%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC358-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 03:06:07 PM UTC 2026
% Result : Unsatisfiable 20.94s 3.16s
% Output : Proof 20.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 23
% Syntax : Number of formulae : 126 ( 70 unt; 0 def)
% Number of atoms : 282 ( 94 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 362 ( 206 ~; 156 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 126 ( 2 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f192,negated_conjecture,
~ segmentP(sk2,sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
~ segmentP(sk2,sk1),
inference(nnf_transformation,[status(thm)],[f192]) ).
fof(f192_sk,plain,
~ segmentP(sk2,sk1),
inference(skolemisation,[status(esa)],[f192_nnf]) ).
cnf(c192,plain,
~ segmentP(sk2,sk1),
inference(cnf_transformation,[status(esa)],[f192_sk]) ).
cnf(t26,plain,
segmentP(sk2,sk1) = false,
inference(equality_encoding,[status(esa)],[c192]) ).
cnf(t629,plain,
segmentP(sk2,sk1) = false,
inference(orient,[status(thm)],[t26]) ).
cnf(f190,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f190_nnf,plain,
sk1 = sk3,
inference(nnf_transformation,[status(thm)],[f190]) ).
cnf(c190,plain,
sk1 = sk3,
inference(cnf_transformation,[status(esa)],[f190_nnf]) ).
cnf(t0,plain,
sk3 = sk1,
inference(equality_encoding,[status(esa)],[c190]) ).
cnf(t649,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t8645,plain,
segmentP(sk2,sk3) = false,
inference(step,[status(thm)],[t629,t649]) ).
cnf(t650,plain,
segmentP(sk2,sk3) = false,
inference(rw,[status(thm)],[t8645]) ).
cnf(f189,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f189_nnf,plain,
sk2 = sk4,
inference(nnf_transformation,[status(thm)],[f189]) ).
cnf(c189,plain,
sk2 = sk4,
inference(cnf_transformation,[status(esa)],[f189_nnf]) ).
cnf(t1,plain,
sk4 = sk2,
inference(equality_encoding,[status(esa)],[c189]) ).
cnf(t657,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t1]) ).
cnf(t8647,plain,
segmentP(sk4,sk3) = false,
inference(step,[status(thm)],[t650,t657]) ).
cnf(t8217,plain,
segmentP(sk4,sk3) = false,
inference(orient,[status(thm)],[t8647]) ).
cnf(t73,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t234,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t73]) ).
cnf(f196,negated_conjecture,
( segmentP(sk4,sk3)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f196_nnf,plain,
( segmentP(sk4,sk3)
| nil = sk3 ),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
( segmentP(sk4,sk3)
| nil = sk3 ),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c196,plain,
( segmentP(sk4,sk3)
| nil = sk3 ),
inference(cnf_transformation,[status(esa)],[f196_sk]) ).
cnf(t76,plain,
or(eq(nil,sk3),segmentP(sk4,sk3)) = true,
inference(equality_encoding,[status(esa)],[c196]) ).
cnf(t589,plain,
or(eq(nil,sk3),segmentP(sk4,sk3)) = true,
inference(orient,[status(thm)],[t76]) ).
cnf(t8650,plain,
or(eq(nil,sk3),false) = true,
inference(step,[status(thm)],[t589,t8217]) ).
cnf(t22,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t263,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t22]) ).
cnf(t8651,plain,
eq(nil,sk3) = true,
inference(step,[status(thm)],[t8650,t263]) ).
cnf(t8227,plain,
eq(nil,sk3) = true,
inference(rw,[status(thm)],[t8651]) ).
cnf(f194,negated_conjecture,
( segmentP(sk4,sk3)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f194_nnf,plain,
( segmentP(sk4,sk3)
| nil = sk4 ),
inference(nnf_transformation,[status(thm)],[f194]) ).
fof(f194_sk,plain,
( segmentP(sk4,sk3)
| nil = sk4 ),
inference(skolemisation,[status(esa)],[f194_nnf]) ).
cnf(c194,plain,
( segmentP(sk4,sk3)
| nil = sk4 ),
inference(cnf_transformation,[status(esa)],[f194_sk]) ).
cnf(t78,plain,
or(eq(nil,sk4),segmentP(sk4,sk3)) = true,
inference(equality_encoding,[status(esa)],[c194]) ).
cnf(t591,plain,
or(eq(nil,sk4),segmentP(sk4,sk3)) = true,
inference(orient,[status(thm)],[t78]) ).
cnf(t8648,plain,
or(eq(nil,sk4),false) = true,
inference(step,[status(thm)],[t591,t8217]) ).
cnf(t8649,plain,
eq(nil,sk4) = true,
inference(step,[status(thm)],[t8648,t263]) ).
cnf(t8226,plain,
eq(nil,sk4) = true,
inference(rw,[status(thm)],[t8649]) ).
cnf(t8506,plain,
eq(nil,sk4) = true,
inference(orient,[status(thm)],[t8226]) ).
cnf(t8507,plain,
sk4 = ifeq(true,true,nil,sk4),
inference(cp,[status(thm)],[t234,t8506]) ).
cnf(t69,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t221,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t69]) ).
cnf(t8676,plain,
sk4 = nil,
inference(step,[status(thm)],[t8507,t221]) ).
cnf(t8525,plain,
nil = sk4,
inference(orient,[status(thm)],[t8676]) ).
cnf(t8756,plain,
eq(sk4,sk3) = true,
inference(step,[status(thm)],[t8227,t8525]) ).
cnf(t8611,plain,
eq(sk4,sk3) = true,
inference(orient,[status(thm)],[t8756]) ).
cnf(t8612,plain,
sk3 = ifeq(true,true,sk4,sk3),
inference(cp,[status(thm)],[t234,t8611]) ).
cnf(t8757,plain,
sk3 = sk4,
inference(step,[status(thm)],[t8612,t221]) ).
cnf(t8619,plain,
sk3 = sk4,
inference(orient,[status(thm)],[t8757]) ).
cnf(t8760,plain,
segmentP(sk4,sk4) = false,
inference(step,[status(thm)],[t8217,t8619]) ).
cnf(f56,axiom,
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
fof(f56_nnf,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t87,plain,
ifeq(ssList(X1),true,segmentP(X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t538,plain,
ifeq(ssList(X1),true,segmentP(X1,X1),true) = true,
inference(orient,[status(thm)],[t87]) ).
cnf(f188,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f188_nnf,plain,
ssList(sk4),
inference(nnf_transformation,[status(thm)],[f188]) ).
cnf(c188,plain,
ssList(sk4),
inference(cnf_transformation,[status(esa)],[f188_nnf]) ).
cnf(t14,plain,
ssList(sk4) = true,
inference(equality_encoding,[status(esa)],[c188]) ).
cnf(t3047,plain,
ssList(sk4) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t3051,plain,
true = ifeq(true,true,segmentP(sk4,sk4),true),
inference(cp,[status(thm)],[t538,t3047]) ).
cnf(t8671,plain,
true = segmentP(sk4,sk4),
inference(step,[status(thm)],[t3051,t221]) ).
cnf(t8434,plain,
segmentP(sk4,sk4) = true,
inference(orient,[status(thm)],[t8671]) ).
cnf(t8761,plain,
true = false,
inference(step,[status(thm)],[t8760,t8434]) ).
cnf(t8622,plain,
true = false,
inference(rw,[status(thm)],[t8761]) ).
cnf(t8623,plain,
false = true,
inference(orient,[status(thm)],[t8622]) ).
cnf(f10,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
fof(f10_nnf,plain,
~ singletonP(nil),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ singletonP(nil),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f53,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
fof(f53_nnf,plain,
skac3 != skac2,
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
skac3 != skac2,
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
skac3 != skac2,
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(f62,axiom,
( ~ ssItem(U)
| ~ lt(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
fof(f62_nnf,plain,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c62,plain,
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(f70,axiom,
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
fof(f70_nnf,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(f97,axiom,
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
fof(f97_nnf,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
inference(nnf_transformation,[status(thm)],[f97]) ).
fof(f97_sk,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
inference(skolemisation,[status(esa)],[f97_nnf]) ).
cnf(c97,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(esa)],[f97_sk]) ).
cnf(f98,axiom,
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
fof(f98_nnf,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
inference(nnf_transformation,[status(thm)],[f98]) ).
fof(f98_sk,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
inference(skolemisation,[status(esa)],[f98_nnf]) ).
cnf(c98,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(f109,axiom,
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
fof(f109_nnf,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(f110,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
fof(f110_nnf,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f110]) ).
fof(f110_sk,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f110_nnf]) ).
cnf(c110,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f110_sk]) ).
cnf(f113,axiom,
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
fof(f113_nnf,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(f114,axiom,
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
fof(f114_nnf,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f114_nnf]) ).
cnf(c114,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(f116,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
fof(f116_nnf,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f178,axiom,
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause179) ).
fof(f178_nnf,plain,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
inference(nnf_transformation,[status(thm)],[f178]) ).
fof(f178_sk,plain,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
inference(skolemisation,[status(esa)],[f178_nnf]) ).
cnf(c178,plain,
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
inference(cnf_transformation,[status(esa)],[f178_sk]) ).
cnf(f184,axiom,
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).
fof(f184_nnf,plain,
! [U,V,W,X,Y,Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
inference(nnf_transformation,[status(thm)],[f184]) ).
fof(f184_sk,plain,
! [U,V,W,X,Y,Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
inference(skolemisation,[status(esa)],[f184_nnf]) ).
cnf(c184,plain,
( ~ ssList(X5)
| ~ cyclefreeP(X5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f184_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c10,c53,c62,c70,c97,c98,c109,c110,c113,c114,c116,c178,c184,c192]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t8623]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC358-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n003.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 17:50:51 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.94/3.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.94/3.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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