
% 3.97/4.28 inference(transitivity,[status(thm)],[45, 56, 47])).
% 3.97/4.28 tff(61,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun______(X17!0, X17!0))),
% 3.97/4.28 inference(monotonicity,[status(thm)],[60])).
% 3.97/4.28 tff(62,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun______(X17!0, X17!0)) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)),
% 3.97/4.28 inference(symmetry,[status(thm)],[61])).
% 3.97/4.28 tff(63,plain,
% 3.97/4.28 (^[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))))),
% 3.97/4.28 inference(bind,[status(th)],[])).
% 3.97/4.28 tff(64,plain,
% 3.97/4.28 (![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)))),
% 3.97/4.28 inference(quant_intro,[status(thm)],[63])).
% 3.97/4.28 tff(65,plain,
% 3.97/4.28 (![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)))),
% 3.97/4.28 inference(rewrite,[status(thm)],[])).
% 3.97/4.28 tff(66,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_08')).
% 3.97/4.28 tff(67,plain,
% 3.97/4.28 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 3.97/4.28 inference(modus_ponens,[status(thm)],[66, 65])).
% 3.97/4.28 tff(68,plain,(
% 3.97/4.28 ![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 3.97/4.28 inference(skolemize,[status(sab)],[67])).
% 3.97/4.28 tff(69,plain,
% 3.97/4.28 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 3.97/4.28 inference(modus_ponens,[status(thm)],[68, 64])).
% 3.97/4.28 tff(70,plain,
% 3.97/4.28 ((~![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______(tptp_fun____(X17!0, X17!0), X17!0)), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun______(X17!0, X17!0)))),
% 3.97/4.28 inference(quant_inst,[status(thm)],[])).
% 3.97/4.28 tff(71,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun______(X17!0, X17!0))),
% 3.97/4.28 inference(unit_resolution,[status(thm)],[70, 69])).
% 3.97/4.28 tff(72,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), tptp_fun______(X17!0, X17!0))),
% 3.97/4.28 inference(monotonicity,[status(thm)],[60])).
% 3.97/4.28 tff(73,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), tptp_fun______(X17!0, X17!0)) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), X17!0)),
% 3.97/4.28 inference(symmetry,[status(thm)],[72])).
% 3.97/4.28 tff(74,plain,
% 3.97/4.28 ((~![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, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), tptp_fun______(X17!0, X17!0)))),
% 3.97/4.28 inference(quant_inst,[status(thm)],[])).
% 3.97/4.28 tff(75,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), tptp_fun______(X17!0, X17!0))),
% 3.97/4.28 inference(unit_resolution,[status(thm)],[74, 69])).
% 3.97/4.28 tff(76,plain,
% 3.97/4.28 ((~![A: $i, B: $i] : (tptp_fun____(A, tptp_fun______(A, B)) = tptp_fun____(B, tptp_fun______(B, A)))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)) = tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))),
% 3.97/4.28 inference(quant_inst,[status(thm)],[])).
% 3.97/4.28 tff(77,plain,
% 3.97/4.28 (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)) = tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))),
% 3.97/4.28 inference(unit_resolution,[status(thm)],[76, 17])).
% 3.97/4.28 tff(78,plain,
% 3.97/4.28 (^[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))))),
% 3.97/4.28 inference(bind,[status(th)],[])).
% 3.97/4.28 tff(79,plain,
% 3.97/4.28 (![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)))),
% 3.97/4.28 inference(quant_intro,[status(thm)],[78])).
% 3.97/4.28 tff(80,plain,
% 3.97/4.28 (![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)))),
% 3.97/4.28 inference(rewrite,[status(thm)],[])).
% 3.97/4.28 tff(81,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')).
% 3.97/4.28 tff(82,plain,
% 3.97/4.28 (![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))),
% 3.97/4.28 inference(modus_ponens,[status(thm)],[81, 80])).
% 3.97/4.28 tff(83,plain,(
% 3.97/4.28 ![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))),
% 3.97/4.28 inference(skolemize,[status(sab)],[82])).
% 3.97/4.28 tff(84,plain,
% 3.97/4.28 (![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))),
% 3.97/4.28 inference(modus_ponens,[status(thm)],[83, 79])).
% 3.97/4.28 tff(85,plain,
% 3.97/4.28 ((~![A: $i, B: $i, C: $i] : (tptp_fun____(tptp_fun____(A, B), C) = tptp_fun____(A, tptp_fun____(B, C)))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)) = tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))))),
% 3.97/4.28 inference(quant_inst,[status(thm)],[])).
% 3.97/4.28 tff(86,plain,
% 3.97/4.28 (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)) = tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))),
% 3.97/4.28 inference(unit_resolution,[status(thm)],[85, 84])).
% 3.97/4.28 tff(87,plain,
% 3.97/4.28 (tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))) = tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 3.97/4.28 inference(symmetry,[status(thm)],[86])).
% 3.97/4.28 tff(88,plain,
% 3.97/4.28 (tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))) = tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))),
% 3.97/4.28 inference(transitivity,[status(thm)],[87, 77])).
% 3.97/4.28 tff(89,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))), X17!0)),
% 3.97/4.28 inference(monotonicity,[status(thm)],[88])).
% 3.97/4.28 tff(90,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))), X17!0)),
% 3.97/4.28 inference(symmetry,[status(thm)],[89])).
% 3.97/4.28 tff(91,plain,
% 3.97/4.28 ((~![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, tptp_fun____(X17!0, X17!0))), X17!0) <=> tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0)))),
% 3.97/4.28 inference(quant_inst,[status(thm)],[])).
% 3.97/4.28 tff(92,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))), X17!0) <=> tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0))),
% 3.97/4.28 inference(unit_resolution,[status(thm)],[91, 69])).
% 3.97/4.28 tff(93,plain,
% 3.97/4.28 ((~![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, X17!0), X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(X17!0, X17!0)))),
% 3.97/4.28 inference(quant_inst,[status(thm)],[])).
% 3.97/4.28 tff(94,plain,
% 3.97/4.28 (tptp_fun_____(tptp_fun____(X17!0, X17!0), X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(X17!0, X17!0))),
% 3.97/4.28 inference(unit_resolution,[status(thm)],[93, 69])).
% 3.97/4.28 tff(95,plain,
% 3.97/4.28 (tptp_fun______(h(X17!0), X17!0) = h(X17!0)),
% 3.97/4.28 inference(symmetry,[status(thm)],[56])).
% 3.97/4.28 tff(96,plain,
% 3.97/4.28 (tptp_fun______(X17!0, X17!0) = X17!0),
% 3.97/4.28 inference(transitivity,[status(thm)],[46, 95, 44])).
% 3.97/4.28 tff(97,plain,
% 3.97/4.28 (tptp_fun_____(X17!0, tptp_fun______(X17!0, X17!0)) <=> tptp_fun_____(X17!0, X17!0)),
% 3.97/4.28 inference(monotonicity,[status(thm)],[96])).
% 3.97/4.28 tff(98,plain,
% 3.97/4.28 (tptp_fun_____(X17!0, X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(X17!0, X17!0))),
% 3.97/4.28 inference(symmetry,[status(thm)],[97])).
% 3.97/4.28 tff(99,assumption,(~tptp_fun_____(X17!0, X17!0)), introduced(assumption)).
% 3.97/4.28 tff(100,plain,
% 3.97/4.28 (^[A: $i] : refl(tptp_fun_____(A, A) <=> tptp_fun_____(A, A))),
% 3.97/4.28 inference(bind,[status(th)],[])).
% 3.97/4.28 tff(101,plain,
% 3.97/4.28 (![A: $i] : tptp_fun_____(A, A) <=> ![A: $i] : tptp_fun_____(A, A)),
% 3.97/4.28 inference(quant_intro,[status(thm)],[100])).
% 3.97/4.28 tff(102,plain,
% 3.97/4.28 (![A: $i] : tptp_fun_____(A, A) <=> ![A: $i] : tptp_fun_____(A, A)),
% 3.97/4.28 inference(rewrite,[status(thm)],[])).
% 3.97/4.28 tff(103,axiom,(![A: $i] : tptp_fun_____(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_05')).
% 3.97/4.28 tff(104,plain,
% 3.97/4.28 (![A: $i] : tptp_fun_____(A, A)),
% 3.97/4.28 inference(modus_ponens,[status(thm)],[103, 102])).
% 3.97/4.28 tff(105,plain,(
% 3.97/4.28 ![A: $i] : tptp_fun_____(A, A)),
% 3.97/4.28 inference(skolemize,[status(sab)],[104])).
% 3.97/4.28 tff(106,plain,
% 3.97/4.28 (![A: $i] : tptp_fun_____(A, A)),
% 3.97/4.28 inference(modus_ponens,[status(thm)],[105, 101])).
% 3.97/4.28 tff(107,plain,
% 3.97/4.28 ((~![A: $i] : tptp_fun_____(A, A)) | tptp_fun_____(X17!0, X17!0)),
% 3.97/4.28 inference(quant_inst,[status(thm)],[])).
% 3.97/4.28 tff(108,plain,
% 3.97/4.28 ($false),
% 3.97/4.28 inference(unit_resolution,[status(thm)],[107, 106, 99])).
% 3.97/4.28 tff(109,plain,(tptp_fun_____(X17!0, X17!0)), inference(lemma,lemma(discharge,[]))).
% 3.97/4.29 tff(110,plain,
% 3.97/4.29 (tptp_fun_____(X17!0, tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[109, 98])).
% 3.97/4.29 tff(111,plain,
% 3.97/4.29 ((~(tptp_fun_____(tptp_fun____(X17!0, X17!0), X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(X17!0, X17!0)))) | tptp_fun_____(tptp_fun____(X17!0, X17!0), X17!0) | (~tptp_fun_____(X17!0, tptp_fun______(X17!0, X17!0)))),
% 3.97/4.29 inference(tautology,[status(thm)],[])).
% 3.97/4.29 tff(112,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, X17!0), X17!0)),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[111, 110, 94])).
% 3.97/4.29 tff(113,plain,
% 3.97/4.29 (^[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))))),
% 3.97/4.29 inference(bind,[status(th)],[])).
% 3.97/4.29 tff(114,plain,
% 3.97/4.29 (![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)))),
% 3.97/4.29 inference(quant_intro,[status(thm)],[113])).
% 3.97/4.29 tff(115,plain,
% 3.97/4.29 (![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)))),
% 3.97/4.29 inference(rewrite,[status(thm)],[])).
% 3.97/4.29 tff(116,plain,
% 3.97/4.29 (^[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))))),
% 3.97/4.29 inference(bind,[status(th)],[])).
% 3.97/4.29 tff(117,plain,
% 3.97/4.29 (![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)))),
% 3.97/4.29 inference(quant_intro,[status(thm)],[116])).
% 3.97/4.29 tff(118,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_12')).
% 3.97/4.29 tff(119,plain,
% 3.97/4.29 (![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[118, 117])).
% 3.97/4.29 tff(120,plain,
% 3.97/4.29 (![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[119, 115])).
% 3.97/4.29 tff(121,plain,(
% 3.97/4.29 ![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 3.97/4.29 inference(skolemize,[status(sab)],[120])).
% 3.97/4.29 tff(122,plain,
% 3.97/4.29 (![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[121, 114])).
% 3.97/4.29 tff(123,plain,
% 3.97/4.29 (((~![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, X17!0), X17!0)) | tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, 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____(X17!0, X17!0), X17!0)) | tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0)))),
% 3.97/4.29 inference(rewrite,[status(thm)],[])).
% 3.97/4.29 tff(124,plain,
% 3.97/4.29 ((~![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, X17!0), X17!0)) | tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0)))),
% 3.97/4.29 inference(quant_inst,[status(thm)],[])).
% 3.97/4.29 tff(125,plain,
% 3.97/4.29 ((~![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, X17!0), X17!0)) | tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[124, 123])).
% 3.97/4.29 tff(126,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[125, 122, 112])).
% 3.97/4.29 tff(127,plain,
% 3.97/4.29 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))), X17!0) <=> tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0)))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))), X17!0) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0)))),
% 3.97/4.29 inference(tautology,[status(thm)],[])).
% 3.97/4.29 tff(128,plain,
% 3.97/4.29 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))), X17!0) <=> tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0)))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))), X17!0)),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[127, 126])).
% 3.97/4.29 tff(129,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))), X17!0)),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[128, 92])).
% 3.97/4.29 tff(130,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))), X17!0)),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[129, 90])).
% 3.97/4.29 tff(131,plain,
% 3.97/4.29 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), tptp_fun______(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))), X17!0)) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(tautology,[status(thm)],[])).
% 3.97/4.29 tff(132,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[131, 130, 75])).
% 3.97/4.29 tff(133,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), X17!0)),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[132, 73])).
% 3.97/4.29 tff(134,plain,
% 3.97/4.29 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun______(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(tautology,[status(thm)],[])).
% 3.97/4.29 tff(135,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[134, 133, 71])).
% 3.97/4.29 tff(136,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[135, 62])).
% 3.97/4.29 tff(137,plain,
% 3.97/4.29 ((~![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, X17!0), X17!0), X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))),
% 3.97/4.29 inference(quant_inst,[status(thm)],[])).
% 3.97/4.29 tff(138,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[137, 69])).
% 3.97/4.29 tff(139,plain,
% 3.97/4.29 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 3.97/4.29 inference(quant_inst,[status(thm)],[])).
% 3.97/4.29 tff(140,plain,
% 3.97/4.29 (tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[139, 7])).
% 3.97/4.29 tff(141,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)),
% 3.97/4.29 inference(monotonicity,[status(thm)],[140])).
% 3.97/4.29 tff(142,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), X17!0) <=> tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), X17!0)),
% 3.97/4.29 inference(symmetry,[status(thm)],[141])).
% 3.97/4.29 tff(143,plain,
% 3.97/4.29 ((~![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, X17!0)), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun______(X17!0, X17!0)))),
% 3.97/4.29 inference(quant_inst,[status(thm)],[])).
% 3.97/4.29 tff(144,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[143, 69])).
% 3.97/4.29 tff(145,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun______(X17!0, X17!0)) <=> tptp_fun_____(tptp_fun____(X17!0, X17!0), X17!0)),
% 3.97/4.29 inference(monotonicity,[status(thm)],[96])).
% 3.97/4.29 tff(146,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, X17!0), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(symmetry,[status(thm)],[145])).
% 3.97/4.29 tff(147,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun______(X17!0, X17!0))),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[112, 146])).
% 3.97/4.29 tff(148,plain,
% 3.97/4.29 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun______(X17!0, X17!0)))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), X17!0) | (~tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun______(X17!0, X17!0)))),
% 3.97/4.29 inference(tautology,[status(thm)],[])).
% 3.97/4.29 tff(149,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[148, 147, 144])).
% 3.97/4.29 tff(150,plain,
% 3.97/4.29 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), X17!0)),
% 3.97/4.29 inference(modus_ponens,[status(thm)],[149, 142])).
% 3.97/4.29 tff(151,plain,
% 3.97/4.29 ((~(tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), X17!0) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))) | (~tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), X17!0)) | tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 3.97/4.29 inference(tautology,[status(thm)],[])).
% 3.97/4.29 tff(152,plain,
% 3.97/4.29 (tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 3.97/4.29 inference(unit_resolution,[status(thm)],[151, 150, 138])).
% 3.97/4.29 tff(153,plain,
% 3.97/4.29 (![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)))),
% 3.97/4.29 inference(rewrite,[status(thm)],[])).
% 3.97/4.29 tff(154,plain,
% 3.97/4.29 (^[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)))))),
% 4.07/4.30 inference(bind,[status(th)],[])).
% 4.07/4.30 tff(155,plain,
% 4.07/4.30 (![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)))),
% 4.07/4.30 inference(quant_intro,[status(thm)],[154])).
% 4.07/4.30 tff(156,plain,
% 4.07/4.30 (![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))),
% 4.07/4.30 inference(rewrite,[status(thm)],[])).
% 4.07/4.30 tff(157,plain,
% 4.07/4.30 (^[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)))),
% 4.07/4.30 inference(bind,[status(th)],[])).
% 4.07/4.30 tff(158,plain,
% 4.07/4.30 (![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))),
% 4.07/4.30 inference(quant_intro,[status(thm)],[157])).
% 4.07/4.30 tff(159,axiom,(![X3: $i, X4: $i] : ((tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3)) => (X3 = X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_07')).
% 4.07/4.30 tff(160,plain,
% 4.07/4.30 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 4.07/4.30 inference(modus_ponens,[status(thm)],[159, 158])).
% 4.07/4.30 tff(161,plain,
% 4.07/4.30 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 4.07/4.30 inference(modus_ponens,[status(thm)],[160, 156])).
% 4.07/4.30 tff(162,plain,(
% 4.07/4.30 ![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 4.07/4.30 inference(skolemize,[status(sab)],[161])).
% 4.07/4.30 tff(163,plain,
% 4.07/4.30 (![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 4.07/4.30 inference(modus_ponens,[status(thm)],[162, 155])).
% 4.07/4.30 tff(164,plain,
% 4.07/4.30 (![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 4.07/4.30 inference(modus_ponens,[status(thm)],[163, 153])).
% 4.07/4.30 tff(165,plain,
% 4.07/4.30 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)) | (X17!0 = tptp_fun______(tptp_fun____(X17!0, 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, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)) | (X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))),
% 4.07/4.30 inference(rewrite,[status(thm)],[])).
% 4.07/4.30 tff(166,plain,
% 4.07/4.30 (((X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0))) <=> ((~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)) | (X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))),
% 4.07/4.30 inference(rewrite,[status(thm)],[])).
% 4.07/4.30 tff(167,plain,
% 4.07/4.30 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), 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, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)) | (X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))))),
% 4.07/4.30 inference(monotonicity,[status(thm)],[166])).
% 4.07/4.30 tff(168,plain,
% 4.07/4.30 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), 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, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)) | (X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))),
% 4.07/4.30 inference(transitivity,[status(thm)],[167, 165])).
% 4.07/4.30 tff(169,plain,
% 4.07/4.30 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)))),
% 4.07/4.30 inference(quant_inst,[status(thm)],[])).
% 4.07/4.30 tff(170,plain,
% 4.07/4.30 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)) | (X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 4.07/4.30 inference(modus_ponens,[status(thm)],[169, 168])).
% 4.07/4.30 tff(171,plain,
% 4.07/4.30 ((~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0), X17!0)) | (X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 4.07/4.30 inference(unit_resolution,[status(thm)],[170, 164, 152])).
% 4.07/4.30 tff(172,plain,
% 4.07/4.30 (X17!0 = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)),
% 4.07/4.30 inference(unit_resolution,[status(thm)],[171, 136])).
% 4.07/4.30 tff(173,plain,
% 4.07/4.30 (tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0) = X17!0),
% 4.07/4.30 inference(symmetry,[status(thm)],[172])).
% 4.07/4.30 tff(174,plain,
% 4.07/4.30 (tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0) <=> tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0))),
% 4.07/4.30 inference(monotonicity,[status(thm)],[60])).
% 4.07/4.30 tff(175,plain,
% 4.07/4.30 (tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun______(X17!0, X17!0)) <=> tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)),
% 4.07/4.30 inference(symmetry,[status(thm)],[174])).
% 4.07/4.30 tff(176,plain,
% 4.07/4.30 (tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)),
% 4.07/4.30 inference(modus_ponens,[status(thm)],[126, 175])).
% 4.07/4.30 tff(177,plain,
% 4.07/4.30 ((~![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, X17!0), tptp_fun____(X17!0, X17!0)) <=> tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.30 inference(quant_inst,[status(thm)],[])).
% 4.07/4.30 tff(178,plain,
% 4.07/4.30 (tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, X17!0)) <=> tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.30 inference(unit_resolution,[status(thm)],[177, 69])).
% 4.07/4.30 tff(179,plain,
% 4.07/4.30 (^[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))))),
% 4.07/4.30 inference(bind,[status(th)],[])).
% 4.07/4.30 tff(180,plain,
% 4.07/4.30 (![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)))),
% 4.07/4.30 inference(quant_intro,[status(thm)],[179])).
% 4.07/4.30 tff(181,plain,
% 4.07/4.30 (![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)))),
% 4.07/4.30 inference(rewrite,[status(thm)],[])).
% 4.07/4.30 tff(182,plain,
% 4.07/4.30 (^[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))))),
% 4.07/4.31 inference(bind,[status(th)],[])).
% 4.07/4.31 tff(183,plain,
% 4.07/4.31 (![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)))),
% 4.07/4.31 inference(quant_intro,[status(thm)],[182])).
% 4.07/4.31 tff(184,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_10')).
% 4.07/4.31 tff(185,plain,
% 4.07/4.31 (![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 4.07/4.31 inference(modus_ponens,[status(thm)],[184, 183])).
% 4.07/4.31 tff(186,plain,
% 4.07/4.31 (![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 4.07/4.31 inference(modus_ponens,[status(thm)],[185, 181])).
% 4.07/4.31 tff(187,plain,(
% 4.07/4.31 ![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 4.07/4.31 inference(skolemize,[status(sab)],[186])).
% 4.07/4.31 tff(188,plain,
% 4.07/4.31 (![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))),
% 4.07/4.31 inference(modus_ponens,[status(thm)],[187, 180])).
% 4.07/4.31 tff(189,plain,
% 4.07/4.31 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!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_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, X17!0)))),
% 4.07/4.31 inference(rewrite,[status(thm)],[])).
% 4.07/4.31 tff(190,plain,
% 4.07/4.31 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, X17!0)))),
% 4.07/4.31 inference(quant_inst,[status(thm)],[])).
% 4.07/4.31 tff(191,plain,
% 4.07/4.31 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, X17!0))),
% 4.07/4.31 inference(modus_ponens,[status(thm)],[190, 189])).
% 4.07/4.31 tff(192,plain,
% 4.07/4.31 (tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, X17!0))),
% 4.07/4.31 inference(unit_resolution,[status(thm)],[191, 188, 109])).
% 4.07/4.31 tff(193,plain,
% 4.07/4.31 ((~(tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, X17!0)) <=> tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))) | (~tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, X17!0))) | tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.31 inference(tautology,[status(thm)],[])).
% 4.07/4.31 tff(194,plain,
% 4.07/4.31 ((~(tptp_fun_____(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, X17!0)) <=> tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))) | tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.31 inference(unit_resolution,[status(thm)],[193, 192])).
% 4.07/4.31 tff(195,plain,
% 4.07/4.31 (tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.31 inference(unit_resolution,[status(thm)],[194, 178])).
% 4.07/4.31 tff(196,plain,
% 4.07/4.31 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)) | (X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)) | (X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.31 inference(rewrite,[status(thm)],[])).
% 4.07/4.31 tff(197,plain,
% 4.07/4.31 (((X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))) | (~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0))) <=> ((~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)) | (X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.31 inference(rewrite,[status(thm)],[])).
% 4.07/4.31 tff(198,plain,
% 4.07/4.31 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))) | (~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)) | (X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.31 inference(monotonicity,[status(thm)],[197])).
% 4.07/4.31 tff(199,plain,
% 4.07/4.31 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))) | (~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)) | (X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.31 inference(transitivity,[status(thm)],[198, 196])).
% 4.07/4.31 tff(200,plain,
% 4.07/4.31 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))) | (~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)))),
% 4.07/4.31 inference(quant_inst,[status(thm)],[])).
% 4.07/4.31 tff(201,plain,
% 4.07/4.31 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)) | (X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.31 inference(modus_ponens,[status(thm)],[200, 199])).
% 4.07/4.31 tff(202,plain,
% 4.07/4.31 ((~tptp_fun_____(tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)) | (X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.31 inference(unit_resolution,[status(thm)],[201, 164, 195])).
% 4.07/4.31 tff(203,plain,
% 4.07/4.31 (X17!0 = tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))),
% 4.07/4.31 inference(unit_resolution,[status(thm)],[202, 176])).
% 4.07/4.31 tff(204,plain,
% 4.07/4.31 (tptp_fun____(X17!0, X17!0) = tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.31 inference(monotonicity,[status(thm)],[203])).
% 4.07/4.31 tff(205,plain,
% 4.07/4.31 (tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))) = tptp_fun____(X17!0, X17!0)),
% 4.07/4.31 inference(symmetry,[status(thm)],[204])).
% 4.07/4.31 tff(206,plain,
% 4.07/4.31 (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)) = tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0)),
% 4.07/4.31 inference(monotonicity,[status(thm)],[173])).
% 4.07/4.31 tff(207,plain,
% 4.07/4.31 (tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0) = tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 4.07/4.31 inference(symmetry,[status(thm)],[206])).
% 4.07/4.31 tff(208,plain,
% 4.07/4.31 (tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)) = tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0)),
% 4.07/4.31 inference(symmetry,[status(thm)],[140])).
% 4.07/4.32 tff(209,plain,
% 4.07/4.32 (tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, X17!0))),
% 4.07/4.32 inference(monotonicity,[status(thm)],[205])).
% 4.07/4.32 tff(210,plain,
% 4.07/4.32 (tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, X17!0)) = tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(symmetry,[status(thm)],[209])).
% 4.07/4.32 tff(211,plain,
% 4.07/4.32 ((~![A: $i, B: $i] : (tptp_fun____(A, B) = tptp_fun____(B, A))) | (tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, X17!0)) = tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.32 inference(quant_inst,[status(thm)],[])).
% 4.07/4.32 tff(212,plain,
% 4.07/4.32 (tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, X17!0)) = tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(unit_resolution,[status(thm)],[211, 7])).
% 4.07/4.32 tff(213,plain,
% 4.07/4.32 (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, X17!0))),
% 4.07/4.32 inference(symmetry,[status(thm)],[212])).
% 4.07/4.32 tff(214,plain,
% 4.07/4.32 (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(transitivity,[status(thm)],[213, 210])).
% 4.07/4.32 tff(215,plain,
% 4.07/4.32 (tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))),
% 4.07/4.32 inference(monotonicity,[status(thm)],[205])).
% 4.07/4.32 tff(216,plain,
% 4.07/4.32 (tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)) = tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(symmetry,[status(thm)],[215])).
% 4.07/4.32 tff(217,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.32 inference(monotonicity,[status(thm)],[216, 214])).
% 4.07/4.32 tff(218,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.32 inference(symmetry,[status(thm)],[217])).
% 4.07/4.32 tff(219,plain,
% 4.07/4.32 ((~![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, X17!0), X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.32 inference(quant_inst,[status(thm)],[])).
% 4.07/4.32 tff(220,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(unit_resolution,[status(thm)],[219, 69])).
% 4.07/4.32 tff(221,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) <=> tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.32 inference(monotonicity,[status(thm)],[140])).
% 4.07/4.32 tff(222,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) <=> tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.32 inference(symmetry,[status(thm)],[221])).
% 4.07/4.32 tff(223,plain,
% 4.07/4.32 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!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_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(rewrite,[status(thm)],[])).
% 4.07/4.32 tff(224,plain,
% 4.07/4.32 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(quant_inst,[status(thm)],[])).
% 4.07/4.32 tff(225,plain,
% 4.07/4.32 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.32 inference(modus_ponens,[status(thm)],[224, 223])).
% 4.07/4.32 tff(226,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.32 inference(unit_resolution,[status(thm)],[225, 188, 109])).
% 4.07/4.32 tff(227,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.32 inference(modus_ponens,[status(thm)],[226, 222])).
% 4.07/4.32 tff(228,plain,
% 4.07/4.32 ((~(tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) <=> tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | (~tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(tautology,[status(thm)],[])).
% 4.07/4.32 tff(229,plain,
% 4.07/4.32 (tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(unit_resolution,[status(thm)],[228, 227, 220])).
% 4.07/4.32 tff(230,plain,
% 4.07/4.32 (((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!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_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))))),
% 4.07/4.32 inference(rewrite,[status(thm)],[])).
% 4.07/4.32 tff(231,plain,
% 4.07/4.32 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | ((~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0))))))),
% 4.07/4.32 inference(quant_inst,[status(thm)],[])).
% 4.07/4.32 tff(232,plain,
% 4.07/4.32 ((~![X8: $i, X9: $i, X10: $i] : ((~tptp_fun_____(X8, X9)) | tptp_fun_____(tptp_fun____(X8, X10), tptp_fun____(X9, X10)))) | (~tptp_fun_____(X17!0, tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.32 inference(modus_ponens,[status(thm)],[231, 230])).
% 4.07/4.32 tff(233,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun____(X17!0, tptp_fun______(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.32 inference(unit_resolution,[status(thm)],[232, 188, 229])).
% 4.07/4.32 tff(234,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.32 inference(modus_ponens,[status(thm)],[233, 218])).
% 4.07/4.32 tff(235,plain,
% 4.07/4.32 ((~![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, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.32 inference(quant_inst,[status(thm)],[])).
% 4.07/4.32 tff(236,plain,
% 4.07/4.32 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.32 inference(unit_resolution,[status(thm)],[235, 69])).
% 4.07/4.32 tff(237,plain,
% 4.07/4.32 (((~![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, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, 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____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.33 inference(rewrite,[status(thm)],[])).
% 4.07/4.33 tff(238,plain,
% 4.07/4.33 ((~![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, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.33 inference(quant_inst,[status(thm)],[])).
% 4.07/4.33 tff(239,plain,
% 4.07/4.33 ((~![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, tptp_fun____(X17!0, X17!0)), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.33 inference(modus_ponens,[status(thm)],[238, 237])).
% 4.07/4.33 tff(240,plain,
% 4.07/4.33 (tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.33 inference(unit_resolution,[status(thm)],[239, 122, 226])).
% 4.07/4.33 tff(241,plain,
% 4.07/4.33 ((~(tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.33 inference(tautology,[status(thm)],[])).
% 4.07/4.33 tff(242,plain,
% 4.07/4.33 ((~(tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.33 inference(unit_resolution,[status(thm)],[241, 240])).
% 4.07/4.33 tff(243,plain,
% 4.07/4.33 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.33 inference(unit_resolution,[status(thm)],[242, 236])).
% 4.07/4.33 tff(244,plain,
% 4.07/4.33 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!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, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.33 inference(rewrite,[status(thm)],[])).
% 4.07/4.33 tff(245,plain,
% 4.07/4.33 (((tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) | (~tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))))) <=> ((~tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.33 inference(rewrite,[status(thm)],[])).
% 4.07/4.33 tff(246,plain,
% 4.07/4.33 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) | (~tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!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, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.33 inference(monotonicity,[status(thm)],[245])).
% 4.07/4.33 tff(247,plain,
% 4.07/4.33 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) | (~tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!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, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.34 inference(transitivity,[status(thm)],[246, 244])).
% 4.07/4.34 tff(248,plain,
% 4.07/4.34 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))) | (~tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))))),
% 4.07/4.34 inference(quant_inst,[status(thm)],[])).
% 4.07/4.34 tff(249,plain,
% 4.07/4.34 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.34 inference(modus_ponens,[status(thm)],[248, 247])).
% 4.07/4.34 tff(250,plain,
% 4.07/4.34 ((~tptp_fun_____(tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)), tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))) | (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))),
% 4.07/4.34 inference(unit_resolution,[status(thm)],[249, 164, 243])).
% 4.07/4.34 tff(251,plain,
% 4.07/4.34 (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))),
% 4.07/4.34 inference(unit_resolution,[status(thm)],[250, 234])).
% 4.07/4.34 tff(252,plain,
% 4.07/4.34 (tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))) = tptp_fun____(X17!0, X17!0)),
% 4.07/4.34 inference(transitivity,[status(thm)],[251, 208, 207, 77, 205])).
% 4.07/4.34 tff(253,plain,
% 4.07/4.34 (tptp_fun______(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0) = tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)),
% 4.07/4.34 inference(monotonicity,[status(thm)],[252])).
% 4.07/4.34 tff(254,plain,
% 4.07/4.34 (tptp_fun______(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0) = X17!0),
% 4.07/4.34 inference(transitivity,[status(thm)],[253, 173])).
% 4.07/4.34 tff(255,plain,
% 4.07/4.34 (tptp_fun_____(|'0'|, tptp_fun______(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0)) <=> tptp_fun_____(|'0'|, X17!0)),
% 4.07/4.34 inference(monotonicity,[status(thm)],[254])).
% 4.07/4.34 tff(256,plain,
% 4.07/4.34 ((~![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, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), |'0'|), X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0)))),
% 4.07/4.34 inference(quant_inst,[status(thm)],[])).
% 4.07/4.34 tff(257,plain,
% 4.07/4.34 (tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), |'0'|), X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0))),
% 4.07/4.34 inference(unit_resolution,[status(thm)],[256, 69])).
% 4.07/4.34 tff(258,plain,
% 4.07/4.34 ((~![A: $i] : (tptp_fun____(A, |'0'|) = A)) | (tptp_fun____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), |'0'|) = tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))))),
% 4.07/4.34 inference(quant_inst,[status(thm)],[])).
% 4.07/4.34 tff(259,plain,
% 4.07/4.34 (tptp_fun____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), |'0'|) = tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))))),
% 4.07/4.34 inference(unit_resolution,[status(thm)],[258, 28])).
% 4.07/4.34 tff(260,plain,
% 4.07/4.34 (tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), |'0'|), X17!0) <=> tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0)),
% 4.07/4.34 inference(monotonicity,[status(thm)],[259])).
% 4.07/4.34 tff(261,plain,
% 4.07/4.34 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0) <=> tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), |'0'|), X17!0)),
% 4.07/4.34 inference(symmetry,[status(thm)],[260])).
% 4.07/4.34 tff(262,plain,
% 4.07/4.34 ((~![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, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))),
% 4.07/4.34 inference(quant_inst,[status(thm)],[])).
% 4.07/4.34 tff(263,plain,
% 4.07/4.34 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 4.07/4.34 inference(unit_resolution,[status(thm)],[262, 69])).
% 4.07/4.34 tff(264,plain,
% 4.07/4.34 (((~![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, tptp_fun____(X17!0, X17!0)), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), 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____(X17!0, tptp_fun____(X17!0, X17!0)), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))),
% 4.07/4.35 inference(rewrite,[status(thm)],[])).
% 4.07/4.35 tff(265,plain,
% 4.07/4.35 ((~![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, tptp_fun____(X17!0, X17!0)), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))),
% 4.07/4.35 inference(quant_inst,[status(thm)],[])).
% 4.07/4.35 tff(266,plain,
% 4.07/4.35 ((~![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, tptp_fun____(X17!0, X17!0)), X17!0)) | tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[265, 264])).
% 4.07/4.35 tff(267,plain,
% 4.07/4.35 (tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0))),
% 4.07/4.35 inference(unit_resolution,[status(thm)],[266, 122, 149])).
% 4.07/4.35 tff(268,plain,
% 4.07/4.35 ((~(tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))) | tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0) | (~tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))),
% 4.07/4.35 inference(tautology,[status(thm)],[])).
% 4.07/4.35 tff(269,plain,
% 4.07/4.35 ((~(tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0) <=> tptp_fun_____(tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0))), tptp_fun______(tptp_fun____(X17!0, X17!0), X17!0)))) | tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0)),
% 4.07/4.35 inference(unit_resolution,[status(thm)],[268, 267])).
% 4.07/4.35 tff(270,plain,
% 4.07/4.35 (tptp_fun_____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0)),
% 4.07/4.35 inference(unit_resolution,[status(thm)],[269, 263])).
% 4.07/4.35 tff(271,plain,
% 4.07/4.35 (tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), |'0'|), X17!0)),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[270, 261])).
% 4.07/4.35 tff(272,plain,
% 4.07/4.35 ((~(tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), |'0'|), X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0)))) | (~tptp_fun_____(tptp_fun____(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), |'0'|), X17!0)) | tptp_fun_____(|'0'|, tptp_fun______(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0))),
% 4.07/4.35 inference(tautology,[status(thm)],[])).
% 4.07/4.35 tff(273,plain,
% 4.07/4.35 (tptp_fun_____(|'0'|, tptp_fun______(tptp_fun____(tptp_fun____(X17!0, X17!0), tptp_fun______(tptp_fun____(X17!0, X17!0), tptp_fun____(X17!0, tptp_fun____(X17!0, X17!0)))), X17!0))),
% 4.07/4.35 inference(unit_resolution,[status(thm)],[272, 271, 257])).
% 4.07/4.35 tff(274,plain,
% 4.07/4.35 (tptp_fun_____(|'0'|, X17!0)),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[273, 255])).
% 4.07/4.35 tff(275,plain,
% 4.07/4.35 (^[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))))),
% 4.07/4.35 inference(bind,[status(th)],[])).
% 4.07/4.35 tff(276,plain,
% 4.07/4.35 (![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)))),
% 4.07/4.35 inference(quant_intro,[status(thm)],[275])).
% 4.07/4.35 tff(277,plain,
% 4.07/4.35 (![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)))),
% 4.07/4.35 inference(rewrite,[status(thm)],[])).
% 4.07/4.35 tff(278,plain,
% 4.07/4.35 (^[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))))),
% 4.07/4.35 inference(bind,[status(th)],[])).
% 4.07/4.35 tff(279,plain,
% 4.07/4.35 (![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)))),
% 4.07/4.35 inference(quant_intro,[status(thm)],[278])).
% 4.07/4.35 tff(280,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_11')).
% 4.07/4.35 tff(281,plain,
% 4.07/4.35 (![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[280, 279])).
% 4.07/4.35 tff(282,plain,
% 4.07/4.35 (![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[281, 277])).
% 4.07/4.35 tff(283,plain,(
% 4.07/4.35 ![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 4.07/4.35 inference(skolemize,[status(sab)],[282])).
% 4.07/4.35 tff(284,plain,
% 4.07/4.35 (![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[283, 276])).
% 4.07/4.35 tff(285,plain,
% 4.07/4.35 (((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, X17!0), tptp_fun______(|'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_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, X17!0), tptp_fun______(|'0'|, X17!0)))),
% 4.07/4.35 inference(rewrite,[status(thm)],[])).
% 4.07/4.35 tff(286,plain,
% 4.07/4.35 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, X17!0), tptp_fun______(|'0'|, X17!0)))),
% 4.07/4.35 inference(quant_inst,[status(thm)],[])).
% 4.07/4.35 tff(287,plain,
% 4.07/4.35 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, X17!0), tptp_fun______(|'0'|, X17!0))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[286, 285])).
% 4.07/4.35 tff(288,plain,
% 4.07/4.35 ((~tptp_fun_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, X17!0), tptp_fun______(|'0'|, X17!0))),
% 4.07/4.35 inference(unit_resolution,[status(thm)],[287, 284])).
% 4.07/4.35 tff(289,plain,
% 4.07/4.35 (tptp_fun_____(tptp_fun______(X17!0, X17!0), tptp_fun______(|'0'|, X17!0))),
% 4.07/4.35 inference(unit_resolution,[status(thm)],[288, 274])).
% 4.07/4.35 tff(290,plain,
% 4.07/4.35 (tptp_fun_____(tptp_fun____(X17!0, |'0'|), tptp_fun____(tptp_fun______(|'0'|, X17!0), |'0'|))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[289, 59])).
% 4.07/4.35 tff(291,plain,
% 4.07/4.35 (tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[290, 33])).
% 4.07/4.35 tff(292,plain,
% 4.07/4.35 (![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)))),
% 4.07/4.35 inference(rewrite,[status(thm)],[])).
% 4.07/4.35 tff(293,plain,
% 4.07/4.35 (^[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)))))),
% 4.07/4.35 inference(bind,[status(th)],[])).
% 4.07/4.35 tff(294,plain,
% 4.07/4.35 (![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)))),
% 4.07/4.35 inference(quant_intro,[status(thm)],[293])).
% 4.07/4.35 tff(295,plain,
% 4.07/4.35 (![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))),
% 4.07/4.35 inference(rewrite,[status(thm)],[])).
% 4.07/4.35 tff(296,plain,
% 4.07/4.35 (^[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)))),
% 4.07/4.35 inference(bind,[status(th)],[])).
% 4.07/4.35 tff(297,plain,
% 4.07/4.35 (![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))),
% 4.07/4.35 inference(quant_intro,[status(thm)],[296])).
% 4.07/4.35 tff(298,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_06')).
% 4.07/4.35 tff(299,plain,
% 4.07/4.35 (![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[298, 297])).
% 4.07/4.35 tff(300,plain,
% 4.07/4.35 (![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[299, 295])).
% 4.07/4.35 tff(301,plain,(
% 4.07/4.35 ![X0: $i, X1: $i, X2: $i] : ((~(tptp_fun_____(X0, X1) & tptp_fun_____(X1, X2))) | tptp_fun_____(X0, X2))),
% 4.07/4.35 inference(skolemize,[status(sab)],[300])).
% 4.07/4.35 tff(302,plain,
% 4.07/4.35 (![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[301, 294])).
% 4.07/4.35 tff(303,plain,
% 4.07/4.35 (![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))),
% 4.07/4.35 inference(modus_ponens,[status(thm)],[302, 292])).
% 4.07/4.36 tff(304,plain,
% 4.07/4.36 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))))),
% 4.07/4.36 inference(rewrite,[status(thm)],[])).
% 4.07/4.36 tff(305,plain,
% 4.07/4.36 ((tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))) | (~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))))) <=> ((~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))))),
% 4.07/4.36 inference(rewrite,[status(thm)],[])).
% 4.07/4.36 tff(306,plain,
% 4.07/4.36 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))) | (~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | ((~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))),
% 4.07/4.36 inference(monotonicity,[status(thm)],[305])).
% 4.07/4.36 tff(307,plain,
% 4.07/4.36 (((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))) | (~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))))),
% 4.07/4.36 inference(transitivity,[status(thm)],[306, 304])).
% 4.07/4.36 tff(308,plain,
% 4.07/4.36 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))) | (~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))),
% 4.07/4.36 inference(quant_inst,[status(thm)],[])).
% 4.07/4.36 tff(309,plain,
% 4.07/4.36 ((~![X0: $i, X1: $i, X2: $i] : (tptp_fun_____(X0, X2) | (~tptp_fun_____(X0, X1)) | (~tptp_fun_____(X1, X2)))) | (~tptp_fun_____(|'0'|, X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))),
% 4.07/4.36 inference(modus_ponens,[status(thm)],[308, 307])).
% 4.07/4.36 tff(310,plain,
% 4.07/4.36 (tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))),
% 4.07/4.36 inference(unit_resolution,[status(thm)],[309, 303, 274, 291])).
% 4.07/4.36 tff(311,plain,
% 4.07/4.36 ((~![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, |'0'|)), |'0'|) <=> tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|)))),
% 4.07/4.36 inference(quant_inst,[status(thm)],[])).
% 4.07/4.36 tff(312,plain,
% 4.07/4.36 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|) <=> tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|))),
% 4.07/4.36 inference(unit_resolution,[status(thm)],[311, 69])).
% 4.07/4.36 tff(313,plain,
% 4.07/4.36 (((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|)))) <=> ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|)))),
% 4.07/4.36 inference(rewrite,[status(thm)],[])).
% 4.07/4.36 tff(314,plain,
% 4.07/4.36 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | ((~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|)))),
% 4.07/4.36 inference(quant_inst,[status(thm)],[])).
% 4.07/4.36 tff(315,plain,
% 4.07/4.36 ((~![X11: $i, X12: $i, X13: $i] : ((~tptp_fun_____(X11, X12)) | tptp_fun_____(tptp_fun______(X12, X13), tptp_fun______(X11, X13)))) | (~tptp_fun_____(X17!0, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|))),
% 4.07/4.36 inference(modus_ponens,[status(thm)],[314, 313])).
% 4.07/4.36 tff(316,plain,
% 4.07/4.36 (tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|))),
% 4.07/4.36 inference(unit_resolution,[status(thm)],[315, 284, 109])).
% 4.07/4.36 tff(317,plain,
% 4.07/4.36 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|) <=> tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|)))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|) | (~tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|)))),
% 4.07/4.36 inference(tautology,[status(thm)],[])).
% 4.07/4.36 tff(318,plain,
% 4.07/4.36 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|) <=> tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, |'0'|)))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)),
% 4.07/4.36 inference(unit_resolution,[status(thm)],[317, 316])).
% 4.07/4.36 tff(319,plain,
% 4.07/4.36 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)),
% 4.07/4.36 inference(unit_resolution,[status(thm)],[318, 312])).
% 4.07/4.36 tff(320,plain,
% 4.07/4.36 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|))),
% 4.07/4.36 inference(rewrite,[status(thm)],[])).
% 4.07/4.36 tff(321,plain,
% 4.07/4.36 (((tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))))) <=> ((~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|))),
% 4.07/4.36 inference(rewrite,[status(thm)],[])).
% 4.07/4.36 tff(322,plain,
% 4.07/4.36 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|)))),
% 4.07/4.36 inference(monotonicity,[status(thm)],[321])).
% 4.07/4.36 tff(323,plain,
% 4.07/4.36 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|))),
% 4.07/4.37 inference(transitivity,[status(thm)],[322, 320])).
% 4.07/4.37 tff(324,plain,
% 4.07/4.37 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))),
% 4.07/4.37 inference(quant_inst,[status(thm)],[])).
% 4.07/4.37 tff(325,plain,
% 4.07/4.37 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), |'0'|)) | (~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|)),
% 4.07/4.37 inference(modus_ponens,[status(thm)],[324, 323])).
% 4.07/4.37 tff(326,plain,
% 4.07/4.37 ((~tptp_fun_____(|'0'|, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|)),
% 4.07/4.37 inference(unit_resolution,[status(thm)],[325, 164, 319])).
% 4.07/4.37 tff(327,plain,
% 4.07/4.37 (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = |'0'|),
% 4.07/4.37 inference(unit_resolution,[status(thm)],[326, 310])).
% 4.07/4.37 tff(328,plain,
% 4.07/4.37 ((~![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, |'0'|)), X17!0) <=> tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0)))),
% 4.07/4.37 inference(quant_inst,[status(thm)],[])).
% 4.07/4.37 tff(329,plain,
% 4.07/4.37 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0) <=> tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0))),
% 4.07/4.37 inference(unit_resolution,[status(thm)],[328, 69])).
% 4.07/4.37 tff(330,plain,
% 4.07/4.37 (((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0)))) <=> ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0)))),
% 4.07/4.37 inference(rewrite,[status(thm)],[])).
% 4.07/4.37 tff(331,plain,
% 4.07/4.37 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | ((~tptp_fun_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0)))),
% 4.07/4.37 inference(quant_inst,[status(thm)],[])).
% 4.07/4.37 tff(332,plain,
% 4.07/4.37 ((~![X14: $i, X15: $i, X16: $i] : ((~tptp_fun_____(X14, X15)) | tptp_fun_____(tptp_fun______(X16, X14), tptp_fun______(X16, X15)))) | (~tptp_fun_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0))),
% 4.07/4.37 inference(modus_ponens,[status(thm)],[331, 330])).
% 4.07/4.37 tff(333,plain,
% 4.07/4.37 ((~tptp_fun_____(|'0'|, X17!0)) | tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0))),
% 4.07/4.37 inference(unit_resolution,[status(thm)],[332, 122])).
% 4.07/4.37 tff(334,plain,
% 4.07/4.37 (tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0))),
% 4.07/4.37 inference(unit_resolution,[status(thm)],[333, 274])).
% 4.07/4.37 tff(335,plain,
% 4.07/4.37 ((~(tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0) <=> tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0)))) | tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0) | (~tptp_fun_____(tptp_fun______(X17!0, |'0'|), tptp_fun______(X17!0, X17!0)))),
% 4.07/4.37 inference(tautology,[status(thm)],[])).
% 4.07/4.37 tff(336,plain,
% 4.07/4.37 (tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)),
% 4.07/4.38 inference(unit_resolution,[status(thm)],[335, 334, 329])).
% 4.07/4.38 tff(337,plain,
% 4.07/4.38 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0))),
% 4.07/4.38 inference(rewrite,[status(thm)],[])).
% 4.07/4.38 tff(338,plain,
% 4.07/4.38 (((tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))))) <=> ((~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0))),
% 4.07/4.38 inference(rewrite,[status(thm)],[])).
% 4.07/4.38 tff(339,plain,
% 4.07/4.38 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0)))),
% 4.07/4.38 inference(monotonicity,[status(thm)],[338])).
% 4.07/4.38 tff(340,plain,
% 4.07/4.38 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0))),
% 4.07/4.38 inference(transitivity,[status(thm)],[339, 337])).
% 4.07/4.38 tff(341,plain,
% 4.07/4.38 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))))),
% 4.07/4.38 inference(quant_inst,[status(thm)],[])).
% 4.07/4.38 tff(342,plain,
% 4.07/4.38 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (~tptp_fun_____(tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)), X17!0)) | (~tptp_fun_____(X17!0, tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)))) | (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0)),
% 4.07/4.38 inference(modus_ponens,[status(thm)],[341, 340])).
% 4.07/4.38 tff(343,plain,
% 4.07/4.38 (tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|)) = X17!0),
% 4.07/4.38 inference(unit_resolution,[status(thm)],[342, 164, 336, 291])).
% 4.07/4.38 tff(344,plain,
% 4.07/4.38 (X17!0 = tptp_fun____(X17!0, tptp_fun______(X17!0, |'0'|))),
% 4.07/4.38 inference(symmetry,[status(thm)],[343])).
% 4.07/4.38 tff(345,plain,
% 4.07/4.38 (X17!0 = |'0'|),
% 4.07/4.38 inference(transitivity,[status(thm)],[344, 327])).
% 4.07/4.38 tff(346,plain,
% 4.07/4.38 (~(X17!0 = |'0'|)),
% 4.07/4.38 inference(or_elim,[status(thm)],[43])).
% 4.07/4.38 tff(347,plain,
% 4.07/4.38 ($false),
% 4.07/4.38 inference(unit_resolution,[status(thm)],[346, 345])).
% 4.07/4.38 % SZS output end Proof
% 0.22/4.41 % E exiting
%------------------------------------------------------------------------------