%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC119+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 : n004.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 03:07:58 PM UTC 2026
% Result : Theorem 231.56s 35.69s
% Output : CNFRefutation 231.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 135 ( 26 unt; 0 def)
% Number of atoms : 526 ( 147 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 692 ( 301 ~; 288 |; 68 &)
% ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 195 ( 0 sgn 169 !; 26 ?; 66 :)
% 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/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| ( nil = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| 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)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| ( nil = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| 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)
& ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ssItem(X4)
& memberP(X3,X4)
& cons(X4,nil) = X2 ) )
& ( nil != X0
| nil != X1 )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ssItem(X4)
& memberP(X3,X4)
& cons(X4,nil) = X2 ) )
& ( nil != X0
| nil != X1 )
& ( nil != X3
| nil = X2 )
& 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(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f109,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f114,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(f117,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(f118,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,[],[f117]) ).
fof(f124,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(f125,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f134,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) )
& ( ~ neq(sK3,nil)
| ( ssItem(sK4)
& memberP(sK3,sK4)
& sK2 = cons(sK4,nil) ) )
& ( nil != sK0
| nil != sK1 )
& ( nil != sK3
| nil = sK2 )
& 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(f137,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f109]) ).
fof(f143,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,[],[f114]) ).
fof(f144,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,[],[f143]) ).
fof(f145,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))],[f144]) ).
fof(f147,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,[],[f124]) ).
fof(f148,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,[],[f147]) ).
fof(f149,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))],[f148]) ).
fof(f152,plain,
ssList(sK0),
inference(cnf_transformation,[],[f134]) ).
fof(f153,plain,
ssList(sK1),
inference(cnf_transformation,[],[f134]) ).
fof(f156,plain,
( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(cnf_transformation,[],[f134]) ).
fof(f157,plain,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(cnf_transformation,[],[f134]) ).
fof(f158,plain,
( ~ neq(sK3,nil)
| memberP(sK3,sK4) ),
inference(cnf_transformation,[],[f134]) ).
fof(f159,plain,
( ~ neq(sK3,nil)
| sK2 = cons(sK4,nil) ),
inference(cnf_transformation,[],[f134]) ).
fof(f160,plain,
( nil != sK0
| nil != sK1 ),
inference(cnf_transformation,[],[f134]) ).
fof(f161,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f134]) ).
fof(f162,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f134]) ).
fof(f163,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f134]) ).
fof(f167,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f169,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f176,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f178,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f181,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f189,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0 ),
inference(cnf_transformation,[],[f145]) ).
fof(f190,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| ssList(sK10(X0,X1)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f191,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| ssList(sK9(X0,X1)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f196,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,[],[f118]) ).
fof(f203,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,[],[f149]) ).
fof(f204,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f211,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f132]) ).
fof(f213,plain,
( nil != sK2
| nil != sK3 ),
inference(definition_unfolding,[],[f160,f163,f162]) ).
fof(f214,plain,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(definition_unfolding,[],[f156,f162,f163,f162]) ).
fof(f215,plain,
ssList(sK3),
inference(definition_unfolding,[],[f153,f163]) ).
fof(f216,plain,
ssList(sK2),
inference(definition_unfolding,[],[f152,f162]) ).
fof(f222,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,[],[f203]) ).
tcf(c_49,negated_conjecture,
( ( nil = sK2 )
| ( nil != sK3 ) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_50,negated_conjecture,
( ( nil != sK3 )
| ( nil != sK2 ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_51,negated_conjecture,
( ( cons(sK4,nil) = sK2 )
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_52,negated_conjecture,
( memberP(sK3,sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_53,negated_conjecture,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_54,negated_conjecture,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_57,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f215]) ).
tcf(c_58,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f216]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_76,plain,
ssList(nil),
inference(cnf_transformation,[],[f181]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ssList(sK9(X0,X1))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ssList(sK10(X0,X1))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_87,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,[],[f189]) ).
tcf(c_91,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,[],[f196]) ).
tcf(c_95,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,[],[f222]) ).
tcf(c_99,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_106,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_139,negated_conjecture,
nil != sK3,
inference(global_subsumption_just,[status(thm)],[c_49,c_49,c_50]) ).
tcf(c_888,plain,
! [X0: $i,X1: $i] :
( ssItem(sK4)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != sK3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_72]) ).
tcf(c_889,plain,
( ssItem(sK4)
| ( nil = sK3 )
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_888]) ).
tcf(c_890,plain,
ssItem(sK4),
inference(global_subsumption_just,[status(thm)],[c_889,c_57,c_76,c_49,c_50,c_889]) ).
tcf(c_908,plain,
! [X0: $i,X1: $i] :
( memberP(sK3,sK4)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != sK3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_72]) ).
tcf(c_909,plain,
( memberP(sK3,sK4)
| ( nil = sK3 )
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_908]) ).
tcf(c_910,plain,
memberP(sK3,sK4),
inference(global_subsumption_just,[status(thm)],[c_909,c_57,c_76,c_139,c_909]) ).
tcf(c_928,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( cons(sK4,nil) = sK2 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != sK3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_72]) ).
tcf(c_929,plain,
( ( nil = sK3 )
| ( cons(sK4,nil) = sK2 )
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_928]) ).
tcf(c_930,plain,
cons(sK4,nil) = sK2,
inference(global_subsumption_just,[status(thm)],[c_929,c_57,c_76,c_49,c_50,c_929]) ).
tcf(c_949,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK3,sK2)
| ( X1 != sK2 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_72]) ).
tcf(c_950,plain,
( ( nil = sK2 )
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ segmentP(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_949]) ).
tcf(c_951,plain,
( ( nil = sK2 )
| ~ segmentP(sK3,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_950,c_58,c_76,c_950]) ).
tcf(c_1635,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1637,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2444,plain,
app(sK3,nil) = sK3,
inference(superposition,[status(thm)],[c_57,c_99]) ).
tcf(c_2562,plain,
( ~ ssList(nil)
| ~ ssItem(sK4)
| ( nil != sK2 ) ),
inference(superposition,[status(thm)],[c_930,c_64]) ).
tcf(c_2563,plain,
nil != sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_2562,c_76,c_890]) ).
tcf(c_2564,plain,
~ segmentP(sK3,sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_951,c_2563]) ).
tcf(c_3001,plain,
! [X0: $i] :
( ssList(sK9(X0,sK4))
| ~ ssItem(sK4)
| ~ ssList(X0)
| ~ memberP(X0,sK4) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_3067,plain,
! [X0: $i] :
( ssList(sK10(X0,sK4))
| ~ ssItem(sK4)
| ~ ssList(X0)
| ~ memberP(X0,sK4) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_3624,plain,
! [X0: $i,X1: $i] :
( ( sK3 = X0 )
| ( sK3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1637]) ).
tcf(c_3850,plain,
( ( app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3 )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_910,c_87]) ).
tcf(c_3865,plain,
app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_3850,c_57,c_890]) ).
tcf(c_4707,plain,
( ssList(sK9(sK3,sK4))
| ~ ssList(sK3)
| ~ ssItem(sK4)
| ~ memberP(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_3001]) ).
tcf(c_4734,plain,
( ssList(sK10(sK3,sK4))
| ~ ssList(sK3)
| ~ ssItem(sK4)
| ~ memberP(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_3067]) ).
tcf(c_4769,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_3865,c_91]) ).
tcf(c_4956,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_1635]) ).
tcf(c_5207,plain,
sK2 = sK2,
inference(instantiation,[status(thm)],[c_1635]) ).
tcf(c_9274,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ( sK3 != sK3 )
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_3624]) ).
tcf(c_23932,plain,
( ( sK3 = app(sK3,nil) )
| ( sK3 != sK3 )
| ( app(sK3,nil) != sK3 ) ),
inference(instantiation,[status(thm)],[c_9274]) ).
tcf(c_102702,plain,
! [X0: $i,X1: $i] :
( segmentP(sK3,sK2)
| ~ segmentP(X1,X0)
| ( sK3 != X1 )
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_1641]) ).
tcf(c_147415,plain,
! [X0: $i] :
( segmentP(sK3,sK2)
| ~ segmentP(app(sK3,nil),X0)
| ( sK3 != app(sK3,nil) )
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_102702]) ).
tcf(c_158137,plain,
( segmentP(sK3,sK2)
| ~ segmentP(app(sK3,nil),sK2)
| ( sK3 != app(sK3,nil) )
| ( sK2 != sK2 ) ),
inference(instantiation,[status(thm)],[c_147415]) ).
tcf(c_243773,plain,
! [X0: $i] :
( ( app(cons(sK4,nil),X0) = cons(sK4,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_890,c_62]) ).
tcf(c_243774,plain,
! [X0: $i] :
( ( cons(sK4,X0) = app(sK2,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_243773,c_930]) ).
tcf(c_244037,plain,
( ( app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3 )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_910,c_87]) ).
tcf(c_244045,plain,
app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_244037,c_57,c_890]) ).
tcf(c_244444,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_58,c_106]) ).
tcf(c_244609,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK2),X0)) ),
inference(superposition,[status(thm)],[c_244444,c_95]) ).
tcf(c_244630,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_244609,c_244444]) ).
tcf(c_244631,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_244630,c_58,c_76]) ).
tcf(c_244648,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_86,c_243774]) ).
tcf(c_246763,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_244045,c_91]) ).
tcf(c_256025,plain,
( ( cons(sK4,sK10(sK3,sK4)) = app(sK2,sK10(sK3,sK4)) )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_910,c_244648]) ).
tcf(c_256043,plain,
cons(sK4,sK10(sK3,sK4)) = app(sK2,sK10(sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_256025,c_57,c_890]) ).
tcf(c_302338,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK3,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(cons(sK4,sK10(sK3,sK4)),X0)
| ~ ssList(cons(sK4,sK10(sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_246763,c_57,c_76,c_49,c_50,c_889,c_909,c_4707,c_4769]) ).
tcf(c_302339,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK3,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(cons(sK4,sK10(sK3,sK4)))
| ~ segmentP(cons(sK4,sK10(sK3,sK4)),X0) ),
inference(renaming,[status(thm)],[c_302338]) ).
tcf(c_302340,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK3,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK2,sK10(sK3,sK4)))
| ~ segmentP(app(sK2,sK10(sK3,sK4)),X0) ),
inference(light_normalisation,[status(thm)],[c_302339,c_256043]) ).
tcf(c_302360,plain,
! [X0: $i] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(sK10(sK3,sK4))
| ~ ssList(app(sK2,sK10(sK3,sK4))) ),
inference(superposition,[status(thm)],[c_244631,c_302340]) ).
tcf(c_302366,plain,
! [X0: $i] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(X0)
| ~ ssList(sK10(sK3,sK4))
| ~ ssList(app(sK2,sK10(sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_302360,c_58]) ).
tcf(c_302383,plain,
( segmentP(app(sK3,nil),sK2)
| ~ ssList(nil)
| ~ ssList(sK10(sK3,sK4))
| ~ ssList(app(sK2,sK10(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_302366]) ).
tcf(c_328939,plain,
( ssList(app(sK2,sK10(sK3,sK4)))
| ~ ssItem(sK4)
| ~ ssList(sK10(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_256043,c_71]) ).
tcf(c_328953,plain,
( ssList(app(sK2,sK10(sK3,sK4)))
| ~ ssList(sK10(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_328939,c_890]) ).
tcf(c_329049,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_328953,c_302383,c_158137,c_23932,c_5207,c_4956,c_4734,c_2564,c_2444,c_909,c_889,c_139,c_76,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC119+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 16:29:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 231.56/35.69 % SZS status Started for theBenchmark.p
% 231.56/35.69 % SZS status Theorem for theBenchmark.p
% 231.56/35.69
% 231.56/35.69 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 231.56/35.69
% 231.56/35.69 % ------ iProver source info
% 231.56/35.69
% 231.56/35.69 % git: date: 2026-07-19 20:42:38 +0200
% 231.56/35.69 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 231.56/35.69 % git: non_committed_changes: false
% 231.56/35.69
% 231.56/35.69 % ------ Parsing...
% 231.56/35.69 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 231.56/35.69
% 231.56/35.69 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 231.56/35.69
% 231.56/35.69 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 231.56/35.69
% 231.56/35.69 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 231.56/35.69 % ------ Proving...
% 231.56/35.69 % ------ Problem Properties
% 231.56/35.69
% 231.56/35.69 %
% 231.56/35.69 % clauses 52
% 231.56/35.69 % conjectures 3
% 231.56/35.69 % EPR 17
% 231.56/35.69 % Horn 47
% 231.56/35.69 % unary 12
% 231.56/35.69 % binary 6
% 231.56/35.69 % lits 170
% 231.56/35.69 % lits eq 33
% 231.56/35.69 % fd_pure 0
% 231.56/35.69 % fd_pseudo 0
% 231.56/35.69 % fd_cond 5
% 231.56/35.69 % fd_pseudo_cond 6
% 231.56/35.69 % AC symbols 0
% 231.56/35.69
% 231.56/35.69 % ------ Schedule dynamic 5 is on
% 231.56/35.69
% 231.56/35.69 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 231.56/35.69
% 231.56/35.69
% 231.56/35.69 % ------
% 231.56/35.69 % Current options:
% 231.56/35.69 % ------
% 231.56/35.69
% 231.56/35.69
% 231.56/35.69 %
% 231.56/35.69
% 231.56/35.69 % ------ Proving...
% 231.56/35.69 % Proof_search_loop: time out after: 3513 full_loop iterations
% 231.56/35.69
% 231.56/35.69 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 231.56/35.69
% 231.56/35.69
% 231.56/35.69 % ------
% 231.56/35.69 % Current options:
% 231.56/35.69 % ------
% 231.56/35.69
% 231.56/35.69
% 231.56/35.69 %
% 231.56/35.69
% 231.56/35.69 % ------ Proving...
% 231.56/35.69 % Proof_search_loop: time out after: 4725 full_loop iterations
% 231.56/35.69
% 231.56/35.69 % ------ Option_1: Negative Selections Time Limit: 35.
% 231.56/35.69
% 231.56/35.69
% 231.56/35.69 % ------
% 231.56/35.69 % Current options:
% 231.56/35.69 % ------
% 231.56/35.69
% 231.56/35.69
% 231.56/35.69 %
% 231.56/35.69
% 231.56/35.69 % ------ Proving...
% 231.56/35.69 %
% 231.56/35.69
% 231.56/35.69 % SZS status Theorem for theBenchmark.p
% 231.56/35.69
% 231.56/35.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 231.56/35.69
% 231.56/35.69
%------------------------------------------------------------------------------