%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC345+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 : n010.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 03:09:23 PM UTC 2026
% Result : Theorem 136.07s 35.26s
% Output : CNFRefutation 136.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 155 ( 29 unt; 0 def)
% Number of atoms : 560 ( 134 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 697 ( 292 ~; 303 |; 69 &)
% ( 4 <=>; 29 =>; 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 208 ( 0 sgn 180 !; 28 ?; 76 :)
% 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(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(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(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax68) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax69) ).
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)
=> ( ( strictorderedP(X0)
& segmentP(X1,X0) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X4,X5)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,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)
=> ( ( strictorderedP(X0)
& segmentP(X1,X0) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X4,X5)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,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)
& ( ~ strictorderedP(X0)
| ~ segmentP(X1,X0) )
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,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)
& ( ~ strictorderedP(X0)
| ~ segmentP(X1,X0) )
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,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(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(f134,plain,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f68]) ).
fof(f137,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f144,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f145,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f169,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ~ strictorderedP(sK0)
| ~ segmentP(sK1,sK0) )
& ( ( nil = sK2
& nil = sK3 )
| ( ssItem(sK4)
& ! [X5] :
( ~ leq(sK4,X5)
| ~ memberP(sK3,X5)
| sK4 = X5
| ~ ssItem(X5) )
& memberP(sK3,sK4)
& sK2 = cons(sK4,nil) ) )
& 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(f176,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(f177,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,[],[f176]) ).
fof(f178,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))],[f177]) ).
fof(f180,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(f181,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,[],[f180]) ).
fof(f182,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))],[f181]) ).
fof(f194,plain,
ssList(sK0),
inference(cnf_transformation,[],[f169]) ).
fof(f195,plain,
ssList(sK1),
inference(cnf_transformation,[],[f169]) ).
fof(f198,plain,
( ~ strictorderedP(sK0)
| ~ segmentP(sK1,sK0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f199,plain,
( nil = sK2
| ssItem(sK4) ),
inference(cnf_transformation,[],[f169]) ).
fof(f200,plain,
( nil = sK3
| ssItem(sK4) ),
inference(cnf_transformation,[],[f169]) ).
fof(f203,plain,
( nil = sK2
| memberP(sK3,sK4) ),
inference(cnf_transformation,[],[f169]) ).
fof(f204,plain,
( nil = sK3
| memberP(sK3,sK4) ),
inference(cnf_transformation,[],[f169]) ).
fof(f205,plain,
( nil = sK2
| sK2 = cons(sK4,nil) ),
inference(cnf_transformation,[],[f169]) ).
fof(f206,plain,
( nil = sK3
| sK2 = cons(sK4,nil) ),
inference(cnf_transformation,[],[f169]) ).
fof(f207,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f169]) ).
fof(f208,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f169]) ).
fof(f212,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f221,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f222,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f230,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0 ),
inference(cnf_transformation,[],[f178]) ).
fof(f231,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| ssList(sK10(X0,X1)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f232,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| ssList(sK9(X0,X1)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f237,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(f238,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f244,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,[],[f182]) ).
fof(f258,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f259,plain,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f268,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f137]) ).
fof(f275,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f276,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f292,plain,
( ~ strictorderedP(sK2)
| ~ segmentP(sK3,sK2) ),
inference(definition_unfolding,[],[f198,f208,f207,f207]) ).
fof(f293,plain,
ssList(sK3),
inference(definition_unfolding,[],[f195,f208]) ).
fof(f294,plain,
ssList(sK2),
inference(definition_unfolding,[],[f194,f207]) ).
fof(f298,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,[],[f244]) ).
tcf(c_49,negated_conjecture,
( ( nil = sK3 )
| ( cons(sK4,nil) = sK2 ) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_50,negated_conjecture,
( ( sK2 = nil )
| ( cons(sK4,nil) = sK2 ) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_51,negated_conjecture,
( memberP(sK3,sK4)
| ( nil = sK3 ) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_52,negated_conjecture,
( memberP(sK3,sK4)
| ( sK2 = nil ) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_55,negated_conjecture,
( ssItem(sK4)
| ( nil = sK3 ) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_56,negated_conjecture,
( ssItem(sK4)
| ( sK2 = nil ) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_57,negated_conjecture,
( ~ strictorderedP(sK2)
| ~ segmentP(sK3,sK2) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_60,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f293]) ).
tcf(c_61,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f294]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_75,plain,
ssList(nil),
inference(cnf_transformation,[],[f222]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( ssList(sK9(X0,X1))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ssList(sK10(X0,X1))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
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,[],[f230]) ).
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,[],[f237]) ).
tcf(c_91,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f238]) ).
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,[],[f298]) ).
tcf(c_110,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f258]) ).
tcf(c_111,plain,
! [X0: $i] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_120,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_127,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_145,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_2728,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2730,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2736,plain,
! [X0: $i,X1: $i] :
( strictorderedP(X0)
| ~ strictorderedP(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4242,plain,
( strictorderedP(sK2)
| ( sK2 = nil )
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_50,c_111]) ).
tcf(c_4250,plain,
( strictorderedP(sK2)
| ( sK2 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_4242,c_56,c_4242]) ).
tcf(c_4334,plain,
app(sK3,nil) = sK3,
inference(superposition,[status(thm)],[c_60,c_120]) ).
tcf(c_4452,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_61,c_127]) ).
tcf(c_5117,plain,
! [X0: $i] :
( strictorderedP(sK2)
| ~ strictorderedP(X0)
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_2736]) ).
tcf(c_5118,plain,
( strictorderedP(sK2)
| ~ strictorderedP(nil)
| ( sK2 != nil ) ),
inference(instantiation,[status(thm)],[c_5117]) ).
tcf(c_6095,negated_conjecture,
~ segmentP(sK3,sK2),
inference(global_subsumption_just,[status(thm)],[c_57,c_110,c_57,c_4250,c_5118]) ).
tcf(c_6258,plain,
! [X0: $i,X1: $i] :
( segmentP(sK3,sK2)
| ~ segmentP(X1,X0)
| ( sK3 != X1 )
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_2735]) ).
tcf(c_8941,plain,
! [X0: $i] :
( segmentP(sK3,sK2)
| ~ segmentP(sK3,X0)
| ( sK3 != sK3 )
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_6258]) ).
tcf(c_8942,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_2728]) ).
tcf(c_8943,plain,
( segmentP(sK3,sK2)
| ~ segmentP(sK3,nil)
| ( sK3 != sK3 )
| ( sK2 != nil ) ),
inference(instantiation,[status(thm)],[c_8941]) ).
tcf(c_8944,plain,
! [X0: $i,X1: $i] :
( ( sK3 = X0 )
| ( sK3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_2730]) ).
tcf(c_10998,plain,
( ( sK2 = nil )
| ( app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3 )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_52,c_86]) ).
tcf(c_10999,plain,
( ( nil = sK3 )
| ( app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3 )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_51,c_86]) ).
tcf(c_11026,plain,
( ( nil = sK3 )
| ( app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3 )
| ~ ssItem(sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10999,c_60]) ).
tcf(c_11030,plain,
( ( sK2 = nil )
| ( app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3 )
| ~ ssItem(sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10998,c_60]) ).
tcf(c_14155,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK3,X1),X0)
| ~ ssList(sK3)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(superposition,[status(thm)],[c_4334,c_90]) ).
tcf(c_14218,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK3,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14155,c_60,c_75]) ).
tcf(c_14554,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_4452,c_94]) ).
tcf(c_14595,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_14554,c_4452]) ).
tcf(c_14596,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14595,c_75,c_61]) ).
tcf(c_18705,plain,
! [X0: $i] :
( segmentP(sK3,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(superposition,[status(thm)],[c_4334,c_14218]) ).
tcf(c_18709,plain,
! [X0: $i] :
( segmentP(sK3,X0)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18705,c_75]) ).
tcf(c_18731,plain,
( segmentP(sK3,nil)
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_18709]) ).
tcf(c_23359,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ( sK3 != sK3 )
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_8944]) ).
tcf(c_23556,plain,
sK2 = sK2,
inference(instantiation,[status(thm)],[c_2728]) ).
tcf(c_26730,plain,
( ssList(sK9(sK3,sK4))
| ~ ssList(sK3)
| ~ ssItem(sK4)
| ~ memberP(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_27313,plain,
( ssList(sK10(sK3,sK4))
| ~ ssList(sK3)
| ~ ssItem(sK4)
| ~ memberP(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_27805,plain,
app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3,
inference(global_subsumption_just,[status(thm)],[c_11026,c_110,c_75,c_56,c_145,c_57,c_4250,c_5118,c_8943,c_8942,c_11030,c_18731]) ).
tcf(c_27809,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_27805,c_90]) ).
tcf(c_88601,plain,
( ( sK3 = app(sK3,nil) )
| ( sK3 != sK3 )
| ( app(sK3,nil) != sK3 ) ),
inference(instantiation,[status(thm)],[c_23359]) ).
tcf(c_186000,plain,
! [X0: $i] :
( ssList(app(sK2,X0))
| ~ ssList(sK2)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_199088,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_61,c_127]) ).
tcf(c_199584,plain,
! [X0: $i] :
( ssList(cons(sK4,X0))
| ~ ssItem(sK4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_199854,plain,
! [X0: $i,X1: $i] :
( segmentP(sK3,sK2)
| ~ segmentP(X1,X0)
| ( sK3 != X1 )
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_2735]) ).
tcf(c_200533,negated_conjecture,
ssItem(sK4),
inference(global_subsumption_just,[status(thm)],[c_55,c_110,c_75,c_56,c_145,c_57,c_4250,c_5118,c_8943,c_8942,c_18731]) ).
tcf(c_206219,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_199088,c_94]) ).
tcf(c_206263,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_206219,c_199088]) ).
tcf(c_206264,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_206263,c_75,c_61]) ).
tcf(c_207111,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_206264,c_61,c_14596,c_186000]) ).
tcf(c_246490,plain,
! [X0: $i] :
( segmentP(sK3,sK2)
| ~ segmentP(app(sK3,nil),X0)
| ( sK3 != app(sK3,nil) )
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_199854]) ).
tcf(c_257478,plain,
( segmentP(sK3,sK2)
| ~ segmentP(app(sK3,nil),sK2)
| ( sK3 != app(sK3,nil) )
| ( sK2 != sK2 ) ),
inference(instantiation,[status(thm)],[c_246490]) ).
tcf(c_262629,plain,
( ssList(cons(sK4,sK10(sK3,sK4)))
| ~ ssItem(sK4)
| ~ ssList(sK10(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_199584]) ).
tcf(c_372405,negated_conjecture,
cons(sK4,nil) = sK2,
inference(global_subsumption_just,[status(thm)],[c_49,c_110,c_75,c_145,c_57,c_50,c_4250,c_5118,c_8943,c_8942,c_18731]) ).
tcf(c_372407,negated_conjecture,
memberP(sK3,sK4),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_145,c_52,c_6095,c_8943,c_8942,c_18731]) ).
tcf(c_372461,plain,
! [X0: $i] :
( ( app(cons(sK4,nil),X0) = cons(sK4,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_200533,c_65]) ).
tcf(c_372462,plain,
! [X0: $i] :
( ( cons(sK4,X0) = app(sK2,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_372461,c_372405]) ).
tcf(c_372720,plain,
( ( app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3 )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_372407,c_86]) ).
tcf(c_372728,plain,
app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4))) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_372720,c_60,c_200533]) ).
tcf(c_373135,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_61,c_127]) ).
tcf(c_373231,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_373135,c_94]) ).
tcf(c_373233,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_373231,c_373135]) ).
tcf(c_373234,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_373233,c_75,c_61]) ).
tcf(c_373694,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_372462]) ).
tcf(c_377244,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_372728,c_90]) ).
tcf(c_383524,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_373234,c_207111]) ).
tcf(c_391271,plain,
( ( cons(sK4,sK10(sK3,sK4)) = app(sK2,sK10(sK3,sK4)) )
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_372407,c_373694]) ).
tcf(c_391282,plain,
cons(sK4,sK10(sK3,sK4)) = app(sK2,sK10(sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_391271,c_60,c_200533]) ).
tcf(c_475042,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_377244,c_60,c_75,c_56,c_145,c_52,c_6095,c_8943,c_8942,c_18731,c_26730,c_27313,c_27809,c_262629]) ).
tcf(c_475044,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_475042,c_391282]) ).
tcf(c_475062,plain,
! [X0: $i] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(sK10(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_383524,c_475044]) ).
tcf(c_475063,plain,
! [X0: $i] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(X0)
| ~ ssList(sK10(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_475062,c_61]) ).
tcf(c_475077,plain,
( segmentP(app(sK3,nil),sK2)
| ~ ssList(nil)
| ~ ssList(sK10(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_475063]) ).
tcf(c_475078,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_475077,c_257478,c_88601,c_27313,c_23556,c_18731,c_8942,c_8943,c_6095,c_4334,c_52,c_145,c_56,c_75,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC345+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/1.03 % Computer : n010.cluster.edu
% 0.11/1.03 % Model : x86_64 x86_64
% 0.11/1.03 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/1.03 % Memory : 8046.5625MB
% 0.11/1.03 % OS : Linux 6.8.0-71-generic
% 0.04/1.03 % CPULimit : 300
% 0.04/1.03 % WCLimit : 300
% 0.04/1.03 % DateTime : Thu Sep 24 17:45:27 UTC 2026
% 0.04/1.03 % CPUTime :
% 0.04/1.03 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/1.07 Running first-order theorem proving
% 0.04/1.07 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
% 0.04/1.08
% 0.04/1.08 % ======== iProver multi-core TPTP/SMT =========
% 0.04/1.08
% 0.04/1.08 % Detected problem language: tptp
% 0.04/1.09 % Proving...
% 136.07/35.26 % SZS status Started for theBenchmark.p
% 136.07/35.26 % SZS status Theorem for theBenchmark.p
% 136.07/35.26
% 136.07/35.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 136.07/35.26
% 136.07/35.26 % ------ iProver source info
% 136.07/35.26
% 136.07/35.26 % git: date: 2026-07-19 20:42:38 +0200
% 136.07/35.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 136.07/35.26 % git: non_committed_changes: false
% 136.07/35.26
% 136.07/35.26 % ------ Parsing...
% 136.07/35.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 136.07/35.26
% 136.07/35.26 % ------ 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 %
% 136.07/35.26
% 136.07/35.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 136.07/35.26
% 136.07/35.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 136.07/35.26 % ------ Proving...
% 136.07/35.26 % ------ Problem Properties
% 136.07/35.26
% 136.07/35.26 %
% 136.07/35.26 % clauses 90
% 136.07/35.26 % conjectures 11
% 136.07/35.26 % EPR 30
% 136.07/35.26 % Horn 57
% 136.07/35.26 % unary 9
% 136.07/35.26 % binary 15
% 136.07/35.26 % lits 318
% 136.07/35.26 % lits eq 69
% 136.07/35.26 % fd_pure 0
% 136.07/35.26 % fd_pseudo 0
% 136.07/35.26 % fd_cond 18
% 136.07/35.26 % fd_pseudo_cond 9
% 136.07/35.26 % AC symbols 0
% 136.07/35.26
% 136.07/35.26 % ------ Schedule dynamic 5 is on
% 136.07/35.26
% 136.07/35.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 136.07/35.26
% 136.07/35.26
% 136.07/35.26 % ------
% 136.07/35.26 % Current options:
% 136.07/35.26 % ------
% 136.07/35.26
% 136.07/35.26
% 136.07/35.26 %
% 136.07/35.26
% 136.07/35.26 % ------ Proving...
% 136.07/35.26 % Proof_search_loop: time out after: 7463 full_loop iterations
% 136.07/35.26
% 136.07/35.26 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 136.07/35.26
% 136.07/35.26
% 136.07/35.26 % ------
% 136.07/35.26 % Current options:
% 136.07/35.26 % ------
% 136.07/35.26
% 136.07/35.26
% 136.07/35.26 %
% 136.07/35.26
% 136.07/35.26 % ------ Proving...
% 136.07/35.26 % Proof_search_loop: time out after: 8806 full_loop iterations
% 136.07/35.26
% 136.07/35.26 % ------ Option_1: Negative Selections Time Limit: 35.
% 136.07/35.26
% 136.07/35.26
% 136.07/35.26 % ------
% 136.07/35.26 % Current options:
% 136.07/35.26 % ------
% 136.07/35.26
% 136.07/35.26
% 136.07/35.26 %
% 136.07/35.26
% 136.07/35.26 % ------ Proving...
% 136.07/35.26 %
% 136.07/35.26
% 136.07/35.26 % SZS status Theorem for theBenchmark.p
% 136.07/35.26
% 136.07/35.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 136.07/35.27
% 136.07/35.27
%------------------------------------------------------------------------------