%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC339-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 03:06:02 PM UTC 2026
% Result : Unsatisfiable 114.28s 15.26s
% Output : Proof 114.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 29
% Syntax : Number of formulae : 148 ( 88 unt; 0 def)
% Number of atoms : 364 ( 116 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 498 ( 282 ~; 216 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-4 aty)
% Number of variables : 180 ( 2 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f172,axiom,
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
fof(f172_nnf,plain,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
inference(nnf_transformation,[status(thm)],[f172]) ).
fof(f172_sk,plain,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
inference(skolemisation,[status(esa)],[f172_nnf]) ).
cnf(c172,plain,
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
inference(cnf_transformation,[status(esa)],[f172_sk]) ).
cnf(t204,plain,
ifeq(app(app(X1,X2),X3),X4,ifeq(ssList(X3),true,ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X4),true,segmentP(X4,X2),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c172]) ).
cnf(t311,plain,
ifeq(app(app(X1,X2),X3),X4,ifeq(ssList(X3),true,ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X4),true,segmentP(X4,X2),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t204]) ).
cnf(t71,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t225,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t71]) ).
cnf(t312,plain,
true = ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(ssList(app(app(X2,X3),X1)),true,segmentP(app(app(X2,X3),X1),X3),true),true),true),true),
inference(cp,[status(thm)],[t311,t225]) ).
cnf(t101174,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(ssList(app(app(X2,X3),X1)),true,segmentP(app(app(X2,X3),X1),X3),true),true),true),true) = true,
inference(orient,[status(thm)],[t312]) ).
cnf(f193,negated_conjecture,
app(app(sk5,sk3),sk6) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f193_nnf,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(nnf_transformation,[status(thm)],[f193]) ).
cnf(c193,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(cnf_transformation,[status(esa)],[f193_nnf]) ).
cnf(t70,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(equality_encoding,[status(esa)],[c193]) ).
cnf(t600,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(orient,[status(thm)],[t70]) ).
cnf(t101966,plain,
true = ifeq(ssList(sk6),true,ifeq(ssList(sk5),true,ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,segmentP(app(app(sk5,sk3),sk6),sk3),true),true),true),true),
inference(cp,[status(thm)],[t101174,t600]) ).
cnf(f192,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
ssList(sk6),
inference(nnf_transformation,[status(thm)],[f192]) ).
cnf(c192,plain,
ssList(sk6),
inference(cnf_transformation,[status(esa)],[f192_nnf]) ).
cnf(t16,plain,
ssList(sk6) = true,
inference(equality_encoding,[status(esa)],[c192]) ).
cnf(t3408,plain,
ssList(sk6) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t107422,plain,
true = ifeq(true,true,ifeq(ssList(sk5),true,ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,segmentP(app(app(sk5,sk3),sk6),sk3),true),true),true),true),
inference(step,[status(thm)],[t101966,t3408]) ).
cnf(t107423,plain,
true = ifeq(ssList(sk5),true,ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,segmentP(app(app(sk5,sk3),sk6),sk3),true),true),true),
inference(step,[status(thm)],[t107422,t225]) ).
cnf(f191,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f191_nnf,plain,
ssList(sk5),
inference(nnf_transformation,[status(thm)],[f191]) ).
cnf(c191,plain,
ssList(sk5),
inference(cnf_transformation,[status(esa)],[f191_nnf]) ).
cnf(t15,plain,
ssList(sk5) = true,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t3600,plain,
ssList(sk5) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t107424,plain,
true = ifeq(true,true,ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,segmentP(app(app(sk5,sk3),sk6),sk3),true),true),true),
inference(step,[status(thm)],[t107423,t3600]) ).
cnf(t107425,plain,
true = ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,segmentP(app(app(sk5,sk3),sk6),sk3),true),true),
inference(step,[status(thm)],[t107424,t225]) ).
cnf(f187,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f187_nnf,plain,
ssList(sk3),
inference(nnf_transformation,[status(thm)],[f187]) ).
cnf(c187,plain,
ssList(sk3),
inference(cnf_transformation,[status(esa)],[f187_nnf]) ).
cnf(t13,plain,
ssList(sk3) = true,
inference(equality_encoding,[status(esa)],[c187]) ).
cnf(t3024,plain,
ssList(sk3) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t107426,plain,
true = ifeq(true,true,ifeq(ssList(sk4),true,segmentP(app(app(sk5,sk3),sk6),sk3),true),true),
inference(step,[status(thm)],[t107425,t3024]) ).
cnf(t107427,plain,
true = ifeq(ssList(sk4),true,segmentP(app(app(sk5,sk3),sk6),sk3),true),
inference(step,[status(thm)],[t107426,t225]) ).
cnf(f188,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/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(t3216,plain,
ssList(sk4) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t107428,plain,
true = ifeq(true,true,segmentP(app(app(sk5,sk3),sk6),sk3),true),
inference(step,[status(thm)],[t107427,t3216]) ).
cnf(t107429,plain,
true = segmentP(app(app(sk5,sk3),sk6),sk3),
inference(step,[status(thm)],[t107428,t225]) ).
cnf(t107430,plain,
true = segmentP(sk4,sk3),
inference(step,[status(thm)],[t107429,t600]) ).
cnf(t74,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t339,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t74]) ).
cnf(f198,negated_conjecture,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f198_nnf,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(nnf_transformation,[status(thm)],[f198]) ).
fof(f198_sk,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(skolemisation,[status(esa)],[f198_nnf]) ).
cnf(c198,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(cnf_transformation,[status(esa)],[f198_sk]) ).
cnf(t89,plain,
or(not(segmentP(sk2,sk1)),not(totalorderedP(sk1))) = true,
inference(equality_encoding,[status(esa)],[c198]) ).
cnf(t595,plain,
or(not(segmentP(sk2,sk1)),not(totalorderedP(sk1))) = true,
inference(orient,[status(thm)],[t89]) ).
cnf(f190,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/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(t666,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t102392,plain,
or(not(segmentP(sk2,sk3)),not(totalorderedP(sk1))) = true,
inference(step,[status(thm)],[t595,t666]) ).
cnf(t102393,plain,
or(not(segmentP(sk2,sk3)),not(totalorderedP(sk3))) = true,
inference(step,[status(thm)],[t102392,t666]) ).
cnf(t667,plain,
or(not(segmentP(sk2,sk3)),not(totalorderedP(sk3))) = true,
inference(rw,[status(thm)],[t102393]) ).
cnf(f189,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/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(t680,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t1]) ).
cnf(t104091,plain,
or(not(segmentP(sk4,sk3)),not(totalorderedP(sk3))) = true,
inference(step,[status(thm)],[t667,t680]) ).
cnf(f194,negated_conjecture,
totalorderedP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f194_nnf,plain,
totalorderedP(sk3),
inference(nnf_transformation,[status(thm)],[f194]) ).
cnf(c194,plain,
totalorderedP(sk3),
inference(cnf_transformation,[status(esa)],[f194_nnf]) ).
cnf(t21,plain,
totalorderedP(sk3) = true,
inference(equality_encoding,[status(esa)],[c194]) ).
cnf(t8994,plain,
totalorderedP(sk3) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t104092,plain,
or(not(segmentP(sk4,sk3)),not(true)) = true,
inference(step,[status(thm)],[t104091,t8994]) ).
cnf(t6,plain,
not(true) = false,
introduced(definition) ).
cnf(t629,plain,
not(true) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t104093,plain,
or(not(segmentP(sk4,sk3)),false) = true,
inference(step,[status(thm)],[t104092,t629]) ).
cnf(t24,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t267,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t24]) ).
cnf(t104094,plain,
not(segmentP(sk4,sk3)) = true,
inference(step,[status(thm)],[t104093,t267]) ).
cnf(t15931,plain,
not(segmentP(sk4,sk3)) = true,
inference(orient,[status(thm)],[t104094]) ).
cnf(t15932,plain,
false = ifeq(true,true,segmentP(sk4,sk3),false),
inference(cp,[status(thm)],[t339,t15931]) ).
cnf(t104095,plain,
false = segmentP(sk4,sk3),
inference(step,[status(thm)],[t15932,t225]) ).
cnf(t15933,plain,
segmentP(sk4,sk3) = false,
inference(orient,[status(thm)],[t104095]) ).
cnf(t107431,plain,
true = false,
inference(step,[status(thm)],[t107430,t15933]) ).
cnf(t102266,plain,
false = true,
inference(orient,[status(thm)],[t107431]) ).
cnf(f10,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f195,negated_conjecture,
( ~ leq(A,C)
| app(cons(C,nil),D) != sk3
| ~ ssList(D)
| ~ ssItem(C)
| app(B,cons(A,nil)) != sk5
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f195_nnf,plain,
! [A,B,C,D] :
( ~ leq(A,C)
| app(cons(C,nil),D) != sk3
| ~ ssList(D)
| ~ ssItem(C)
| app(B,cons(A,nil)) != sk5
| ~ ssList(B)
| ~ ssItem(A) ),
inference(nnf_transformation,[status(thm)],[f195]) ).
fof(f195_sk,plain,
! [A,B,C,D] :
( ~ leq(A,C)
| app(cons(C,nil),D) != sk3
| ~ ssList(D)
| ~ ssItem(C)
| app(B,cons(A,nil)) != sk5
| ~ ssList(B)
| ~ ssItem(A) ),
inference(skolemisation,[status(esa)],[f195_nnf]) ).
cnf(c195,plain,
( ~ leq(X0,X2)
| app(cons(X2,nil),X3) != sk3
| ~ ssList(X3)
| ~ ssItem(X2)
| app(X1,cons(X0,nil)) != sk5
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f195_sk]) ).
cnf(f196,negated_conjecture,
( ~ leq(C,A)
| app(D,cons(C,nil)) != sk3
| ~ ssList(D)
| ~ ssItem(C)
| app(cons(A,nil),B) != sk6
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f196_nnf,plain,
! [A,B,C,D] :
( ~ leq(C,A)
| app(D,cons(C,nil)) != sk3
| ~ ssList(D)
| ~ ssItem(C)
| app(cons(A,nil),B) != sk6
| ~ ssList(B)
| ~ ssItem(A) ),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
! [A,B,C,D] :
( ~ leq(C,A)
| app(D,cons(C,nil)) != sk3
| ~ ssList(D)
| ~ ssItem(C)
| app(cons(A,nil),B) != sk6
| ~ ssList(B)
| ~ ssItem(A) ),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c196,plain,
( ~ leq(X2,X0)
| app(X3,cons(X2,nil)) != sk3
| ~ ssList(X3)
| ~ ssItem(X2)
| app(cons(X0,nil),X1) != sk6
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f196_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,c195,c196,c198]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t102266]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC339-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.57 % Computer : n010.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Thu Sep 24 17:43:32 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 114.28/15.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 114.28/15.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------