%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN656-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:39:46 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN656-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:40:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(p3_type, type, (
% 0.21/0.39 p3: ( $i * $i ) > $o)).
% 0.21/0.39 tff(f13_type, type, (
% 0.21/0.39 f13: ( $i * $i ) > $i)).
% 0.21/0.39 tff(c34_type, type, (
% 0.21/0.39 c34: $i)).
% 0.21/0.39 tff(c31_type, type, (
% 0.21/0.39 c31: $i)).
% 0.21/0.39 tff(f15_type, type, (
% 0.21/0.39 f15: ( $i * $i ) > $i)).
% 0.21/0.39 tff(c35_type, type, (
% 0.21/0.39 c35: $i)).
% 0.21/0.39 tff(f17_type, type, (
% 0.21/0.39 f17: ( $i * $i ) > $i)).
% 0.21/0.39 tff(c33_type, type, (
% 0.21/0.39 c33: $i)).
% 0.21/0.39 tff(p25_type, type, (
% 0.21/0.39 p25: ( $i * $i ) > $o)).
% 0.21/0.39 tff(f5_type, type, (
% 0.21/0.39 f5: ( $i * $i ) > $i)).
% 0.21/0.39 tff(f7_type, type, (
% 0.21/0.39 f7: ( $i * $i ) > $i)).
% 0.21/0.39 tff(c29_type, type, (
% 0.21/0.39 c29: $i)).
% 0.21/0.39 tff(c28_type, type, (
% 0.21/0.39 c28: $i)).
% 0.21/0.39 tff(c32_type, type, (
% 0.21/0.39 c32: $i)).
% 0.21/0.39 tff(p4_type, type, (
% 0.21/0.39 p4: ( $i * $i ) > $o)).
% 0.21/0.39 tff(p2_type, type, (
% 0.21/0.39 p2: ( $i * $i ) > $o)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[X58: $i] : refl(p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58)) <=> p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![X58: $i] : p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58)) <=> ![X58: $i] : p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![X58: $i] : p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58)) <=> ![X58: $i] : p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(4,axiom,(![X58: $i] : p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_31')).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![X58: $i] : p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.39 tff(6,plain,(
% 0.21/0.39 ![X58: $i] : p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58))),
% 0.21/0.39 inference(skolemize,[status(sab)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![X58: $i] : p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~![X58: $i] : p25(f5(c29, f13(c31, f15(c32, X58))), f13(c31, X58))) | p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (^[X62: $i, X57: $i, X56: $i, X55: $i] : refl((p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62))) <=> (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62))) <=> ![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62))) <=> ![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (^[X62: $i, X57: $i, X56: $i, X55: $i] : trans(monotonicity(rewrite((p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X62))) <=> (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X62)))), (((p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X62))) | (~p25(f5(f7(c28, X55), X62), X57))) <=> ((p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X62))) | (~p25(f5(f7(c28, X55), X62), X57))))), rewrite(((p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X62))) | (~p25(f5(f7(c28, X55), X62), X57))) <=> (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))), (((p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X62))) | (~p25(f5(f7(c28, X55), X62), X57))) <=> (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (![X62: $i, X57: $i, X56: $i, X55: $i] : ((p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X62))) | (~p25(f5(f7(c28, X55), X62), X57))) <=> ![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.40 tff(15,axiom,(![X62: $i, X57: $i, X56: $i, X55: $i] : ((p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X62))) | (~p25(f5(f7(c28, X55), X62), X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_46')).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.40 tff(18,plain,(
% 0.21/0.40 ![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[17])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 ((~p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))) <=> (~p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(21,axiom,(~p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p25_45')).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (~p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (((~![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))) | (p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))))) <=> ((~![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))) | p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 ((p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35))))) <=> (p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (((~![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))) | (p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))))) <=> ((~![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))) | (p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (((~![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))) | (p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))))) <=> ((~![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))) | p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[25, 23])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 ((~![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))) | (p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 ((~![X62: $i, X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(f7(c28, X55), X62), X57)) | (~p25(f5(X55, X56), X62)))) | p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (~p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[28, 22, 19, 9])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (^[X63: $i] : refl((p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34))) <=> (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34))) <=> ![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34))) <=> ![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(33,axiom,(![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_49')).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.40 tff(35,plain,(
% 0.21/0.40 ![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[34])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (((~![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))) | (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34)))) <=> ((~![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))) | p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 ((~![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))) | (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ((~![X63: $i] : (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), X63))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), X63))), f13(c31, c34)))) | p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35))) | p25(f5(f7(c28, c29), f13(c31, f15(f17(c33, c34), c35))), f13(c31, c34))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[40, 29])).
% 0.21/0.41 tff(42,assumption,(~p3(f13(c31, c34), f13(c31, c34))), introduced(assumption)).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (^[X64: $i] : refl(p3(X64, X64) <=> p3(X64, X64))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![X64: $i] : p3(X64, X64) <=> ![X64: $i] : p3(X64, X64)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![X64: $i] : p3(X64, X64) <=> ![X64: $i] : p3(X64, X64)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(46,axiom,(![X64: $i] : p3(X64, X64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_6')).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![X64: $i] : p3(X64, X64)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.41 tff(48,plain,(
% 0.21/0.41 ![X64: $i] : p3(X64, X64)),
% 0.21/0.41 inference(skolemize,[status(sab)],[47])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (![X64: $i] : p3(X64, X64)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 ((~![X64: $i] : p3(X64, X64)) | p3(f13(c31, c34), f13(c31, c34))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[50, 49, 42])).
% 0.21/0.41 tff(52,plain,(p3(f13(c31, c34), f13(c31, c34))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (^[X64: $i, X66: $i, X65: $i] : refl(((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66)) <=> ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66)) <=> ![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66)) <=> ![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (^[X64: $i, X66: $i, X65: $i] : trans(monotonicity(rewrite((p3(X65, X66) | (~p3(X64, X65))) <=> ((~p3(X64, X65)) | p3(X65, X66))), (((p3(X65, X66) | (~p3(X64, X65))) | (~p3(X64, X66))) <=> (((~p3(X64, X65)) | p3(X65, X66)) | (~p3(X64, X66))))), rewrite((((~p3(X64, X65)) | p3(X65, X66)) | (~p3(X64, X66))) <=> ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))), (((p3(X65, X66) | (~p3(X64, X65))) | (~p3(X64, X66))) <=> ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![X64: $i, X66: $i, X65: $i] : ((p3(X65, X66) | (~p3(X64, X65))) | (~p3(X64, X66))) <=> ![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.41 tff(58,axiom,(![X64: $i, X66: $i, X65: $i] : ((p3(X65, X66) | (~p3(X64, X65))) | (~p3(X64, X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_22')).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.41 tff(61,plain,(
% 0.21/0.41 ![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))),
% 0.21/0.41 inference(skolemize,[status(sab)],[60])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (((~![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))) | ((~p3(f13(c31, c34), f13(c31, c34))) | (~p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35)))) | p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34)))) <=> ((~![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))) | (~p3(f13(c31, c34), f13(c31, c34))) | (~p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35)))) | p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((~![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))) | ((~p3(f13(c31, c34), f13(c31, c34))) | (~p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35)))) | p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((~![X64: $i, X66: $i, X65: $i] : ((~p3(X64, X66)) | (~p3(X64, X65)) | p3(X65, X66))) | (~p3(f13(c31, c34), f13(c31, c34))) | (~p3(f13(c31, c34), f13(c31, f15(f17(c33, c34), c35)))) | p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[65, 62, 52, 41])).
% 0.21/0.41 tff(67,assumption,(~p3(f13(c31, f15(c32, f15(f17(c33, c34), c35))), f13(c31, f15(c32, f15(f17(c33, c34), c35))))), introduced(assumption)).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ((~![X64: $i] : p3(X64, X64)) | p3(f13(c31, f15(c32, f15(f17(c33, c34), c35))), f13(c31, f15(c32, f15(f17(c33, c34), c35))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[68, 49, 67])).
% 0.21/0.41 tff(70,plain,(p3(f13(c31, f15(c32, f15(f17(c33, c34), c35))), f13(c31, f15(c32, f15(f17(c33, c34), c35))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(71,assumption,(~p2(c29, c29)), introduced(assumption)).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (^[X27: $i] : refl(p2(X27, X27) <=> p2(X27, X27))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (![X27: $i] : p2(X27, X27) <=> ![X27: $i] : p2(X27, X27)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (![X27: $i] : p2(X27, X27) <=> ![X27: $i] : p2(X27, X27)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(75,axiom,(![X27: $i] : p2(X27, X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_9')).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (![X27: $i] : p2(X27, X27)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.41 tff(77,plain,(
% 0.21/0.41 ![X27: $i] : p2(X27, X27)),
% 0.21/0.41 inference(skolemize,[status(sab)],[76])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (![X27: $i] : p2(X27, X27)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 ((~![X27: $i] : p2(X27, X27)) | p2(c29, c29)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[79, 78, 71])).
% 0.21/0.41 tff(81,plain,(p2(c29, c29)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (^[X80: $i, X81: $i, X78: $i, X79: $i] : refl(((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81))) <=> ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81))) <=> ![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81))) <=> ![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 (^[X80: $i, X81: $i, X78: $i, X79: $i] : trans(monotonicity(rewrite((p4(f5(X78, X79), f5(X80, X81)) | (~p2(X78, X80))) <=> ((~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))), (((p4(f5(X78, X79), f5(X80, X81)) | (~p2(X78, X80))) | (~p3(X79, X81))) <=> (((~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81))) | (~p3(X79, X81))))), rewrite((((~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81))) | (~p3(X79, X81))) <=> ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))), (((p4(f5(X78, X79), f5(X80, X81)) | (~p2(X78, X80))) | (~p3(X79, X81))) <=> ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (![X80: $i, X81: $i, X78: $i, X79: $i] : ((p4(f5(X78, X79), f5(X80, X81)) | (~p2(X78, X80))) | (~p3(X79, X81))) <=> ![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.41 tff(87,axiom,(![X80: $i, X81: $i, X78: $i, X79: $i] : ((p4(f5(X78, X79), f5(X80, X81)) | (~p2(X78, X80))) | (~p3(X79, X81)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_44')).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.21/0.41 tff(90,plain,(
% 0.21/0.41 ![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[89])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (((~![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))) | ((~p3(f13(c31, f15(c32, f15(f17(c33, c34), c35))), f13(c31, f15(c32, f15(f17(c33, c34), c35))))) | (~p2(c29, c29)) | p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35))))))) <=> ((~![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))) | (~p3(f13(c31, f15(c32, f15(f17(c33, c34), c35))), f13(c31, f15(c32, f15(f17(c33, c34), c35))))) | (~p2(c29, c29)) | p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 ((~![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))) | ((~p3(f13(c31, f15(c32, f15(f17(c33, c34), c35))), f13(c31, f15(c32, f15(f17(c33, c34), c35))))) | (~p2(c29, c29)) | p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ((~![X80: $i, X81: $i, X78: $i, X79: $i] : ((~p3(X79, X81)) | (~p2(X78, X80)) | p4(f5(X78, X79), f5(X80, X81)))) | (~p3(f13(c31, f15(c32, f15(f17(c33, c34), c35))), f13(c31, f15(c32, f15(f17(c33, c34), c35))))) | (~p2(c29, c29)) | p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 ((~p3(f13(c31, f15(c32, f15(f17(c33, c34), c35))), f13(c31, f15(c32, f15(f17(c33, c34), c35))))) | (~p2(c29, c29)) | p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[94, 91])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 81, 70])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (^[X57: $i, X56: $i, X55: $i] : refl(((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57)) <=> ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57)) <=> ![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57)) <=> ![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (^[X57: $i, X56: $i, X55: $i] : rewrite((p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X57))) <=> ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (![X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X57))) <=> ![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.42 tff(102,axiom,(![X57: $i, X56: $i, X55: $i] : (p25(f5(f7(c28, X55), X56), X57) | (~p25(f5(X55, X56), X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_32')).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.21/0.42 tff(105,plain,(
% 0.21/0.42 ![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))),
% 0.21/0.42 inference(skolemize,[status(sab)],[104])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (((~![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))) | ((~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))) | p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)))) <=> ((~![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))) | p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 ((~![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))) | ((~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))) | p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 ((~![X57: $i, X56: $i, X55: $i] : ((~p25(f5(X55, X56), X57)) | p25(f5(f7(c28, X55), X56), X57))) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))) | p25(f5(f7(c28, c29), f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[109, 106, 22])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (^[X53: $i, X52: $i, X51: $i, X54: $i] : refl(((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52)) <=> ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52)) <=> ![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52)) <=> ![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (^[X53: $i, X52: $i, X51: $i, X54: $i] : trans(monotonicity(trans(monotonicity(rewrite((p25(X51, X52) | (~p3(X54, X52))) <=> ((~p3(X54, X52)) | p25(X51, X52))), (((p25(X51, X52) | (~p3(X54, X52))) | (~p4(X53, X51))) <=> (((~p3(X54, X52)) | p25(X51, X52)) | (~p4(X53, X51))))), rewrite((((~p3(X54, X52)) | p25(X51, X52)) | (~p4(X53, X51))) <=> ((~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))), (((p25(X51, X52) | (~p3(X54, X52))) | (~p4(X53, X51))) <=> ((~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52)))), ((((p25(X51, X52) | (~p3(X54, X52))) | (~p4(X53, X51))) | (~p25(X53, X54))) <=> (((~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52)) | (~p25(X53, X54))))), rewrite((((~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52)) | (~p25(X53, X54))) <=> ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))), ((((p25(X51, X52) | (~p3(X54, X52))) | (~p4(X53, X51))) | (~p25(X53, X54))) <=> ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (![X53: $i, X52: $i, X51: $i, X54: $i] : (((p25(X51, X52) | (~p3(X54, X52))) | (~p4(X53, X51))) | (~p25(X53, X54))) <=> ![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.42 tff(116,axiom,(![X53: $i, X52: $i, X51: $i, X54: $i] : (((p25(X51, X52) | (~p3(X54, X52))) | (~p4(X53, X51))) | (~p25(X53, X54)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_35')).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.21/0.42 tff(119,plain,(
% 0.21/0.42 ![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))),
% 0.21/0.42 inference(skolemize,[status(sab)],[118])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))) | (p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))))) <=> ((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))) | p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(122,plain,
% 0.21/0.43 (((~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34))) <=> (p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 (((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))) | ((~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)))) <=> ((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))) | (p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[122])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 (((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))) | ((~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)))) <=> ((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))) | p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[123, 121])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 ((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))) | ((~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 ((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p25(X53, X54)) | (~p4(X53, X51)) | (~p3(X54, X52)) | p25(X51, X52))) | p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, c34)) | (~p25(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f13(c31, f15(f17(c33, c34), c35)))) | (~p3(f13(c31, f15(f17(c33, c34), c35)), f13(c31, c34))) | (~p4(f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35)))), f5(c29, f13(c31, f15(c32, f15(f17(c33, c34), c35))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[126, 120, 110, 9, 96, 66])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------