%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN586-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:39:38 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN586-1 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 12:40:16 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(p2_type, type, (
% 0.21/0.39 p2: ( $i * $i ) > $o)).
% 0.21/0.39 tff(c20_type, type, (
% 0.21/0.39 c20: $i)).
% 0.21/0.39 tff(f4_type, type, (
% 0.21/0.39 f4: ( $i * $i ) > $i)).
% 0.21/0.39 tff(f11_type, type, (
% 0.21/0.39 f11: $i > $i)).
% 0.21/0.39 tff(c19_type, type, (
% 0.21/0.39 c19: $i)).
% 0.21/0.39 tff(f6_type, type, (
% 0.21/0.39 f6: ( $i * $i ) > $i)).
% 0.21/0.39 tff(c18_type, type, (
% 0.21/0.39 c18: $i)).
% 0.21/0.39 tff(f7_type, type, (
% 0.21/0.39 f7: $i > $i)).
% 0.21/0.39 tff(f8_type, type, (
% 0.21/0.39 f8: $i > $i)).
% 0.21/0.39 tff(f9_type, type, (
% 0.21/0.39 f9: $i > $i)).
% 0.21/0.39 tff(c17_type, type, (
% 0.21/0.39 c17: $i)).
% 0.21/0.39 tff(f10_type, type, (
% 0.21/0.39 f10: $i > $i)).
% 0.21/0.39 tff(c16_type, type, (
% 0.21/0.39 c16: $i)).
% 0.21/0.39 tff(c21_type, type, (
% 0.21/0.39 c21: $i)).
% 0.21/0.39 tff(p5_type, type, (
% 0.21/0.39 p5: ( $i * $i ) > $o)).
% 0.21/0.39 tff(p3_type, type, (
% 0.21/0.39 p3: ( $i * $i ) > $o)).
% 0.21/0.39 tff(p15_type, type, (
% 0.21/0.39 p15: ( $i * $i ) > $o)).
% 0.21/0.39 tff(1,assumption,(~p2(c20, c20)), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (^[X13: $i] : refl(p2(X13, X13) <=> p2(X13, X13))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![X13: $i] : p2(X13, X13) <=> ![X13: $i] : p2(X13, X13)),
% 0.21/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (![X13: $i] : p2(X13, X13) <=> ![X13: $i] : p2(X13, X13)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(5,axiom,(![X13: $i] : p2(X13, X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (![X13: $i] : p2(X13, X13)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.39 tff(7,plain,(
% 0.21/0.39 ![X13: $i] : p2(X13, X13)),
% 0.21/0.39 inference(skolemize,[status(sab)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![X13: $i] : p2(X13, X13)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 ((~![X13: $i] : p2(X13, X13)) | p2(c20, c20)),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.39 tff(11,plain,(p2(c20, c20)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(12,assumption,(~p5(c16, c16)), introduced(assumption)).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (^[X37: $i] : refl(p5(X37, X37) <=> p5(X37, X37))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![X37: $i] : p5(X37, X37) <=> ![X37: $i] : p5(X37, X37)),
% 0.21/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![X37: $i] : p5(X37, X37) <=> ![X37: $i] : p5(X37, X37)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(16,axiom,(![X37: $i] : p5(X37, X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_2')).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (![X37: $i] : p5(X37, X37)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.39 tff(18,plain,(
% 0.21/0.39 ![X37: $i] : p5(X37, X37)),
% 0.21/0.39 inference(skolemize,[status(sab)],[17])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (![X37: $i] : p5(X37, X37)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 ((~![X37: $i] : p5(X37, X37)) | p5(c16, c16)),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.21/0.39 tff(22,plain,(p5(c16, c16)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (^[X41: $i, X40: $i] : refl(((~p5(X40, X41)) | p5(f10(X40), f10(X41))) <=> ((~p5(X40, X41)) | p5(f10(X40), f10(X41))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41))) <=> ![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41))) <=> ![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (^[X41: $i, X40: $i] : rewrite((p5(f10(X40), f10(X41)) | (~p5(X40, X41))) <=> ((~p5(X40, X41)) | p5(f10(X40), f10(X41))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (![X41: $i, X40: $i] : (p5(f10(X40), f10(X41)) | (~p5(X40, X41))) <=> ![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.39 tff(28,axiom,(![X41: $i, X40: $i] : (p5(f10(X40), f10(X41)) | (~p5(X40, X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_9')).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.40 tff(31,plain,(
% 0.21/0.40 ![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[30])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (((~![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))) | ((~p5(c16, c16)) | p5(f10(c16), f10(c16)))) <=> ((~![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))) | (~p5(c16, c16)) | p5(f10(c16), f10(c16)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 ((~![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))) | ((~p5(c16, c16)) | p5(f10(c16), f10(c16)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ((~![X41: $i, X40: $i] : ((~p5(X40, X41)) | p5(f10(X40), f10(X41)))) | (~p5(c16, c16)) | p5(f10(c16), f10(c16))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 ((~p5(c16, c16)) | p5(f10(c16), f10(c16))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (p5(f10(c16), f10(c16))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[36, 22])).
% 0.21/0.40 tff(38,assumption,(~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))), introduced(assumption)).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ((~![X13: $i] : p2(X13, X13)) | p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[39, 8, 38])).
% 0.21/0.40 tff(41,plain,(p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (^[X22: $i, X21: $i, X20: $i, X23: $i] : refl(((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23))) <=> ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23))) <=> ![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23))) <=> ![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (^[X22: $i, X21: $i, X20: $i, X23: $i] : trans(monotonicity(rewrite((p2(f6(X20, X21), f6(X22, X23)) | (~p2(X21, X23))) <=> ((~p2(X21, X23)) | p2(f6(X20, X21), f6(X22, X23)))), (((p2(f6(X20, X21), f6(X22, X23)) | (~p2(X21, X23))) | (~p5(X20, X22))) <=> (((~p2(X21, X23)) | p2(f6(X20, X21), f6(X22, X23))) | (~p5(X20, X22))))), rewrite((((~p2(X21, X23)) | p2(f6(X20, X21), f6(X22, X23))) | (~p5(X20, X22))) <=> ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))), (((p2(f6(X20, X21), f6(X22, X23)) | (~p2(X21, X23))) | (~p5(X20, X22))) <=> ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (![X22: $i, X21: $i, X20: $i, X23: $i] : ((p2(f6(X20, X21), f6(X22, X23)) | (~p2(X21, X23))) | (~p5(X20, X22))) <=> ![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.40 tff(47,axiom,(![X22: $i, X21: $i, X20: $i, X23: $i] : ((p2(f6(X20, X21), f6(X22, X23)) | (~p2(X21, X23))) | (~p5(X20, X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_21')).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.40 tff(50,plain,(
% 0.21/0.40 ![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[49])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (((~![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))) | (p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))) | (~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16))))) <=> ((~![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))) | p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))) | (~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (((~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16))) | p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) <=> (p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))) | (~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (((~![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))) | ((~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16))) | p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))))) <=> ((~![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))) | (p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))) | (~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (((~![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))) | ((~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16))) | p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))))) <=> ((~![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))) | p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))) | (~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 ((~![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))) | ((~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16))) | p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 ((~![X22: $i, X21: $i, X20: $i, X23: $i] : ((~p2(X21, X23)) | (~p5(X20, X22)) | p2(f6(X20, X21), f6(X22, X23)))) | p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))) | (~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))) | (~p2(f6(f7(f8(f9(c17))), c18), f6(f7(f8(f9(c17))), c18))) | (~p5(f10(c16), f10(c16)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[57, 51])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[58, 41, 37])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (^[X27: $i, X28: $i] : refl(((~p3(X27, X28)) | p3(f11(X27), f11(X28))) <=> ((~p3(X27, X28)) | p3(f11(X27), f11(X28))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28))) <=> ![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28))) <=> ![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (^[X27: $i, X28: $i] : rewrite((p3(f11(X27), f11(X28)) | (~p3(X27, X28))) <=> ((~p3(X27, X28)) | p3(f11(X27), f11(X28))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (![X27: $i, X28: $i] : (p3(f11(X27), f11(X28)) | (~p3(X27, X28))) <=> ![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.40 tff(65,axiom,(![X27: $i, X28: $i] : (p3(f11(X27), f11(X28)) | (~p3(X27, X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_12')).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.40 tff(68,plain,(
% 0.21/0.40 ![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[67])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (p3(c21, c19) <=> p3(c21, c19)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(71,axiom,(p3(c21, c19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_5')).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (p3(c21, c19)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (((~![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))) | ((~p3(c21, c19)) | p3(f11(c21), f11(c19)))) <=> ((~![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))) | (~p3(c21, c19)) | p3(f11(c21), f11(c19)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((~![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))) | ((~p3(c21, c19)) | p3(f11(c21), f11(c19)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 ((~![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f11(X27), f11(X28)))) | (~p3(c21, c19)) | p3(f11(c21), f11(c19))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (p3(f11(c21), f11(c19))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[75, 72, 69])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (^[X17: $i, X16: $i, X18: $i, X19: $i] : refl(((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) <=> ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) <=> ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) <=> ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (^[X17: $i, X16: $i, X18: $i, X19: $i] : trans(monotonicity(rewrite((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) <=> ((~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))), (((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) | (~p3(X17, X19))) <=> (((~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) | (~p3(X17, X19))))), rewrite((((~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) | (~p3(X17, X19))) <=> ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))), (((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) | (~p3(X17, X19))) <=> ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) | (~p3(X17, X19))) <=> ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.41 tff(82,axiom,(![X17: $i, X16: $i, X18: $i, X19: $i] : ((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) | (~p3(X17, X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_20')).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.21/0.41 tff(85,plain,(
% 0.21/0.41 ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[84])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | ((~p3(f11(c21), f11(c19))) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19))))) <=> ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | (~p3(f11(c21), f11(c19))) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | ((~p3(f11(c21), f11(c19))) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | (~p3(f11(c21), f11(c19))) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 ((~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[89, 86, 76])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[90, 59])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 ((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)) <=> (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(93,axiom,(~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p15_23')).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20) <=> p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(96,axiom,(p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15_22')).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 (^[X9: $i, X12: $i, X11: $i, X10: $i] : refl(((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) <=> ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 (^[X9: $i, X12: $i, X11: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((p15(X9, X10) | (~p2(X11, X9))) <=> ((~p2(X11, X9)) | p15(X9, X10))), (((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) <=> (((~p2(X11, X9)) | p15(X9, X10)) | (~p2(X12, X10))))), rewrite((((~p2(X11, X9)) | p15(X9, X10)) | (~p2(X12, X10))) <=> ((~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))), (((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) <=> ((~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)))), ((((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) | (~p15(X11, X12))) <=> (((~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) | (~p15(X11, X12))))), rewrite((((~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) | (~p15(X11, X12))) <=> ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))), ((((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) | (~p15(X11, X12))) <=> ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 (![X9: $i, X12: $i, X11: $i, X10: $i] : (((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) | (~p15(X11, X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.41 tff(103,axiom,(![X9: $i, X12: $i, X11: $i, X10: $i] : (((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) | (~p15(X11, X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15_17')).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.21/0.41 tff(106,plain,(
% 0.21/0.41 ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.21/0.41 inference(skolemize,[status(sab)],[105])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)) | (~p2(c20, c20)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)) <=> (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | ((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)) | (~p2(c20, c20)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | ((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)) | (~p2(c20, c20)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[110, 108])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | ((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)) | (~p2(c20, c20)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[113, 107, 97, 94, 91, 11])).
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------