%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN615-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:39:41 AM UTC 2025
% Result : Unsatisfiable 0.80s 0.98s
% Output : Proof 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN615-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:39:18 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.80/0.98 % SZS status Unsatisfiable
% 0.80/0.98 % SZS output start Proof
% 0.80/0.98 tff(p7_type, type, (
% 0.80/0.98 p7: ( $i * $i ) > $o)).
% 0.80/0.98 tff(c25_type, type, (
% 0.80/0.98 c25: $i)).
% 0.80/0.98 tff(f8_type, type, (
% 0.80/0.98 f8: ( $i * $i ) > $i)).
% 0.80/0.98 tff(f9_type, type, (
% 0.80/0.98 f9: ( $i * $i ) > $i)).
% 0.80/0.98 tff(f10_type, type, (
% 0.80/0.98 f10: ( $i * $i ) > $i)).
% 0.80/0.98 tff(c27_type, type, (
% 0.80/0.98 c27: $i)).
% 0.80/0.98 tff(f11_type, type, (
% 0.80/0.98 f11: $i > $i)).
% 0.80/0.98 tff(f3_type, type, (
% 0.80/0.98 f3: $i > $i)).
% 0.80/0.98 tff(f4_type, type, (
% 0.80/0.98 f4: $i > $i)).
% 0.80/0.98 tff(f5_type, type, (
% 0.80/0.98 f5: $i > $i)).
% 0.80/0.98 tff(c22_type, type, (
% 0.80/0.98 c22: $i)).
% 0.80/0.98 tff(c24_type, type, (
% 0.80/0.98 c24: $i)).
% 0.80/0.98 tff(c26_type, type, (
% 0.80/0.98 c26: $i)).
% 0.80/0.98 tff(c23_type, type, (
% 0.80/0.98 c23: $i)).
% 0.80/0.98 tff(f12_type, type, (
% 0.80/0.98 f12: $i > $i)).
% 0.80/0.98 tff(f14_type, type, (
% 0.80/0.98 f14: ( $i * $i ) > $i)).
% 0.80/0.98 tff(f16_type, type, (
% 0.80/0.98 f16: ( $i * $i ) > $i)).
% 0.80/0.98 tff(f17_type, type, (
% 0.80/0.98 f17: ( $i * $i ) > $i)).
% 0.80/0.98 tff(c21_type, type, (
% 0.80/0.98 c21: $i)).
% 0.80/0.98 tff(c28_type, type, (
% 0.80/0.98 c28: $i)).
% 0.80/0.98 tff(p2_type, type, (
% 0.80/0.98 p2: ( $i * $i ) > $o)).
% 0.80/0.98 tff(p19_type, type, (
% 0.80/0.98 p19: ( $i * $i ) > $o)).
% 0.80/0.98 tff(p20_type, type, (
% 0.80/0.98 p20: ( $i * $i ) > $o)).
% 0.80/0.98 tff(f6_type, type, (
% 0.80/0.98 f6: ( $i * $i ) > $i)).
% 0.80/0.98 tff(1,assumption,(~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))), introduced(assumption)).
% 0.80/0.98 tff(2,plain,
% 0.80/0.98 (^[X43: $i] : refl(p7(X43, X43) <=> p7(X43, X43))),
% 0.80/0.98 inference(bind,[status(th)],[])).
% 0.80/0.98 tff(3,plain,
% 0.80/0.98 (![X43: $i] : p7(X43, X43) <=> ![X43: $i] : p7(X43, X43)),
% 0.80/0.98 inference(quant_intro,[status(thm)],[2])).
% 0.80/0.98 tff(4,plain,
% 0.80/0.98 (![X43: $i] : p7(X43, X43) <=> ![X43: $i] : p7(X43, X43)),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(5,axiom,(![X43: $i] : p7(X43, X43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_2')).
% 0.80/0.98 tff(6,plain,
% 0.80/0.98 (![X43: $i] : p7(X43, X43)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.80/0.98 tff(7,plain,(
% 0.80/0.98 ![X43: $i] : p7(X43, X43)),
% 0.80/0.98 inference(skolemize,[status(sab)],[6])).
% 0.80/0.98 tff(8,plain,
% 0.80/0.98 (![X43: $i] : p7(X43, X43)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.80/0.98 tff(9,plain,
% 0.80/0.98 ((~![X43: $i] : p7(X43, X43)) | p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))),
% 0.80/0.98 inference(quant_inst,[status(thm)],[])).
% 0.80/0.98 tff(10,plain,
% 0.80/0.98 ($false),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.80/0.98 tff(11,plain,(p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.98 tff(12,plain,
% 0.80/0.98 (^[X47: $i, X49: $i, X46: $i, X48: $i] : refl(((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49))) <=> ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49))))),
% 0.80/0.98 inference(bind,[status(th)],[])).
% 0.80/0.98 tff(13,plain,
% 0.80/0.98 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49))) <=> ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))),
% 0.80/0.98 inference(quant_intro,[status(thm)],[12])).
% 0.80/0.98 tff(14,plain,
% 0.80/0.98 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49))) <=> ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(15,plain,
% 0.80/0.99 (^[X47: $i, X49: $i, X46: $i, X48: $i] : trans(monotonicity(rewrite((p7(f10(X46, X47), f10(X48, X49)) | (~p2(X47, X49))) <=> ((~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))), (((p7(f10(X46, X47), f10(X48, X49)) | (~p2(X47, X49))) | (~p7(X46, X48))) <=> (((~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49))) | (~p7(X46, X48))))), rewrite((((~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49))) | (~p7(X46, X48))) <=> ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))), (((p7(f10(X46, X47), f10(X48, X49)) | (~p2(X47, X49))) | (~p7(X46, X48))) <=> ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(16,plain,
% 0.80/0.99 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((p7(f10(X46, X47), f10(X48, X49)) | (~p2(X47, X49))) | (~p7(X46, X48))) <=> ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[15])).
% 0.80/0.99 tff(17,axiom,(![X47: $i, X49: $i, X46: $i, X48: $i] : ((p7(f10(X46, X47), f10(X48, X49)) | (~p2(X47, X49))) | (~p7(X46, X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_24')).
% 0.80/0.99 tff(18,plain,
% 0.80/0.99 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.80/0.99 tff(19,plain,
% 0.80/0.99 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.80/0.99 tff(20,plain,(
% 0.80/0.99 ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))),
% 0.80/0.99 inference(skolemize,[status(sab)],[19])).
% 0.80/0.99 tff(21,plain,
% 0.80/0.99 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.80/0.99 tff(22,plain,
% 0.80/0.99 (p2(c26, f14(f16(c28, f17(c21, c27)), c25)) <=> p2(c26, f14(f16(c28, f17(c21, c27)), c25))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(23,axiom,(p2(c26, f14(f16(c28, f17(c21, c27)), c25))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_14')).
% 0.80/0.99 tff(24,plain,
% 0.80/0.99 (p2(c26, f14(f16(c28, f17(c21, c27)), c25))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.80/0.99 tff(25,plain,
% 0.80/0.99 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))) | ((~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | (~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25))))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | (~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25))))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(26,plain,
% 0.80/0.99 (((~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))) <=> ((~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | (~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25))))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(27,plain,
% 0.80/0.99 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))) | ((~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25))))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))) | ((~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | (~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))))),
% 0.80/0.99 inference(monotonicity,[status(thm)],[26])).
% 0.80/0.99 tff(28,plain,
% 0.80/0.99 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))) | ((~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25))))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | (~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25))))),
% 0.80/0.99 inference(transitivity,[status(thm)],[27, 25])).
% 0.80/0.99 tff(29,plain,
% 0.80/0.99 ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))) | ((~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25))))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(30,plain,
% 0.80/0.99 ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p2(X47, X49)) | p7(f10(X46, X47), f10(X48, X49)))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))) | (~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.80/0.99 tff(31,plain,
% 0.80/0.99 ((~p7(f11(f3(f4(f5(c22)))), f11(f3(f4(f5(c22)))))) | p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[30, 24, 21])).
% 0.80/0.99 tff(32,plain,
% 0.80/0.99 (p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[31, 11])).
% 0.80/0.99 tff(33,assumption,(~p7(f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), introduced(assumption)).
% 0.80/0.99 tff(34,plain,
% 0.80/0.99 ((~![X43: $i] : p7(X43, X43)) | p7(f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(35,plain,
% 0.80/0.99 ($false),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[34, 8, 33])).
% 0.80/0.99 tff(36,plain,(p7(f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.99 tff(37,plain,
% 0.80/0.99 (^[X57: $i, X56: $i, X55: $i, X54: $i] : refl(((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57))) <=> ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(38,plain,
% 0.80/0.99 (![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57))) <=> ![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[37])).
% 0.80/0.99 tff(39,plain,
% 0.80/0.99 (![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57))) <=> ![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(40,plain,
% 0.80/0.99 (^[X57: $i, X56: $i, X55: $i, X54: $i] : trans(monotonicity(rewrite((p7(f8(X54, X55), f8(X56, X57)) | (~p7(X54, X56))) <=> ((~p7(X54, X56)) | p7(f8(X54, X55), f8(X56, X57)))), (((p7(f8(X54, X55), f8(X56, X57)) | (~p7(X54, X56))) | (~p7(X55, X57))) <=> (((~p7(X54, X56)) | p7(f8(X54, X55), f8(X56, X57))) | (~p7(X55, X57))))), rewrite((((~p7(X54, X56)) | p7(f8(X54, X55), f8(X56, X57))) | (~p7(X55, X57))) <=> ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))), (((p7(f8(X54, X55), f8(X56, X57)) | (~p7(X54, X56))) | (~p7(X55, X57))) <=> ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(41,plain,
% 0.80/0.99 (![X57: $i, X56: $i, X55: $i, X54: $i] : ((p7(f8(X54, X55), f8(X56, X57)) | (~p7(X54, X56))) | (~p7(X55, X57))) <=> ![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[40])).
% 0.80/0.99 tff(42,axiom,(![X57: $i, X56: $i, X55: $i, X54: $i] : ((p7(f8(X54, X55), f8(X56, X57)) | (~p7(X54, X56))) | (~p7(X55, X57)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_23')).
% 0.80/0.99 tff(43,plain,
% 0.80/0.99 (![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.80/0.99 tff(44,plain,
% 0.80/0.99 (![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.80/0.99 tff(45,plain,(
% 0.80/0.99 ![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))),
% 0.80/0.99 inference(skolemize,[status(sab)],[44])).
% 0.80/0.99 tff(46,plain,
% 0.80/0.99 (![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.80/0.99 tff(47,plain,
% 0.80/0.99 (((~![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))) | ((~p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))) | (~p7(f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))) | p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) <=> ((~![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))) | (~p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))) | (~p7(f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))) | p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(48,plain,
% 0.80/0.99 ((~![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))) | ((~p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))) | (~p7(f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))) | p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(49,plain,
% 0.80/0.99 ((~![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))) | (~p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))) | (~p7(f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))) | p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.80/0.99 tff(50,plain,
% 0.80/0.99 ((~p7(f10(f11(f3(f4(f5(c22)))), c26), f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)))) | (~p7(f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))) | p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.80/0.99 tff(51,plain,
% 0.80/0.99 (p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[50, 36, 32])).
% 0.80/0.99 tff(52,assumption,(~p7(f10(f12(f11(f3(f5(c22)))), c23), f10(f12(f11(f3(f5(c22)))), c23))), introduced(assumption)).
% 0.80/0.99 tff(53,plain,
% 0.80/0.99 ((~![X43: $i] : p7(X43, X43)) | p7(f10(f12(f11(f3(f5(c22)))), c23), f10(f12(f11(f3(f5(c22)))), c23))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(54,plain,
% 0.80/0.99 ($false),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[53, 8, 52])).
% 0.80/0.99 tff(55,plain,(p7(f10(f12(f11(f3(f5(c22)))), c23), f10(f12(f11(f3(f5(c22)))), c23))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.99 tff(56,plain,
% 0.80/0.99 (((~![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))) | ((~p7(f10(f12(f11(f3(f5(c22)))), c23), f10(f12(f11(f3(f5(c22)))), c23))) | (~p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))))) <=> ((~![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))) | (~p7(f10(f12(f11(f3(f5(c22)))), c23), f10(f12(f11(f3(f5(c22)))), c23))) | (~p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(57,plain,
% 0.80/0.99 ((~![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))) | ((~p7(f10(f12(f11(f3(f5(c22)))), c23), f10(f12(f11(f3(f5(c22)))), c23))) | (~p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(58,plain,
% 0.80/0.99 ((~![X57: $i, X56: $i, X55: $i, X54: $i] : ((~p7(X54, X56)) | (~p7(X55, X57)) | p7(f8(X54, X55), f8(X56, X57)))) | (~p7(f10(f12(f11(f3(f5(c22)))), c23), f10(f12(f11(f3(f5(c22)))), c23))) | (~p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.80/0.99 tff(59,plain,
% 0.80/0.99 ((~p7(f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[58, 46, 55])).
% 0.80/0.99 tff(60,plain,
% 0.80/0.99 (p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[59, 51])).
% 0.80/0.99 tff(61,assumption,(~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))), introduced(assumption)).
% 0.80/0.99 tff(62,plain,
% 0.80/0.99 (^[X18: $i, X20: $i, X19: $i] : refl((p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(63,plain,
% 0.80/0.99 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[62])).
% 0.80/0.99 tff(64,plain,
% 0.80/0.99 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(65,plain,
% 0.80/0.99 (^[X18: $i, X20: $i, X19: $i] : trans(monotonicity(rewrite((p2(X19, X20) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))))), rewrite(((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(66,plain,
% 0.80/0.99 (![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[65])).
% 0.80/0.99 tff(67,axiom,(![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_17')).
% 0.80/0.99 tff(68,plain,
% 0.80/0.99 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.80/0.99 tff(69,plain,
% 0.80/0.99 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.80/0.99 tff(70,plain,(
% 0.80/0.99 ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.80/0.99 inference(skolemize,[status(sab)],[69])).
% 0.80/0.99 tff(71,plain,
% 0.80/0.99 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.80/0.99 tff(72,plain,
% 0.80/0.99 (p2(c26, f3(c22)) <=> p2(c26, f3(c22))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(73,axiom,(p2(c26, f3(c22))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_5')).
% 0.80/0.99 tff(74,plain,
% 0.80/0.99 (p2(c26, f3(c22))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.80/0.99 tff(75,plain,
% 0.80/0.99 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22)) | (~p2(c26, f3(c22))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22)) | (~p2(c26, f3(c22))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(76,plain,
% 0.80/0.99 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22)) | (~p2(c26, f3(c22))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25))))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(77,plain,
% 0.80/0.99 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22)) | (~p2(c26, f3(c22))) | (~p2(c26, f14(f16(c28, f17(c21, c27)), c25)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.80/0.99 tff(78,plain,
% 0.80/0.99 ($false),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[77, 74, 24, 71, 61])).
% 0.80/0.99 tff(79,plain,(p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.99 tff(80,plain,
% 0.80/0.99 (^[X62: $i, X63: $i] : refl(((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22)))))) <=> ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22)))))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(81,plain,
% 0.80/0.99 (![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22)))))) <=> ![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))),
% 0.80/1.00 inference(quant_intro,[status(thm)],[80])).
% 0.80/1.00 tff(82,plain,
% 0.80/1.00 (![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22)))))) <=> ![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(83,plain,
% 0.80/1.00 (^[X62: $i, X63: $i] : trans(monotonicity(rewrite((((~p19(X62, f3(f4(f5(c22))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21)))) | (~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22)))) <=> ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))), (((((~p19(X62, f3(f4(f5(c22))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21)))) | (~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22)))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27))))))) <=> (((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22)))))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27))))))))), rewrite((((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22)))))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27))))))) <=> ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))), (((((~p19(X62, f3(f4(f5(c22))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21)))) | (~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22)))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27))))))) <=> ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))))),
% 0.80/1.00 inference(bind,[status(th)],[])).
% 0.80/1.00 tff(84,plain,
% 0.80/1.00 (![X62: $i, X63: $i] : ((((~p19(X62, f3(f4(f5(c22))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21)))) | (~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22)))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27))))))) <=> ![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))),
% 0.80/1.00 inference(quant_intro,[status(thm)],[83])).
% 0.80/1.00 tff(85,axiom,(![X62: $i, X63: $i] : ((((~p19(X62, f3(f4(f5(c22))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21)))) | (~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22)))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p19_30')).
% 0.80/1.00 tff(86,plain,
% 0.80/1.00 (![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.80/1.00 tff(87,plain,
% 0.80/1.00 (![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.80/1.00 tff(88,plain,(
% 0.80/1.00 ![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))),
% 0.80/1.00 inference(skolemize,[status(sab)],[87])).
% 0.80/1.00 tff(89,plain,
% 0.80/1.00 (![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.80/1.00 tff(90,plain,
% 0.80/1.00 (p20(c24, f6(f3(f4(f5(c22))), c21)) <=> p20(c24, f6(f3(f4(f5(c22))), c21))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(91,axiom,(p20(c24, f6(f3(f4(f5(c22))), c21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p20_8')).
% 0.80/1.00 tff(92,plain,
% 0.80/1.00 (p20(c24, f6(f3(f4(f5(c22))), c21))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.80/1.00 tff(93,plain,
% 0.80/1.00 (p19(c23, f3(f4(f5(c22)))) <=> p19(c23, f3(f4(f5(c22))))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(94,axiom,(p19(c23, f3(f4(f5(c22))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p19_7')).
% 0.80/1.00 tff(95,plain,
% 0.80/1.00 (p19(c23, f3(f4(f5(c22))))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.80/1.00 tff(96,plain,
% 0.80/1.00 (((~![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))) | ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p19(c23, f3(f4(f5(c22))))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21))))) <=> ((~![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))) | (~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p19(c23, f3(f4(f5(c22))))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21))))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(97,plain,
% 0.80/1.00 (((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21))) | (~p19(c23, f3(f4(f5(c22)))))) <=> ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p19(c23, f3(f4(f5(c22))))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21))))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(98,plain,
% 0.80/1.00 (((~![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))) | ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21))) | (~p19(c23, f3(f4(f5(c22))))))) <=> ((~![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))) | ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p19(c23, f3(f4(f5(c22))))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21)))))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[97])).
% 0.80/1.00 tff(99,plain,
% 0.80/1.00 (((~![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))) | ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21))) | (~p19(c23, f3(f4(f5(c22))))))) <=> ((~![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))) | (~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p19(c23, f3(f4(f5(c22))))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21))))),
% 0.80/1.00 inference(transitivity,[status(thm)],[98, 96])).
% 0.80/1.00 tff(100,plain,
% 0.80/1.00 ((~![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))) | ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21))) | (~p19(c23, f3(f4(f5(c22))))))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(101,plain,
% 0.80/1.00 ((~![X62: $i, X63: $i] : ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), X62), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(X63), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(X63, f6(f3(f4(f5(c22))), c21))) | (~p19(X62, f3(f4(f5(c22))))))) | (~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p19(c23, f3(f4(f5(c22))))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p20(c24, f6(f3(f4(f5(c22))), c21)))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.80/1.00 tff(102,plain,
% 0.80/1.00 ((~p2(f14(f16(c28, f17(c21, c27)), c25), f3(c22))) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))))),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[101, 95, 92, 89])).
% 0.80/1.00 tff(103,plain,
% 0.80/1.00 (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[102, 79])).
% 0.80/1.00 tff(104,plain,
% 0.80/1.00 (^[X43: $i, X45: $i, X44: $i] : refl((p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44))) <=> (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44))))),
% 0.80/1.00 inference(bind,[status(th)],[])).
% 0.80/1.00 tff(105,plain,
% 0.80/1.00 (![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44))) <=> ![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))),
% 0.80/1.00 inference(quant_intro,[status(thm)],[104])).
% 0.80/1.00 tff(106,plain,
% 0.80/1.00 (![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44))) <=> ![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(107,plain,
% 0.80/1.00 (^[X43: $i, X45: $i, X44: $i] : trans(monotonicity(rewrite((p7(X44, X45) | (~p7(X43, X44))) <=> (p7(X44, X45) | (~p7(X43, X44)))), (((p7(X44, X45) | (~p7(X43, X44))) | (~p7(X43, X45))) <=> ((p7(X44, X45) | (~p7(X43, X44))) | (~p7(X43, X45))))), rewrite(((p7(X44, X45) | (~p7(X43, X44))) | (~p7(X43, X45))) <=> (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))), (((p7(X44, X45) | (~p7(X43, X44))) | (~p7(X43, X45))) <=> (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))))),
% 0.80/1.00 inference(bind,[status(th)],[])).
% 0.80/1.00 tff(108,plain,
% 0.80/1.00 (![X43: $i, X45: $i, X44: $i] : ((p7(X44, X45) | (~p7(X43, X44))) | (~p7(X43, X45))) <=> ![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))),
% 0.80/1.00 inference(quant_intro,[status(thm)],[107])).
% 0.80/1.00 tff(109,axiom,(![X43: $i, X45: $i, X44: $i] : ((p7(X44, X45) | (~p7(X43, X44))) | (~p7(X43, X45)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_16')).
% 0.80/1.00 tff(110,plain,
% 0.80/1.00 (![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.80/1.00 tff(111,plain,
% 0.80/1.00 (![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.80/1.00 tff(112,plain,(
% 0.80/1.00 ![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))),
% 0.80/1.00 inference(skolemize,[status(sab)],[111])).
% 0.80/1.00 tff(113,plain,
% 0.80/1.00 (![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.80/1.00 tff(114,plain,
% 0.80/1.00 (((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | (p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) | (~p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25)))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) | (~p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(115,plain,
% 0.80/1.00 ((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | (p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) | (~p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25)))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(116,plain,
% 0.80/1.00 ((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) | (~p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), f14(f16(c28, f17(c21, c27)), c25)), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))) | (~p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.80/1.00 tff(117,plain,
% 0.80/1.00 (~p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[116, 113, 103, 60])).
% 0.80/1.00 tff(118,plain,
% 0.80/1.00 ((~![X43: $i] : p7(X43, X43)) | p7(c25, c25)),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(119,plain,
% 0.80/1.00 (p7(c25, c25)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[118, 8])).
% 0.80/1.00 tff(120,plain,
% 0.80/1.00 (p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))) <=> p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(121,axiom,(p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_29')).
% 0.80/1.00 tff(122,plain,
% 0.80/1.00 (p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.80/1.00 tff(123,plain,
% 0.80/1.00 (((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | ((~p7(c25, c25)) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | (~p7(c25, c25)) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(124,plain,
% 0.80/1.00 ((p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, c25)) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))))) <=> ((~p7(c25, c25)) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(125,plain,
% 0.80/1.00 (((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | (p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, c25)) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | ((~p7(c25, c25)) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))))))),
% 0.80/1.01 inference(monotonicity,[status(thm)],[124])).
% 0.80/1.01 tff(126,plain,
% 0.80/1.01 (((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | (p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, c25)) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | (~p7(c25, c25)) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))))),
% 0.80/1.01 inference(transitivity,[status(thm)],[125, 123])).
% 0.80/1.01 tff(127,plain,
% 0.80/1.01 ((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | (p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, c25)) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))))))),
% 0.80/1.01 inference(quant_inst,[status(thm)],[])).
% 0.80/1.01 tff(128,plain,
% 0.80/1.01 ((~![X43: $i, X45: $i, X44: $i] : (p7(X44, X45) | (~p7(X43, X45)) | (~p7(X43, X44)))) | (~p7(c25, c25)) | p7(f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27)))), c25) | (~p7(c25, f8(f10(f12(f11(f3(f5(c22)))), c23), f8(f10(f11(f3(f4(f5(c22)))), c26), f9(f11(c24), f10(f11(f3(f4(f5(c22)))), c27))))))),
% 0.80/1.01 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.80/1.01 tff(129,plain,
% 0.80/1.01 ($false),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[128, 113, 122, 119, 117])).
% 0.80/1.01 % SZS output end Proof
% 0.80/1.01 % E exiting
%------------------------------------------------------------------------------