%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC118+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 : n008.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 03:05:24 PM UTC 2026
% Result : Theorem 155.56s 20.35s
% Output : Proof 155.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 22
% Syntax : Number of formulae : 169 ( 108 unt; 0 def)
% Number of atoms : 540 ( 202 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 628 ( 257 ~; 207 |; 112 &)
% ( 6 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 11 con; 0-4 aty)
% Number of variables : 238 ( 2 sgn 122 !; 40 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( segmentP(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f95_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( segmentP(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& ( nil != U
| nil != V )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ leq(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [X1,X2,X3,X4,X5,X6,X7,X8] :
( ( ~ segmentP(sk48,sk47)
| ~ neq(sk47,nil) )
& ( nil != sk47
| nil != sk48 )
& ( nil != sk49
| nil = sk50 )
& ( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != sk49
| ~ ssList(X8)
| ~ ssItem(X7)
| app(cons(X5,nil),X6) != sk52
| ~ ssList(X6)
| ~ ssItem(X5) )
& ( ~ leq(X1,X3)
| app(cons(X3,nil),X4) != sk49
| ~ ssList(X4)
| ~ ssItem(X3)
| app(X2,cons(X1,nil)) != sk51
| ~ ssList(X2)
| ~ ssItem(X1) )
& totalorderedP(sk49)
& app(app(sk51,sk49),sk52) = sk50
& ssList(sk52)
& ssList(sk51)
& sk47 = sk49
& sk48 = sk50
& ssList(sk50)
& ssList(sk49)
& ssList(sk48)
& ssList(sk47) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48,sk49,sk50,sk51,sk52])],[f95_nnf]) ).
cnf(c203,plain,
( nil != sk47
| nil != sk48 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t73,plain,
ifeq(nil,sk48,ifeq(nil,sk47,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c203]) ).
cnf(t290,plain,
ifeq(nil,sk48,ifeq(nil,sk47,false,true),true) = true,
inference(orient,[status(thm)],[t73]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t0,plain,
sk49 = sk47,
inference(equality_encoding,[status(esa)],[c195]) ).
cnf(t916,plain,
sk47 = sk49,
inference(orient,[status(thm)],[t0]) ).
cnf(t180018,plain,
ifeq(nil,sk48,ifeq(nil,sk49,false,true),true) = true,
inference(step,[status(thm)],[t290,t916]) ).
cnf(t920,plain,
ifeq(nil,sk48,ifeq(nil,sk49,false,true),true) = true,
inference(rw,[status(thm)],[t180018]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t1,plain,
sk50 = sk48,
inference(equality_encoding,[status(esa)],[c194]) ).
cnf(t924,plain,
sk48 = sk50,
inference(orient,[status(thm)],[t1]) ).
cnf(t184724,plain,
ifeq(nil,sk50,ifeq(nil,sk49,false,true),true) = true,
inference(step,[status(thm)],[t920,t924]) ).
cnf(t177406,plain,
ifeq(nil,sk50,ifeq(nil,sk49,false,true),true) = true,
inference(orient,[status(thm)],[t184724]) ).
cnf(t59,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t257,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t59]) ).
fof(f14,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f14_nnf,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [U,V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c81,plain,
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t159,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X1,X2),eq(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(t417,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X1,X2),eq(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t159]) ).
cnf(t55,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t292,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t55]) ).
cnf(c204,plain,
( ~ segmentP(sk48,sk47)
| ~ neq(sk47,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t82,plain,
or(not(neq(sk47,nil)),not(segmentP(sk48,sk47))) = true,
inference(equality_encoding,[status(esa)],[c204]) ).
cnf(t489,plain,
or(not(neq(sk47,nil)),not(segmentP(sk48,sk47))) = true,
inference(orient,[status(thm)],[t82]) ).
cnf(t180019,plain,
or(not(neq(sk49,nil)),not(segmentP(sk48,sk47))) = true,
inference(step,[status(thm)],[t489,t916]) ).
cnf(t180020,plain,
or(not(neq(sk49,nil)),not(segmentP(sk48,sk49))) = true,
inference(step,[status(thm)],[t180019,t916]) ).
cnf(t921,plain,
or(not(neq(sk49,nil)),not(segmentP(sk48,sk49))) = true,
inference(rw,[status(thm)],[t180020]) ).
cnf(t184725,plain,
or(not(neq(sk49,nil)),not(segmentP(sk50,sk49))) = true,
inference(step,[status(thm)],[t921,t924]) ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f6_nnf,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [U,V,W,X] :
( ( ( app(app(W,V),X) != U
| ~ ssList(X)
| ~ ssList(W)
| segmentP(U,V) )
& ( ( app(app(sk7(U,V),V),sk8(U,V)) = U
& ssList(sk8(U,V))
& ssList(sk7(U,V)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8])],[f6_nnf]) ).
cnf(c21,plain,
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t236,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(ssList(X4),true,ifeq(app(app(X3,X2),X4),X1,segmentP(X1,X2),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t411,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(ssList(X4),true,ifeq(app(app(X3,X2),X4),X1,segmentP(X1,X2),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t236]) ).
cnf(t52,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t52]) ).
cnf(t412,plain,
true = ifeq(ssList(app(app(X1,X2),X3)),true,ifeq(ssList(X2),true,ifeq(ssList(X1),true,ifeq(ssList(X3),true,segmentP(app(app(X1,X2),X3),X2),true),true),true),true),
inference(cp,[status(thm)],[t411,t256]) ).
cnf(t81567,plain,
ifeq(ssList(app(app(X1,X2),X3)),true,ifeq(ssList(X2),true,ifeq(ssList(X1),true,ifeq(ssList(X3),true,segmentP(app(app(X1,X2),X3),X2),true),true),true),true) = true,
inference(orient,[status(thm)],[t412]) ).
cnf(c198,plain,
app(app(sk51,sk49),sk52) = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t51,plain,
app(app(sk51,sk49),sk52) = sk50,
inference(equality_encoding,[status(esa)],[c198]) ).
cnf(t590,plain,
app(app(sk51,sk49),sk52) = sk50,
inference(orient,[status(thm)],[t51]) ).
cnf(t81568,plain,
true = ifeq(ssList(sk50),true,ifeq(ssList(sk49),true,ifeq(ssList(sk51),true,ifeq(ssList(sk52),true,segmentP(app(app(sk51,sk49),sk52),sk49),true),true),true),true),
inference(cp,[status(thm)],[t81567,t590]) ).
cnf(c191,plain,
ssList(sk48),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t12,plain,
ssList(sk48) = true,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t180025,plain,
ssList(sk50) = true,
inference(step,[status(thm)],[t12,t924]) ).
cnf(t1365,plain,
ssList(sk50) = true,
inference(orient,[status(thm)],[t180025]) ).
cnf(t182979,plain,
true = ifeq(true,true,ifeq(ssList(sk49),true,ifeq(ssList(sk51),true,ifeq(ssList(sk52),true,segmentP(app(app(sk51,sk49),sk52),sk49),true),true),true),true),
inference(step,[status(thm)],[t81568,t1365]) ).
cnf(t182980,plain,
true = ifeq(ssList(sk49),true,ifeq(ssList(sk51),true,ifeq(ssList(sk52),true,segmentP(app(app(sk51,sk49),sk52),sk49),true),true),true),
inference(step,[status(thm)],[t182979,t256]) ).
cnf(c190,plain,
ssList(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t11,plain,
ssList(sk47) = true,
inference(equality_encoding,[status(esa)],[c190]) ).
cnf(t180024,plain,
ssList(sk49) = true,
inference(step,[status(thm)],[t11,t916]) ).
cnf(t1122,plain,
ssList(sk49) = true,
inference(orient,[status(thm)],[t180024]) ).
cnf(t182981,plain,
true = ifeq(true,true,ifeq(ssList(sk51),true,ifeq(ssList(sk52),true,segmentP(app(app(sk51,sk49),sk52),sk49),true),true),true),
inference(step,[status(thm)],[t182980,t1122]) ).
cnf(t182982,plain,
true = ifeq(ssList(sk51),true,ifeq(ssList(sk52),true,segmentP(app(app(sk51,sk49),sk52),sk49),true),true),
inference(step,[status(thm)],[t182981,t256]) ).
cnf(c196,plain,
ssList(sk51),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t15,plain,
ssList(sk51) = true,
inference(equality_encoding,[status(esa)],[c196]) ).
cnf(t1608,plain,
ssList(sk51) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t182983,plain,
true = ifeq(true,true,ifeq(ssList(sk52),true,segmentP(app(app(sk51,sk49),sk52),sk49),true),true),
inference(step,[status(thm)],[t182982,t1608]) ).
cnf(t182984,plain,
true = ifeq(ssList(sk52),true,segmentP(app(app(sk51,sk49),sk52),sk49),true),
inference(step,[status(thm)],[t182983,t256]) ).
cnf(c197,plain,
ssList(sk52),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t16,plain,
ssList(sk52) = true,
inference(equality_encoding,[status(esa)],[c197]) ).
cnf(t1851,plain,
ssList(sk52) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t182985,plain,
true = ifeq(true,true,segmentP(app(app(sk51,sk49),sk52),sk49),true),
inference(step,[status(thm)],[t182984,t1851]) ).
cnf(t182986,plain,
true = segmentP(app(app(sk51,sk49),sk52),sk49),
inference(step,[status(thm)],[t182985,t256]) ).
cnf(t182987,plain,
true = segmentP(sk50,sk49),
inference(step,[status(thm)],[t182986,t590]) ).
cnf(t82299,plain,
segmentP(sk50,sk49) = true,
inference(orient,[status(thm)],[t182987]) ).
cnf(t184726,plain,
or(not(neq(sk49,nil)),not(true)) = true,
inference(step,[status(thm)],[t184725,t82299]) ).
cnf(t6,plain,
not(true) = false,
introduced(definition) ).
cnf(t651,plain,
not(true) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t184727,plain,
or(not(neq(sk49,nil)),false) = true,
inference(step,[status(thm)],[t184726,t651]) ).
cnf(t31,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t288,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t31]) ).
cnf(t184728,plain,
not(neq(sk49,nil)) = true,
inference(step,[status(thm)],[t184727,t288]) ).
cnf(t177407,plain,
not(neq(sk49,nil)) = true,
inference(orient,[status(thm)],[t184728]) ).
cnf(t177408,plain,
false = ifeq(true,true,neq(sk49,nil),false),
inference(cp,[status(thm)],[t292,t177407]) ).
cnf(t184729,plain,
false = neq(sk49,nil),
inference(step,[status(thm)],[t177408,t256]) ).
cnf(t177409,plain,
neq(sk49,nil) = false,
inference(orient,[status(thm)],[t184729]) ).
cnf(t177410,plain,
true = ifeq(ssList(sk49),true,ifeq(ssList(nil),true,or(false,eq(sk49,nil)),true),true),
inference(cp,[status(thm)],[t417,t177409]) ).
cnf(t184730,plain,
true = ifeq(true,true,ifeq(ssList(nil),true,or(false,eq(sk49,nil)),true),true),
inference(step,[status(thm)],[t177410,t1122]) ).
cnf(t184731,plain,
true = ifeq(ssList(nil),true,or(false,eq(sk49,nil)),true),
inference(step,[status(thm)],[t184730,t256]) ).
fof(f16,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f16_nnf,plain,
ssList(nil),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c83,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(t10,plain,
ssList(nil) = true,
inference(equality_encoding,[status(esa)],[c83]) ).
cnf(t925,plain,
ssList(nil) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t184732,plain,
true = ifeq(true,true,or(false,eq(sk49,nil)),true),
inference(step,[status(thm)],[t184731,t925]) ).
cnf(t184733,plain,
true = or(false,eq(sk49,nil)),
inference(step,[status(thm)],[t184732,t256]) ).
cnf(t33,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t289,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t33]) ).
cnf(t184734,plain,
true = eq(sk49,nil),
inference(step,[status(thm)],[t184733,t289]) ).
cnf(t177414,plain,
eq(sk49,nil) = true,
inference(orient,[status(thm)],[t184734]) ).
cnf(t177415,plain,
nil = ifeq(true,true,sk49,nil),
inference(cp,[status(thm)],[t257,t177414]) ).
cnf(t184735,plain,
nil = sk49,
inference(step,[status(thm)],[t177415,t256]) ).
cnf(t177422,plain,
nil = sk49,
inference(orient,[status(thm)],[t184735]) ).
cnf(t184806,plain,
ifeq(sk49,sk50,ifeq(nil,sk49,false,true),true) = true,
inference(step,[status(thm)],[t177406,t177422]) ).
cnf(t184807,plain,
ifeq(sk49,sk50,ifeq(sk49,sk49,false,true),true) = true,
inference(step,[status(thm)],[t184806,t177422]) ).
cnf(t184808,plain,
ifeq(sk49,sk50,false,true) = true,
inference(step,[status(thm)],[t184807,t256]) ).
cnf(t177471,plain,
ifeq(sk49,sk50,false,true) = true,
inference(rw,[status(thm)],[t184808]) ).
cnf(c202,plain,
( nil != sk49
| nil = sk50 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t53,plain,
ifeq(nil,sk49,nil,sk50) = sk50,
inference(equality_encoding,[status(esa)],[c202]) ).
cnf(t291,plain,
ifeq(nil,sk49,nil,sk50) = sk50,
inference(orient,[status(thm)],[t53]) ).
cnf(t184803,plain,
ifeq(sk49,sk49,nil,sk50) = sk50,
inference(step,[status(thm)],[t291,t177422]) ).
cnf(t184804,plain,
nil = sk50,
inference(step,[status(thm)],[t184803,t256]) ).
cnf(t184805,plain,
sk49 = sk50,
inference(step,[status(thm)],[t184804,t177422]) ).
cnf(t177470,plain,
sk49 = sk50,
inference(rw,[status(thm)],[t184805]) ).
cnf(t178572,plain,
sk49 = sk50,
inference(orient,[status(thm)],[t177470]) ).
cnf(t187195,plain,
ifeq(sk50,sk50,false,true) = true,
inference(step,[status(thm)],[t177471,t178572]) ).
cnf(t187196,plain,
false = true,
inference(step,[status(thm)],[t187195,t256]) ).
cnf(t179965,plain,
false = true,
inference(orient,[status(thm)],[t187196]) ).
fof(f0,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f0_nnf,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [U,V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 != X1
| ~ neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f1_nnf,plain,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
( sk0 != sk1
& ssItem(sk1)
& ssItem(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f1_nnf]) ).
cnf(c4,plain,
sk0 != sk1,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ( cyclefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ~ ( leq(W,V)
& leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
fof(f7_nnf,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( leq(W,V)
& leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,V,W,X,Y,Z] :
( ( ( ( leq(sk10(U),sk9(U))
& leq(sk9(U),sk10(U))
& app(app(sk11(U),cons(sk9(U),sk12(U))),cons(sk10(U),sk13(U))) = U
& ssList(sk13(U))
& ssList(sk12(U))
& ssList(sk11(U))
& ssItem(sk10(U))
& ssItem(sk9(U)) )
| cyclefreeP(U) )
& ( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z)
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10,sk11,sk12,sk13])],[f7_nnf]) ).
cnf(c22,plain,
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f12,axiom,
! [U] :
( ssList(U)
=> ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
fof(f12_nnf,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( V = W
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [U,V,W,X,Y,Z] :
( ( ( ( sk34(U) = sk35(U)
& app(app(sk36(U),cons(sk34(U),sk37(U))),cons(sk35(U),sk38(U))) = U
& ssList(sk38(U))
& ssList(sk37(U))
& ssList(sk36(U))
& ssItem(sk35(U))
& ssItem(sk34(U)) )
| duplicatefreeP(U) )
& ( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z)
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk34,sk35,sk36,sk37,sk38])],[f12_nnf]) ).
cnf(c65,plain,
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(c80,plain,
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f17,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f17_nnf,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [U,V] :
( cons(V,U) != U
| ~ ssItem(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c84,plain,
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f20,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f20_nnf,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [U,V] :
( nil != cons(V,U)
| ~ ssItem(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c90,plain,
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f32,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
=> ~ lt(V,U) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
fof(f32_nnf,plain,
! [U] :
( ! [V] :
( ~ lt(V,U)
| ~ lt(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [U,V] :
( ~ lt(V,U)
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c103,plain,
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f37_nnf,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c113,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
fof(f38,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f38_nnf,plain,
~ singletonP(nil),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
~ singletonP(nil),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c114,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
fof(f89,axiom,
! [U] :
( ssItem(U)
=> ~ lt(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
fof(f89_nnf,plain,
! [U] :
( ~ lt(U,U)
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f89]) ).
fof(f89_sk,plain,
! [U] :
( ~ lt(U,U)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f89_nnf]) ).
cnf(c182,plain,
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f89_sk]) ).
fof(f92,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( leq(U,V)
& U != V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
fof(f92_nnf,plain,
! [U] :
( ! [V] :
( ( ( ~ leq(U,V)
| U = V
| lt(U,V) )
& ( ( leq(U,V)
& U != V )
| ~ lt(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f92]) ).
fof(f92_sk,plain,
! [U,V] :
( ( ( ~ leq(U,V)
| U = V
| lt(U,V) )
& ( ( leq(U,V)
& U != V )
| ~ lt(U,V) ) )
| ~ ssItem(V)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f92_nnf]) ).
cnf(c185,plain,
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f92_sk]) ).
fof(f93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( gt(U,V)
=> ~ gt(V,U) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94) ).
fof(f93_nnf,plain,
! [U] :
( ! [V] :
( ~ gt(V,U)
| ~ gt(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f93]) ).
fof(f93_sk,plain,
! [U,V] :
( ~ gt(V,U)
| ~ gt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f93_nnf]) ).
cnf(c188,plain,
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(c200,plain,
( ~ leq(X6,X8)
| app(cons(X8,nil),X9) != sk49
| ~ ssList(X9)
| ~ ssItem(X8)
| app(X7,cons(X6,nil)) != sk51
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c201,plain,
( ~ leq(X12,X10)
| app(X13,cons(X12,nil)) != sk49
| ~ ssList(X13)
| ~ ssItem(X12)
| app(cons(X10,nil),X11) != sk52
| ~ ssList(X11)
| ~ ssItem(X10) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c4,c22,c65,c80,c84,c90,c103,c113,c114,c182,c185,c188,c200,c201,c203,c204]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t179965]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC118+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.61 % Computer : n008.cluster.edu
% 0.14/0.61 % Model : x86_64 x86_64
% 0.14/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.61 % Memory : 8046.5625MB
% 0.14/0.61 % OS : Linux 6.8.0-71-generic
% 0.14/0.61 % CPULimit : 300
% 0.14/0.61 % WCLimit : 300
% 0.14/0.61 % DateTime : Thu Sep 24 16:30:25 UTC 2026
% 0.14/0.62 % CPUTime :
% 0.14/0.62 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 155.56/20.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 155.56/20.35 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------