%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC368+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 03:09:29 PM UTC 2026
% Result : Theorem 130.55s 32.68s
% Output : CNFRefutation 130.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 157 ( 35 unt; 0 def)
% Number of atoms : 559 ( 148 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 689 ( 287 ~; 292 |; 75 &)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 216 ( 0 sgn 182 !; 34 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X5,X4)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| segmentP(X1,X0)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X5,X4)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| segmentP(X1,X0)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ~ leq(X5,X4)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2 ) )
& ~ segmentP(X1,X0)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ~ leq(X5,X4)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2 ) )
& ~ segmentP(X1,X0)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f102,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f103,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(ennf_transformation,[],[f20]) ).
fof(f104,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(flattening,[],[f103]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f112,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f115,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1) ) ) ) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f122,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f133,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f140,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f141,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f147,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( nil = sK2
& nil = sK3 )
| ( ssItem(sK4)
& ! [X5] :
( ~ leq(X5,sK4)
| ~ memberP(sK3,X5)
| sK4 = X5
| ~ ssItem(X5) )
& memberP(sK3,sK4)
& sK2 = cons(sK4,nil) ) )
& ~ segmentP(sK1,sK0)
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f149,plain,
! [X0] :
( ~ ssList(X0)
| ( cons(sK8(X0),sK7(X0)) = X0
& ssItem(sK8(X0))
& ssList(sK7(X0)) )
| nil = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f104]) ).
fof(f154,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f112]) ).
fof(f155,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(rectify,[],[f154]) ).
fof(f156,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0
& ssList(sK10(X0,X1))
& ssList(sK9(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f155]) ).
fof(f158,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f122]) ).
fof(f159,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(rectify,[],[f158]) ).
fof(f160,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK11(X0,X1),X1),sK12(X0,X1)) = X0
& ssList(sK12(X0,X1))
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X4,sK11(X0,X1)),skolemize(X5,sK12(X0,X1))],[f159]) ).
fof(f165,plain,
ssList(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f166,plain,
ssList(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f169,plain,
( nil = sK2
| ssItem(sK4) ),
inference(cnf_transformation,[],[f147]) ).
fof(f170,plain,
( nil = sK3
| ssItem(sK4) ),
inference(cnf_transformation,[],[f147]) ).
fof(f173,plain,
( nil = sK2
| memberP(sK3,sK4) ),
inference(cnf_transformation,[],[f147]) ).
fof(f174,plain,
( nil = sK3
| memberP(sK3,sK4) ),
inference(cnf_transformation,[],[f147]) ).
fof(f175,plain,
( nil = sK2
| sK2 = cons(sK4,nil) ),
inference(cnf_transformation,[],[f147]) ).
fof(f176,plain,
( nil = sK3
| sK2 = cons(sK4,nil) ),
inference(cnf_transformation,[],[f147]) ).
fof(f177,plain,
~ segmentP(sK1,sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f178,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f147]) ).
fof(f179,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f147]) ).
fof(f183,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f185,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f186,plain,
! [X0] :
( ~ ssList(X0)
| cons(sK8(X0),sK7(X0)) = X0
| nil = X0 ),
inference(cnf_transformation,[],[f149]) ).
fof(f192,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f193,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f201,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0 ),
inference(cnf_transformation,[],[f156]) ).
fof(f202,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| ssList(sK10(X0,X1)) ),
inference(cnf_transformation,[],[f156]) ).
fof(f203,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| ssList(sK9(X0,X1)) ),
inference(cnf_transformation,[],[f156]) ).
fof(f208,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f209,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
fof(f224,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f133]) ).
fof(f231,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f140]) ).
fof(f232,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f141]) ).
fof(f236,plain,
~ segmentP(sK3,sK2),
inference(definition_unfolding,[],[f177,f179,f178]) ).
fof(f237,plain,
ssList(sK3),
inference(definition_unfolding,[],[f166,f179]) ).
fof(f238,plain,
ssList(sK2),
inference(definition_unfolding,[],[f165,f178]) ).
fof(f242,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f215]) ).
tcf(c_49,negated_conjecture,
~ segmentP(sK3,sK2),
inference(cnf_transformation,[],[f236]) ).
tcf(c_50,negated_conjecture,
( ( sK3 = nil )
| ( cons(sK4,nil) = sK2 ) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_51,negated_conjecture,
( ( sK2 = nil )
| ( cons(sK4,nil) = sK2 ) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_52,negated_conjecture,
( memberP(sK3,sK4)
| ( sK3 = nil ) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_53,negated_conjecture,
( memberP(sK3,sK4)
| ( sK2 = nil ) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_56,negated_conjecture,
( ssItem(sK4)
| ( sK3 = nil ) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_57,negated_conjecture,
( ssItem(sK4)
| ( sK2 = nil ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_60,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f237]) ).
tcf(c_61,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f238]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_70,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(sK8(X0),sK7(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_75,plain,
ssList(nil),
inference(cnf_transformation,[],[f193]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( ssList(sK9(X0,X1))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ssList(sK10(X0,X1))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ( app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0 )
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_91,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_106,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_113,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_119,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1949,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1951,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3049,plain,
app(sK3,nil) = sK3,
inference(superposition,[status(thm)],[c_60,c_106]) ).
tcf(c_3081,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_61,c_113]) ).
tcf(c_3312,plain,
( ( sK3 = nil )
| ~ ssList(nil)
| ~ ssItem(sK4)
| ( sK2 != nil ) ),
inference(superposition,[status(thm)],[c_50,c_67]) ).
tcf(c_3314,plain,
( ( sK3 = nil )
| ~ ssItem(sK4)
| ( sK2 != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3312,c_75]) ).
tcf(c_3819,plain,
! [X0: $i,X1: $i] :
( segmentP(sK3,sK2)
| ~ segmentP(X0,X1)
| ( sK2 != X1 )
| ( sK3 != X0 ) ),
inference(instantiation,[status(thm)],[c_1952]) ).
tcf(c_3820,plain,
( segmentP(sK3,sK2)
| ~ segmentP(nil,nil)
| ( sK2 != nil )
| ( sK3 != nil ) ),
inference(instantiation,[status(thm)],[c_3819]) ).
tcf(c_3885,plain,
( ( sK2 = nil )
| ( cons(sK8(sK2),sK7(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_61,c_70]) ).
tcf(c_4050,plain,
cons(sK8(sK2),sK7(sK2)) = sK2,
inference(global_subsumption_just,[status(thm)],[c_3885,c_75,c_49,c_57,c_56,c_119,c_3314,c_3820,c_3885]) ).
tcf(c_4053,plain,
( ~ ssList(sK7(sK2))
| ~ ssItem(sK8(sK2))
| ( sK2 != nil ) ),
inference(superposition,[status(thm)],[c_4050,c_67]) ).
tcf(c_4314,plain,
sK2 = sK2,
inference(instantiation,[status(thm)],[c_1949]) ).
tcf(c_4738,plain,
! [X0: $i] :
( ssList(sK10(X0,sK4))
| ~ ssItem(sK4)
| ~ ssList(X0)
| ~ memberP(X0,sK4) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_4739,plain,
! [X0: $i] :
( ssList(sK9(X0,sK4))
| ~ ssItem(sK4)
| ~ ssList(X0)
| ~ memberP(X0,sK4) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_4902,negated_conjecture,
ssItem(sK4),
inference(global_subsumption_just,[status(thm)],[c_56,c_75,c_49,c_57,c_56,c_119,c_3820]) ).
tcf(c_4906,negated_conjecture,
memberP(sK3,sK4),
inference(global_subsumption_just,[status(thm)],[c_52,c_75,c_49,c_119,c_53,c_52,c_3820]) ).
tcf(c_4910,negated_conjecture,
cons(sK4,nil) = sK2,
inference(global_subsumption_just,[status(thm)],[c_50,c_75,c_49,c_57,c_56,c_119,c_51,c_3314,c_3820]) ).
tcf(c_5966,plain,
( ~ ssList(nil)
| ~ ssItem(sK4)
| ( sK2 != nil ) ),
inference(superposition,[status(thm)],[c_4910,c_67]) ).
tcf(c_5970,plain,
sK2 != nil,
inference(forward_subsumption_resolution,[status(thm)],[c_5966,c_75,c_4902]) ).
tcf(c_7280,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK2),X0)) ),
inference(superposition,[status(thm)],[c_3081,c_94]) ).
tcf(c_7318,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_7280,c_3081]) ).
tcf(c_7319,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7318,c_75,c_61]) ).
tcf(c_7830,plain,
( ssList(sK10(sK3,sK4))
| ~ ssList(sK3)
| ~ ssItem(sK4)
| ~ memberP(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_4738]) ).
tcf(c_7861,plain,
( ssList(sK9(sK3,sK4))
| ~ ssList(sK3)
| ~ ssItem(sK4)
| ~ memberP(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_4739]) ).
tcf(c_8036,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_1949]) ).
tcf(c_9738,plain,
sK2 != nil,
inference(global_subsumption_just,[status(thm)],[c_4053,c_5970]) ).
tcf(c_9742,plain,
ssItem(sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_9738]) ).
tcf(c_9744,plain,
memberP(sK3,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_53,c_9738]) ).
tcf(c_9767,plain,
( ( app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3 )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_9744,c_86]) ).
tcf(c_9768,plain,
app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_9767,c_60,c_9742]) ).
tcf(c_9805,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK3,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK9(sK3,sK4))
| ~ ssList(cons(sK4,sK10(sK3,sK4)))
| ~ segmentP(cons(sK4,sK10(sK3,sK4)),X0) ),
inference(superposition,[status(thm)],[c_9768,c_90]) ).
tcf(c_27402,plain,
! [X0: $i] :
( ssList(app(sK2,X0))
| ~ ssList(sK2)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_33266,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_61,c_113]) ).
tcf(c_37377,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK2),X0)) ),
inference(superposition,[status(thm)],[c_33266,c_94]) ).
tcf(c_37422,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_37377,c_33266]) ).
tcf(c_37423,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37422,c_75,c_61]) ).
tcf(c_39893,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_37423,c_61,c_7319,c_27402]) ).
tcf(c_145052,plain,
! [X0: $i] :
( ssList(cons(sK4,X0))
| ~ ssItem(sK4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_241106,plain,
( ssList(cons(sK4,sK10(sK3,sK4)))
| ~ ssItem(sK4)
| ~ ssList(sK10(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_145052]) ).
tcf(c_314210,negated_conjecture,
cons(sK4,nil) = sK2,
inference(global_subsumption_just,[status(thm)],[c_50,c_75,c_49,c_57,c_56,c_119,c_51,c_3314,c_3820]) ).
tcf(c_314212,negated_conjecture,
memberP(sK3,sK4),
inference(global_subsumption_just,[status(thm)],[c_52,c_4906]) ).
tcf(c_314234,plain,
! [X0: $i] :
( ( app(cons(sK4,nil),X0) = cons(sK4,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_4902,c_65]) ).
tcf(c_314235,plain,
! [X0: $i] :
( ( cons(sK4,X0) = app(sK2,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_314234,c_314210]) ).
tcf(c_314522,plain,
( ( app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3 )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_314212,c_86]) ).
tcf(c_314530,plain,
app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_314522,c_60,c_4902]) ).
tcf(c_314900,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_61,c_113]) ).
tcf(c_315034,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK2),X0)) ),
inference(superposition,[status(thm)],[c_314900,c_94]) ).
tcf(c_315036,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_315034,c_314900]) ).
tcf(c_315037,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_315036,c_75,c_61]) ).
tcf(c_315173,plain,
! [X0: $i,X1: $i] :
( ( cons(sK4,sK10(X0,X1)) = app(sK2,sK10(X0,X1)) )
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(superposition,[status(thm)],[c_85,c_314235]) ).
tcf(c_315576,plain,
! [X0: $i,X1: $i] :
( segmentP(sK3,sK2)
| ~ segmentP(X0,X1)
| ( sK2 != X1 )
| ( sK3 != X0 ) ),
inference(instantiation,[status(thm)],[c_1952]) ).
tcf(c_316587,plain,
! [X0: $i,X1: $i] :
( ( sK3 = X0 )
| ( sK3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1951]) ).
tcf(c_317356,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK3,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK9(sK3,sK4))
| ~ ssList(cons(sK4,sK10(sK3,sK4)))
| ~ segmentP(cons(sK4,sK10(sK3,sK4)),X0) ),
inference(superposition,[status(thm)],[c_314530,c_90]) ).
tcf(c_324041,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_315037,c_39893]) ).
tcf(c_324560,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ( sK3 != sK3 )
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_316587]) ).
tcf(c_326521,plain,
( ( cons(sK4,sK10(sK3,sK4)) = app(sK2,sK10(sK3,sK4)) )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_314212,c_315173]) ).
tcf(c_326538,plain,
cons(sK4,sK10(sK3,sK4)) = app(sK2,sK10(sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_326521,c_60,c_4902]) ).
tcf(c_351543,plain,
( ( sK3 = app(sK3,nil) )
| ( sK3 != sK3 )
| ( app(sK3,nil) != sK3 ) ),
inference(instantiation,[status(thm)],[c_324560]) ).
tcf(c_370658,plain,
! [X0: $i] :
( segmentP(sK3,sK2)
| ~ segmentP(app(sK3,nil),X0)
| ( sK2 != X0 )
| ( sK3 != app(sK3,nil) ) ),
inference(instantiation,[status(thm)],[c_315576]) ).
tcf(c_375779,plain,
( segmentP(sK3,sK2)
| ~ segmentP(app(sK3,nil),sK2)
| ( sK2 != sK2 )
| ( sK3 != app(sK3,nil) ) ),
inference(instantiation,[status(thm)],[c_370658]) ).
tcf(c_379105,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK3,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(cons(sK4,sK10(sK3,sK4)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_317356,c_60,c_4902,c_4906,c_7830,c_7861,c_9805,c_241106]) ).
tcf(c_379107,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK3,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(app(sK2,sK10(sK3,sK4)),X0) ),
inference(light_normalisation,[status(thm)],[c_379105,c_326538]) ).
tcf(c_379125,plain,
! [X0: $i] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(sK10(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_324041,c_379107]) ).
tcf(c_379126,plain,
! [X0: $i] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(X0)
| ~ ssList(sK10(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_379125,c_61]) ).
tcf(c_379140,plain,
( segmentP(app(sK3,nil),sK2)
| ~ ssList(nil)
| ~ ssList(sK10(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_379126]) ).
tcf(c_379141,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_379140,c_375779,c_351543,c_8036,c_7830,c_4906,c_4902,c_4314,c_3049,c_49,c_75,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC368+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 17:52:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.44
% 0.14/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.44
% 0.14/0.44 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 130.55/32.68 % SZS status Started for theBenchmark.p
% 130.55/32.68 % SZS status Theorem for theBenchmark.p
% 130.55/32.68
% 130.55/32.68 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 130.55/32.68
% 130.55/32.68 % ------ iProver source info
% 130.55/32.68
% 130.55/32.68 % git: date: 2026-07-19 20:42:38 +0200
% 130.55/32.68 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 130.55/32.68 % git: non_committed_changes: false
% 130.55/32.68
% 130.55/32.68 % ------ Parsing...
% 130.55/32.68 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 130.55/32.68
% 130.55/32.68 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 130.55/32.68
% 130.55/32.68 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 130.55/32.68
% 130.55/32.68 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 130.55/32.68 % ------ Proving...
% 130.55/32.68 % ------ Problem Properties
% 130.55/32.68
% 130.55/32.68 %
% 130.55/32.68 % clauses 65
% 130.55/32.68 % conjectures 11
% 130.55/32.68 % EPR 29
% 130.55/32.68 % Horn 51
% 130.55/32.68 % unary 9
% 130.55/32.68 % binary 13
% 130.55/32.68 % lits 227
% 130.55/32.68 % lits eq 44
% 130.55/32.68 % fd_pure 0
% 130.55/32.68 % fd_pseudo 0
% 130.55/32.68 % fd_cond 7
% 130.55/32.68 % fd_pseudo_cond 8
% 130.55/32.68 % AC symbols 0
% 130.55/32.68
% 130.55/32.68 % ------ Schedule dynamic 5 is on
% 130.55/32.68
% 130.55/32.68 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 130.55/32.68
% 130.55/32.68
% 130.55/32.68 % ------
% 130.55/32.68 % Current options:
% 130.55/32.68 % ------
% 130.55/32.68
% 130.55/32.68
% 130.55/32.68 %
% 130.55/32.68
% 130.55/32.68 % ------ Proving...
% 130.55/32.68 % Proof_search_loop: time out after: 4366 full_loop iterations
% 130.55/32.68
% 130.55/32.68 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 130.55/32.68
% 130.55/32.68
% 130.55/32.68 % ------
% 130.55/32.68 % Current options:
% 130.55/32.68 % ------
% 130.55/32.68
% 130.55/32.68
% 130.55/32.68 %
% 130.55/32.68
% 130.55/32.68 % ------ Proving...
% 130.55/32.68 % Proof_search_loop: time out after: 5465 full_loop iterations
% 130.55/32.68
% 130.55/32.68 % ------ Option_1: Negative Selections Time Limit: 35.
% 130.55/32.68
% 130.55/32.68
% 130.55/32.68 % ------
% 130.55/32.68 % Current options:
% 130.55/32.68 % ------
% 130.55/32.68
% 130.55/32.68
% 130.55/32.68 %
% 130.55/32.68
% 130.55/32.68 % ------ Proving...
% 130.55/32.68 %
% 130.55/32.68
% 130.55/32.68 % SZS status Theorem for theBenchmark.p
% 130.55/32.68
% 130.55/32.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 130.55/32.69
% 130.55/32.69
%------------------------------------------------------------------------------