TSTP Solution File: SYN700-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN700-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Thu Sep 29 23:56:59 EDT 2022
% Result : Unsatisfiable 7.70s 5.25s
% Output : Proof 7.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN700-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 06:33:32 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 7.70/5.25 % SZS status Unsatisfiable
% 7.70/5.25 % SZS output start Proof
% 7.70/5.25 tff(p2_type, type, (
% 7.70/5.25 p2: ( $i * $i ) > $o)).
% 7.70/5.25 tff(f11_type, type, (
% 7.70/5.25 f11: ( $i * $i ) > $i)).
% 7.70/5.25 tff(c43_type, type, (
% 7.70/5.25 c43: $i)).
% 7.70/5.25 tff(f4_type, type, (
% 7.70/5.25 f4: $i > $i)).
% 7.70/5.25 tff(f23_type, type, (
% 7.70/5.25 f23: ( $i * $i ) > $i)).
% 7.70/5.25 tff(f9_type, type, (
% 7.70/5.25 f9: $i > $i)).
% 7.70/5.25 tff(f20_type, type, (
% 7.70/5.25 f20: $i > $i)).
% 7.70/5.25 tff(c37_type, type, (
% 7.70/5.25 c37: $i)).
% 7.70/5.25 tff(c44_type, type, (
% 7.70/5.25 c44: $i)).
% 7.70/5.25 tff(c46_type, type, (
% 7.70/5.25 c46: $i)).
% 7.70/5.25 tff(p10_type, type, (
% 7.70/5.25 p10: ( $i * $i ) > $o)).
% 7.70/5.25 tff(p3_type, type, (
% 7.70/5.25 p3: ( $i * $i ) > $o)).
% 7.70/5.25 tff(1,plain,
% 7.70/5.25 (^[X43: $i] : refl(p2(X43, X43) <=> p2(X43, X43))),
% 7.70/5.25 inference(bind,[status(th)],[])).
% 7.70/5.25 tff(2,plain,
% 7.70/5.25 (![X43: $i] : p2(X43, X43) <=> ![X43: $i] : p2(X43, X43)),
% 7.70/5.25 inference(quant_intro,[status(thm)],[1])).
% 7.70/5.25 tff(3,plain,
% 7.70/5.25 (![X43: $i] : p2(X43, X43) <=> ![X43: $i] : p2(X43, X43)),
% 7.70/5.25 inference(rewrite,[status(thm)],[])).
% 7.70/5.25 tff(4,axiom,(![X43: $i] : p2(X43, X43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_12')).
% 7.70/5.25 tff(5,plain,
% 7.70/5.25 (![X43: $i] : p2(X43, X43)),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[4, 3])).
% 7.70/5.25 tff(6,plain,(
% 7.70/5.25 ![X43: $i] : p2(X43, X43)),
% 7.70/5.25 inference(skolemize,[status(sab)],[5])).
% 7.70/5.25 tff(7,plain,
% 7.70/5.25 (![X43: $i] : p2(X43, X43)),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[6, 2])).
% 7.70/5.25 tff(8,plain,
% 7.70/5.25 ((~![X43: $i] : p2(X43, X43)) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 7.70/5.25 inference(quant_inst,[status(thm)],[])).
% 7.70/5.25 tff(9,plain,
% 7.70/5.25 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 7.70/5.25 inference(unit_resolution,[status(thm)],[8, 7])).
% 7.70/5.25 tff(10,plain,
% 7.70/5.25 ((~p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) <=> (~p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 7.70/5.25 inference(rewrite,[status(thm)],[])).
% 7.70/5.25 tff(11,axiom,(~p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p2_57')).
% 7.70/5.25 tff(12,plain,
% 7.70/5.25 (~p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[11, 10])).
% 7.70/5.25 tff(13,plain,
% 7.70/5.25 (^[X43: $i, X45: $i, X44: $i] : refl((p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44))) <=> (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44))))),
% 7.70/5.25 inference(bind,[status(th)],[])).
% 7.70/5.25 tff(14,plain,
% 7.70/5.25 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44))) <=> ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 7.70/5.25 inference(quant_intro,[status(thm)],[13])).
% 7.70/5.25 tff(15,plain,
% 7.70/5.25 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44))) <=> ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 7.70/5.25 inference(rewrite,[status(thm)],[])).
% 7.70/5.25 tff(16,plain,
% 7.70/5.25 (^[X43: $i, X45: $i, X44: $i] : trans(monotonicity(rewrite((p2(X44, X45) | (~p2(X43, X44))) <=> (p2(X44, X45) | (~p2(X43, X44)))), (((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))) <=> ((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))))), rewrite(((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))) <=> (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))), (((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))) <=> (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))))),
% 7.70/5.25 inference(bind,[status(th)],[])).
% 7.70/5.25 tff(17,plain,
% 7.70/5.25 (![X43: $i, X45: $i, X44: $i] : ((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))) <=> ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 7.70/5.25 inference(quant_intro,[status(thm)],[16])).
% 7.70/5.25 tff(18,axiom,(![X43: $i, X45: $i, X44: $i] : ((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_43')).
% 7.70/5.25 tff(19,plain,
% 7.70/5.25 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[18, 17])).
% 7.70/5.25 tff(20,plain,
% 7.70/5.25 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[19, 15])).
% 7.70/5.25 tff(21,plain,(
% 7.70/5.25 ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 7.70/5.25 inference(skolemize,[status(sab)],[20])).
% 7.70/5.25 tff(22,plain,
% 7.70/5.25 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[21, 14])).
% 7.70/5.25 tff(23,plain,
% 7.70/5.25 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43))))),
% 7.70/5.25 inference(rewrite,[status(thm)],[])).
% 7.70/5.25 tff(24,plain,
% 7.70/5.25 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43))))),
% 7.70/5.25 inference(quant_inst,[status(thm)],[])).
% 7.70/5.25 tff(25,plain,
% 7.70/5.25 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[24, 23])).
% 7.70/5.25 tff(26,plain,
% 7.70/5.25 (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43))),
% 7.70/5.25 inference(unit_resolution,[status(thm)],[25, 22, 12, 9])).
% 7.70/5.25 tff(27,assumption,(~p10(c43, c43)), introduced(assumption)).
% 7.70/5.25 tff(28,plain,
% 7.70/5.25 (^[X5: $i] : refl(p10(X5, X5) <=> p10(X5, X5))),
% 7.70/5.25 inference(bind,[status(th)],[])).
% 7.70/5.25 tff(29,plain,
% 7.70/5.25 (![X5: $i] : p10(X5, X5) <=> ![X5: $i] : p10(X5, X5)),
% 7.70/5.25 inference(quant_intro,[status(thm)],[28])).
% 7.70/5.25 tff(30,plain,
% 7.70/5.25 (![X5: $i] : p10(X5, X5) <=> ![X5: $i] : p10(X5, X5)),
% 7.70/5.25 inference(rewrite,[status(thm)],[])).
% 7.70/5.25 tff(31,axiom,(![X5: $i] : p10(X5, X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_7')).
% 7.70/5.25 tff(32,plain,
% 7.70/5.25 (![X5: $i] : p10(X5, X5)),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[31, 30])).
% 7.70/5.25 tff(33,plain,(
% 7.70/5.25 ![X5: $i] : p10(X5, X5)),
% 7.70/5.25 inference(skolemize,[status(sab)],[32])).
% 7.70/5.25 tff(34,plain,
% 7.70/5.25 (![X5: $i] : p10(X5, X5)),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[33, 29])).
% 7.70/5.25 tff(35,plain,
% 7.70/5.25 ((~![X5: $i] : p10(X5, X5)) | p10(c43, c43)),
% 7.70/5.25 inference(quant_inst,[status(thm)],[])).
% 7.70/5.25 tff(36,plain,
% 7.70/5.25 ($false),
% 7.70/5.25 inference(unit_resolution,[status(thm)],[35, 34, 27])).
% 7.70/5.25 tff(37,plain,(p10(c43, c43)), inference(lemma,lemma(discharge,[]))).
% 7.70/5.25 tff(38,plain,
% 7.70/5.25 (^[X91: $i, X92: $i] : refl(((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ((~p2(X91, X92)) | p3(f4(X91), f4(X92))))),
% 7.70/5.25 inference(bind,[status(th)],[])).
% 7.70/5.25 tff(39,plain,
% 7.70/5.25 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 7.70/5.25 inference(quant_intro,[status(thm)],[38])).
% 7.70/5.25 tff(40,plain,
% 7.70/5.25 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 7.70/5.25 inference(rewrite,[status(thm)],[])).
% 7.70/5.25 tff(41,plain,
% 7.70/5.25 (^[X91: $i, X92: $i] : rewrite((p3(f4(X91), f4(X92)) | (~p2(X91, X92))) <=> ((~p2(X91, X92)) | p3(f4(X91), f4(X92))))),
% 7.70/5.25 inference(bind,[status(th)],[])).
% 7.70/5.25 tff(42,plain,
% 7.70/5.25 (![X91: $i, X92: $i] : (p3(f4(X91), f4(X92)) | (~p2(X91, X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 7.70/5.25 inference(quant_intro,[status(thm)],[41])).
% 7.70/5.25 tff(43,axiom,(![X91: $i, X92: $i] : (p3(f4(X91), f4(X92)) | (~p2(X91, X92)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_37')).
% 7.70/5.25 tff(44,plain,
% 7.70/5.25 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[43, 42])).
% 7.70/5.25 tff(45,plain,
% 7.70/5.25 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[44, 40])).
% 7.70/5.25 tff(46,plain,(
% 7.70/5.25 ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 7.70/5.25 inference(skolemize,[status(sab)],[45])).
% 7.70/5.25 tff(47,plain,
% 7.70/5.25 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[46, 39])).
% 7.70/5.25 tff(48,plain,
% 7.70/5.25 (p2(c44, c46) <=> p2(c44, c46)),
% 7.70/5.25 inference(rewrite,[status(thm)],[])).
% 7.70/5.25 tff(49,axiom,(p2(c44, c46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_16')).
% 7.70/5.25 tff(50,plain,
% 7.70/5.25 (p2(c44, c46)),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[49, 48])).
% 7.70/5.25 tff(51,plain,
% 7.70/5.25 (((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | ((~p2(c44, c46)) | p3(f4(c44), f4(c46)))) <=> ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | (~p2(c44, c46)) | p3(f4(c44), f4(c46)))),
% 7.70/5.25 inference(rewrite,[status(thm)],[])).
% 7.70/5.25 tff(52,plain,
% 7.70/5.25 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | ((~p2(c44, c46)) | p3(f4(c44), f4(c46)))),
% 7.70/5.25 inference(quant_inst,[status(thm)],[])).
% 7.70/5.25 tff(53,plain,
% 7.70/5.25 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | (~p2(c44, c46)) | p3(f4(c44), f4(c46))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[52, 51])).
% 7.70/5.25 tff(54,plain,
% 7.70/5.25 (p3(f4(c44), f4(c46))),
% 7.70/5.25 inference(unit_resolution,[status(thm)],[53, 50, 47])).
% 7.70/5.25 tff(55,plain,
% 7.70/5.25 (^[X47: $i, X49: $i, X46: $i, X48: $i] : refl(((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) <=> ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))))),
% 7.70/5.25 inference(bind,[status(th)],[])).
% 7.70/5.25 tff(56,plain,
% 7.70/5.25 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) <=> ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 7.70/5.25 inference(quant_intro,[status(thm)],[55])).
% 7.70/5.25 tff(57,plain,
% 7.70/5.25 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) <=> ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 7.70/5.25 inference(rewrite,[status(thm)],[])).
% 7.70/5.25 tff(58,plain,
% 7.70/5.25 (^[X47: $i, X49: $i, X46: $i, X48: $i] : trans(monotonicity(rewrite((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) <=> ((~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))), (((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) | (~p3(X46, X48))) <=> (((~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) | (~p3(X46, X48))))), rewrite((((~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) | (~p3(X46, X48))) <=> ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))), (((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) | (~p3(X46, X48))) <=> ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))))),
% 7.70/5.25 inference(bind,[status(th)],[])).
% 7.70/5.25 tff(59,plain,
% 7.70/5.25 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) | (~p3(X46, X48))) <=> ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 7.70/5.25 inference(quant_intro,[status(thm)],[58])).
% 7.70/5.25 tff(60,axiom,(![X47: $i, X49: $i, X46: $i, X48: $i] : ((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) | (~p3(X46, X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_62')).
% 7.70/5.25 tff(61,plain,
% 7.70/5.25 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[60, 59])).
% 7.70/5.25 tff(62,plain,
% 7.70/5.25 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 7.70/5.25 inference(modus_ponens,[status(thm)],[61, 57])).
% 7.70/5.25 tff(63,plain,(
% 7.70/5.25 ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 7.70/5.25 inference(skolemize,[status(sab)],[62])).
% 7.70/5.25 tff(64,plain,
% 7.70/5.25 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 7.70/5.26 inference(modus_ponens,[status(thm)],[63, 56])).
% 7.70/5.26 tff(65,plain,
% 7.70/5.26 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p10(c43, c43)) | (~p3(f4(c44), f4(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | (~p10(c43, c43)) | (~p3(f4(c44), f4(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))),
% 7.70/5.26 inference(rewrite,[status(thm)],[])).
% 7.70/5.26 tff(66,plain,
% 7.70/5.26 (((~p3(f4(c44), f4(c46))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c46), c43))) <=> ((~p10(c43, c43)) | (~p3(f4(c44), f4(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))),
% 7.70/5.26 inference(rewrite,[status(thm)],[])).
% 7.70/5.26 tff(67,plain,
% 7.70/5.26 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p3(f4(c44), f4(c46))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p10(c43, c43)) | (~p3(f4(c44), f4(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43))))),
% 7.70/5.26 inference(monotonicity,[status(thm)],[66])).
% 7.70/5.26 tff(68,plain,
% 7.70/5.26 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p3(f4(c44), f4(c46))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | (~p10(c43, c43)) | (~p3(f4(c44), f4(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))),
% 7.70/5.26 inference(transitivity,[status(thm)],[67, 65])).
% 7.70/5.26 tff(69,plain,
% 7.70/5.26 ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p3(f4(c44), f4(c46))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))),
% 7.70/5.26 inference(quant_inst,[status(thm)],[])).
% 7.70/5.26 tff(70,plain,
% 7.70/5.26 ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | (~p10(c43, c43)) | (~p3(f4(c44), f4(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43))),
% 7.70/5.26 inference(modus_ponens,[status(thm)],[69, 68])).
% 7.70/5.26 tff(71,plain,
% 7.70/5.26 (p2(f11(f4(c44), c43), f11(f4(c46), c43))),
% 7.70/5.26 inference(unit_resolution,[status(thm)],[70, 64, 54, 37])).
% 7.70/5.26 tff(72,plain,
% 7.70/5.26 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | ((~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 7.70/5.26 inference(rewrite,[status(thm)],[])).
% 7.70/5.26 tff(73,plain,
% 7.70/5.26 ((p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))) <=> ((~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 7.70/5.26 inference(rewrite,[status(thm)],[])).
% 7.70/5.26 tff(74,plain,
% 7.70/5.26 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | ((~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))))),
% 7.70/5.26 inference(monotonicity,[status(thm)],[73])).
% 7.70/5.26 tff(75,plain,
% 7.70/5.26 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 7.70/5.26 inference(transitivity,[status(thm)],[74, 72])).
% 7.70/5.26 tff(76,plain,
% 7.70/5.26 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 7.70/5.26 inference(quant_inst,[status(thm)],[])).
% 7.70/5.26 tff(77,plain,
% 7.70/5.26 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 7.70/5.26 inference(modus_ponens,[status(thm)],[76, 75])).
% 7.70/5.26 tff(78,plain,
% 7.70/5.26 (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 7.70/5.26 inference(unit_resolution,[status(thm)],[77, 22, 71, 26])).
% 7.70/5.26 tff(79,plain,
% 7.70/5.26 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43)) <=> p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))),
% 7.70/5.26 inference(rewrite,[status(thm)],[])).
% 7.70/5.26 tff(80,axiom,(p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_56')).
% 7.70/5.26 tff(81,plain,
% 7.70/5.26 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))),
% 7.70/5.26 inference(modus_ponens,[status(thm)],[80, 79])).
% 7.70/5.26 tff(82,plain,
% 7.70/5.26 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | ((~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 7.70/5.26 inference(rewrite,[status(thm)],[])).
% 7.70/5.26 tff(83,plain,
% 7.70/5.26 ((p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43)))) <=> ((~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 7.70/5.26 inference(rewrite,[status(thm)],[])).
% 7.70/5.26 tff(84,plain,
% 7.70/5.26 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | ((~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 7.70/5.26 inference(monotonicity,[status(thm)],[83])).
% 7.70/5.26 tff(85,plain,
% 7.70/5.26 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 7.82/5.26 inference(transitivity,[status(thm)],[84, 82])).
% 7.82/5.26 tff(86,plain,
% 7.82/5.26 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))))),
% 7.82/5.26 inference(quant_inst,[status(thm)],[])).
% 7.82/5.26 tff(87,plain,
% 7.82/5.26 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 7.82/5.26 inference(modus_ponens,[status(thm)],[86, 85])).
% 7.82/5.26 tff(88,plain,
% 7.82/5.26 ($false),
% 7.82/5.26 inference(unit_resolution,[status(thm)],[87, 22, 81, 9, 78])).
% 7.82/5.26 % SZS output end Proof
%------------------------------------------------------------------------------