%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN639-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:39:44 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.49s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN639-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:39:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.49 % SZS status Unsatisfiable
% 0.18/0.49 % SZS output start Proof
% 0.18/0.49 tff(p2_type, type, (
% 0.18/0.49 p2: ( $i * $i ) > $o)).
% 0.18/0.49 tff(f13_type, type, (
% 0.18/0.49 f13: $i > $i)).
% 0.18/0.49 tff(f11_type, type, (
% 0.18/0.49 f11: $i > $i)).
% 0.18/0.49 tff(c25_type, type, (
% 0.18/0.49 c25: $i)).
% 0.18/0.49 tff(c23_type, type, (
% 0.18/0.49 c23: $i)).
% 0.18/0.49 tff(f7_type, type, (
% 0.18/0.49 f7: $i > $i)).
% 0.18/0.49 tff(f8_type, type, (
% 0.18/0.49 f8: $i > $i)).
% 0.18/0.49 tff(f9_type, type, (
% 0.18/0.49 f9: $i > $i)).
% 0.18/0.49 tff(c24_type, type, (
% 0.18/0.49 c24: $i)).
% 0.18/0.49 tff(p4_type, type, (
% 0.18/0.49 p4: ( $i * $i ) > $o)).
% 0.18/0.49 tff(f15_type, type, (
% 0.18/0.49 f15: $i > $i)).
% 0.18/0.49 tff(f5_type, type, (
% 0.18/0.49 f5: ( $i * $i ) > $i)).
% 0.18/0.49 tff(f6_type, type, (
% 0.18/0.49 f6: ( $i * $i ) > $i)).
% 0.18/0.49 tff(p10_type, type, (
% 0.18/0.49 p10: ( $i * $i ) > $o)).
% 0.18/0.49 tff(c22_type, type, (
% 0.18/0.49 c22: $i)).
% 0.18/0.49 tff(p19_type, type, (
% 0.18/0.49 p19: ( $i * $i ) > $o)).
% 0.18/0.49 tff(p20_type, type, (
% 0.18/0.49 p20: ( $i * $i ) > $o)).
% 0.18/0.49 tff(f17_type, type, (
% 0.18/0.49 f17: $i > $i)).
% 0.18/0.49 tff(f12_type, type, (
% 0.18/0.49 f12: $i > $i)).
% 0.18/0.49 tff(1,plain,
% 0.18/0.49 (p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c25) <=> p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c25)),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(2,axiom,(p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_42')).
% 0.18/0.49 tff(3,plain,
% 0.18/0.49 (p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c25)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.18/0.49 tff(4,plain,
% 0.18/0.49 (^[X52: $i, X51: $i] : refl(((~p10(X51, X52)) | p4(f11(X51), f11(X52))) <=> ((~p10(X51, X52)) | p4(f11(X51), f11(X52))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(5,plain,
% 0.18/0.49 (![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52))) <=> ![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.49 tff(6,plain,
% 0.18/0.49 (![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52))) <=> ![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(7,plain,
% 0.18/0.49 (^[X52: $i, X51: $i] : rewrite((p4(f11(X51), f11(X52)) | (~p10(X51, X52))) <=> ((~p10(X51, X52)) | p4(f11(X51), f11(X52))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(8,plain,
% 0.18/0.49 (![X52: $i, X51: $i] : (p4(f11(X51), f11(X52)) | (~p10(X51, X52))) <=> ![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[7])).
% 0.18/0.49 tff(9,axiom,(![X52: $i, X51: $i] : (p4(f11(X51), f11(X52)) | (~p10(X51, X52)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_14')).
% 0.18/0.49 tff(10,plain,
% 0.18/0.49 (![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.49 tff(11,plain,
% 0.18/0.49 (![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.18/0.49 tff(12,plain,(
% 0.18/0.49 ![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[11])).
% 0.18/0.49 tff(13,plain,
% 0.18/0.49 (![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.18/0.49 tff(14,plain,
% 0.18/0.49 (((~![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))) | ((~p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c25)) | p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25)))) <=> ((~![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))) | (~p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c25)) | p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(15,plain,
% 0.18/0.49 ((~![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))) | ((~p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c25)) | p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(16,plain,
% 0.18/0.49 ((~![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))) | (~p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c25)) | p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.50 tff(17,plain,
% 0.18/0.50 (p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[16, 13, 3])).
% 0.18/0.50 tff(18,plain,
% 0.18/0.50 (^[X49: $i, X50: $i, X48: $i] : refl(((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50)) <=> ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(19,plain,
% 0.18/0.50 (![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50)) <=> ![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[18])).
% 0.18/0.50 tff(20,plain,
% 0.18/0.50 (![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50)) <=> ![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(21,plain,
% 0.18/0.50 (^[X49: $i, X50: $i, X48: $i] : trans(monotonicity(rewrite((p4(X49, X50) | (~p4(X48, X49))) <=> ((~p4(X48, X49)) | p4(X49, X50))), (((p4(X49, X50) | (~p4(X48, X49))) | (~p4(X48, X50))) <=> (((~p4(X48, X49)) | p4(X49, X50)) | (~p4(X48, X50))))), rewrite((((~p4(X48, X49)) | p4(X49, X50)) | (~p4(X48, X50))) <=> ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))), (((p4(X49, X50) | (~p4(X48, X49))) | (~p4(X48, X50))) <=> ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(22,plain,
% 0.18/0.50 (![X49: $i, X50: $i, X48: $i] : ((p4(X49, X50) | (~p4(X48, X49))) | (~p4(X48, X50))) <=> ![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[21])).
% 0.18/0.50 tff(23,axiom,(![X49: $i, X50: $i, X48: $i] : ((p4(X49, X50) | (~p4(X48, X49))) | (~p4(X48, X50)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_24')).
% 0.18/0.50 tff(24,plain,
% 0.18/0.50 (![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.50 tff(25,plain,
% 0.18/0.50 (![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.18/0.50 tff(26,plain,(
% 0.18/0.50 ![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))),
% 0.18/0.50 inference(skolemize,[status(sab)],[25])).
% 0.18/0.50 tff(27,plain,
% 0.18/0.50 (![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.18/0.50 tff(28,plain,
% 0.18/0.50 (((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25)))) <=> ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(29,plain,
% 0.18/0.50 (((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25))) <=> ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(30,plain,
% 0.18/0.50 (((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25)))) <=> ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[29])).
% 0.18/0.50 tff(31,plain,
% 0.18/0.50 (((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25)))) <=> ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[30, 28])).
% 0.18/0.50 tff(32,plain,
% 0.18/0.50 ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(33,plain,
% 0.18/0.50 ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f9(f9(f9(f9(f8(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c25))) | p4(f11(c25), f11(c25))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.50 tff(34,plain,
% 0.18/0.50 (p4(f11(c25), f11(c25))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[33, 27, 17])).
% 0.18/0.50 tff(35,plain,
% 0.18/0.50 (^[X22: $i, X21: $i] : refl(((~p4(X21, X22)) | p2(f13(X21), f13(X22))) <=> ((~p4(X21, X22)) | p2(f13(X21), f13(X22))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(36,plain,
% 0.18/0.50 (![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22))) <=> ![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[35])).
% 0.18/0.50 tff(37,plain,
% 0.18/0.50 (![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22))) <=> ![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(38,plain,
% 0.18/0.50 (^[X22: $i, X21: $i] : rewrite((p2(f13(X21), f13(X22)) | (~p4(X21, X22))) <=> ((~p4(X21, X22)) | p2(f13(X21), f13(X22))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(39,plain,
% 0.18/0.50 (![X22: $i, X21: $i] : (p2(f13(X21), f13(X22)) | (~p4(X21, X22))) <=> ![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[38])).
% 0.18/0.50 tff(40,axiom,(![X22: $i, X21: $i] : (p2(f13(X21), f13(X22)) | (~p4(X21, X22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_18')).
% 0.18/0.50 tff(41,plain,
% 0.18/0.50 (![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.50 tff(42,plain,
% 0.18/0.50 (![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.18/0.50 tff(43,plain,(
% 0.18/0.50 ![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))),
% 0.18/0.50 inference(skolemize,[status(sab)],[42])).
% 0.18/0.50 tff(44,plain,
% 0.18/0.50 (![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.18/0.50 tff(45,plain,
% 0.18/0.50 (((~![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))) | ((~p4(f11(c25), f11(c25))) | p2(f13(f11(c25)), f13(f11(c25))))) <=> ((~![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))) | (~p4(f11(c25), f11(c25))) | p2(f13(f11(c25)), f13(f11(c25))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(46,plain,
% 0.18/0.50 ((~![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))) | ((~p4(f11(c25), f11(c25))) | p2(f13(f11(c25)), f13(f11(c25))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(47,plain,
% 0.18/0.50 ((~![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))) | (~p4(f11(c25), f11(c25))) | p2(f13(f11(c25)), f13(f11(c25)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.50 tff(48,plain,
% 0.18/0.50 (p2(f13(f11(c25)), f13(f11(c25)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[47, 44, 34])).
% 0.18/0.50 tff(49,plain,
% 0.18/0.50 (p2(f13(f11(c25)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))) <=> p2(f13(f11(c25)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(50,axiom,(p2(f13(f11(c25)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_34')).
% 0.18/0.50 tff(51,plain,
% 0.18/0.50 (p2(f13(f11(c25)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.50 tff(52,plain,
% 0.18/0.50 (^[X17: $i, X16: $i, X18: $i] : refl(((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18)) <=> ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(53,plain,
% 0.18/0.50 (![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18)) <=> ![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.50 tff(54,plain,
% 0.18/0.50 (![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18)) <=> ![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(55,plain,
% 0.18/0.50 (^[X17: $i, X16: $i, X18: $i] : trans(monotonicity(rewrite((p2(X17, X18) | (~p2(X16, X17))) <=> ((~p2(X16, X17)) | p2(X17, X18))), (((p2(X17, X18) | (~p2(X16, X17))) | (~p2(X16, X18))) <=> (((~p2(X16, X17)) | p2(X17, X18)) | (~p2(X16, X18))))), rewrite((((~p2(X16, X17)) | p2(X17, X18)) | (~p2(X16, X18))) <=> ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))), (((p2(X17, X18) | (~p2(X16, X17))) | (~p2(X16, X18))) <=> ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(56,plain,
% 0.18/0.50 (![X17: $i, X16: $i, X18: $i] : ((p2(X17, X18) | (~p2(X16, X17))) | (~p2(X16, X18))) <=> ![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[55])).
% 0.18/0.50 tff(57,axiom,(![X17: $i, X16: $i, X18: $i] : ((p2(X17, X18) | (~p2(X16, X17))) | (~p2(X16, X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_26')).
% 0.18/0.50 tff(58,plain,
% 0.18/0.50 (![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.18/0.50 tff(59,plain,
% 0.18/0.50 (![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.18/0.50 tff(60,plain,(
% 0.18/0.50 ![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))),
% 0.18/0.50 inference(skolemize,[status(sab)],[59])).
% 0.18/0.50 tff(61,plain,
% 0.18/0.50 (![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.18/0.50 tff(62,plain,
% 0.18/0.50 (((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | ((~p2(f13(f11(c25)), f13(f11(c25)))) | (~p2(f13(f11(c25)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))) | p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25))))) <=> ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | (~p2(f13(f11(c25)), f13(f11(c25)))) | (~p2(f13(f11(c25)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))) | p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(63,plain,
% 0.18/0.50 ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | ((~p2(f13(f11(c25)), f13(f11(c25)))) | (~p2(f13(f11(c25)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))) | p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(64,plain,
% 0.18/0.50 ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | (~p2(f13(f11(c25)), f13(f11(c25)))) | (~p2(f13(f11(c25)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))) | p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.50 tff(65,plain,
% 0.18/0.50 (p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[64, 61, 51, 48])).
% 0.18/0.50 tff(66,plain,
% 0.18/0.50 (p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c23) <=> p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c23)),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(67,axiom,(p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_41')).
% 0.18/0.50 tff(68,plain,
% 0.18/0.50 (p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c23)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.50 tff(69,plain,
% 0.18/0.50 (((~![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))) | ((~p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c23)) | p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23)))) <=> ((~![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))) | (~p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c23)) | p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(70,plain,
% 0.18/0.50 ((~![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))) | ((~p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c23)) | p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(71,plain,
% 0.18/0.50 ((~![X52: $i, X51: $i] : ((~p10(X51, X52)) | p4(f11(X51), f11(X52)))) | (~p10(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24)))))))))))))))))))))))))), c23)) | p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.50 tff(72,plain,
% 0.18/0.50 (p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[71, 13, 68])).
% 0.18/0.50 tff(73,plain,
% 0.18/0.50 (((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23)))) <=> ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(74,plain,
% 0.18/0.50 (((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23))) <=> ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(75,plain,
% 0.18/0.50 (((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23)))) <=> ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[74])).
% 0.18/0.50 tff(76,plain,
% 0.18/0.50 (((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23)))) <=> ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[75, 73])).
% 0.18/0.50 tff(77,plain,
% 0.18/0.50 ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | ((~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(78,plain,
% 0.18/0.50 ((~![X49: $i, X50: $i, X48: $i] : ((~p4(X48, X50)) | (~p4(X48, X49)) | p4(X49, X50))) | (~p4(f11(f15(f5(f7(c24), f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f7(f8(f8(f8(f8(f9(f9(f8(f9(f9(f9(f8(f8(f9(f8(f9(f8(f9(f8(f8(f8(f9(f8(c24))))))))))))))))))))))))))), f11(c23))) | p4(f11(c23), f11(c23))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.50 tff(79,plain,
% 0.18/0.50 (p4(f11(c23), f11(c23))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[78, 27, 72])).
% 0.18/0.50 tff(80,plain,
% 0.18/0.50 (((~![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))) | ((~p4(f11(c23), f11(c23))) | p2(f13(f11(c23)), f13(f11(c23))))) <=> ((~![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))) | (~p4(f11(c23), f11(c23))) | p2(f13(f11(c23)), f13(f11(c23))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(81,plain,
% 0.18/0.50 ((~![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))) | ((~p4(f11(c23), f11(c23))) | p2(f13(f11(c23)), f13(f11(c23))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(82,plain,
% 0.18/0.50 ((~![X22: $i, X21: $i] : ((~p4(X21, X22)) | p2(f13(X21), f13(X22)))) | (~p4(f11(c23), f11(c23))) | p2(f13(f11(c23)), f13(f11(c23)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.50 tff(83,plain,
% 0.18/0.50 (p2(f13(f11(c23)), f13(f11(c23)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[82, 44, 79])).
% 0.18/0.50 tff(84,plain,
% 0.18/0.50 (p2(f13(f11(c23)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))) <=> p2(f13(f11(c23)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(85,axiom,(p2(f13(f11(c23)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_33')).
% 0.18/0.50 tff(86,plain,
% 0.18/0.50 (p2(f13(f11(c23)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.50 tff(87,plain,
% 0.18/0.50 (((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | ((~p2(f13(f11(c23)), f13(f11(c23)))) | (~p2(f13(f11(c23)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))) | p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23))))) <=> ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | (~p2(f13(f11(c23)), f13(f11(c23)))) | (~p2(f13(f11(c23)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))) | p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(88,plain,
% 0.18/0.50 ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | ((~p2(f13(f11(c23)), f13(f11(c23)))) | (~p2(f13(f11(c23)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))) | p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(89,plain,
% 0.18/0.50 ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | (~p2(f13(f11(c23)), f13(f11(c23)))) | (~p2(f13(f11(c23)), f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))) | p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.50 tff(90,plain,
% 0.18/0.50 (p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[89, 61, 86, 83])).
% 0.18/0.50 tff(91,plain,
% 0.18/0.50 (((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | (p2(f13(f11(c23)), f13(f11(c25))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))))) <=> ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | p2(f13(f11(c23)), f13(f11(c25))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(92,plain,
% 0.18/0.51 (((~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))) | p2(f13(f11(c23)), f13(f11(c25)))) <=> (p2(f13(f11(c23)), f13(f11(c25))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(93,plain,
% 0.18/0.51 (((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | ((~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))) | p2(f13(f11(c23)), f13(f11(c25))))) <=> ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | (p2(f13(f11(c23)), f13(f11(c25))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[92])).
% 0.18/0.51 tff(94,plain,
% 0.18/0.51 (((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | ((~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))) | p2(f13(f11(c23)), f13(f11(c25))))) <=> ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | p2(f13(f11(c23)), f13(f11(c25))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[93, 91])).
% 0.18/0.51 tff(95,plain,
% 0.18/0.51 ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | ((~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23)))) | p2(f13(f11(c23)), f13(f11(c25))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(96,plain,
% 0.18/0.51 ((~![X17: $i, X16: $i, X18: $i] : ((~p2(X16, X18)) | (~p2(X16, X17)) | p2(X17, X18))) | p2(f13(f11(c23)), f13(f11(c25))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c25)))) | (~p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))), f13(f11(c23))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.51 tff(97,plain,
% 0.18/0.51 (p2(f13(f11(c23)), f13(f11(c25)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[96, 61, 90, 65])).
% 0.18/0.51 tff(98,assumption,(~p2(f13(f11(c22)), f13(f11(c22)))), introduced(assumption)).
% 0.18/0.51 tff(99,plain,
% 0.18/0.51 (^[X16: $i] : refl(p2(X16, X16) <=> p2(X16, X16))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(100,plain,
% 0.18/0.51 (![X16: $i] : p2(X16, X16) <=> ![X16: $i] : p2(X16, X16)),
% 0.18/0.51 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.51 tff(101,plain,
% 0.18/0.51 (![X16: $i] : p2(X16, X16) <=> ![X16: $i] : p2(X16, X16)),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(102,axiom,(![X16: $i] : p2(X16, X16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_5')).
% 0.18/0.51 tff(103,plain,
% 0.18/0.51 (![X16: $i] : p2(X16, X16)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.51 tff(104,plain,(
% 0.18/0.51 ![X16: $i] : p2(X16, X16)),
% 0.18/0.51 inference(skolemize,[status(sab)],[103])).
% 0.18/0.51 tff(105,plain,
% 0.18/0.51 (![X16: $i] : p2(X16, X16)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.18/0.51 tff(106,plain,
% 0.18/0.51 ((~![X16: $i] : p2(X16, X16)) | p2(f13(f11(c22)), f13(f11(c22)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(107,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[106, 105, 98])).
% 0.18/0.51 tff(108,plain,(p2(f13(f11(c22)), f13(f11(c22)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(109,plain,
% 0.18/0.51 (^[X35: $i, X36: $i] : refl(((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36))) <=> ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(110,plain,
% 0.18/0.51 (![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36))) <=> ![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[109])).
% 0.18/0.51 tff(111,plain,
% 0.18/0.51 (![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36))) <=> ![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(112,plain,
% 0.18/0.51 (^[X35: $i, X36: $i] : trans(monotonicity(trans(monotonicity(rewrite((p20(f17(X35), f17(X36)) | (~p2(f12(f11(X36)), f7(c24)))) <=> ((~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))), (((p20(f17(X35), f17(X36)) | (~p2(f12(f11(X36)), f7(c24)))) | (~p2(f12(f11(X35)), f7(c24)))) <=> (((~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36))) | (~p2(f12(f11(X35)), f7(c24)))))), rewrite((((~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36))) | (~p2(f12(f11(X35)), f7(c24)))) <=> ((~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))), (((p20(f17(X35), f17(X36)) | (~p2(f12(f11(X36)), f7(c24)))) | (~p2(f12(f11(X35)), f7(c24)))) <=> ((~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36))))), ((((p20(f17(X35), f17(X36)) | (~p2(f12(f11(X36)), f7(c24)))) | (~p2(f12(f11(X35)), f7(c24)))) | (~p19(f13(f11(X35)), f13(f11(X36))))) <=> (((~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36))) | (~p19(f13(f11(X35)), f13(f11(X36))))))), rewrite((((~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36))) | (~p19(f13(f11(X35)), f13(f11(X36))))) <=> ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))), ((((p20(f17(X35), f17(X36)) | (~p2(f12(f11(X36)), f7(c24)))) | (~p2(f12(f11(X35)), f7(c24)))) | (~p19(f13(f11(X35)), f13(f11(X36))))) <=> ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(113,plain,
% 0.18/0.51 (![X35: $i, X36: $i] : (((p20(f17(X35), f17(X36)) | (~p2(f12(f11(X36)), f7(c24)))) | (~p2(f12(f11(X35)), f7(c24)))) | (~p19(f13(f11(X35)), f13(f11(X36))))) <=> ![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[112])).
% 0.18/0.51 tff(114,axiom,(![X35: $i, X36: $i] : (((p20(f17(X35), f17(X36)) | (~p2(f12(f11(X36)), f7(c24)))) | (~p2(f12(f11(X35)), f7(c24)))) | (~p19(f13(f11(X35)), f13(f11(X36)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p20_35')).
% 0.18/0.51 tff(115,plain,
% 0.18/0.51 (![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.51 tff(116,plain,
% 0.18/0.51 (![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.18/0.51 tff(117,plain,(
% 0.18/0.51 ![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))),
% 0.18/0.51 inference(skolemize,[status(sab)],[116])).
% 0.18/0.51 tff(118,plain,
% 0.18/0.51 (![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.18/0.51 tff(119,plain,
% 0.18/0.51 (p2(f12(f11(c22)), f7(c24)) <=> p2(f12(f11(c22)), f7(c24))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(120,axiom,(p2(f12(f11(c22)), f7(c24))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_10')).
% 0.18/0.51 tff(121,plain,
% 0.18/0.51 (p2(f12(f11(c22)), f7(c24))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.18/0.51 tff(122,plain,
% 0.18/0.51 (p2(f12(f11(c25)), f7(c24)) <=> p2(f12(f11(c25)), f7(c24))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(123,axiom,(p2(f12(f11(c25)), f7(c24))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_9')).
% 0.18/0.51 tff(124,plain,
% 0.18/0.51 (p2(f12(f11(c25)), f7(c24))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.18/0.51 tff(125,plain,
% 0.18/0.51 ((~p20(f17(c25), f17(c22))) <=> (~p20(f17(c25), f17(c22)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(126,axiom,(~p20(f17(c25), f17(c22))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p20_7')).
% 0.18/0.51 tff(127,plain,
% 0.18/0.51 (~p20(f17(c25), f17(c22))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.18/0.51 tff(128,plain,
% 0.18/0.51 (((~![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))) | (p20(f17(c25), f17(c22)) | (~p2(f12(f11(c25)), f7(c24))) | (~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c22)), f7(c24))))) <=> ((~![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))) | p20(f17(c25), f17(c22)) | (~p2(f12(f11(c25)), f7(c24))) | (~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c22)), f7(c24))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(129,plain,
% 0.18/0.51 (((~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c25)), f7(c24))) | (~p2(f12(f11(c22)), f7(c24))) | p20(f17(c25), f17(c22))) <=> (p20(f17(c25), f17(c22)) | (~p2(f12(f11(c25)), f7(c24))) | (~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c22)), f7(c24))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(130,plain,
% 0.18/0.51 (((~![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))) | ((~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c25)), f7(c24))) | (~p2(f12(f11(c22)), f7(c24))) | p20(f17(c25), f17(c22)))) <=> ((~![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))) | (p20(f17(c25), f17(c22)) | (~p2(f12(f11(c25)), f7(c24))) | (~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c22)), f7(c24)))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[129])).
% 0.18/0.51 tff(131,plain,
% 0.18/0.51 (((~![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))) | ((~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c25)), f7(c24))) | (~p2(f12(f11(c22)), f7(c24))) | p20(f17(c25), f17(c22)))) <=> ((~![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))) | p20(f17(c25), f17(c22)) | (~p2(f12(f11(c25)), f7(c24))) | (~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c22)), f7(c24))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[130, 128])).
% 0.18/0.51 tff(132,plain,
% 0.18/0.51 ((~![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))) | ((~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c25)), f7(c24))) | (~p2(f12(f11(c22)), f7(c24))) | p20(f17(c25), f17(c22)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(133,plain,
% 0.18/0.51 ((~![X35: $i, X36: $i] : ((~p19(f13(f11(X35)), f13(f11(X36)))) | (~p2(f12(f11(X35)), f7(c24))) | (~p2(f12(f11(X36)), f7(c24))) | p20(f17(X35), f17(X36)))) | p20(f17(c25), f17(c22)) | (~p2(f12(f11(c25)), f7(c24))) | (~p19(f13(f11(c25)), f13(f11(c22)))) | (~p2(f12(f11(c22)), f7(c24)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.18/0.51 tff(134,plain,
% 0.18/0.51 (~p19(f13(f11(c25)), f13(f11(c22)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[133, 127, 124, 121, 118])).
% 0.18/0.51 tff(135,plain,
% 0.18/0.51 (^[X14: $i, X12: $i, X13: $i, X15: $i] : refl(((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13)) <=> ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13)))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(136,plain,
% 0.18/0.51 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13)) <=> ![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[135])).
% 0.18/0.51 tff(137,plain,
% 0.18/0.51 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13)) <=> ![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(138,plain,
% 0.18/0.51 (^[X14: $i, X12: $i, X13: $i, X15: $i] : trans(monotonicity(trans(monotonicity(rewrite((p19(X12, X13) | (~p2(X14, X12))) <=> ((~p2(X14, X12)) | p19(X12, X13))), (((p19(X12, X13) | (~p2(X14, X12))) | (~p2(X15, X13))) <=> (((~p2(X14, X12)) | p19(X12, X13)) | (~p2(X15, X13))))), rewrite((((~p2(X14, X12)) | p19(X12, X13)) | (~p2(X15, X13))) <=> ((~p2(X15, X13)) | (~p2(X14, X12)) | p19(X12, X13))), (((p19(X12, X13) | (~p2(X14, X12))) | (~p2(X15, X13))) <=> ((~p2(X15, X13)) | (~p2(X14, X12)) | p19(X12, X13)))), ((((p19(X12, X13) | (~p2(X14, X12))) | (~p2(X15, X13))) | (~p19(X14, X15))) <=> (((~p2(X15, X13)) | (~p2(X14, X12)) | p19(X12, X13)) | (~p19(X14, X15))))), rewrite((((~p2(X15, X13)) | (~p2(X14, X12)) | p19(X12, X13)) | (~p19(X14, X15))) <=> ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))), ((((p19(X12, X13) | (~p2(X14, X12))) | (~p2(X15, X13))) | (~p19(X14, X15))) <=> ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(139,plain,
% 0.18/0.51 (![X14: $i, X12: $i, X13: $i, X15: $i] : (((p19(X12, X13) | (~p2(X14, X12))) | (~p2(X15, X13))) | (~p19(X14, X15))) <=> ![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[138])).
% 0.18/0.51 tff(140,axiom,(![X14: $i, X12: $i, X13: $i, X15: $i] : (((p19(X12, X13) | (~p2(X14, X12))) | (~p2(X15, X13))) | (~p19(X14, X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p19_28')).
% 0.18/0.51 tff(141,plain,
% 0.18/0.51 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.18/0.51 tff(142,plain,
% 0.18/0.51 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.18/0.51 tff(143,plain,(
% 0.18/0.51 ![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))),
% 0.18/0.51 inference(skolemize,[status(sab)],[142])).
% 0.18/0.51 tff(144,plain,
% 0.18/0.51 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.18/0.51 tff(145,plain,
% 0.18/0.51 (p19(f13(f11(c23)), f13(f11(c22))) <=> p19(f13(f11(c23)), f13(f11(c22)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(146,axiom,(p19(f13(f11(c23)), f13(f11(c22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p19_12')).
% 0.18/0.51 tff(147,plain,
% 0.18/0.51 (p19(f13(f11(c23)), f13(f11(c22)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.18/0.51 tff(148,plain,
% 0.18/0.51 (((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))) | (p19(f13(f11(c25)), f13(f11(c22))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c22)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25)))))) <=> ((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))) | p19(f13(f11(c25)), f13(f11(c22))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c22)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(149,plain,
% 0.18/0.51 (((~p2(f13(f11(c22)), f13(f11(c22)))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25)))) | p19(f13(f11(c25)), f13(f11(c22)))) <=> (p19(f13(f11(c25)), f13(f11(c22))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c22)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(150,plain,
% 0.18/0.51 (((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))) | ((~p2(f13(f11(c22)), f13(f11(c22)))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25)))) | p19(f13(f11(c25)), f13(f11(c22))))) <=> ((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))) | (p19(f13(f11(c25)), f13(f11(c22))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c22)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[149])).
% 0.18/0.51 tff(151,plain,
% 0.18/0.51 (((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))) | ((~p2(f13(f11(c22)), f13(f11(c22)))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25)))) | p19(f13(f11(c25)), f13(f11(c22))))) <=> ((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))) | p19(f13(f11(c25)), f13(f11(c22))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c22)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[150, 148])).
% 0.18/0.51 tff(152,plain,
% 0.18/0.51 ((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))) | ((~p2(f13(f11(c22)), f13(f11(c22)))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25)))) | p19(f13(f11(c25)), f13(f11(c22))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(153,plain,
% 0.18/0.51 ((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p2(X15, X13)) | (~p19(X14, X15)) | (~p2(X14, X12)) | p19(X12, X13))) | p19(f13(f11(c25)), f13(f11(c22))) | (~p19(f13(f11(c23)), f13(f11(c22)))) | (~p2(f13(f11(c22)), f13(f11(c22)))) | (~p2(f13(f11(c23)), f13(f11(c25))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.18/0.51 tff(154,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[153, 147, 144, 134, 108, 97])).
% 0.18/0.51 % SZS output end Proof
% 0.18/0.52 % E exiting
%------------------------------------------------------------------------------