%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC397+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 : n014.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 03:09:37 PM UTC 2026
% Result : Theorem 7.21s 1.75s
% Output : CNFRefutation 7.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 101 ( 21 unt; 0 def)
% Number of atoms : 449 ( 105 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 564 ( 216 ~; 266 |; 52 &)
% ( 6 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 107 !; 14 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
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(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X2 ) ) ) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| 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)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X2 ) ) ) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(f146,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f147,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2 ) ) )
& ( nil != X3
| nil = X2 )
& ? [X4] :
( ssItem(X4)
& ~ memberP(X1,X4)
& memberP(X0,X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2 ) ) )
& ( nil != X3
| nil = X2 )
& ? [X4] :
( ssItem(X4)
& ~ memberP(X1,X4)
& memberP(X0,X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f277,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f146]) ).
fof(f278,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f277]) ).
fof(f279,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f147]) ).
fof(f280,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f279]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ~ neq(sK56,nil)
| ( ssItem(sK58)
& ssList(sK59)
& sK56 = app(sK59,cons(sK58,nil))
& sK55 = app(cons(sK58,nil),sK59) ) )
& ( nil != sK56
| nil = sK55 )
& ssItem(sK57)
& ~ memberP(sK54,sK57)
& memberP(sK53,sK57)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59)],[f222]) ).
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(f413,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f416,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f280]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| ssItem(sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( ~ neq(sK56,nil)
| ssList(sK59) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( ~ neq(sK56,nil)
| sK56 = app(sK59,cons(sK58,nil)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( ~ neq(sK56,nil)
| sK55 = app(cons(sK58,nil),sK59) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
~ memberP(sK54,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
memberP(sK53,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
memberP(sK55,sK57),
inference(definition_unfolding,[],[f507,f508]) ).
fof(f511,plain,
~ memberP(sK56,sK57),
inference(definition_unfolding,[],[f506,f509]) ).
fof(f512,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f509]) ).
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_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f415]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f414]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| memberP(X0,X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ memberP(app(X0,X1),X2) ),
inference(cnf_transformation,[],[f413]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[],[f416]) ).
tcf(c_246,negated_conjecture,
memberP(sK55,sK57),
inference(cnf_transformation,[],[f510]) ).
tcf(c_247,negated_conjecture,
~ memberP(sK56,sK57),
inference(cnf_transformation,[],[f511]) ).
tcf(c_248,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f505]) ).
tcf(c_249,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_250,negated_conjecture,
( ( app(cons(sK58,nil),sK59) = sK55 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_251,negated_conjecture,
( ( app(sK59,cons(sK58,nil)) = sK56 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_252,negated_conjecture,
( ssList(sK59)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_253,negated_conjecture,
( ssItem(sK58)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_256,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f512]) ).
tcf(c_411,plain,
( ( nil = sK56 )
| ( app(cons(sK58,nil),sK59) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_250]) ).
tcf(c_412,plain,
( ( nil = sK56 )
| ( app(sK59,cons(sK58,nil)) = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_251]) ).
tcf(c_413,plain,
( ssList(sK59)
| ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_252]) ).
tcf(c_414,plain,
( ssItem(sK58)
| ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_253]) ).
tcf(c_737,plain,
( ssItem(sK58)
| ( nil = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_414,c_256,c_141,c_414]) ).
tcf(c_758,plain,
( ssList(sK59)
| ( nil = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_413,c_256,c_141,c_413]) ).
tcf(c_816,plain,
( ( nil = sK56 )
| ( app(cons(sK58,nil),sK59) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_250]) ).
tcf(c_817,plain,
( ( nil = sK56 )
| ( app(sK59,cons(sK58,nil)) = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_251]) ).
tcf(c_820,plain,
( ( nil = sK56 )
| ( app(sK59,cons(sK58,nil)) = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_412,c_256,c_141,c_412]) ).
tcf(c_835,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK59,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_820,c_165]) ).
tcf(c_836,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(superposition,[status(thm)],[c_820,c_166]) ).
tcf(c_856,plain,
( ( nil = sK56 )
| ( app(cons(sK58,nil),sK59) = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_411,c_256,c_141,c_411]) ).
tcf(c_864,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_856,c_167]) ).
tcf(c_1482,plain,
( ( nil = sK56 )
| ( app(sK59,cons(sK58,nil)) = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_817,c_820]) ).
tcf(c_1497,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK59,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1482,c_165]) ).
tcf(c_1498,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(superposition,[status(thm)],[c_1482,c_166]) ).
tcf(c_1542,plain,
( ( nil = sK56 )
| ( app(cons(sK58,nil),sK59) = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_816,c_856]) ).
tcf(c_1550,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1542,c_167]) ).
tcf(c_1781,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK59,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_835,c_256,c_141,c_413,c_835]) ).
tcf(c_1782,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK59,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_1781]) ).
tcf(c_1794,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(superposition,[status(thm)],[c_140,c_1782]) ).
tcf(c_1818,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ memberP(cons(sK58,nil),X0)
| ~ ssList(cons(sK58,nil))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_836,c_256,c_141,c_413,c_836]) ).
tcf(c_1819,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(renaming,[status(thm)],[c_1818]) ).
tcf(c_1948,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK55,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_864,c_758,c_864]) ).
tcf(c_1949,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_1948]) ).
tcf(c_1965,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1949,c_1819]) ).
tcf(c_3154,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ memberP(sK59,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1497,c_256,c_141,c_414,c_1794]) ).
tcf(c_3155,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(renaming,[status(thm)],[c_3154]) ).
tcf(c_3188,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ memberP(cons(sK58,nil),X0)
| ~ ssList(cons(sK58,nil))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1498,c_1819]) ).
tcf(c_3189,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(renaming,[status(thm)],[c_3188]) ).
tcf(c_3361,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK55,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1550,c_1949]) ).
tcf(c_3362,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_3361]) ).
tcf(c_3375,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(nil,X0)
| ( nil = sK56 )
| ( X0 = sK58 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_3362,c_170]) ).
tcf(c_3377,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_3362,c_3189]) ).
tcf(c_5148,plain,
! [X0: $i] :
( ~ ssList(cons(sK58,nil))
| ~ memberP(sK55,X0)
| ~ ssItem(X0)
| ( nil = sK56 )
| memberP(sK56,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1965,c_1965,c_3155]) ).
tcf(c_5149,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_5148]) ).
tcf(c_5161,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_140,c_5149]) ).
tcf(c_9566,plain,
! [X0: $i] :
( ~ memberP(sK55,X0)
| ~ ssItem(X0)
| ( nil = sK56 )
| memberP(sK56,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3377,c_141,c_737,c_5161]) ).
tcf(c_9567,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(renaming,[status(thm)],[c_9566]) ).
tcf(c_9577,plain,
( memberP(sK56,sK57)
| ( nil = sK56 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_246,c_9567]) ).
tcf(c_9579,plain,
nil = sK56,
inference(global_subsumption_just,[status(thm)],[c_3375,c_248,c_247,c_9577]) ).
tcf(c_9605,plain,
nil = sK55,
inference(superposition,[status(thm)],[c_9579,c_249]) ).
tcf(c_9608,plain,
~ memberP(nil,sK57),
inference(superposition,[status(thm)],[c_9579,c_247]) ).
tcf(c_9664,plain,
memberP(nil,sK57),
inference(demodulation,[status(thm)],[c_246,c_9605]) ).
tcf(c_9666,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9608,c_9664]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC397+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 18:01:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 7.21/1.75 % SZS status Started for theBenchmark.p
% 7.21/1.75 % SZS status Theorem for theBenchmark.p
% 7.21/1.75
% 7.21/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.21/1.75
% 7.21/1.75 % ------ iProver source info
% 7.21/1.75
% 7.21/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 7.21/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.21/1.75 % git: non_committed_changes: false
% 7.21/1.75
% 7.21/1.75 % ------ Parsing...
% 7.21/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.21/1.75 % ------ Proving...
% 7.21/1.75 % ------ Problem Properties
% 7.21/1.75
% 7.21/1.75 %
% 7.21/1.75 % clauses 209
% 7.21/1.75 % conjectures 12
% 7.21/1.75 % EPR 74
% 7.21/1.75 % Horn 138
% 7.21/1.75 % unary 19
% 7.21/1.75 % binary 58
% 7.21/1.75 % lits 687
% 7.21/1.75 % lits eq 85
% 7.21/1.75 % fd_pure 0
% 7.21/1.75 % fd_pseudo 0
% 7.21/1.75 % fd_cond 21
% 7.21/1.75 % fd_pseudo_cond 17
% 7.21/1.75 % AC symbols 0
% 7.21/1.75
% 7.21/1.75 % ------ Input Options Time Limit: Unbounded
% 7.21/1.75
% 7.21/1.75
% 7.21/1.75 % ------
% 7.21/1.75 % Current options:
% 7.21/1.75 % ------
% 7.21/1.75
% 7.21/1.75
% 7.21/1.75 %
% 7.21/1.75
% 7.21/1.75 % ------ Proving...
% 7.21/1.75 %
% 7.21/1.75
% 7.21/1.75 % SZS status Theorem for theBenchmark.p
% 7.21/1.75
% 7.21/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.21/1.76
% 7.21/1.76
%------------------------------------------------------------------------------