%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC080+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 : 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 03:07:48 PM UTC 2026
% Result : Theorem 64.29s 12.10s
% Output : CNFRefutation 64.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 90 ( 21 unt; 1 def)
% Number of atoms : 414 ( 62 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 479 ( 198 ~; 189 |; 75 &)
% ( 4 <=>; 13 =>; 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 : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 192 ( 0 sgn 166 !; 26 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
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(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X5] :
( ~ frontsegP(X2,X5)
| ~ frontsegP(X3,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X5] :
( ~ frontsegP(X2,X5)
| ~ frontsegP(X3,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X5] :
( frontsegP(X2,X5)
& frontsegP(X3,X5)
& neq(X5,nil)
& ssList(X5) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f114,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
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(f138,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f139,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f145,plain,
( ssList(sK2)
& ssList(sK3)
& ssList(sK4)
& ( ( ~ neq(sK5,nil)
& neq(sK3,nil) )
| sP0(sK3,sK2,sK5,sK4) )
& sK2 = sK4
& sK3 = sK5
& ssList(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f141]) ).
fof(f153,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,[],[f114]) ).
fof(f154,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,[],[f153]) ).
fof(f155,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK10(X0,X1)) = X0
& ssList(sK10(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X3,sK10(X0,X1))],[f154]) ).
fof(f157,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(f158,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,[],[f157]) ).
fof(f159,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))],[f158]) ).
fof(f168,plain,
ssList(sK2),
inference(cnf_transformation,[],[f145]) ).
fof(f169,plain,
ssList(sK3),
inference(cnf_transformation,[],[f145]) ).
fof(f171,plain,
( ~ neq(sK5,nil)
| sP0(sK3,sK2,sK5,sK4) ),
inference(cnf_transformation,[],[f145]) ).
fof(f172,plain,
( neq(sK3,nil)
| sP0(sK3,sK2,sK5,sK4) ),
inference(cnf_transformation,[],[f145]) ).
fof(f173,plain,
sK2 = sK4,
inference(cnf_transformation,[],[f145]) ).
fof(f174,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f145]) ).
fof(f187,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f198,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(X1,sK10(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f155]) ).
fof(f199,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ssList(sK10(X0,X1)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f211,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,[],[f159]) ).
fof(f225,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f138]) ).
fof(f226,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f227,plain,
( neq(sK5,nil)
| sP0(sK5,sK4,sK5,sK4) ),
inference(definition_unfolding,[],[f172,f174,f173,f174]) ).
fof(f228,plain,
( ~ neq(sK5,nil)
| sP0(sK5,sK4,sK5,sK4) ),
inference(definition_unfolding,[],[f171,f174,f173]) ).
fof(f229,plain,
ssList(sK5),
inference(definition_unfolding,[],[f169,f174]) ).
fof(f230,plain,
ssList(sK4),
inference(definition_unfolding,[],[f168,f173]) ).
fof(f237,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,[],[f211]) ).
tcf(c_56,negated_conjecture,
( neq(sK5,nil)
| sP0(sK5,sK4,sK5,sK4) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_57,negated_conjecture,
( sP0(sK5,sK4,sK5,sK4)
| ~ neq(sK5,nil) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_59,negated_conjecture,
ssList(sK5),
inference(cnf_transformation,[],[f229]) ).
tcf(c_60,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f230]) ).
tcf(c_72,plain,
ssList(nil),
inference(cnf_transformation,[],[f187]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( ssList(sK10(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ( app(X1,sK10(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_93,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,[],[f237]) ).
tcf(c_110,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_153,negated_conjecture,
sP0(sK5,sK4,sK5,sK4),
inference(global_subsumption_just,[status(thm)],[c_56,c_56,c_57]) ).
tcf(c_155,negated_conjecture,
sP0(sK5,sK4,sK5,sK4),
inference(global_subsumption_just,[status(thm)],[c_57,c_153]) ).
tcf(c_27448,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(app(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_31484,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_93,c_111,c_93,c_27448]) ).
tcf(c_108613,plain,
( ssList(sK10(sK4,sK1(sK5,sK4)))
| ~ ssList(sK4)
| ~ ssList(sK1(sK5,sK4))
| ~ frontsegP(sK4,sK1(sK5,sK4)) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_108616,plain,
( ssList(sK10(sK5,sK1(sK5,sK4)))
| ~ ssList(sK5)
| ~ ssList(sK1(sK5,sK4))
| ~ frontsegP(sK5,sK1(sK5,sK4)) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_111473,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_93,c_31484]) ).
fof(f140,definition,
! [X1,X0,X3,X2] :
( ~ sP0(X1,X0,X3,X2)
| ( ? [X5] :
( frontsegP(X2,X5)
& frontsegP(X3,X5)
& neq(X5,nil)
& ssList(X5) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f141,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP0(X1,X0,X3,X2) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(definition_folding,[],[f98,f140]) ).
fof(f142,plain,
! [X1,X0,X3,X2] :
( ~ sP0(X1,X0,X3,X2)
| ( ? [X5] :
( frontsegP(X2,X5)
& frontsegP(X3,X5)
& neq(X5,nil)
& ssList(X5) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f140]) ).
fof(f143,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ? [X5] :
( frontsegP(X3,X5)
& frontsegP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
& ! [X4] :
( ~ segmentP(X1,X4)
| ~ segmentP(X0,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X0,nil) ) ),
inference(rectify,[],[f142]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( frontsegP(X3,sK1(X2,X3))
& frontsegP(X2,sK1(X2,X3))
& neq(sK1(X2,X3),nil)
& ssList(sK1(X2,X3))
& ! [X4] :
( ~ segmentP(X1,X4)
| ~ segmentP(X0,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X5,sK1(X2,X3))],[f143]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| frontsegP(X3,sK1(X2,X3)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| frontsegP(X2,sK1(X2,X3)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f164,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| neq(sK1(X2,X3),nil) ),
inference(cnf_transformation,[],[f144]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f166,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(X0,X1,X2,X3)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK1(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( neq(sK1(X2,X3),nil)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X2,sK1(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X3,sK1(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X3,sK1(X2,X3))
| ( X3 != sK4 )
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_155]) ).
tcf(c_932,plain,
frontsegP(sK4,sK1(sK5,sK4)),
inference(unflattening,[status(thm)],[c_931]) ).
tcf(c_936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X2,sK1(X2,X3))
| ( X3 != sK4 )
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_155]) ).
tcf(c_937,plain,
frontsegP(sK5,sK1(sK5,sK4)),
inference(unflattening,[status(thm)],[c_936]) ).
tcf(c_941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( neq(sK1(X2,X3),nil)
| ( X3 != sK4 )
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_155]) ).
tcf(c_942,plain,
neq(sK1(sK5,sK4),nil),
inference(unflattening,[status(thm)],[c_941]) ).
tcf(c_946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK1(X2,X3))
| ( X3 != sK4 )
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_155]) ).
tcf(c_947,plain,
ssList(sK1(sK5,sK4)),
inference(unflattening,[status(thm)],[c_946]) ).
tcf(c_951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4)
| ( X3 != sK4 )
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_155]) ).
tcf(c_952,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK4,X0)
| ~ segmentP(sK5,X0)
| ~ neq(X0,nil) ),
inference(unflattening,[status(thm)],[c_951]) ).
tcf(c_1027,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK4,X0)
| ~ segmentP(sK5,X0)
| ( nil != nil )
| ( sK1(sK5,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_952,c_942]) ).
tcf(c_1028,plain,
( ~ ssList(sK1(sK5,sK4))
| ~ segmentP(sK4,sK1(sK5,sK4))
| ~ segmentP(sK5,sK1(sK5,sK4)) ),
inference(unflattening,[status(thm)],[c_1027]) ).
tcf(c_108948,plain,
app(nil,sK1(sK5,sK4)) = sK1(sK5,sK4),
inference(superposition,[status(thm)],[c_947,c_110]) ).
tcf(c_109606,plain,
( ( app(sK1(sK5,sK4),sK10(sK4,sK1(sK5,sK4))) = sK4 )
| ~ ssList(sK4)
| ~ ssList(sK1(sK5,sK4)) ),
inference(superposition,[status(thm)],[c_932,c_85]) ).
tcf(c_109607,plain,
( ( app(sK1(sK5,sK4),sK10(sK5,sK1(sK5,sK4))) = sK5 )
| ~ ssList(sK5)
| ~ ssList(sK1(sK5,sK4)) ),
inference(superposition,[status(thm)],[c_937,c_85]) ).
tcf(c_109634,plain,
app(sK1(sK5,sK4),sK10(sK5,sK1(sK5,sK4))) = sK5,
inference(forward_subsumption_resolution,[status(thm)],[c_109607,c_59,c_947]) ).
tcf(c_109635,plain,
app(sK1(sK5,sK4),sK10(sK4,sK1(sK5,sK4))) = sK4,
inference(forward_subsumption_resolution,[status(thm)],[c_109606,c_60,c_947]) ).
tcf(c_111490,plain,
! [X0: $i] :
( segmentP(app(sK1(sK5,sK4),X0),sK1(sK5,sK4))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK1(sK5,sK4)) ),
inference(superposition,[status(thm)],[c_108948,c_111473]) ).
tcf(c_111578,plain,
! [X0: $i] :
( segmentP(app(sK1(sK5,sK4),X0),sK1(sK5,sK4))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111490,c_72,c_947]) ).
tcf(c_116813,plain,
( segmentP(sK4,sK1(sK5,sK4))
| ~ ssList(sK10(sK4,sK1(sK5,sK4))) ),
inference(superposition,[status(thm)],[c_109635,c_111578]) ).
tcf(c_116814,plain,
( segmentP(sK5,sK1(sK5,sK4))
| ~ ssList(sK10(sK5,sK1(sK5,sK4))) ),
inference(superposition,[status(thm)],[c_109634,c_111578]) ).
tcf(c_116839,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_116813,c_116814,c_108616,c_108613,c_1028,c_947,c_937,c_932,c_59,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC080+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 16:19:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 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
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 64.29/12.10 % SZS status Started for theBenchmark.p
% 64.29/12.10 % SZS status Theorem for theBenchmark.p
% 64.29/12.10
% 64.29/12.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 64.29/12.10
% 64.29/12.10 % ------ iProver source info
% 64.29/12.10
% 64.29/12.10 % git: date: 2026-07-19 20:42:38 +0200
% 64.29/12.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 64.29/12.10 % git: non_committed_changes: false
% 64.29/12.10
% 64.29/12.10 % ------ Parsing...
% 64.29/12.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 64.29/12.10
% 64.29/12.10 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 64.29/12.10
% 64.29/12.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 64.29/12.10
% 64.29/12.10 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 64.29/12.10 % ------ Proving...
% 64.29/12.10 % ------ Problem Properties
% 64.29/12.10
% 64.29/12.10 %
% 64.29/12.10 % clauses 57
% 64.29/12.10 % conjectures 2
% 64.29/12.10 % EPR 21
% 64.29/12.10 % Horn 54
% 64.29/12.10 % unary 14
% 64.29/12.10 % binary 8
% 64.29/12.10 % lits 180
% 64.29/12.10 % lits eq 35
% 64.29/12.10 % fd_pure 0
% 64.29/12.10 % fd_pseudo 0
% 64.29/12.10 % fd_cond 7
% 64.29/12.10 % fd_pseudo_cond 7
% 64.29/12.10 % AC symbols 0
% 64.29/12.10
% 64.29/12.10 % ------ Schedule dynamic 5 is on
% 64.29/12.10
% 64.29/12.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 64.29/12.10
% 64.29/12.10
% 64.29/12.10 % ------
% 64.29/12.10 % Current options:
% 64.29/12.10 % ------
% 64.29/12.10
% 64.29/12.10
% 64.29/12.10 %
% 64.29/12.10
% 64.29/12.10 % ------ Proving...
% 64.29/12.10 % Proof_search_loop: time out after: 4624 full_loop iterations
% 64.29/12.10
% 64.29/12.10 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 64.29/12.10
% 64.29/12.10
% 64.29/12.10 % ------
% 64.29/12.10 % Current options:
% 64.29/12.10 % ------
% 64.29/12.10
% 64.29/12.10
% 64.29/12.10 %
% 64.29/12.10
% 64.29/12.10 % ------ Proving...
% 64.29/12.10 %
% 64.29/12.10
% 64.29/12.10 % SZS status Theorem for theBenchmark.p
% 64.29/12.10
% 64.29/12.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 64.29/12.10
% 64.29/12.10
%------------------------------------------------------------------------------