%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC002+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 : n011.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 03:07:27 PM UTC 2026
% Result : Theorem 0.74s 1.18s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 95 ( 16 unt; 2 def)
% Number of atoms : 511 ( 144 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 724 ( 308 ~; 294 |; 106 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 6 ( 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; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 280 ( 0 sgn 240 !; 40 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X11] :
( geq(X11,X8)
& memberP(X3,X11)
& X8 != X11
& ssItem(X11) )
| app(X9,X10) != X2
| app(app(X9,cons(X8,nil)),X10) != X3 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( X4 = X7
| ~ geq(X7,X4)
| ~ memberP(X1,X7) ) )
& app(X5,X6) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| 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)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X11] :
( geq(X11,X8)
& memberP(X3,X11)
& X8 != X11
& ssItem(X11) )
| app(X9,X10) != X2
| app(app(X9,cons(X8,nil)),X10) != X3 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( X4 = X7
| ~ geq(X7,X4)
| ~ memberP(X1,X7) ) )
& app(X5,X6) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| 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)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X11] :
( ~ geq(X11,X8)
| ~ memberP(X3,X11)
| X8 = X11
| ~ ssItem(X11) )
& app(X9,X10) = X2
& app(app(X9,cons(X8,nil)),X10) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& X4 != X7
& geq(X7,X4)
& memberP(X1,X7) )
| app(X5,X6) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X11] :
( ~ geq(X11,X8)
| ~ memberP(X3,X11)
| X8 = X11
| ~ ssItem(X11) )
& app(X9,X10) = X2
& app(app(X9,cons(X8,nil)),X10) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& X4 != X7
& geq(X7,X4)
& memberP(X1,X7) )
| app(X5,X6) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f148,plain,
! [X1,X0,X2,X3] :
( ~ sP1(X1,X0,X2,X3)
| ( sP0(X3,X2)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& X4 != X7
& geq(X7,X4)
& memberP(X1,X7) )
| app(X5,X6) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f146]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( ~ sP1(X0,X1,X2,X3)
| ( sP0(X3,X2)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& X4 != X7
& geq(X7,X4)
& memberP(X0,X7) )
| app(X5,X6) != X1
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(rectify,[],[f148]) ).
fof(f150,plain,
! [X0,X1,X2,X3] :
( ~ sP1(X0,X1,X2,X3)
| ( sP0(X3,X2)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ssItem(sK2(X0,X4))
& sK2(X0,X4) != X4
& geq(sK2(X0,X4),X4)
& memberP(X0,sK2(X0,X4)) )
| app(X5,X6) != X1
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X7,sK2(X0,X4))],[f149]) ).
fof(f154,plain,
( ssList(sK6)
& ssList(sK7)
& ssList(sK8)
& ssList(sK9)
& ( ( ~ neq(sK9,nil)
& neq(sK7,nil) )
| sP1(sK7,sK6,sK8,sK9) )
& sK6 = sK8
& sK7 = sK9 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f147]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1,X2,X3)
| sP0(X3,X2) ),
inference(cnf_transformation,[],[f150]) ).
fof(f172,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(X0,X1,X2,X3)
| ssItem(sK2(X0,X4))
| app(X5,X6) != X1
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f150]) ).
fof(f173,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(X0,X1,X2,X3)
| sK2(X0,X4) != X4
| app(X5,X6) != X1
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f150]) ).
fof(f174,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(X0,X1,X2,X3)
| geq(sK2(X0,X4),X4)
| app(X5,X6) != X1
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f150]) ).
fof(f175,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(X0,X1,X2,X3)
| memberP(X0,sK2(X0,X4))
| app(X5,X6) != X1
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f150]) ).
fof(f187,plain,
( ~ neq(sK9,nil)
| sP1(sK7,sK6,sK8,sK9) ),
inference(cnf_transformation,[],[f154]) ).
fof(f188,plain,
( neq(sK7,nil)
| sP1(sK7,sK6,sK8,sK9) ),
inference(cnf_transformation,[],[f154]) ).
fof(f189,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f154]) ).
fof(f190,plain,
sK7 = sK9,
inference(cnf_transformation,[],[f154]) ).
fof(f245,plain,
( neq(sK9,nil)
| sP1(sK9,sK8,sK8,sK9) ),
inference(definition_unfolding,[],[f188,f190,f189,f190]) ).
fof(f246,plain,
( ~ neq(sK9,nil)
| sP1(sK9,sK8,sK8,sK9) ),
inference(definition_unfolding,[],[f187,f190,f189]) ).
fof(f249,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ sP1(app(app(X5,cons(X4,nil)),X6),X1,X2,X3)
| memberP(app(app(X5,cons(X4,nil)),X6),sK2(app(app(X5,cons(X4,nil)),X6),X4))
| app(X5,X6) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f175]) ).
fof(f250,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP1(app(app(X5,cons(X4,nil)),X6),app(X5,X6),X2,X3)
| memberP(app(app(X5,cons(X4,nil)),X6),sK2(app(app(X5,cons(X4,nil)),X6),X4))
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f249]) ).
fof(f251,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ sP1(app(app(X5,cons(X4,nil)),X6),X1,X2,X3)
| geq(sK2(app(app(X5,cons(X4,nil)),X6),X4),X4)
| app(X5,X6) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f174]) ).
fof(f252,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP1(app(app(X5,cons(X4,nil)),X6),app(X5,X6),X2,X3)
| geq(sK2(app(app(X5,cons(X4,nil)),X6),X4),X4)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f251]) ).
fof(f253,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ sP1(app(app(X5,cons(X4,nil)),X6),X1,X2,X3)
| sK2(app(app(X5,cons(X4,nil)),X6),X4) != X4
| app(X5,X6) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f173]) ).
fof(f254,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP1(app(app(X5,cons(X4,nil)),X6),app(X5,X6),X2,X3)
| sK2(app(app(X5,cons(X4,nil)),X6),X4) != X4
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f253]) ).
fof(f255,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ sP1(app(app(X5,cons(X4,nil)),X6),X1,X2,X3)
| ssItem(sK2(app(app(X5,cons(X4,nil)),X6),X4))
| app(X5,X6) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f172]) ).
fof(f256,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP1(app(app(X5,cons(X4,nil)),X6),app(X5,X6),X2,X3)
| ssItem(sK2(app(app(X5,cons(X4,nil)),X6),X4))
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f255]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( memberP(app(app(X0,cons(X1,nil)),X2),sK2(app(app(X0,cons(X1,nil)),X2),X1))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ sP1(app(app(X0,cons(X1,nil)),X2),app(X0,X2),X3,X4) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( geq(sK2(app(app(X0,cons(X1,nil)),X2),X1),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ sP1(app(app(X0,cons(X1,nil)),X2),app(X0,X2),X3,X4) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ sP1(app(app(X0,cons(X1,nil)),X2),app(X0,X2),X3,X4)
| ( sK2(app(app(X0,cons(X1,nil)),X2),X1) != X1 ) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ssItem(sK2(app(app(X0,cons(X1,nil)),X2),X1))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ sP1(app(app(X0,cons(X1,nil)),X2),app(X0,X2),X3,X4) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X3,X2)
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_61,negated_conjecture,
( neq(sK9,nil)
| sP1(sK9,sK8,sK8,sK9) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_62,negated_conjecture,
( sP1(sK9,sK8,sK8,sK9)
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_161,negated_conjecture,
sP1(sK9,sK8,sK8,sK9),
inference(global_subsumption_just,[status(thm)],[c_61,c_61,c_62]) ).
tcf(c_163,negated_conjecture,
sP1(sK9,sK8,sK8,sK9),
inference(global_subsumption_just,[status(thm)],[c_62,c_161]) ).
tcf(c_1178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X3,X2)
| ( X3 != sK9 )
| ( X2 != sK8 )
| ( X1 != sK8 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_163]) ).
tcf(c_1179,plain,
sP0(sK9,sK8),
inference(unflattening,[status(thm)],[c_1178]) ).
tcf(c_1188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ssItem(sK2(app(app(X0,cons(X1,nil)),X2),X1))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( X4 != sK9 )
| ( X3 != sK8 )
| ( app(X0,X2) != sK8 )
| ( app(app(X0,cons(X1,nil)),X2) != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_163]) ).
tcf(c_1189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sK2(app(app(X0,cons(X1,nil)),X2),X1))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(X0,X2) != sK8 )
| ( app(app(X0,cons(X1,nil)),X2) != sK9 ) ),
inference(unflattening,[status(thm)],[c_1188]) ).
tcf(c_1209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( X4 != sK9 )
| ( X3 != sK8 )
| ( app(X0,X2) != sK8 )
| ( app(app(X0,cons(X1,nil)),X2) != sK9 )
| ( sK2(app(app(X0,cons(X1,nil)),X2),X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_163]) ).
tcf(c_1210,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(X0,X2) != sK8 )
| ( app(app(X0,cons(X1,nil)),X2) != sK9 )
| ( sK2(app(app(X0,cons(X1,nil)),X2),X1) != X1 ) ),
inference(unflattening,[status(thm)],[c_1209]) ).
tcf(c_1230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( geq(sK2(app(app(X0,cons(X1,nil)),X2),X1),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( X4 != sK9 )
| ( X3 != sK8 )
| ( app(X0,X2) != sK8 )
| ( app(app(X0,cons(X1,nil)),X2) != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_163]) ).
tcf(c_1231,plain,
! [X0: $i,X1: $i,X2: $i] :
( geq(sK2(app(app(X0,cons(X1,nil)),X2),X1),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(X0,X2) != sK8 )
| ( app(app(X0,cons(X1,nil)),X2) != sK9 ) ),
inference(unflattening,[status(thm)],[c_1230]) ).
tcf(c_1251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( memberP(app(app(X0,cons(X1,nil)),X2),sK2(app(app(X0,cons(X1,nil)),X2),X1))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( X4 != sK9 )
| ( X3 != sK8 )
| ( app(X0,X2) != sK8 )
| ( app(app(X0,cons(X1,nil)),X2) != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_163]) ).
tcf(c_1252,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(app(X0,cons(X1,nil)),X2),sK2(app(app(X0,cons(X1,nil)),X2),X1))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(X0,X2) != sK8 )
| ( app(app(X0,cons(X1,nil)),X2) != sK9 ) ),
inference(unflattening,[status(thm)],[c_1251]) ).
fof(f145,definition,
! [X3,X2] :
( ~ sP0(X3,X2)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X11] :
( ~ geq(X11,X8)
| ~ memberP(X3,X11)
| X8 = X11
| ~ ssItem(X11) )
& app(X9,X10) = X2
& app(app(X9,cons(X8,nil)),X10) = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f146,definition,
! [X1,X0,X2,X3] :
( ~ sP1(X1,X0,X2,X3)
| ( sP0(X3,X2)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& X4 != X7
& geq(X7,X4)
& memberP(X1,X7) )
| app(X5,X6) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f147,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP1(X1,X0,X2,X3) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f99,f146,f145]) ).
fof(f151,plain,
! [X3,X2] :
( ~ sP0(X3,X2)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X11] :
( ~ geq(X11,X8)
| ~ memberP(X3,X11)
| X8 = X11
| ~ ssItem(X11) )
& app(X9,X10) = X2
& app(app(X9,cons(X8,nil)),X10) = X3 ) ) ) ),
inference(nnf_transformation,[],[f145]) ).
fof(f152,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ~ geq(X5,X2)
| ~ memberP(X0,X5)
| X2 = X5
| ~ ssItem(X5) )
& app(X3,X4) = X1
& app(app(X3,cons(X2,nil)),X4) = X0 ) ) ) ),
inference(rectify,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( ssItem(sK3(X0,X1))
& ssList(sK4(X0,X1))
& ssList(sK5(X0,X1))
& ! [X5] :
( ~ geq(X5,sK3(X0,X1))
| ~ memberP(X0,X5)
| sK3(X0,X1) = X5
| ~ ssItem(X5) )
& app(sK4(X0,X1),sK5(X0,X1)) = X1
& app(app(sK4(X0,X1),cons(sK3(X0,X1),nil)),sK5(X0,X1)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X3,sK4(X0,X1)),skolemize(X4,sK5(X0,X1))],[f152]) ).
fof(f177,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssItem(sK3(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f178,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK4(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK5(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f180,plain,
! [X0,X1,X5] :
( ~ sP0(X0,X1)
| ~ geq(X5,sK3(X0,X1))
| ~ memberP(X0,X5)
| sK3(X0,X1) = X5
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f153]) ).
fof(f181,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| app(sK4(X0,X1),sK5(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f153]) ).
fof(f182,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| app(app(sK4(X0,X1),cons(sK3(X0,X1),nil)),sK5(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( app(app(sK4(X0,X1),cons(sK3(X0,X1),nil)),sK5(X0,X1)) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( app(sK4(X0,X1),sK5(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK3(X1,X2) = X0 )
| ~ ssItem(X0)
| ~ sP0(X1,X2)
| ~ memberP(X1,X0)
| ~ geq(X0,sK3(X1,X2)) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ssList(sK5(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ssList(sK4(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ssItem(sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_1298,plain,
! [X0: $i,X1: $i] :
( ssItem(sK3(X0,X1))
| ( X1 != sK8 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_1179]) ).
tcf(c_1299,plain,
ssItem(sK3(sK9,sK8)),
inference(unflattening,[status(thm)],[c_1298]) ).
tcf(c_1303,plain,
! [X0: $i,X1: $i] :
( ssList(sK4(X0,X1))
| ( X1 != sK8 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_1179]) ).
tcf(c_1304,plain,
ssList(sK4(sK9,sK8)),
inference(unflattening,[status(thm)],[c_1303]) ).
tcf(c_1308,plain,
! [X0: $i,X1: $i] :
( ssList(sK5(X0,X1))
| ( X1 != sK8 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_1179]) ).
tcf(c_1309,plain,
ssList(sK5(sK9,sK8)),
inference(unflattening,[status(thm)],[c_1308]) ).
tcf(c_1313,plain,
! [X0: $i,X1: $i] :
( ( app(sK4(X0,X1),sK5(X0,X1)) = X1 )
| ( X1 != sK8 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_1179]) ).
tcf(c_1314,plain,
app(sK4(sK9,sK8),sK5(sK9,sK8)) = sK8,
inference(unflattening,[status(thm)],[c_1313]) ).
tcf(c_1318,plain,
! [X0: $i,X1: $i] :
( ( app(app(sK4(X0,X1),cons(sK3(X0,X1),nil)),sK5(X0,X1)) = X0 )
| ( X1 != sK8 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_1179]) ).
tcf(c_1319,plain,
app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)) = sK9,
inference(unflattening,[status(thm)],[c_1318]) ).
tcf(c_1323,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK3(X0,X1) = X2 )
| ~ ssItem(X2)
| ~ memberP(X0,X2)
| ~ geq(X2,sK3(X0,X1))
| ( X1 != sK8 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_1179]) ).
tcf(c_1324,plain,
! [X0: $i] :
( ( sK3(sK9,sK8) = X0 )
| ~ ssItem(X0)
| ~ memberP(sK9,X0)
| ~ geq(X0,sK3(sK9,sK8)) ),
inference(unflattening,[status(thm)],[c_1323]) ).
tcf(c_3305,plain,
( memberP(app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)),sK2(app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)),sK3(sK9,sK8)))
| ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8))
| ( app(sK4(sK9,sK8),sK5(sK9,sK8)) != sK8 ) ),
inference(superposition,[status(thm)],[c_1319,c_1252]) ).
tcf(c_3306,plain,
( ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8))
| ( sK2(sK9,sK3(sK9,sK8)) != sK3(sK9,sK8) )
| ( app(sK4(sK9,sK8),sK5(sK9,sK8)) != sK8 )
| ( app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)) != sK9 ) ),
inference(superposition,[status(thm)],[c_1319,c_1210]) ).
tcf(c_3307,plain,
( geq(sK2(app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)),sK3(sK9,sK8)),sK3(sK9,sK8))
| ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8))
| ( app(sK4(sK9,sK8),sK5(sK9,sK8)) != sK8 ) ),
inference(superposition,[status(thm)],[c_1319,c_1231]) ).
tcf(c_3308,plain,
( ssItem(sK2(app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)),sK3(sK9,sK8)))
| ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8))
| ( app(sK4(sK9,sK8),sK5(sK9,sK8)) != sK8 ) ),
inference(superposition,[status(thm)],[c_1319,c_1189]) ).
tcf(c_3309,plain,
( ssItem(sK2(app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)),sK3(sK9,sK8)))
| ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8)) ),
inference(ground_joinability,[status(thm)],[c_3308,c_1314]) ).
tcf(c_3310,plain,
( ssItem(sK2(sK9,sK3(sK9,sK8)))
| ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8)) ),
inference(light_normalisation,[status(thm)],[c_3309,c_1319]) ).
tcf(c_3311,plain,
ssItem(sK2(sK9,sK3(sK9,sK8))),
inference(forward_subsumption_resolution,[status(thm)],[c_3310,c_1309,c_1304,c_1299]) ).
tcf(c_3312,plain,
( geq(sK2(app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)),sK3(sK9,sK8)),sK3(sK9,sK8))
| ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8)) ),
inference(ground_joinability,[status(thm)],[c_3307,c_1314]) ).
tcf(c_3313,plain,
( geq(sK2(sK9,sK3(sK9,sK8)),sK3(sK9,sK8))
| ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8)) ),
inference(light_normalisation,[status(thm)],[c_3312,c_1319]) ).
tcf(c_3314,plain,
geq(sK2(sK9,sK3(sK9,sK8)),sK3(sK9,sK8)),
inference(forward_subsumption_resolution,[status(thm)],[c_3313,c_1309,c_1304,c_1299]) ).
tcf(c_3315,plain,
( ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8))
| ( sK2(sK9,sK3(sK9,sK8)) != sK3(sK9,sK8) )
| ( app(sK4(sK9,sK8),sK5(sK9,sK8)) != sK8 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3306,c_1319]) ).
tcf(c_3316,plain,
( ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8))
| ( sK2(sK9,sK3(sK9,sK8)) != sK3(sK9,sK8) ) ),
inference(ground_joinability,[status(thm)],[c_3315,c_1314]) ).
tcf(c_3317,plain,
sK2(sK9,sK3(sK9,sK8)) != sK3(sK9,sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_3316,c_1309,c_1304,c_1299]) ).
tcf(c_3318,plain,
( memberP(app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)),sK2(app(app(sK4(sK9,sK8),cons(sK3(sK9,sK8),nil)),sK5(sK9,sK8)),sK3(sK9,sK8)))
| ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8)) ),
inference(ground_joinability,[status(thm)],[c_3305,c_1314]) ).
tcf(c_3319,plain,
( memberP(sK9,sK2(sK9,sK3(sK9,sK8)))
| ~ ssList(sK5(sK9,sK8))
| ~ ssList(sK4(sK9,sK8))
| ~ ssItem(sK3(sK9,sK8)) ),
inference(light_normalisation,[status(thm)],[c_3318,c_1319]) ).
tcf(c_3320,plain,
memberP(sK9,sK2(sK9,sK3(sK9,sK8))),
inference(forward_subsumption_resolution,[status(thm)],[c_3319,c_1309,c_1304,c_1299]) ).
tcf(c_3330,plain,
( ( sK2(sK9,sK3(sK9,sK8)) = sK3(sK9,sK8) )
| ~ ssItem(sK2(sK9,sK3(sK9,sK8)))
| ~ memberP(sK9,sK2(sK9,sK3(sK9,sK8))) ),
inference(superposition,[status(thm)],[c_3314,c_1324]) ).
tcf(c_3331,plain,
sK2(sK9,sK3(sK9,sK8)) = sK3(sK9,sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_3330,c_3311,c_3320]) ).
tcf(c_3335,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3331,c_3317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC002+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 15:51:29 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.39 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 0.74/1.18 % SZS status Started for theBenchmark.p
% 0.74/1.18 % SZS status Theorem for theBenchmark.p
% 0.74/1.18
% 0.74/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.74/1.18
% 0.74/1.18 % ------ iProver source info
% 0.74/1.18
% 0.74/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 0.74/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.74/1.18 % git: non_committed_changes: false
% 0.74/1.18
% 0.74/1.18 % ------ Parsing...
% 0.74/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.74/1.18
% 0.74/1.18 % ------ 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 %
% 0.74/1.18
% 0.74/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.74/1.18
% 0.74/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.74/1.18 % ------ Proving...
% 0.74/1.18 % ------ Problem Properties
% 0.74/1.18
% 0.74/1.18 %
% 0.74/1.18 % clauses 61
% 0.74/1.18 % conjectures 2
% 0.74/1.18 % EPR 22
% 0.74/1.18 % Horn 55
% 0.74/1.18 % unary 13
% 0.74/1.18 % binary 6
% 0.74/1.18 % lits 217
% 0.74/1.18 % lits eq 43
% 0.74/1.18 % fd_pure 0
% 0.74/1.18 % fd_pseudo 0
% 0.74/1.18 % fd_cond 5
% 0.74/1.18 % fd_pseudo_cond 8
% 0.74/1.18 % AC symbols 0
% 0.74/1.18
% 0.74/1.18 % ------ Schedule dynamic 5 is on
% 0.74/1.18
% 0.74/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 % ------
% 0.74/1.18 % Current options:
% 0.74/1.18 % ------
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 %
% 0.74/1.18
% 0.74/1.18 % ------ Proving...
% 0.74/1.18 %
% 0.74/1.18
% 0.74/1.18 % SZS status Theorem for theBenchmark.p
% 0.74/1.18
% 0.74/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.74/1.19
% 0.74/1.19
%------------------------------------------------------------------------------