%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC031+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 : n002.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 03:07:35 PM UTC 2026
% Result : Theorem 10.60s 2.17s
% Output : CNFRefutation 10.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 146 ( 26 unt; 0 def)
% Number of atoms : 494 ( 168 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 583 ( 235 ~; 246 |; 62 &)
% ( 8 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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; 5 con; 0-2 aty)
% Number of variables : 158 ( 0 sgn 138 !; 20 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
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(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
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(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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ? [X4] :
( totalorderedP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| ~ totalorderedP(X2)
| ~ frontsegP(X3,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)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ? [X4] :
( totalorderedP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| ~ totalorderedP(X2)
| ~ frontsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
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(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f126]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f158,plain,
! [X0] :
( ~ ssList(X0)
| ( frontsegP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f175,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(ennf_transformation,[],[f57]) ).
fof(f176,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f180,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f65]) ).
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(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f240,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f241,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X3] :
( app(X1,X3) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f240]) ).
fof(f242,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f241]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f283,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ frontsegP(nil,X0)
| nil = X0 )
& ( nil != X0
| frontsegP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f158]) ).
fof(f285,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f176]) ).
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)
& ( ( nil != sK54
& nil = sK53 )
| ( nil != sK53
& nil = sK54 ) )
& ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,sK55)
| ~ frontsegP(sK56,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4) )
& totalorderedP(sK55)
& frontsegP(sK56,sK55)
& 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(f311,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f242]) ).
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(f396,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f397,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f429,plain,
! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f283]) ).
fof(f442,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(cnf_transformation,[],[f175]) ).
fof(f443,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f444,plain,
! [X0] :
( ~ ssList(X0)
| nil != X0
| segmentP(nil,X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f451,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f180]) ).
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(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil != sK54
| nil != sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK53
| nil = sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,sK55)
| ~ frontsegP(sK56,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
( nil = sK55
| nil = sK56 ),
inference(definition_unfolding,[],[f503,f508,f507]) ).
fof(f512,plain,
( nil != sK56
| nil != sK55 ),
inference(definition_unfolding,[],[f500,f507,f508]) ).
fof(f513,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f508]) ).
fof(f514,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f507]) ).
fof(f518,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f311]) ).
fof(f534,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f444]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f518]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
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_148,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f396]) ).
tcf(c_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_182,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f429]) ).
tcf(c_194,plain,
! [X0: $i] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f442]) ).
tcf(c_195,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f534]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_203,plain,
! [X0: $i] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f451]) ).
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_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f477]) ).
tcf(c_246,negated_conjecture,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f506]) ).
tcf(c_248,negated_conjecture,
! [X0: $i] :
( ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0)
| ~ neq(sK55,X0) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_249,negated_conjecture,
( ( nil = sK55 )
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f509]) ).
tcf(c_250,negated_conjecture,
( ( nil != sK55 )
| ( nil != sK56 ) ),
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_304,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
tcf(c_3698,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ totalorderedP(X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X2,sK55)
| ~ frontsegP(sK56,X2)
| ( X1 != X2 )
| ( X0 != sK55 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_248]) ).
tcf(c_3699,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ ssList(sK55)
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3698]) ).
tcf(c_3701,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ totalorderedP(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3699,c_254,c_3699]) ).
tcf(c_3702,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3701]) ).
tcf(c_9758,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3702]) ).
tcf(c_9759,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_9760,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_9761,negated_conjecture,
( ( nil != sK55 )
| ( nil != sK56 ) ),
inference(demodulation,[status(thm)],[c_250]) ).
tcf(c_9762,negated_conjecture,
( ( nil = sK55 )
| ( nil = sK56 ) ),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_9764,negated_conjecture,
frontsegP(sK56,sK55),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_9767,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_13481,plain,
( frontsegP(nil,sK55)
| ( nil = sK55 ) ),
inference(superposition,[status(thm)],[c_9762,c_9764]) ).
tcf(c_14723,plain,
( ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_13481,c_182]) ).
tcf(c_14724,plain,
nil = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_14723,c_9759]) ).
tcf(c_14725,plain,
nil != sK56,
inference(backward_subsumption_resolution,[status(thm)],[c_9761,c_14724]) ).
tcf(c_14731,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,nil)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_9758,c_14724]) ).
tcf(c_14773,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ frontsegP(sK56,X0) ),
inference(global_subsumption_just,[status(thm)],[c_14731,c_194,c_14731]) ).
tcf(c_15306,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( sK56 != X0 )
| ( nil != X0 ) ),
inference(instantiation,[status(thm)],[c_9767]) ).
tcf(c_15307,plain,
( ( nil = sK56 )
| ( sK56 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_15306]) ).
tcf(c_16096,plain,
( ( nil = sK56 )
| ( hd(sK56) = sK51(sK56) ) ),
inference(superposition,[status(thm)],[c_9760,c_220]) ).
tcf(c_16097,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_16096,c_14725]) ).
tcf(c_16246,plain,
( ssItem(hd(sK56))
| ( sK56 = nil )
| ~ ssList(sK56) ),
inference(instantiation,[status(thm)],[c_149]) ).
tcf(c_16288,plain,
( ( nil = sK56 )
| ( tl(sK56) = sK52(sK56) ) ),
inference(superposition,[status(thm)],[c_9760,c_222]) ).
tcf(c_16289,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_16288,c_14725]) ).
tcf(c_16387,plain,
( ssItem(hd(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_16097,c_219]) ).
tcf(c_16388,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_16387,c_14725,c_9760]) ).
tcf(c_16397,plain,
( ssList(tl(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_16289,c_221]) ).
tcf(c_16398,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_16397,c_14725,c_9760]) ).
tcf(c_18534,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_9760,c_224]) ).
tcf(c_18537,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_18534,c_14725]) ).
tcf(c_18744,plain,
! [X0: $i] :
( ( app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_16388,c_227]) ).
tcf(c_18914,plain,
app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
inference(superposition,[status(thm)],[c_16398,c_18744]) ).
tcf(c_18916,plain,
app(cons(hd(sK56),nil),tl(sK56)) = sK56,
inference(light_normalisation,[status(thm)],[c_18914,c_18537]) ).
tcf(c_19564,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(superposition,[status(thm)],[c_18916,c_377]) ).
tcf(c_19568,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19564,c_16398]) ).
tcf(c_21954,plain,
( ( cons(hd(sK56),nil) = nil )
| ~ totalorderedP(cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(superposition,[status(thm)],[c_19568,c_14773]) ).
tcf(c_23130,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(hd(sK56))
| ( cons(hd(sK56),X0) != nil ) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_23131,plain,
! [X0: $i] :
( ssList(cons(hd(sK56),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_23139,plain,
( totalorderedP(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_203]) ).
tcf(c_23141,plain,
( ssList(cons(hd(sK56),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_23131]) ).
tcf(c_23142,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK56))
| ( cons(hd(sK56),nil) != nil ) ),
inference(instantiation,[status(thm)],[c_23130]) ).
tcf(c_23143,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_23142,c_23141,c_23139,c_21954,c_16246,c_15307,c_14724,c_304,c_250,c_195,c_141,c_253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC031+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n002.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 16:03:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 10.60/2.17 % SZS status Started for theBenchmark.p
% 10.60/2.17 % SZS status Theorem for theBenchmark.p
% 10.60/2.17
% 10.60/2.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.60/2.17
% 10.60/2.17 % ------ iProver source info
% 10.60/2.17
% 10.60/2.17 % git: date: 2026-07-19 20:42:38 +0200
% 10.60/2.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.60/2.17 % git: non_committed_changes: false
% 10.60/2.17
% 10.60/2.17 % ------ Parsing...
% 10.60/2.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.60/2.17
% 10.60/2.17 % ------ 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 %
% 10.60/2.17
% 10.60/2.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.60/2.17
% 10.60/2.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.60/2.17 % ------ Proving...
% 10.60/2.17 % ------ Problem Properties
% 10.60/2.17
% 10.60/2.17 %
% 10.60/2.17 % clauses 187
% 10.60/2.17 % conjectures 6
% 10.60/2.17 % EPR 56
% 10.60/2.17 % Horn 118
% 10.60/2.17 % unary 20
% 10.60/2.17 % binary 42
% 10.60/2.17 % lits 631
% 10.60/2.17 % lits eq 83
% 10.60/2.17 % fd_pure 0
% 10.60/2.17 % fd_pseudo 0
% 10.60/2.17 % fd_cond 22
% 10.60/2.17 % fd_pseudo_cond 14
% 10.60/2.17 % AC symbols 0
% 10.60/2.17
% 10.60/2.17 % ------ Schedule dynamic 5 is on
% 10.60/2.17
% 10.60/2.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.60/2.17
% 10.60/2.17
% 10.60/2.17 % ------
% 10.60/2.17 % Current options:
% 10.60/2.17 % ------
% 10.60/2.17
% 10.60/2.17
% 10.60/2.17 %
% 10.60/2.17
% 10.60/2.17 % ------ Proving...
% 10.60/2.17 %
% 10.60/2.17
% 10.60/2.17 % SZS status Theorem for theBenchmark.p
% 10.60/2.17
% 10.60/2.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.60/2.17
% 10.60/2.17
%------------------------------------------------------------------------------