%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN713-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:35:32 PM UTC 2026
% Result : Unsatisfiable 18.75s 3.00s
% Output : Proof 18.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 15
% Syntax : Number of formulae : 113 ( 89 unt; 0 def)
% Number of atoms : 157 ( 62 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 17 con; 0-4 aty)
% Number of variables : 183 ( 2 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f73,negated_conjecture,
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p57_74) ).
fof(f73_nnf,plain,
! [X186,X187,X188] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [X186,X187,X188] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( ~ p57(f26(X0,X1),X2)
| p57(f26(f28(c71,X0),X1),X2) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t88,plain,
ifeq(p57(f26(X1,X2),X3),true,p57(f26(f28(c71,X1),X2),X3),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t239,plain,
ifeq(p57(f26(X1,X2),X3),true,p57(f26(f28(c71,X1),X2),X3),true) = true,
inference(orient,[status(thm)],[t88]) ).
cnf(f100,negated_conjecture,
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p57_101) ).
fof(f100_nnf,plain,
! [X181,X179,X180] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ),
inference(nnf_transformation,[status(thm)],[f100]) ).
fof(f100_sk,plain,
! [X181,X179,X180] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ),
inference(skolemisation,[status(esa)],[f100_nnf]) ).
cnf(c100,plain,
( ~ p56(f11(c65,f14(f17(c66,X1),f23(c74,X2))),X0)
| p57(f26(f41(c78,X0),X1),X2) ),
inference(cnf_transformation,[status(esa)],[f100_sk]) ).
cnf(t133,plain,
ifeq(p56(f11(c65,f14(f17(c66,X1),f23(c74,X2))),X3),true,p57(f26(f41(c78,X3),X1),X2),true) = true,
inference(equality_encoding,[status(esa)],[c100]) ).
cnf(t238,plain,
ifeq(p56(f11(c65,f14(f17(c66,X1),f23(c74,X2))),X3),true,p57(f26(f41(c78,X3),X1),X2),true) = true,
inference(orient,[status(thm)],[t133]) ).
cnf(f75,negated_conjecture,
( ~ p4(X177,X175)
| ~ p56(X177,X178)
| ~ p40(X178,X176)
| p56(X175,X176) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p56_76) ).
fof(f75_nnf,plain,
! [X175,X176,X178,X177] :
( ~ p4(X177,X175)
| ~ p56(X177,X178)
| ~ p40(X178,X176)
| p56(X175,X176) ),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
! [X175,X176,X178,X177] :
( ~ p4(X177,X175)
| ~ p56(X177,X178)
| ~ p40(X178,X176)
| p56(X175,X176) ),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
( ~ p4(X3,X0)
| ~ p56(X3,X2)
| ~ p40(X2,X1)
| p56(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(t131,plain,
ifeq(p40(X1,X2),true,ifeq(p56(X3,X1),true,ifeq(p4(X3,X4),true,p56(X4,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(t223,plain,
ifeq(p40(X1,X2),true,ifeq(p56(X3,X1),true,ifeq(p4(X3,X4),true,p56(X4,X2),true),true),true) = true,
inference(orient,[status(thm)],[t131]) ).
cnf(f13,negated_conjecture,
p40(X129,X129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p40_14) ).
fof(f13_nnf,plain,
! [X129] : p40(X129,X129),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X129] : p40(X129,X129),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
p40(X0,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t25,plain,
p40(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t775,plain,
p40(X1,X1) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t779,plain,
true = ifeq(true,true,ifeq(p56(X1,X2),true,ifeq(p4(X1,X3),true,p56(X3,X2),true),true),true),
inference(cp,[status(thm)],[t223,t775]) ).
cnf(t38,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t180,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t38]) ).
cnf(t1861,plain,
true = ifeq(p56(X1,X2),true,ifeq(p4(X1,X3),true,p56(X3,X2),true),true),
inference(step,[status(thm)],[t779,t180]) ).
cnf(t1489,plain,
ifeq(p56(X1,X2),true,ifeq(p4(X1,X3),true,p56(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t1861]) ).
cnf(f37,negated_conjecture,
p56(f11(c65,f14(f17(c66,c67),c68)),c64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p56_38) ).
fof(f37_nnf,plain,
p56(f11(c65,f14(f17(c66,c67),c68)),c64),
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c37,plain,
p56(f11(c65,f14(f17(c66,c67),c68)),c64),
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(t43,plain,
p56(f11(c65,f14(f17(c66,c67),c68)),c64) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t931,plain,
p56(f11(c65,f14(f17(c66,c67),c68)),c64) = true,
inference(orient,[status(thm)],[t43]) ).
cnf(t1490,plain,
true = ifeq(true,true,ifeq(p4(f11(c65,f14(f17(c66,c67),c68)),X1),true,p56(X1,c64),true),true),
inference(cp,[status(thm)],[t1489,t931]) ).
cnf(t1915,plain,
true = ifeq(p4(f11(c65,f14(f17(c66,c67),c68)),X1),true,p56(X1,c64),true),
inference(step,[status(thm)],[t1490,t180]) ).
cnf(t1660,plain,
ifeq(p4(f11(c65,f14(f17(c66,c67),c68)),X1),true,p56(X1,c64),true) = true,
inference(orient,[status(thm)],[t1915]) ).
cnf(f86,negated_conjecture,
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_87) ).
fof(f86_nnf,plain,
! [X121,X122,X123,X124] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ),
inference(nnf_transformation,[status(thm)],[f86]) ).
fof(f86_sk,plain,
! [X121,X122,X123,X124] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ),
inference(skolemisation,[status(esa)],[f86_nnf]) ).
cnf(c86,plain,
( ~ p9(X0,X2)
| ~ p10(X1,X3)
| p4(f11(X0,X1),f11(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
cnf(t107,plain,
ifeq(p10(X1,X2),true,ifeq(p9(X3,X4),true,p4(f11(X3,X1),f11(X4,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c86]) ).
cnf(t193,plain,
ifeq(p10(X1,X2),true,ifeq(p9(X3,X4),true,p4(f11(X3,X1),f11(X4,X2)),true),true) = true,
inference(orient,[status(thm)],[t107]) ).
cnf(f1,negated_conjecture,
p9(X210,X210),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_2) ).
fof(f1_nnf,plain,
! [X210] : p9(X210,X210),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X210] : p9(X210,X210),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
p9(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t37,plain,
p9(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t950,plain,
p9(X1,X1) = true,
inference(orient,[status(thm)],[t37]) ).
cnf(t954,plain,
true = ifeq(p10(X1,X2),true,ifeq(true,true,p4(f11(X3,X1),f11(X3,X2)),true),true),
inference(cp,[status(thm)],[t193,t950]) ).
cnf(t1819,plain,
true = ifeq(p10(X1,X2),true,p4(f11(X3,X1),f11(X3,X2)),true),
inference(step,[status(thm)],[t954,t180]) ).
cnf(t1237,plain,
ifeq(p10(X1,X2),true,p4(f11(X3,X1),f11(X3,X2)),true) = true,
inference(orient,[status(thm)],[t1819]) ).
cnf(f80,negated_conjecture,
( ~ p13(X4,X6)
| ~ p12(X3,X5)
| p10(f14(X3,X4),f14(X5,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_81) ).
fof(f80_nnf,plain,
! [X3,X4,X5,X6] :
( ~ p13(X4,X6)
| ~ p12(X3,X5)
| p10(f14(X3,X4),f14(X5,X6)) ),
inference(nnf_transformation,[status(thm)],[f80]) ).
fof(f80_sk,plain,
! [X3,X4,X5,X6] :
( ~ p13(X4,X6)
| ~ p12(X3,X5)
| p10(f14(X3,X4),f14(X5,X6)) ),
inference(skolemisation,[status(esa)],[f80_nnf]) ).
cnf(c80,plain,
( ~ p13(X1,X3)
| ~ p12(X0,X2)
| p10(f14(X0,X1),f14(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f80_sk]) ).
cnf(t108,plain,
ifeq(p12(X1,X2),true,ifeq(p13(X3,X4),true,p10(f14(X1,X3),f14(X2,X4)),true),true) = true,
inference(equality_encoding,[status(esa)],[c80]) ).
cnf(t203,plain,
ifeq(p12(X1,X2),true,ifeq(p13(X3,X4),true,p10(f14(X1,X3),f14(X2,X4)),true),true) = true,
inference(orient,[status(thm)],[t108]) ).
cnf(f33,negated_conjecture,
p12(X7,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_34) ).
fof(f33_nnf,plain,
! [X7] : p12(X7,X7),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X7] : p12(X7,X7),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
p12(X0,X0),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(t5,plain,
p12(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(t658,plain,
p12(X1,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t663,plain,
true = ifeq(true,true,ifeq(p13(X1,X2),true,p10(f14(X3,X1),f14(X3,X2)),true),true),
inference(cp,[status(thm)],[t203,t658]) ).
cnf(t1786,plain,
true = ifeq(p13(X1,X2),true,p10(f14(X3,X1),f14(X3,X2)),true),
inference(step,[status(thm)],[t663,t180]) ).
cnf(t1082,plain,
ifeq(p13(X1,X2),true,p10(f14(X3,X1),f14(X3,X2)),true) = true,
inference(orient,[status(thm)],[t1786]) ).
cnf(f104,negated_conjecture,
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13_105) ).
fof(f104_nnf,plain,
! [X17,X18] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ),
inference(nnf_transformation,[status(thm)],[f104]) ).
fof(f104_sk,plain,
! [X17,X18] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ),
inference(skolemisation,[status(esa)],[f104_nnf]) ).
cnf(c104,plain,
( ~ p59(f38(c72,X1),f35(c73,X0))
| p58(f31(f33(c75,c76),f23(c69,X1)),f19(f22(c70,c69),X0))
| p13(X0,f23(c74,X1)) ),
inference(cnf_transformation,[status(esa)],[f104_sk]) ).
cnf(hi102,negated_conjecture,
ifeq(p59(f38(c72,X0),f35(c73,X1)),true,or(p13(X1,f23(c74,X0)),p58(f31(f33(c75,c76),f23(c69,X0)),f19(f22(c70,c69),X1))),true) = true,
inference(equality_encoding,[status(esa)],[c104]) ).
cnf(f34,negated_conjecture,
p59(f38(c72,c77),f35(c73,c68)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p59_35) ).
fof(f34_nnf,plain,
p59(f38(c72,c77),f35(c73,c68)),
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c34,plain,
p59(f38(c72,c77),f35(c73,c68)),
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(hi34,negated_conjecture,
p59(f38(c72,c77),f35(c73,c68)) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(t127,plain,
or(p13(c68,f23(c74,c77)),p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))) = true,
inference(hyper_resolution,[status(thm)],[hi102,hi34]) ).
cnf(f79,negated_conjecture,
~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p58_80) ).
fof(f79_nnf,plain,
~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)),
inference(nnf_transformation,[status(thm)],[f79]) ).
fof(f79_sk,plain,
~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)),
inference(skolemisation,[status(esa)],[f79_nnf]) ).
cnf(c79,plain,
~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)),
inference(cnf_transformation,[status(esa)],[f79_sk]) ).
cnf(t56,plain,
p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)) = false,
inference(equality_encoding,[status(esa)],[c79]) ).
cnf(t634,plain,
p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)) = false,
inference(orient,[status(thm)],[t56]) ).
cnf(t1693,plain,
or(p13(c68,f23(c74,c77)),false) = true,
inference(step,[status(thm)],[t127,t634]) ).
cnf(t0,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t181,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t1694,plain,
p13(c68,f23(c74,c77)) = true,
inference(step,[status(thm)],[t1693,t181]) ).
cnf(t640,plain,
p13(c68,f23(c74,c77)) = true,
inference(orient,[status(thm)],[t1694]) ).
cnf(t1083,plain,
true = ifeq(true,true,p10(f14(X1,c68),f14(X1,f23(c74,c77))),true),
inference(cp,[status(thm)],[t1082,t640]) ).
cnf(t1787,plain,
true = p10(f14(X1,c68),f14(X1,f23(c74,c77))),
inference(step,[status(thm)],[t1083,t180]) ).
cnf(t1087,plain,
p10(f14(X1,c68),f14(X1,f23(c74,c77))) = true,
inference(orient,[status(thm)],[t1787]) ).
cnf(t1238,plain,
true = ifeq(true,true,p4(f11(X1,f14(X2,c68)),f11(X1,f14(X2,f23(c74,c77)))),true),
inference(cp,[status(thm)],[t1237,t1087]) ).
cnf(t1832,plain,
true = p4(f11(X1,f14(X2,c68)),f11(X1,f14(X2,f23(c74,c77)))),
inference(step,[status(thm)],[t1238,t180]) ).
cnf(t1342,plain,
p4(f11(X1,f14(X2,c68)),f11(X1,f14(X2,f23(c74,c77)))) = true,
inference(orient,[status(thm)],[t1832]) ).
cnf(t1661,plain,
true = ifeq(true,true,p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64),true),
inference(cp,[status(thm)],[t1660,t1342]) ).
cnf(t1916,plain,
true = p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64),
inference(step,[status(thm)],[t1661,t180]) ).
cnf(t1664,plain,
p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64) = true,
inference(orient,[status(thm)],[t1916]) ).
cnf(t1672,plain,
true = ifeq(true,true,p57(f26(f41(c78,c64),c67),c77),true),
inference(cp,[status(thm)],[t238,t1664]) ).
cnf(t1917,plain,
true = p57(f26(f41(c78,c64),c67),c77),
inference(step,[status(thm)],[t1672,t180]) ).
cnf(t1674,plain,
p57(f26(f41(c78,c64),c67),c77) = true,
inference(orient,[status(thm)],[t1917]) ).
cnf(t1679,plain,
true = ifeq(true,true,p57(f26(f28(c71,f41(c78,c64)),c67),c77),true),
inference(cp,[status(thm)],[t239,t1674]) ).
cnf(t1920,plain,
true = p57(f26(f28(c71,f41(c78,c64)),c67),c77),
inference(step,[status(thm)],[t1679,t180]) ).
cnf(f38,negated_conjecture,
~ p57(f26(f28(c71,f41(c78,c64)),c67),c77),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p57_39) ).
fof(f38_nnf,plain,
~ p57(f26(f28(c71,f41(c78,c64)),c67),c77),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
~ p57(f26(f28(c71,f41(c78,c64)),c67),c77),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
~ p57(f26(f28(c71,f41(c78,c64)),c67),c77),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t44,plain,
p57(f26(f28(c71,f41(c78,c64)),c67),c77) = false,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t628,plain,
p57(f26(f28(c71,f41(c78,c64)),c67),c77) = false,
inference(orient,[status(thm)],[t44]) ).
cnf(t1921,plain,
true = false,
inference(step,[status(thm)],[t1920,t628]) ).
cnf(t1683,plain,
false = true,
inference(orient,[status(thm)],[t1921]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c38,c79]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1683]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN713-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.36 % Computer : n006.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 02:09:25 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 18.75/3.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.75/3.00 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------