%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC037+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 : n013.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 03:05:09 PM UTC 2026
% Result : Theorem 65.25s 24.24s
% Output : Proof 65.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 19
% Syntax : Number of formulae : 158 ( 96 unt; 0 def)
% Number of atoms : 442 ( 166 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 489 ( 205 ~; 160 |; 73 &)
% ( 5 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-4 aty)
% Number of variables : 175 ( 2 sgn 103 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
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(c80,plain,
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t186,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(neq(X1,X2),true,ifeq(X1,X2,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c80]) ).
cnf(t395,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(neq(X1,X2),true,ifeq(X1,X2,false,true),true),true),true) = true,
inference(orient,[status(thm)],[t186]) ).
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssList(Y)
=> ( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil) ) ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
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)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssList(Y)
=> ( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil) ) ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( segmentP(W,Y)
& segmentP(X,Y)
& neq(Y,nil)
& ssList(Y) ) )
& nil != U
& U = W
& V = X
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
( ( ( nil = sk49
& nil = sk50 )
| ( segmentP(sk49,sk51)
& segmentP(sk50,sk51)
& neq(sk51,nil)
& ssList(sk51) ) )
& nil != sk47
& sk47 = sk49
& sk48 = sk50
& nil = sk48
& ssList(sk50)
& ssList(sk49)
& ssList(sk48)
& ssList(sk47) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48,sk49,sk50,sk51])],[f95_nnf]) ).
cnf(c201,plain,
( nil = sk49
| neq(sk51,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t63,plain,
or(neq(sk51,nil),eq(nil,sk49)) = true,
inference(equality_encoding,[status(esa)],[c201]) ).
cnf(t505,plain,
or(neq(sk51,nil),eq(nil,sk49)) = true,
inference(orient,[status(thm)],[t63]) ).
cnf(c194,plain,
nil = sk48,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t0,plain,
sk48 = nil,
inference(equality_encoding,[status(esa)],[c194]) ).
cnf(t568,plain,
nil = sk48,
inference(orient,[status(thm)],[t0]) ).
cnf(t12720,plain,
or(neq(sk51,sk48),eq(nil,sk49)) = true,
inference(step,[status(thm)],[t505,t568]) ).
cnf(t12721,plain,
or(neq(sk51,sk48),eq(sk48,sk49)) = true,
inference(step,[status(thm)],[t12720,t568]) ).
cnf(t575,plain,
or(neq(sk51,sk48),eq(sk48,sk49)) = true,
inference(rw,[status(thm)],[t12721]) ).
cnf(c195,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t2,plain,
sk50 = sk48,
inference(equality_encoding,[status(esa)],[c195]) ).
cnf(t911,plain,
sk48 = sk50,
inference(orient,[status(thm)],[t2]) ).
cnf(t13079,plain,
or(neq(sk51,sk50),eq(sk48,sk49)) = true,
inference(step,[status(thm)],[t575,t911]) ).
cnf(t13080,plain,
or(neq(sk51,sk50),eq(sk50,sk49)) = true,
inference(step,[status(thm)],[t13079,t911]) ).
cnf(c197,plain,
nil != sk47,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t24,plain,
eq(nil,sk47) = false,
inference(equality_encoding,[status(esa)],[c197]) ).
cnf(t12797,plain,
eq(sk48,sk47) = false,
inference(step,[status(thm)],[t24,t568]) ).
cnf(t689,plain,
eq(sk48,sk47) = false,
inference(orient,[status(thm)],[t12797]) ).
cnf(c196,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t1,plain,
sk49 = sk47,
inference(equality_encoding,[status(esa)],[c196]) ).
cnf(t905,plain,
sk47 = sk49,
inference(orient,[status(thm)],[t1]) ).
cnf(t12819,plain,
eq(sk48,sk49) = false,
inference(step,[status(thm)],[t689,t905]) ).
cnf(t909,plain,
eq(sk48,sk49) = false,
inference(rw,[status(thm)],[t12819]) ).
cnf(t12864,plain,
eq(sk50,sk49) = false,
inference(step,[status(thm)],[t909,t911]) ).
cnf(t2128,plain,
eq(sk50,sk49) = false,
inference(orient,[status(thm)],[t12864]) ).
cnf(t13081,plain,
or(neq(sk51,sk50),false) = true,
inference(step,[status(thm)],[t13080,t2128]) ).
cnf(t32,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t288,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t32]) ).
cnf(t13082,plain,
neq(sk51,sk50) = true,
inference(step,[status(thm)],[t13081,t288]) ).
cnf(t5728,plain,
neq(sk51,sk50) = true,
inference(orient,[status(thm)],[t13082]) ).
cnf(t5729,plain,
true = ifeq(ssList(sk51),true,ifeq(ssList(sk50),true,ifeq(true,true,ifeq(sk51,sk50,false,true),true),true),true),
inference(cp,[status(thm)],[t395,t5728]) ).
cnf(c199,plain,
( nil = sk49
| ssList(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t58,plain,
or(ssList(sk51),eq(nil,sk49)) = true,
inference(equality_encoding,[status(esa)],[c199]) ).
cnf(t507,plain,
or(ssList(sk51),eq(nil,sk49)) = true,
inference(orient,[status(thm)],[t58]) ).
cnf(t12717,plain,
or(ssList(sk51),eq(sk48,sk49)) = true,
inference(step,[status(thm)],[t507,t568]) ).
cnf(t573,plain,
or(ssList(sk51),eq(sk48,sk49)) = true,
inference(rw,[status(thm)],[t12717]) ).
cnf(t12975,plain,
or(ssList(sk51),eq(sk50,sk49)) = true,
inference(step,[status(thm)],[t573,t911]) ).
cnf(t12976,plain,
or(ssList(sk51),false) = true,
inference(step,[status(thm)],[t12975,t2128]) ).
cnf(t12977,plain,
ssList(sk51) = true,
inference(step,[status(thm)],[t12976,t288]) ).
cnf(t4584,plain,
ssList(sk51) = true,
inference(orient,[status(thm)],[t12977]) ).
cnf(t13092,plain,
true = ifeq(true,true,ifeq(ssList(sk50),true,ifeq(true,true,ifeq(sk51,sk50,false,true),true),true),true),
inference(step,[status(thm)],[t5729,t4584]) ).
cnf(t53,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t53]) ).
cnf(t13093,plain,
true = ifeq(ssList(sk50),true,ifeq(true,true,ifeq(sk51,sk50,false,true),true),true),
inference(step,[status(thm)],[t13092,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(t11,plain,
ssList(nil) = true,
inference(equality_encoding,[status(esa)],[c83]) ).
cnf(t12822,plain,
nil = sk50,
inference(step,[status(thm)],[t568,t911]) ).
cnf(t912,plain,
nil = sk50,
inference(orient,[status(thm)],[t12822]) ).
cnf(t12855,plain,
ssList(sk50) = true,
inference(step,[status(thm)],[t11,t912]) ).
cnf(t1190,plain,
ssList(sk50) = true,
inference(orient,[status(thm)],[t12855]) ).
cnf(t13094,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(sk51,sk50,false,true),true),true),
inference(step,[status(thm)],[t13093,t1190]) ).
cnf(t13095,plain,
true = ifeq(true,true,ifeq(sk51,sk50,false,true),true),
inference(step,[status(thm)],[t13094,t256]) ).
cnf(t13096,plain,
true = ifeq(sk51,sk50,false,true),
inference(step,[status(thm)],[t13095,t256]) ).
cnf(t5740,plain,
ifeq(sk51,sk50,false,true) = true,
inference(orient,[status(thm)],[t13096]) ).
fof(f53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
fof(f53_nnf,plain,
! [U] :
( ! [V] :
( U = V
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [U,V] :
( U = V
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c133,plain,
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(t200,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(segmentP(X1,X2),true,ifeq(segmentP(X2,X1),true,X1,X2),X2),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c133]) ).
cnf(t268,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(segmentP(X1,X2),true,ifeq(segmentP(X2,X1),true,X1,X2),X2),X2),X2) = X2,
inference(orient,[status(thm)],[t200]) ).
fof(f56,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f56_nnf,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c136,plain,
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t78,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(equality_encoding,[status(esa)],[c136]) ).
cnf(t484,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(orient,[status(thm)],[t78]) ).
cnf(t12727,plain,
ifeq(ssList(X1),true,segmentP(X1,sk48),true) = true,
inference(step,[status(thm)],[t484,t568]) ).
cnf(t581,plain,
ifeq(ssList(X1),true,segmentP(X1,sk48),true) = true,
inference(rw,[status(thm)],[t12727]) ).
cnf(t13557,plain,
ifeq(ssList(X1),true,segmentP(X1,sk50),true) = true,
inference(step,[status(thm)],[t581,t911]) ).
cnf(t12487,plain,
ifeq(ssList(X1),true,segmentP(X1,sk50),true) = true,
inference(orient,[status(thm)],[t13557]) ).
cnf(t12516,plain,
true = ifeq(true,true,segmentP(sk51,sk50),true),
inference(cp,[status(thm)],[t12487,t4584]) ).
cnf(t13558,plain,
true = segmentP(sk51,sk50),
inference(step,[status(thm)],[t12516,t256]) ).
cnf(t12532,plain,
segmentP(sk51,sk50) = true,
inference(orient,[status(thm)],[t13558]) ).
cnf(t12535,plain,
sk50 = ifeq(ssList(sk51),true,ifeq(ssList(sk50),true,ifeq(true,true,ifeq(segmentP(sk50,sk51),true,sk51,sk50),sk50),sk50),sk50),
inference(cp,[status(thm)],[t268,t12532]) ).
cnf(t13563,plain,
sk50 = ifeq(true,true,ifeq(ssList(sk50),true,ifeq(true,true,ifeq(segmentP(sk50,sk51),true,sk51,sk50),sk50),sk50),sk50),
inference(step,[status(thm)],[t12535,t4584]) ).
cnf(t13564,plain,
sk50 = ifeq(ssList(sk50),true,ifeq(true,true,ifeq(segmentP(sk50,sk51),true,sk51,sk50),sk50),sk50),
inference(step,[status(thm)],[t13563,t256]) ).
cnf(t13565,plain,
sk50 = ifeq(true,true,ifeq(true,true,ifeq(segmentP(sk50,sk51),true,sk51,sk50),sk50),sk50),
inference(step,[status(thm)],[t13564,t1190]) ).
cnf(t13566,plain,
sk50 = ifeq(true,true,ifeq(segmentP(sk50,sk51),true,sk51,sk50),sk50),
inference(step,[status(thm)],[t13565,t256]) ).
cnf(t13567,plain,
sk50 = ifeq(segmentP(sk50,sk51),true,sk51,sk50),
inference(step,[status(thm)],[t13566,t256]) ).
cnf(c203,plain,
( nil = sk49
| segmentP(sk50,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t67,plain,
or(segmentP(sk50,sk51),eq(nil,sk49)) = true,
inference(equality_encoding,[status(esa)],[c203]) ).
cnf(t503,plain,
or(segmentP(sk50,sk51),eq(nil,sk49)) = true,
inference(orient,[status(thm)],[t67]) ).
cnf(t12723,plain,
or(segmentP(sk50,sk51),eq(sk48,sk49)) = true,
inference(step,[status(thm)],[t503,t568]) ).
cnf(t577,plain,
or(segmentP(sk50,sk51),eq(sk48,sk49)) = true,
inference(rw,[status(thm)],[t12723]) ).
cnf(t13097,plain,
or(segmentP(sk50,sk51),eq(sk50,sk49)) = true,
inference(step,[status(thm)],[t577,t911]) ).
cnf(t13098,plain,
or(segmentP(sk50,sk51),false) = true,
inference(step,[status(thm)],[t13097,t2128]) ).
cnf(t13099,plain,
segmentP(sk50,sk51) = true,
inference(step,[status(thm)],[t13098,t288]) ).
cnf(t5744,plain,
segmentP(sk50,sk51) = true,
inference(orient,[status(thm)],[t13099]) ).
cnf(t13568,plain,
sk50 = ifeq(true,true,sk51,sk50),
inference(step,[status(thm)],[t13567,t5744]) ).
cnf(t13569,plain,
sk50 = sk51,
inference(step,[status(thm)],[t13568,t256]) ).
cnf(t12545,plain,
sk50 = sk51,
inference(orient,[status(thm)],[t13569]) ).
cnf(t13576,plain,
ifeq(sk51,sk51,false,true) = true,
inference(step,[status(thm)],[t5740,t12545]) ).
cnf(t13577,plain,
false = true,
inference(step,[status(thm)],[t13576,t256]) ).
cnf(t12551,plain,
false = true,
inference(rw,[status(thm)],[t13577]) ).
cnf(t12684,plain,
false = true,
inference(orient,[status(thm)],[t12551]) ).
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]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c4,c22,c65,c80,c84,c90,c103,c113,c114,c182,c185,c188,c197]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t12684]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC037+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/15.81 % Computer : n013.cluster.edu
% 0.11/15.81 % Model : x86_64 x86_64
% 0.11/15.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.81 % Memory : 8046.5625MB
% 0.11/15.81 % OS : Linux 6.8.0-71-generic
% 0.11/15.81 % CPULimit : 300
% 0.11/15.81 % WCLimit : 300
% 0.11/15.81 % DateTime : Thu Sep 24 16:02:10 UTC 2026
% 0.11/15.81 % CPUTime :
% 0.11/15.81 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 65.25/24.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 65.25/24.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------