%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN599-1 : 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 05:39:39 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN599-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:39:47 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(p7_type, type, (
% 0.12/0.38 p7: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f8_type, type, (
% 0.12/0.38 f8: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f9_type, type, (
% 0.12/0.38 f9: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f10_type, type, (
% 0.12/0.38 f10: $i > $i)).
% 0.12/0.38 tff(f11_type, type, (
% 0.12/0.38 f11: $i > $i)).
% 0.12/0.38 tff(c23_type, type, (
% 0.12/0.38 c23: $i)).
% 0.12/0.38 tff(f12_type, type, (
% 0.12/0.38 f12: $i > $i)).
% 0.12/0.38 tff(f13_type, type, (
% 0.12/0.38 f13: $i > $i)).
% 0.12/0.38 tff(f14_type, type, (
% 0.12/0.38 f14: $i > $i)).
% 0.12/0.38 tff(c22_type, type, (
% 0.12/0.38 c22: $i)).
% 0.12/0.38 tff(f4_type, type, (
% 0.12/0.38 f4: $i > $i)).
% 0.12/0.38 tff(f6_type, type, (
% 0.12/0.38 f6: $i > $i)).
% 0.12/0.38 tff(c21_type, type, (
% 0.12/0.38 c21: $i)).
% 0.12/0.38 tff(p3_type, type, (
% 0.12/0.38 p3: ( $i * $i ) > $o)).
% 0.12/0.38 tff(p19_type, type, (
% 0.12/0.38 p19: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f15_type, type, (
% 0.12/0.38 f15: $i > $i)).
% 0.12/0.38 tff(f16_type, type, (
% 0.12/0.38 f16: $i > $i)).
% 0.12/0.38 tff(p18_type, type, (
% 0.12/0.38 p18: $i > $o)).
% 0.12/0.38 tff(1,assumption,(~p3(f11(f11(f11(f11(f11(f11(c23)))))), f11(f11(f11(f11(f11(f11(c23)))))))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[X18: $i] : refl(p3(X18, X18) <=> p3(X18, X18))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X18: $i] : p3(X18, X18) <=> ![X18: $i] : p3(X18, X18)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X18: $i] : p3(X18, X18) <=> ![X18: $i] : p3(X18, X18)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,axiom,(![X18: $i] : p3(X18, X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_5')).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![X18: $i] : p3(X18, X18)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.38 tff(7,plain,(
% 0.12/0.38 ![X18: $i] : p3(X18, X18)),
% 0.12/0.38 inference(skolemize,[status(sab)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![X18: $i] : p3(X18, X18)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 ((~![X18: $i] : p3(X18, X18)) | p3(f11(f11(f11(f11(f11(f11(c23)))))), f11(f11(f11(f11(f11(f11(c23)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.38 tff(11,plain,(p3(f11(f11(f11(f11(f11(f11(c23)))))), f11(f11(f11(f11(f11(f11(c23)))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (^[X23: $i, X24: $i] : refl(((~p3(X23, X24)) | p3(f11(X23), f11(X24))) <=> ((~p3(X23, X24)) | p3(f11(X23), f11(X24))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24))) <=> ![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24))) <=> ![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[X23: $i, X24: $i] : rewrite((p3(f11(X23), f11(X24)) | (~p3(X23, X24))) <=> ((~p3(X23, X24)) | p3(f11(X23), f11(X24))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![X23: $i, X24: $i] : (p3(f11(X23), f11(X24)) | (~p3(X23, X24))) <=> ![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,axiom,(![X23: $i, X24: $i] : (p3(f11(X23), f11(X24)) | (~p3(X23, X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_13')).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.38 tff(20,plain,(
% 0.12/0.38 ![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (((~![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))) | ((~p3(f11(f11(f11(f11(f11(f11(c23)))))), f11(f11(f11(f11(f11(f11(c23)))))))) | p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23)))))))))) <=> ((~![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))) | (~p3(f11(f11(f11(f11(f11(f11(c23)))))), f11(f11(f11(f11(f11(f11(c23)))))))) | p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23)))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))) | ((~p3(f11(f11(f11(f11(f11(f11(c23)))))), f11(f11(f11(f11(f11(f11(c23)))))))) | p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23)))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f11(X23), f11(X24)))) | (~p3(f11(f11(f11(f11(f11(f11(c23)))))), f11(f11(f11(f11(f11(f11(c23)))))))) | p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~p3(f11(f11(f11(f11(f11(f11(c23)))))), f11(f11(f11(f11(f11(f11(c23)))))))) | p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23))))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23))))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[25, 11])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[X22: $i, X21: $i] : refl(((~p3(X21, X22)) | p3(f10(X21), f10(X22))) <=> ((~p3(X21, X22)) | p3(f10(X21), f10(X22))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22))) <=> ![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22))) <=> ![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (^[X22: $i, X21: $i] : rewrite((p3(f10(X21), f10(X22)) | (~p3(X21, X22))) <=> ((~p3(X21, X22)) | p3(f10(X21), f10(X22))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![X22: $i, X21: $i] : (p3(f10(X21), f10(X22)) | (~p3(X21, X22))) <=> ![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.38 tff(32,axiom,(![X22: $i, X21: $i] : (p3(f10(X21), f10(X22)) | (~p3(X21, X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_12')).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.38 tff(35,plain,(
% 0.12/0.38 ![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (((~![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))) | ((~p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23))))))))) | p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) <=> ((~![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))) | (~p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23))))))))) | p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ((~![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))) | ((~p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23))))))))) | p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((~![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))) | (~p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23))))))))) | p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ((~p3(f11(f11(f11(f11(f11(f11(f11(c23))))))), f11(f11(f11(f11(f11(f11(f11(c23))))))))) | p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[40, 26])).
% 0.12/0.38 tff(42,assumption,(~p3(f13(f11(c23)), f13(f11(c23)))), introduced(assumption)).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((~![X18: $i] : p3(X18, X18)) | p3(f13(f11(c23)), f13(f11(c23)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[43, 8, 42])).
% 0.12/0.38 tff(45,plain,(p3(f13(f11(c23)), f13(f11(c23)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (((~![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))) | ((~p3(f13(f11(c23)), f13(f11(c23)))) | p3(f10(f13(f11(c23))), f10(f13(f11(c23)))))) <=> ((~![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))) | (~p3(f13(f11(c23)), f13(f11(c23)))) | p3(f10(f13(f11(c23))), f10(f13(f11(c23)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((~![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))) | ((~p3(f13(f11(c23)), f13(f11(c23)))) | p3(f10(f13(f11(c23))), f10(f13(f11(c23)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~![X22: $i, X21: $i] : ((~p3(X21, X22)) | p3(f10(X21), f10(X22)))) | (~p3(f13(f11(c23)), f13(f11(c23)))) | p3(f10(f13(f11(c23))), f10(f13(f11(c23))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 ((~p3(f13(f11(c23)), f13(f11(c23)))) | p3(f10(f13(f11(c23))), f10(f13(f11(c23))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[48, 36])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (p3(f10(f13(f11(c23))), f10(f13(f11(c23))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[49, 45])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (^[X38: $i, X37: $i] : refl(((~p3(X37, X38)) | p7(f12(X37), f12(X38))) <=> ((~p3(X37, X38)) | p7(f12(X37), f12(X38))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38))) <=> ![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38))) <=> ![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (^[X38: $i, X37: $i] : rewrite((p7(f12(X37), f12(X38)) | (~p3(X37, X38))) <=> ((~p3(X37, X38)) | p7(f12(X37), f12(X38))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![X38: $i, X37: $i] : (p7(f12(X37), f12(X38)) | (~p3(X37, X38))) <=> ![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.12/0.38 tff(56,axiom,(![X38: $i, X37: $i] : (p7(f12(X37), f12(X38)) | (~p3(X37, X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_17')).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.12/0.39 tff(59,plain,(
% 0.12/0.39 ![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[58])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (((~![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))) | ((~p3(f10(f13(f11(c23))), f10(f13(f11(c23))))) | p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23))))))) <=> ((~![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))) | (~p3(f10(f13(f11(c23))), f10(f13(f11(c23))))) | p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 ((~![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))) | ((~p3(f10(f13(f11(c23))), f10(f13(f11(c23))))) | p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~![X38: $i, X37: $i] : ((~p3(X37, X38)) | p7(f12(X37), f12(X38)))) | (~p3(f10(f13(f11(c23))), f10(f13(f11(c23))))) | p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[63, 60, 50])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (^[X47: $i, X49: $i, X50: $i, X48: $i] : refl(((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50))) <=> ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50))) <=> ![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50))) <=> ![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (^[X47: $i, X49: $i, X50: $i, X48: $i] : trans(monotonicity(rewrite((p7(f9(X47, X48), f9(X49, X50)) | (~p3(X48, X50))) <=> ((~p3(X48, X50)) | p7(f9(X47, X48), f9(X49, X50)))), (((p7(f9(X47, X48), f9(X49, X50)) | (~p3(X48, X50))) | (~p7(X47, X49))) <=> (((~p3(X48, X50)) | p7(f9(X47, X48), f9(X49, X50))) | (~p7(X47, X49))))), rewrite((((~p3(X48, X50)) | p7(f9(X47, X48), f9(X49, X50))) | (~p7(X47, X49))) <=> ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))), (((p7(f9(X47, X48), f9(X49, X50)) | (~p3(X48, X50))) | (~p7(X47, X49))) <=> ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![X47: $i, X49: $i, X50: $i, X48: $i] : ((p7(f9(X47, X48), f9(X49, X50)) | (~p3(X48, X50))) | (~p7(X47, X49))) <=> ![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.39 tff(70,axiom,(![X47: $i, X49: $i, X50: $i, X48: $i] : ((p7(f9(X47, X48), f9(X49, X50)) | (~p3(X48, X50))) | (~p7(X47, X49)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_25')).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.12/0.39 tff(73,plain,(
% 0.12/0.39 ![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[72])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | ((~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | (~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) <=> ((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | (~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (((~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) <=> ((~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | (~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | ((~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) <=> ((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | ((~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | (~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[76])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 (((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | ((~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) <=> ((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | (~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[77, 75])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 ((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | ((~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 ((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | (~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 ((~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | (~p3(f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))) | p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[80, 74])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[81, 64, 41])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (^[X27: $i, X28: $i] : refl(((~p3(X27, X28)) | p3(f14(X27), f14(X28))) <=> ((~p3(X27, X28)) | p3(f14(X27), f14(X28))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28))) <=> ![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[83])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28))) <=> ![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (^[X27: $i, X28: $i] : rewrite((p3(f14(X27), f14(X28)) | (~p3(X27, X28))) <=> ((~p3(X27, X28)) | p3(f14(X27), f14(X28))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 (![X27: $i, X28: $i] : (p3(f14(X27), f14(X28)) | (~p3(X27, X28))) <=> ![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.12/0.39 tff(88,axiom,(![X27: $i, X28: $i] : (p3(f14(X27), f14(X28)) | (~p3(X27, X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_15')).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.12/0.39 tff(91,plain,(
% 0.12/0.39 ![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[90])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 (![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (p3(f4(f6(c21)), c22) <=> p3(f4(f6(c21)), c22)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(94,axiom,(p3(f4(f6(c21)), c22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_7')).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 (p3(f4(f6(c21)), c22)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 (((~![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))) | ((~p3(f4(f6(c21)), c22)) | p3(f14(f4(f6(c21))), f14(c22)))) <=> ((~![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))) | (~p3(f4(f6(c21)), c22)) | p3(f14(f4(f6(c21))), f14(c22)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 ((~![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))) | ((~p3(f4(f6(c21)), c22)) | p3(f14(f4(f6(c21))), f14(c22)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 ((~![X27: $i, X28: $i] : ((~p3(X27, X28)) | p3(f14(X27), f14(X28)))) | (~p3(f4(f6(c21)), c22)) | p3(f14(f4(f6(c21))), f14(c22))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 (p3(f14(f4(f6(c21))), f14(c22))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[98, 95, 92])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 (((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | ((~p3(f14(f4(f6(c21))), f14(c22))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22))))) <=> ((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | (~p3(f14(f4(f6(c21))), f14(c22))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 ((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | ((~p3(f14(f4(f6(c21))), f14(c22))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 ((~![X47: $i, X49: $i, X50: $i, X48: $i] : ((~p3(X48, X50)) | (~p7(X47, X49)) | p7(f9(X47, X48), f9(X49, X50)))) | (~p3(f14(f4(f6(c21))), f14(c22))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 ((~p3(f14(f4(f6(c21))), f14(c22))) | (~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[102, 74])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 ((~p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23)))))) | p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[103, 99])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[104, 64])).
% 0.12/0.40 tff(106,plain,
% 0.12/0.40 (^[X43: $i, X45: $i, X46: $i, X44: $i] : refl(((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46))) <=> ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46))) <=> ![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[106])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46))) <=> ![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(109,plain,
% 0.12/0.40 (^[X43: $i, X45: $i, X46: $i, X44: $i] : trans(monotonicity(rewrite((p7(f8(X43, X44), f8(X45, X46)) | (~p7(X43, X45))) <=> ((~p7(X43, X45)) | p7(f8(X43, X44), f8(X45, X46)))), (((p7(f8(X43, X44), f8(X45, X46)) | (~p7(X43, X45))) | (~p7(X44, X46))) <=> (((~p7(X43, X45)) | p7(f8(X43, X44), f8(X45, X46))) | (~p7(X44, X46))))), rewrite((((~p7(X43, X45)) | p7(f8(X43, X44), f8(X45, X46))) | (~p7(X44, X46))) <=> ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))), (((p7(f8(X43, X44), f8(X45, X46)) | (~p7(X43, X45))) | (~p7(X44, X46))) <=> ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(110,plain,
% 0.12/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((p7(f8(X43, X44), f8(X45, X46)) | (~p7(X43, X45))) | (~p7(X44, X46))) <=> ![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[109])).
% 0.12/0.40 tff(111,axiom,(![X43: $i, X45: $i, X46: $i, X44: $i] : ((p7(f8(X43, X44), f8(X45, X46)) | (~p7(X43, X45))) | (~p7(X44, X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_26')).
% 0.12/0.40 tff(112,plain,
% 0.12/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.12/0.40 tff(113,plain,
% 0.12/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.12/0.40 tff(114,plain,(
% 0.12/0.40 ![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[113])).
% 0.12/0.40 tff(115,plain,
% 0.12/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.12/0.40 tff(116,plain,
% 0.12/0.40 (((~![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))) | ((~p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22)))) | (~p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))) <=> ((~![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))) | (~p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22)))) | (~p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 ((~![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))) | ((~p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22)))) | (~p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(118,plain,
% 0.12/0.40 ((~![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p7(X43, X45)) | (~p7(X44, X46)) | p7(f8(X43, X44), f8(X45, X46)))) | (~p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22)))) | (~p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.12/0.40 tff(119,plain,
% 0.12/0.40 ((~p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22)))) | (~p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.12/0.40 tff(120,plain,
% 0.12/0.40 (p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[119, 105, 82])).
% 0.12/0.40 tff(121,plain,
% 0.12/0.40 (^[X8: $i] : refl(((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) <=> ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(122,plain,
% 0.12/0.40 (![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) <=> ![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[121])).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 (![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) <=> ![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(124,plain,
% 0.12/0.40 (^[X8: $i] : rewrite((p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | (~p18(X8))) <=> ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(125,plain,
% 0.12/0.40 (![X8: $i] : (p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | (~p18(X8))) <=> ![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[124])).
% 0.12/0.40 tff(126,axiom,(![X8: $i] : (p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | (~p18(X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p19_29')).
% 0.12/0.40 tff(127,plain,
% 0.12/0.40 (![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.12/0.40 tff(128,plain,
% 0.12/0.40 (![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.12/0.40 tff(129,plain,(
% 0.12/0.40 ![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[128])).
% 0.12/0.40 tff(130,plain,
% 0.12/0.40 (![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.12/0.40 tff(131,plain,
% 0.12/0.40 (p18(c21) <=> p18(c21)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(132,axiom,(p18(c21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c21_is_p18_2')).
% 0.12/0.40 tff(133,plain,
% 0.12/0.40 (p18(c21)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.12/0.40 tff(134,plain,
% 0.12/0.40 (((~![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))) | ((~p18(c21)) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))) <=> ((~![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))) | (~p18(c21)) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(135,plain,
% 0.12/0.40 ((~![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))) | ((~p18(c21)) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(136,plain,
% 0.12/0.40 ((~![X8: $i] : ((~p18(X8)) | p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))) | (~p18(c21)) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.12/0.40 tff(137,plain,
% 0.12/0.40 (p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[136, 133, 130])).
% 0.12/0.40 tff(138,assumption,(~p7(f16(c21), f16(c21))), introduced(assumption)).
% 0.12/0.40 tff(139,plain,
% 0.12/0.40 (^[X34: $i] : refl(p7(X34, X34) <=> p7(X34, X34))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(140,plain,
% 0.12/0.40 (![X34: $i] : p7(X34, X34) <=> ![X34: $i] : p7(X34, X34)),
% 0.12/0.40 inference(quant_intro,[status(thm)],[139])).
% 0.12/0.40 tff(141,plain,
% 0.12/0.40 (![X34: $i] : p7(X34, X34) <=> ![X34: $i] : p7(X34, X34)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(142,axiom,(![X34: $i] : p7(X34, X34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_3')).
% 0.12/0.40 tff(143,plain,
% 0.12/0.40 (![X34: $i] : p7(X34, X34)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.12/0.40 tff(144,plain,(
% 0.12/0.40 ![X34: $i] : p7(X34, X34)),
% 0.12/0.40 inference(skolemize,[status(sab)],[143])).
% 0.12/0.40 tff(145,plain,
% 0.12/0.40 (![X34: $i] : p7(X34, X34)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.12/0.40 tff(146,plain,
% 0.12/0.40 ((~![X34: $i] : p7(X34, X34)) | p7(f16(c21), f16(c21))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(147,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[146, 145, 138])).
% 0.12/0.40 tff(148,plain,(p7(f16(c21), f16(c21))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(149,plain,
% 0.12/0.40 (^[X39: $i, X40: $i] : refl(((~p7(X39, X40)) | p7(f15(X39), f15(X40))) <=> ((~p7(X39, X40)) | p7(f15(X39), f15(X40))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(150,plain,
% 0.12/0.40 (![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40))) <=> ![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[149])).
% 0.12/0.40 tff(151,plain,
% 0.12/0.40 (![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40))) <=> ![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(152,plain,
% 0.12/0.40 (^[X39: $i, X40: $i] : rewrite((p7(f15(X39), f15(X40)) | (~p7(X39, X40))) <=> ((~p7(X39, X40)) | p7(f15(X39), f15(X40))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(153,plain,
% 0.12/0.40 (![X39: $i, X40: $i] : (p7(f15(X39), f15(X40)) | (~p7(X39, X40))) <=> ![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[152])).
% 0.12/0.41 tff(154,axiom,(![X39: $i, X40: $i] : (p7(f15(X39), f15(X40)) | (~p7(X39, X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_18')).
% 0.12/0.41 tff(155,plain,
% 0.12/0.41 (![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.12/0.41 tff(156,plain,
% 0.12/0.41 (![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.12/0.41 tff(157,plain,(
% 0.12/0.41 ![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[156])).
% 0.12/0.41 tff(158,plain,
% 0.12/0.41 (![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.12/0.41 tff(159,plain,
% 0.12/0.41 (((~![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))) | ((~p7(f16(c21), f16(c21))) | p7(f15(f16(c21)), f15(f16(c21))))) <=> ((~![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))) | (~p7(f16(c21), f16(c21))) | p7(f15(f16(c21)), f15(f16(c21))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(160,plain,
% 0.12/0.41 ((~![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))) | ((~p7(f16(c21), f16(c21))) | p7(f15(f16(c21)), f15(f16(c21))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(161,plain,
% 0.12/0.41 ((~![X39: $i, X40: $i] : ((~p7(X39, X40)) | p7(f15(X39), f15(X40)))) | (~p7(f16(c21), f16(c21))) | p7(f15(f16(c21)), f15(f16(c21)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.12/0.41 tff(162,plain,
% 0.12/0.41 ((~p7(f16(c21), f16(c21))) | p7(f15(f16(c21)), f15(f16(c21)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.12/0.41 tff(163,plain,
% 0.12/0.41 (p7(f15(f16(c21)), f15(f16(c21)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[162, 148])).
% 0.12/0.41 tff(164,plain,
% 0.12/0.41 ((~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) <=> (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(165,axiom,(~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p19_27')).
% 0.12/0.41 tff(166,plain,
% 0.12/0.41 (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.12/0.41 tff(167,plain,
% 0.12/0.41 (^[X6: $i, X4: $i, X7: $i, X5: $i] : refl(((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5)) <=> ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(168,plain,
% 0.12/0.41 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5)) <=> ![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[167])).
% 0.12/0.41 tff(169,plain,
% 0.12/0.41 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5)) <=> ![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(170,plain,
% 0.12/0.41 (^[X6: $i, X4: $i, X7: $i, X5: $i] : trans(monotonicity(trans(monotonicity(rewrite((p19(X4, X5) | (~p7(X6, X4))) <=> ((~p7(X6, X4)) | p19(X4, X5))), (((p19(X4, X5) | (~p7(X6, X4))) | (~p7(X7, X5))) <=> (((~p7(X6, X4)) | p19(X4, X5)) | (~p7(X7, X5))))), rewrite((((~p7(X6, X4)) | p19(X4, X5)) | (~p7(X7, X5))) <=> ((~p7(X7, X5)) | (~p7(X6, X4)) | p19(X4, X5))), (((p19(X4, X5) | (~p7(X6, X4))) | (~p7(X7, X5))) <=> ((~p7(X7, X5)) | (~p7(X6, X4)) | p19(X4, X5)))), ((((p19(X4, X5) | (~p7(X6, X4))) | (~p7(X7, X5))) | (~p19(X6, X7))) <=> (((~p7(X7, X5)) | (~p7(X6, X4)) | p19(X4, X5)) | (~p19(X6, X7))))), rewrite((((~p7(X7, X5)) | (~p7(X6, X4)) | p19(X4, X5)) | (~p19(X6, X7))) <=> ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))), ((((p19(X4, X5) | (~p7(X6, X4))) | (~p7(X7, X5))) | (~p19(X6, X7))) <=> ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(171,plain,
% 0.12/0.41 (![X6: $i, X4: $i, X7: $i, X5: $i] : (((p19(X4, X5) | (~p7(X6, X4))) | (~p7(X7, X5))) | (~p19(X6, X7))) <=> ![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[170])).
% 0.12/0.41 tff(172,axiom,(![X6: $i, X4: $i, X7: $i, X5: $i] : (((p19(X4, X5) | (~p7(X6, X4))) | (~p7(X7, X5))) | (~p19(X6, X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p19_23')).
% 0.12/0.41 tff(173,plain,
% 0.12/0.41 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.12/0.41 tff(174,plain,
% 0.12/0.41 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.12/0.41 tff(175,plain,(
% 0.12/0.41 ![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))),
% 0.12/0.41 inference(skolemize,[status(sab)],[174])).
% 0.12/0.41 tff(176,plain,
% 0.12/0.41 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.12/0.41 tff(177,plain,
% 0.12/0.41 (((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))) | (p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | (~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | (~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(178,plain,
% 0.20/0.41 (((~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21)))) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) <=> (p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | (~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(179,plain,
% 0.20/0.41 (((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))) | ((~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21)))) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))) | (p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | (~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[178])).
% 0.20/0.41 tff(180,plain,
% 0.20/0.41 (((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))) | ((~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21)))) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | (~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[179, 177])).
% 0.20/0.42 tff(181,plain,
% 0.20/0.42 ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))) | ((~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21)))) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(182,plain,
% 0.20/0.42 ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p7(X7, X5)) | (~p19(X6, X7)) | (~p7(X6, X4)) | p19(X4, X5))) | p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | (~p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))) | (~p7(f15(f16(c21)), f15(f16(c21))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.42 tff(183,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[182, 176, 166, 163, 137, 120])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------