%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN684-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:50 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN684-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:40:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(p2_type, type, (
% 0.19/0.38 p2: ( $i * $i ) > $o)).
% 0.19/0.38 tff(f11_type, type, (
% 0.19/0.38 f11: ( $i * $i ) > $i)).
% 0.19/0.38 tff(c34_type, type, (
% 0.19/0.38 c34: $i)).
% 0.19/0.38 tff(f4_type, type, (
% 0.19/0.38 f4: $i > $i)).
% 0.19/0.38 tff(c33_type, type, (
% 0.19/0.38 c33: $i)).
% 0.19/0.38 tff(c32_type, type, (
% 0.19/0.38 c32: $i)).
% 0.19/0.38 tff(p10_type, type, (
% 0.19/0.38 p10: ( $i * $i ) > $o)).
% 0.19/0.38 tff(p3_type, type, (
% 0.19/0.38 p3: ( $i * $i ) > $o)).
% 0.19/0.38 tff(p25_type, type, (
% 0.19/0.38 p25: ( $i * $i ) > $o)).
% 0.19/0.38 tff(c36_type, type, (
% 0.19/0.38 c36: $i)).
% 0.19/0.38 tff(f18_type, type, (
% 0.19/0.38 f18: ( $i * $i ) > $i)).
% 0.19/0.38 tff(f9_type, type, (
% 0.19/0.38 f9: $i > $i)).
% 0.19/0.38 tff(f17_type, type, (
% 0.19/0.38 f17: $i > $i)).
% 0.19/0.38 tff(c31_type, type, (
% 0.19/0.38 c31: $i)).
% 0.19/0.38 tff(1,assumption,(~p10(c34, c34)), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.19/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(5,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_2')).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![X0: $i] : p10(X0, X0)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.38 tff(7,plain,(
% 0.19/0.38 ![X0: $i] : p10(X0, X0)),
% 0.19/0.38 inference(skolemize,[status(sab)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![X0: $i] : p10(X0, X0)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 ((~![X0: $i] : p10(X0, X0)) | p10(c34, c34)),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.38 tff(11,plain,(p10(c34, c34)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(12,assumption,(~p3(f4(c33), f4(c33))), introduced(assumption)).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (^[X83: $i] : refl(p3(X83, X83) <=> p3(X83, X83))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 0.19/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(16,axiom,(![X83: $i] : p3(X83, X83)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_5')).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (![X83: $i] : p3(X83, X83)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.38 tff(18,plain,(
% 0.19/0.38 ![X83: $i] : p3(X83, X83)),
% 0.19/0.38 inference(skolemize,[status(sab)],[17])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (![X83: $i] : p3(X83, X83)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ((~![X83: $i] : p3(X83, X83)) | p3(f4(c33), f4(c33))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.19/0.38 tff(22,plain,(p3(f4(c33), f4(c33))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (^[X31: $i, X32: $i, X34: $i, X33: $i] : refl(((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))) <=> ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (^[X31: $i, X32: $i, X34: $i, X33: $i] : trans(monotonicity(rewrite((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) <=> ((~p10(X32, X34)) | p2(f11(X31, X32), f11(X33, X34)))), (((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33))) <=> (((~p10(X32, X34)) | p2(f11(X31, X32), f11(X33, X34))) | (~p3(X31, X33))))), rewrite((((~p10(X32, X34)) | p2(f11(X31, X32), f11(X33, X34))) | (~p3(X31, X33))) <=> ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))), (((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33))) <=> ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,axiom,(![X31: $i, X32: $i, X34: $i, X33: $i] : ((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_47')).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.39 tff(31,plain,(
% 0.19/0.39 ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | ((~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))) <=> ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | (~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | ((~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | (~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (p2(f11(f4(c33), c34), f11(f4(c33), c34))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 22, 11])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (^[X36: $i] : refl(((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) <=> ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) <=> ![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) <=> ![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (^[X36: $i] : trans(monotonicity(rewrite((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) <=> (p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))), (((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))) <=> ((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))))), rewrite(((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))) <=> ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))), (((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))) <=> ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![X36: $i] : ((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))) <=> ![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.39 tff(43,axiom,(![X36: $i] : ((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_51')).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.39 tff(46,plain,(
% 0.19/0.39 ![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[45])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (p25(c32, c33) <=> p25(c32, c33)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,axiom,(p25(c32, c33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p25_12')).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (p25(c32, c33)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (p25(c33, c36) <=> p25(c33, c36)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(52,axiom,(p25(c33, c36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p25_11')).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (p25(c33, c36)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | (p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))) <=> ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36))) <=> (p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | ((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36)))) <=> ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | (p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | ((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36)))) <=> ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[56, 54])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | ((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (p2(f11(f4(c33), c34), f11(f4(c32), c34))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[59, 53, 50, 47])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (^[X30: $i, X29: $i, X28: $i] : refl(((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)) <=> ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (^[X30: $i, X29: $i, X28: $i] : trans(monotonicity(rewrite((p2(X29, X30) | (~p2(X28, X29))) <=> ((~p2(X28, X29)) | p2(X29, X30))), (((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30))) <=> (((~p2(X28, X29)) | p2(X29, X30)) | (~p2(X28, X30))))), rewrite((((~p2(X28, X29)) | p2(X29, X30)) | (~p2(X28, X30))) <=> ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))), (((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30))) <=> ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (![X30: $i, X29: $i, X28: $i] : ((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30))) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.39 tff(66,axiom,(![X30: $i, X29: $i, X28: $i] : ((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_31')).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.39 tff(69,plain,(
% 0.19/0.39 ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.19/0.39 inference(skolemize,[status(sab)],[68])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)))) <=> ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (p2(f11(f4(c32), c34), f11(f4(c33), c34))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[73, 70, 60, 37])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (^[X96: $i] : refl((~p2(X96, f18(X96, f9(f17(c31))))) <=> (~p2(X96, f18(X96, f9(f17(c31))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(78,axiom,(![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p2_19')).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.40 tff(80,plain,(
% 0.19/0.40 ![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[79])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))) | (~p2(f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (~p2(f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31)))) <=> p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(85,axiom,(p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_39')).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31)))))) <=> ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[89, 70, 86, 83, 74])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------