%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN584-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:39:37 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN584-1 : TPTP v9.0.0. Released v2.5.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:40:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(p12_type, type, (
% 0.18/0.37 p12: ( $i * $i ) > $o)).
% 0.18/0.37 tff(f13_type, type, (
% 0.18/0.37 f13: ( $i * $i ) > $i)).
% 0.18/0.37 tff(f14_type, type, (
% 0.18/0.37 f14: ( $i * $i ) > $i)).
% 0.18/0.37 tff(c17_type, type, (
% 0.18/0.37 c17: $i)).
% 0.18/0.37 tff(f7_type, type, (
% 0.18/0.37 f7: ( $i * $i ) > $i)).
% 0.18/0.37 tff(f8_type, type, (
% 0.18/0.37 f8: ( $i * $i ) > $i)).
% 0.18/0.37 tff(f9_type, type, (
% 0.18/0.37 f9: ( $i * $i ) > $i)).
% 0.18/0.37 tff(f10_type, type, (
% 0.18/0.37 f10: $i > $i)).
% 0.18/0.37 tff(f11_type, type, (
% 0.18/0.37 f11: $i > $i)).
% 0.18/0.37 tff(c20_type, type, (
% 0.18/0.37 c20: $i)).
% 0.18/0.37 tff(c21_type, type, (
% 0.18/0.37 c21: $i)).
% 0.18/0.37 tff(c19_type, type, (
% 0.18/0.37 c19: $i)).
% 0.18/0.37 tff(c18_type, type, (
% 0.18/0.37 c18: $i)).
% 0.18/0.37 tff(c22_type, type, (
% 0.18/0.37 c22: $i)).
% 0.18/0.37 tff(p2_type, type, (
% 0.18/0.37 p2: ( $i * $i ) > $o)).
% 0.18/0.37 tff(p3_type, type, (
% 0.18/0.37 p3: ( $i * $i ) > $o)).
% 0.18/0.37 tff(f4_type, type, (
% 0.18/0.37 f4: $i > $i)).
% 0.18/0.37 tff(p15_type, type, (
% 0.18/0.37 p15: ( $i * $i ) > $o)).
% 0.18/0.37 tff(1,assumption,(~p12(c17, c17)), introduced(assumption)).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (^[X0: $i] : refl(p12(X0, X0) <=> p12(X0, X0))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![X0: $i] : p12(X0, X0) <=> ![X0: $i] : p12(X0, X0)),
% 0.18/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![X0: $i] : p12(X0, X0) <=> ![X0: $i] : p12(X0, X0)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(5,axiom,(![X0: $i] : p12(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_1')).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (![X0: $i] : p12(X0, X0)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.37 tff(7,plain,(
% 0.18/0.37 ![X0: $i] : p12(X0, X0)),
% 0.18/0.37 inference(skolemize,[status(sab)],[6])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![X0: $i] : p12(X0, X0)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 ((~![X0: $i] : p12(X0, X0)) | p12(c17, c17)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.37 tff(11,plain,(p12(c17, c17)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(12,assumption,(~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))), introduced(assumption)).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (^[X19: $i] : refl(p2(X19, X19) <=> p2(X19, X19))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (![X19: $i] : p2(X19, X19) <=> ![X19: $i] : p2(X19, X19)),
% 0.18/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (![X19: $i] : p2(X19, X19) <=> ![X19: $i] : p2(X19, X19)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(16,axiom,(![X19: $i] : p2(X19, X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_5')).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![X19: $i] : p2(X19, X19)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.37 tff(18,plain,(
% 0.18/0.37 ![X19: $i] : p2(X19, X19)),
% 0.18/0.37 inference(skolemize,[status(sab)],[17])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (![X19: $i] : p2(X19, X19)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 ((~![X19: $i] : p2(X19, X19)) | p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.18/0.37 tff(22,plain,(p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (^[X9: $i, X10: $i, X7: $i, X8: $i] : refl(((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10))) <=> ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10))) <=> ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10))) <=> ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (^[X9: $i, X10: $i, X7: $i, X8: $i] : trans(monotonicity(rewrite((p12(f14(X7, X8), f14(X9, X10)) | (~p12(X8, X10))) <=> ((~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))), (((p12(f14(X7, X8), f14(X9, X10)) | (~p12(X8, X10))) | (~p2(X7, X9))) <=> (((~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10))) | (~p2(X7, X9))))), rewrite((((~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10))) | (~p2(X7, X9))) <=> ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))), (((p12(f14(X7, X8), f14(X9, X10)) | (~p12(X8, X10))) | (~p2(X7, X9))) <=> ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((p12(f14(X7, X8), f14(X9, X10)) | (~p12(X8, X10))) | (~p2(X7, X9))) <=> ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.37 tff(28,axiom,(![X9: $i, X10: $i, X7: $i, X8: $i] : ((p12(f14(X7, X8), f14(X9, X10)) | (~p12(X8, X10))) | (~p2(X7, X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_20')).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.18/0.37 tff(31,plain,(
% 0.18/0.37 ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[30])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))) | (p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)) | (~p12(c17, c17)) | (~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))) <=> ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))) | p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)) | (~p12(c17, c17)) | (~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (((~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p12(c17, c17)) | p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))) <=> (p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)) | (~p12(c17, c17)) | (~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))) | ((~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p12(c17, c17)) | p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) <=> ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))) | (p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)) | (~p12(c17, c17)) | (~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))) | ((~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p12(c17, c17)) | p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) <=> ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))) | p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)) | (~p12(c17, c17)) | (~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[35, 33])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))) | ((~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p12(c17, c17)) | p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X7, X9)) | (~p12(X8, X10)) | p12(f14(X7, X8), f14(X9, X10)))) | p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)) | (~p12(c17, c17)) | (~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)) | (~p12(c17, c17)) | (~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[39, 11, 22])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl(((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6))) <=> ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(rewrite((p12(f13(X3, X4), f13(X5, X6)) | (~p12(X3, X5))) <=> ((~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))), (((p12(f13(X3, X4), f13(X5, X6)) | (~p12(X3, X5))) | (~p12(X4, X6))) <=> (((~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6))) | (~p12(X4, X6))))), rewrite((((~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6))) | (~p12(X4, X6))) <=> ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))), (((p12(f13(X3, X4), f13(X5, X6)) | (~p12(X3, X5))) | (~p12(X4, X6))) <=> ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((p12(f13(X3, X4), f13(X5, X6)) | (~p12(X3, X5))) | (~p12(X4, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.38 tff(46,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((p12(f13(X3, X4), f13(X5, X6)) | (~p12(X3, X5))) | (~p12(X4, X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_16')).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.18/0.38 tff(49,plain,(
% 0.18/0.38 ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[48])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))) | ((~p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))) | (~p12(c17, c17)) | p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))) | (~p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))) | (~p12(c17, c17)) | p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))) | ((~p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))) | (~p12(c17, c17)) | p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X4, X6)) | (~p12(X3, X5)) | p12(f13(X3, X4), f13(X5, X6)))) | (~p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))) | (~p12(c17, c17)) | p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 ((~p12(f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17), f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))) | (~p12(c17, c17)) | p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[53, 50])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 (p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[54, 40, 11])).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 (p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22) <=> p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(57,axiom,(p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_23')).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 (p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 (^[X0: $i, X2: $i, X1: $i] : refl(((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2)) <=> ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(62,plain,
% 0.18/0.38 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p12(X1, X2) | (~p12(X0, X1))) <=> ((~p12(X0, X1)) | p12(X1, X2))), (((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2))) <=> (((~p12(X0, X1)) | p12(X1, X2)) | (~p12(X0, X2))))), rewrite((((~p12(X0, X1)) | p12(X1, X2)) | (~p12(X0, X2))) <=> ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))), (((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2))) <=> ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(63,plain,
% 0.18/0.38 (![X0: $i, X2: $i, X1: $i] : ((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.38 tff(64,axiom,(![X0: $i, X2: $i, X1: $i] : ((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_9')).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.18/0.38 tff(67,plain,(
% 0.18/0.38 ![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))),
% 0.18/0.38 inference(skolemize,[status(sab)],[66])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))) | ((~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 (((~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) <=> ((~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))) | ((~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))) | ((~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[70])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))) | ((~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[71, 69])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))) | ((~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p12(X0, X2)) | (~p12(X0, X1)) | p12(X1, X2))) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)) | (~p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[74, 68, 58, 55])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (^[X30: $i, X29: $i] : refl(((~p2(X29, X30)) | p3(f4(X29), f4(X30))) <=> ((~p2(X29, X30)) | p3(f4(X29), f4(X30))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30))) <=> ![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30))) <=> ![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (^[X30: $i, X29: $i] : rewrite((p3(f4(X29), f4(X30)) | (~p2(X29, X30))) <=> ((~p2(X29, X30)) | p3(f4(X29), f4(X30))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (![X30: $i, X29: $i] : (p3(f4(X29), f4(X30)) | (~p2(X29, X30))) <=> ![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.18/0.39 tff(81,axiom,(![X30: $i, X29: $i] : (p3(f4(X29), f4(X30)) | (~p2(X29, X30)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_7')).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.18/0.39 tff(84,plain,(
% 0.18/0.39 ![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[83])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 (![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (((~![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))) | ((~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))) <=> ((~![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))) | (~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 ((~![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))) | ((~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 ((~![X30: $i, X29: $i] : ((~p2(X29, X30)) | p3(f4(X29), f4(X30)))) | (~p2(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[88, 85, 22])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 ((~p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) <=> (~p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(91,axiom,(~p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p15_25')).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (~p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) <=> p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(94,axiom,(p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15_21')).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 (p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.39 tff(96,plain,
% 0.18/0.39 (^[X14: $i, X12: $i, X11: $i, X13: $i] : refl(((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12)) <=> ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12)) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[96])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12)) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 (^[X14: $i, X12: $i, X11: $i, X13: $i] : trans(monotonicity(trans(monotonicity(rewrite((p15(X11, X12) | (~p15(X13, X14))) <=> ((~p15(X13, X14)) | p15(X11, X12))), (((p15(X11, X12) | (~p15(X13, X14))) | (~p3(X14, X12))) <=> (((~p15(X13, X14)) | p15(X11, X12)) | (~p3(X14, X12))))), rewrite((((~p15(X13, X14)) | p15(X11, X12)) | (~p3(X14, X12))) <=> ((~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))), (((p15(X11, X12) | (~p15(X13, X14))) | (~p3(X14, X12))) <=> ((~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12)))), ((((p15(X11, X12) | (~p15(X13, X14))) | (~p3(X14, X12))) | (~p12(X13, X11))) <=> (((~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12)) | (~p12(X13, X11))))), rewrite((((~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12)) | (~p12(X13, X11))) <=> ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))), ((((p15(X11, X12) | (~p15(X13, X14))) | (~p3(X14, X12))) | (~p12(X13, X11))) <=> ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : (((p15(X11, X12) | (~p15(X13, X14))) | (~p3(X14, X12))) | (~p12(X13, X11))) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.40 tff(101,axiom,(![X14: $i, X12: $i, X11: $i, X13: $i] : (((p15(X11, X12) | (~p15(X13, X14))) | (~p3(X14, X12))) | (~p12(X13, X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15_15')).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.18/0.40 tff(104,plain,(
% 0.18/0.40 ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))),
% 0.18/0.40 inference(skolemize,[status(sab)],[103])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))) | (p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))) | p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 (((~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) <=> (p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))) | ((~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))) | (p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[107])).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))) | ((~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))) | p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[108, 106])).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))) | ((~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(111,plain,
% 0.18/0.40 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p12(X13, X11)) | (~p3(X14, X12)) | (~p15(X13, X14)) | p15(X11, X12))) | p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) | (~p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))) | (~p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.40 tff(112,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[111, 105, 95, 92, 89, 75])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------