%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC071+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 : n013.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 03:07:46 PM UTC 2026
% Result : Theorem 4.56s 1.20s
% Output : CNFRefutation 4.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 86 ( 21 unt; 1 def)
% Number of atoms : 399 ( 111 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 519 ( 206 ~; 184 |; 104 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn 125 !; 41 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
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(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ? [X9] :
( lt(X9,X5)
& memberP(X7,X9)
& ssItem(X9) )
| ? [X8] :
( lt(X5,X8)
& memberP(X6,X8)
& ssItem(X8) )
| app(app(X6,X2),X7) != X3
| cons(X5,nil) != X2 ) ) ) ) )
| ( nil = X0
& nil = X1 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ? [X9] :
( lt(X9,X5)
& memberP(X7,X9)
& ssItem(X9) )
| ? [X8] :
( lt(X5,X8)
& memberP(X6,X8)
& ssItem(X8) )
| app(app(X6,X2),X7) != X3
| cons(X5,nil) != X2 ) ) ) ) )
| ( nil = X0
& nil = X1 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ! [X9] :
( ~ lt(X9,X5)
| ~ memberP(X7,X9)
| ~ ssItem(X9) )
& ! [X8] :
( ~ lt(X5,X8)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& app(app(X6,X2),X7) = X3
& cons(X5,nil) = X2 ) ) ) )
& ( nil != X0
| nil != X1 )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ! [X9] :
( ~ lt(X9,X5)
| ~ memberP(X7,X9)
| ~ ssItem(X9) )
& ! [X8] :
( ~ lt(X5,X8)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& app(app(X6,X2),X7) = X3
& cons(X5,nil) = X2 ) ) ) )
& ( nil != X0
| nil != X1 )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f128,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f133,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(f154,plain,
( ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ssList(sK7)
& ( ( nil = sK6
& nil = sK7 )
| sP0(sK6,sK7) )
& ( nil != sK4
| nil != sK5 )
& ! [X4] :
( ~ segmentP(sK4,X4)
| ~ segmentP(sK5,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& sK4 = sK6
& sK5 = sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f150]) ).
fof(f159,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f169,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,[],[f133]) ).
fof(f170,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,[],[f169]) ).
fof(f171,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
& ssList(sK15(X0,X1))
& ssList(sK14(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X4,sK14(X0,X1)),skolemize(X5,sK15(X0,X1))],[f170]) ).
fof(f181,plain,
ssList(sK4),
inference(cnf_transformation,[],[f154]) ).
fof(f182,plain,
ssList(sK5),
inference(cnf_transformation,[],[f154]) ).
fof(f185,plain,
( nil = sK6
| sP0(sK6,sK7) ),
inference(cnf_transformation,[],[f154]) ).
fof(f186,plain,
( nil = sK7
| sP0(sK6,sK7) ),
inference(cnf_transformation,[],[f154]) ).
fof(f187,plain,
( nil != sK4
| nil != sK5 ),
inference(cnf_transformation,[],[f154]) ).
fof(f188,plain,
! [X4] :
( ~ segmentP(sK4,X4)
| ~ segmentP(sK5,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f154]) ).
fof(f189,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f154]) ).
fof(f190,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f154]) ).
fof(f196,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f214,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
fof(f217,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f233,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f239,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,[],[f171]) ).
fof(f251,plain,
! [X4] :
( ~ segmentP(sK6,X4)
| ~ segmentP(sK7,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f188,f190,f189]) ).
fof(f252,plain,
( nil != sK6
| nil != sK7 ),
inference(definition_unfolding,[],[f187,f190,f189]) ).
fof(f253,plain,
ssList(sK7),
inference(definition_unfolding,[],[f182,f190]) ).
fof(f254,plain,
ssList(sK6),
inference(definition_unfolding,[],[f181,f189]) ).
fof(f262,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,[],[f239]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK6,X0)
| ~ segmentP(sK7,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_57,negated_conjecture,
( ( nil != sK6 )
| ( nil != sK7 ) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_58,negated_conjecture,
( sP0(sK6,sK7)
| ( nil = sK7 ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_59,negated_conjecture,
( sP0(sK6,sK7)
| ( nil = sK6 ) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_62,negated_conjecture,
ssList(sK7),
inference(cnf_transformation,[],[f253]) ).
tcf(c_63,negated_conjecture,
ssList(sK6),
inference(cnf_transformation,[],[f254]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_90,plain,
ssList(nil),
inference(cnf_transformation,[],[f217]) ).
tcf(c_106,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_109,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,[],[f262]) ).
tcf(c_166,negated_conjecture,
sP0(sK6,sK7),
inference(global_subsumption_just,[status(thm)],[c_59,c_59,c_58,c_57]) ).
tcf(c_168,negated_conjecture,
sP0(sK6,sK7),
inference(global_subsumption_just,[status(thm)],[c_58,c_166]) ).
tcf(c_1209,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK6,X0)
| ~ segmentP(sK7,X0)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_86]) ).
tcf(c_1210,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK6,X0)
| ~ segmentP(sK7,X0) ),
inference(unflattening,[status(thm)],[c_1209]) ).
tcf(c_1212,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK7,X0)
| ~ segmentP(sK6,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1210,c_90,c_1210]) ).
tcf(c_1213,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK6,X0)
| ~ segmentP(sK7,X0) ),
inference(renaming,[status(thm)],[c_1212]) ).
tcf(c_3192,plain,
( ( nil = sK6 )
| ~ ssList(sK6)
| ~ segmentP(sK7,sK6) ),
inference(superposition,[status(thm)],[c_106,c_1213]) ).
tcf(c_3193,plain,
( ( nil = sK6 )
| ~ segmentP(sK7,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3192,c_63]) ).
fof(f149,definition,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ! [X9] :
( ~ lt(X9,X5)
| ~ memberP(X7,X9)
| ~ ssItem(X9) )
& ! [X8] :
( ~ lt(X5,X8)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& app(app(X6,X2),X7) = X3
& cons(X5,nil) = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f150,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ( nil != X0
| nil != X1 )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f99,f149]) ).
fof(f151,plain,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ! [X9] :
( ~ lt(X9,X5)
| ~ memberP(X7,X9)
| ~ ssItem(X9) )
& ! [X8] :
( ~ lt(X5,X8)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& app(app(X6,X2),X7) = X3
& cons(X5,nil) = X2 ) ) ) ),
inference(nnf_transformation,[],[f149]) ).
fof(f152,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& ! [X6] :
( ~ lt(X6,X2)
| ~ memberP(X4,X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(X2,X5)
| ~ memberP(X3,X5)
| ~ ssItem(X5) )
& app(app(X3,X0),X4) = X1
& cons(X2,nil) = X0 ) ) ) ),
inference(rectify,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( ssItem(sK1(X0,X1))
& ssList(sK2(X0,X1))
& ssList(sK3(X0,X1))
& ! [X6] :
( ~ lt(X6,sK1(X0,X1))
| ~ memberP(sK3(X0,X1),X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(sK1(X0,X1),X5)
| ~ memberP(sK2(X0,X1),X5)
| ~ ssItem(X5) )
& app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
& cons(sK1(X0,X1),nil) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1)),skolemize(X4,sK3(X0,X1))],[f152]) ).
fof(f174,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssItem(sK1(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f175,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK2(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f176,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK3(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f153]) ).
fof(f180,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| cons(sK1(X0,X1),nil) = X0 ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( cons(sK1(X0,X1),nil) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ssList(sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ssList(sK2(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_1128,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_168]) ).
tcf(c_1129,plain,
ssItem(sK1(sK6,sK7)),
inference(unflattening,[status(thm)],[c_1128]) ).
tcf(c_1133,plain,
! [X0: $i,X1: $i] :
( ssList(sK2(X0,X1))
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_168]) ).
tcf(c_1134,plain,
ssList(sK2(sK6,sK7)),
inference(unflattening,[status(thm)],[c_1133]) ).
tcf(c_1138,plain,
! [X0: $i,X1: $i] :
( ssList(sK3(X0,X1))
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_168]) ).
tcf(c_1139,plain,
ssList(sK3(sK6,sK7)),
inference(unflattening,[status(thm)],[c_1138]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i] :
( ( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_168]) ).
tcf(c_1168,plain,
app(app(sK2(sK6,sK7),sK6),sK3(sK6,sK7)) = sK7,
inference(unflattening,[status(thm)],[c_1167]) ).
tcf(c_1172,plain,
! [X0: $i,X1: $i] :
( ( cons(sK1(X0,X1),nil) = X0 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_168]) ).
tcf(c_1173,plain,
cons(sK1(sK6,sK7),nil) = sK6,
inference(unflattening,[status(thm)],[c_1172]) ).
tcf(c_3311,plain,
( ~ ssList(nil)
| ~ ssItem(sK1(sK6,sK7))
| ( nil != sK6 ) ),
inference(superposition,[status(thm)],[c_1173,c_69]) ).
tcf(c_3312,plain,
nil != sK6,
inference(forward_subsumption_resolution,[status(thm)],[c_3311,c_90,c_1129]) ).
tcf(c_3313,plain,
~ segmentP(sK7,sK6),
inference(backward_subsumption_resolution,[status(thm)],[c_3193,c_3312]) ).
tcf(c_7243,plain,
( segmentP(sK7,sK6)
| ~ ssList(sK6)
| ~ ssList(sK3(sK6,sK7))
| ~ ssList(sK2(sK6,sK7))
| ~ ssList(app(app(sK2(sK6,sK7),sK6),sK3(sK6,sK7))) ),
inference(superposition,[status(thm)],[c_1168,c_109]) ).
tcf(c_7407,plain,
( segmentP(sK7,sK6)
| ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssList(sK3(sK6,sK7))
| ~ ssList(sK2(sK6,sK7)) ),
inference(light_normalisation,[status(thm)],[c_7243,c_1168]) ).
tcf(c_7408,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7407,c_3313,c_63,c_62,c_1139,c_1134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC071+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 : n013.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 16:13:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 4.56/1.20 % SZS status Started for theBenchmark.p
% 4.56/1.20 % SZS status Theorem for theBenchmark.p
% 4.56/1.20
% 4.56/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.56/1.20
% 4.56/1.20 % ------ iProver source info
% 4.56/1.20
% 4.56/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 4.56/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.56/1.20 % git: non_committed_changes: false
% 4.56/1.20
% 4.56/1.20 % ------ Parsing...
% 4.56/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.56/1.20
% 4.56/1.20 % ------ 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 %
% 4.56/1.20
% 4.56/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.56/1.20
% 4.56/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.56/1.20 % ------ Proving...
% 4.56/1.20 % ------ Problem Properties
% 4.56/1.20
% 4.56/1.20 %
% 4.56/1.20 % clauses 65
% 4.56/1.20 % conjectures 3
% 4.56/1.20 % EPR 24
% 4.56/1.20 % Horn 59
% 4.56/1.20 % unary 13
% 4.56/1.20 % binary 8
% 4.56/1.20 % lits 221
% 4.56/1.20 % lits eq 37
% 4.56/1.20 % fd_pure 0
% 4.56/1.20 % fd_pseudo 0
% 4.56/1.20 % fd_cond 6
% 4.56/1.20 % fd_pseudo_cond 8
% 4.56/1.20 % AC symbols 0
% 4.56/1.20
% 4.56/1.20 % ------ Schedule dynamic 5 is on
% 4.56/1.20
% 4.56/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.56/1.20
% 4.56/1.20
% 4.56/1.20 % ------
% 4.56/1.20 % Current options:
% 4.56/1.20 % ------
% 4.56/1.20
% 4.56/1.20
% 4.56/1.20 %
% 4.56/1.20
% 4.56/1.20 % ------ Proving...
% 4.56/1.20 %
% 4.56/1.20
% 4.56/1.20 % SZS status Theorem for theBenchmark.p
% 4.56/1.20
% 4.56/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.56/1.21
% 4.56/1.21
%------------------------------------------------------------------------------