%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC253+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 03:09:01 PM UTC 2026
% Result : Theorem 10.60s 2.27s
% Output : CNFRefutation 10.60s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f548ERROR: Could not build tree for root c_44169ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( singletonP(X0)
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& app(X2,X5) = X4
& tl(X3) = X5
& ssList(X5) )
& X3 != X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( singletonP(X0)
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& app(X2,X5) = X4
& tl(X3) = X5
& ssList(X5) )
& X3 != X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) != X0 ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(flattening,[],[f129]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f186,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f187,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f186]) ).
fof(f188,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f188]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f192]) ).
fof(f194,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X2 = X0 ) ) ),
inference(ennf_transformation,[],[f79]) ).
fof(f195,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X2 = X0 ) ) ),
inference(flattening,[],[f194]) ).
fof(f204,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| nil = X0
| tl(app(X0,X1)) = app(tl(X0),X1) ) ),
inference(ennf_transformation,[],[f86]) ).
fof(f205,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| nil = X0
| tl(app(X0,X1)) = app(tl(X0),X1) ) ),
inference(flattening,[],[f204]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ~ singletonP(X0)
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| app(X2,X5) != X4
| tl(X3) != X5
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ~ singletonP(X0)
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| app(X2,X5) != X4
| tl(X3) != X5
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f237,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f238,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK10(X0),nil) = X0
& ssItem(sK10(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f238]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f290,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(X1,sK51(X0))],[f187]) ).
fof(f291,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X1,sK52(X0))],[f189]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( ~ singletonP(sK53)
& ! [X4] :
( ! [X5] :
( ~ neq(nil,sK56)
| app(sK55,X5) != X4
| tl(sK56) != X5
| ~ ssList(X5) )
| sK56 = X4
| ~ ssList(X4) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f308,plain,
! [X0,X1] :
( ~ ssList(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f390,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f399,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f469,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK51(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f470,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f290]) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK52(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f472,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f291]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f475,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f195]) ).
fof(f484,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| tl(app(X0,X1)) = app(tl(X0),X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| ~ singletonP(sK53) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| app(sK55,X5) != X4
| tl(sK56) != X5
| ~ ssList(X5)
| sK56 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
! [X4,X5] :
( neq(sK54,nil)
| ~ neq(nil,sK56)
| app(sK55,X5) != X4
| tl(sK56) != X5
| ~ ssList(X5)
| sK56 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
! [X4,X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| app(sK55,X5) != X4
| tl(sK56) != X5
| ~ ssList(X5)
| sK56 = X4
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f503,f507]) ).
fof(f512,plain,
( ~ neq(sK56,nil)
| ~ singletonP(sK55) ),
inference(definition_unfolding,[],[f500,f506]) ).
fof(f513,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
fof(f514,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f517,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f308]) ).
fof(f542,plain,
! [X4] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| app(sK55,tl(sK56)) != X4
| ~ ssList(tl(sK56))
| sK56 = X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f510]) ).
fof(f543,plain,
( neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(tl(sK56))
| sK56 = app(sK55,tl(sK56))
| ~ ssList(app(sK55,tl(sK56))) ),
inference(equality_resolution,[],[f542]) ).
fof(f544,plain,
! [X4] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| app(sK55,tl(sK56)) != X4
| ~ ssList(tl(sK56))
| sK56 = X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f502]) ).
fof(f545,plain,
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(tl(sK56))
| sK56 = app(sK55,tl(sK56))
| ~ ssList(app(sK55,tl(sK56))) ),
inference(equality_resolution,[],[f544]) ).
tcf(c_58,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f517]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_139,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f548]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f390]) ).
tcf(c_151,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f399]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f403]) ).
tcf(c_219,plain,
! [X0: $i] :
( ssItem(sK51(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f470]) ).
tcf(c_220,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK51(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f469]) ).
tcf(c_221,plain,
! [X0: $i] :
( ssList(sK52(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f472]) ).
tcf(c_222,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK52(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f471]) ).
tcf(c_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X2,X1) ) ),
inference(cnf_transformation,[],[f475]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ( app(tl(X0),X1) = tl(app(X0,X1)) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f484]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f553]) ).
tcf(c_247,negated_conjecture,
( neq(sK56,nil)
| ( app(sK55,tl(sK56)) = sK56 )
| ~ ssList(tl(sK56))
| ~ neq(nil,sK56)
| ~ ssList(app(sK55,tl(sK56))) ),
inference(cnf_transformation,[],[f543]) ).
tcf(c_248,negated_conjecture,
( ( app(sK55,tl(sK56)) = sK56 )
| ~ ssList(tl(sK56))
| ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(app(sK55,tl(sK56))) ),
inference(cnf_transformation,[],[f545]) ).
tcf(c_250,negated_conjecture,
( ~ singletonP(sK55)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f513]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f514]) ).
tcf(c_369,negated_conjecture,
~ singletonP(sK55),
inference(global_subsumption_just,[status(thm)],[c_250,c_246,c_250]) ).
tcf(c_383,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_247,c_246]) ).
tcf(c_385,plain,
( ( app(sK55,tl(sK56)) = sK56 )
| ~ ssList(tl(sK56))
| ~ ssList(app(sK55,tl(sK56)))
| ~ neq(nil,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_248,c_246,c_248]) ).
tcf(c_386,negated_conjecture,
( ( app(sK55,tl(sK56)) = sK56 )
| ~ ssList(tl(sK56))
| ~ neq(nil,sK56)
| ~ ssList(app(sK55,tl(sK56))) ),
inference(renaming,[status(thm)],[c_385]) ).
tcf(c_3236,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(sK55,tl(sK56)) = sK56 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(tl(sK56))
| ~ ssList(app(sK55,tl(sK56)))
| ( X1 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_386]) ).
tcf(c_3237,plain,
( ( nil = sK56 )
| ( app(sK55,tl(sK56)) = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil)
| ~ ssList(tl(sK56))
| ~ ssList(app(sK55,tl(sK56))) ),
inference(unflattening,[status(thm)],[c_3236]) ).
tcf(c_3238,plain,
( ( nil = sK56 )
| ( app(sK55,tl(sK56)) = sK56 )
| ~ ssList(tl(sK56))
| ~ ssList(app(sK55,tl(sK56))) ),
inference(global_subsumption_just,[status(thm)],[c_3237,c_253,c_141,c_3237]) ).
tcf(c_3256,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_383]) ).
tcf(c_3257,plain,
( ~ ssList(nil)
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3256]) ).
tcf(c_3258,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3257,c_141,c_3257]) ).
tcf(c_3263,plain,
( ( app(sK55,tl(sK56)) = sK56 )
| ~ ssList(tl(sK56))
| ~ ssList(app(sK55,tl(sK56))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3238,c_3258]) ).
tcf(c_8875,definition,
iPr_def_10 = tl(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8876,definition,
iPr_def_11 = app(sK55,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8877,plain,
( ( iPr_def_11 = sK56 )
| ~ ssList(iPr_def_11)
| ~ ssList(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_3263,c_8875,c_8876]) ).
tcf(c_8878,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_3258]) ).
tcf(c_8879,negated_conjecture,
~ singletonP(sK55),
inference(demodulation,[status(thm)],[c_369]) ).
tcf(c_8880,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8881,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_12180,plain,
( ssList(iPr_def_10)
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8875,c_151]) ).
tcf(c_12183,plain,
ssList(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12180,c_8878,c_8881]) ).
tcf(c_12190,plain,
( ( sK56 = iPr_def_11 )
| ~ ssList(iPr_def_11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_8877,c_12183]) ).
tcf(c_12194,plain,
app(nil,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_12183,c_155]) ).
tcf(c_12202,plain,
( ssList(iPr_def_11)
| ~ ssList(iPr_def_10)
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8876,c_153]) ).
tcf(c_12211,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_12202,c_12183,c_8880]) ).
tcf(c_12250,plain,
sK56 = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_12190,c_12190,c_12211]) ).
tcf(c_12254,plain,
tl(iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_8875,c_12250]) ).
tcf(c_12255,plain,
nil != iPr_def_11,
inference(demodulation,[status(thm)],[c_8878,c_12250]) ).
tcf(c_12877,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_140,c_58]) ).
tcf(c_12878,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12877,c_141]) ).
tcf(c_13571,plain,
( ( nil = sK55 )
| ( hd(sK55) = sK51(sK55) ) ),
inference(superposition,[status(thm)],[c_8880,c_220]) ).
tcf(c_13572,plain,
( ( nil = iPr_def_11 )
| ( hd(iPr_def_11) = sK51(iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_12211,c_220]) ).
tcf(c_13576,plain,
hd(iPr_def_11) = sK51(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_13572,c_12255]) ).
tcf(c_13701,plain,
( ssItem(hd(iPr_def_11))
| ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11) ),
inference(superposition,[status(thm)],[c_13576,c_219]) ).
tcf(c_13702,plain,
ssItem(hd(iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_13701,c_12255,c_12211]) ).
tcf(c_13727,plain,
( ssItem(hd(sK55))
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_13571,c_219]) ).
tcf(c_13728,plain,
( ssItem(hd(sK55))
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13727,c_8880]) ).
tcf(c_14025,plain,
( ( nil = sK55 )
| ( tl(sK55) = sK52(sK55) ) ),
inference(superposition,[status(thm)],[c_8880,c_222]) ).
tcf(c_14382,plain,
( ssList(tl(sK55))
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_14025,c_221]) ).
tcf(c_14383,plain,
( ssList(tl(sK55))
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14382,c_8880]) ).
tcf(c_15637,plain,
( ( nil = iPr_def_11 )
| ( cons(hd(iPr_def_11),tl(iPr_def_11)) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_12211,c_224]) ).
tcf(c_15643,plain,
( ( nil = iPr_def_11 )
| ( cons(hd(iPr_def_11),iPr_def_10) = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_15637,c_12254]) ).
tcf(c_15644,plain,
cons(hd(iPr_def_11),iPr_def_10) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_15643,c_12255]) ).
tcf(c_15779,plain,
iPr_def_11 = sK56,
inference(global_subsumption_just,[status(thm)],[c_8877,c_8877,c_12183,c_12211]) ).
tcf(c_15781,plain,
nil != iPr_def_11,
inference(demodulation,[status(thm)],[c_8878,c_15779]) ).
tcf(c_15782,plain,
ssList(iPr_def_11),
inference(demodulation,[status(thm)],[c_8881,c_15779]) ).
tcf(c_15789,plain,
tl(iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_8875,c_15779]) ).
tcf(c_16146,plain,
( ~ ssList(iPr_def_10)
| ~ ssItem(hd(iPr_def_11))
| ( iPr_def_10 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_15644,c_142]) ).
tcf(c_16150,plain,
iPr_def_10 != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_16146,c_12183,c_13702]) ).
tcf(c_17819,plain,
( ssList(iPr_def_10)
| ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11) ),
inference(superposition,[status(thm)],[c_15789,c_151]) ).
tcf(c_17822,plain,
ssList(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_17819,c_15781,c_15782]) ).
tcf(c_19407,plain,
app(nil,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_17822,c_155]) ).
tcf(c_21195,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( app(tl(sK55),X0) = tl(app(sK55,X0)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8880,c_234]) ).
tcf(c_21436,plain,
( ( nil = sK55 )
| ( app(tl(sK55),iPr_def_10) = tl(app(sK55,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_12183,c_21195]) ).
tcf(c_21439,plain,
( ( nil = sK55 )
| ( app(tl(sK55),iPr_def_10) = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_21436,c_8876,c_12254]) ).
tcf(c_23594,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_12878]) ).
tcf(c_32471,plain,
( ( nil = sK55 )
| ( tl(sK55) = sK52(sK55) ) ),
inference(superposition,[status(thm)],[c_8880,c_222]) ).
tcf(c_36000,plain,
( ssList(tl(sK55))
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_32471,c_221]) ).
tcf(c_36001,plain,
( ssList(tl(sK55))
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36000,c_8880]) ).
tcf(c_36009,plain,
( ( nil = sK55 )
| ( tl(sK55) = nil )
| ( tl(tl(sK55)) = sK52(tl(sK55)) ) ),
inference(superposition,[status(thm)],[c_36001,c_222]) ).
tcf(c_38446,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( tl(sK55) = X0 )
| ~ ssList(iPr_def_10)
| ~ ssList(X0)
| ~ ssList(tl(sK55))
| ( app(X0,iPr_def_10) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_21439,c_225]) ).
tcf(c_38488,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( tl(sK55) = X0 )
| ~ ssList(X0)
| ~ ssList(tl(sK55))
| ( app(X0,iPr_def_10) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38446,c_12183]) ).
tcf(c_38501,plain,
( ( nil = sK55 )
| ( tl(sK55) = nil )
| ~ ssList(nil)
| ~ ssList(tl(sK55))
| ( app(nil,iPr_def_10) != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_38488]) ).
tcf(c_40933,plain,
( ( nil = sK55 )
| ( tl(sK55) = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_36009,c_141,c_12194,c_14383,c_38501]) ).
tcf(c_42253,plain,
( ( nil = sK55 )
| ( cons(hd(sK55),tl(sK55)) = sK55 ) ),
inference(superposition,[status(thm)],[c_8880,c_224]) ).
tcf(c_43780,plain,
( ( nil = sK55 )
| ( cons(hd(sK55),nil) = sK55 ) ),
inference(superposition,[status(thm)],[c_40933,c_42253]) ).
tcf(c_44067,plain,
( singletonP(sK55)
| ( nil = sK55 )
| ~ ssItem(hd(sK55)) ),
inference(superposition,[status(thm)],[c_43780,c_23594]) ).
tcf(c_44088,plain,
( ( nil = sK55 )
| ~ ssItem(hd(sK55)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44067,c_8879]) ).
tcf(c_44098,plain,
nil = sK55,
inference(global_subsumption_just,[status(thm)],[c_44088,c_13728,c_44088]) ).
tcf(c_44132,plain,
app(nil,iPr_def_10) = iPr_def_11,
inference(demodulation,[status(thm)],[c_8876,c_44098]) ).
tcf(c_44135,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_44132,c_19407]) ).
tcf(c_44169,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_44135,c_16150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC253+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 17:14:18 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 10.60/2.27 % SZS status Started for theBenchmark.p
% 10.60/2.27 % SZS status Theorem for theBenchmark.p
% 10.60/2.27
% 10.60/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.60/2.27
% 10.60/2.27 % ------ iProver source info
% 10.60/2.27
% 10.60/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 10.60/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.60/2.27 % git: non_committed_changes: false
% 10.60/2.27
% 10.60/2.27 % ------ Parsing...
% 10.60/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.60/2.27
% 10.60/2.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 10.60/2.27
% 10.60/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.60/2.27
% 10.60/2.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.60/2.27 % ------ Proving...
% 10.60/2.27 % ------ Problem Properties
% 10.60/2.27
% 10.60/2.27 %
% 10.60/2.27 % clauses 187
% 10.60/2.27 % conjectures 3
% 10.60/2.27 % EPR 54
% 10.60/2.27 % Horn 119
% 10.60/2.27 % unary 22
% 10.60/2.27 % binary 40
% 10.60/2.27 % lits 627
% 10.60/2.27 % lits eq 82
% 10.60/2.27 % fd_pure 0
% 10.60/2.27 % fd_pseudo 0
% 10.60/2.27 % fd_cond 21
% 10.60/2.27 % fd_pseudo_cond 14
% 10.60/2.27 % AC symbols 0
% 10.60/2.27
% 10.60/2.27 % ------ Schedule dynamic 5 is on
% 10.60/2.27
% 10.60/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.60/2.27
% 10.60/2.27
% 10.60/2.27 % ------
% 10.60/2.27 % Current options:
% 10.60/2.27 % ------
% 10.60/2.27
% 10.60/2.27
% 10.60/2.27 %
% 10.60/2.27
% 10.60/2.27 % ------ Proving...
% 10.60/2.27 %
% 10.60/2.27
% 10.60/2.27 % SZS status Theorem for theBenchmark.p
% 10.60/2.27
% 10.60/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.60/2.27
% 10.60/2.27
%------------------------------------------------------------------------------