%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC392+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 : n018.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 03:09:36 PM UTC 2026
% Result : Theorem 1.09s 1.20s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 18 unt; 0 def)
% Number of atoms : 218 ( 75 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 249 ( 86 ~; 92 |; 51 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 2 ( 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 48 !; 14 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
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(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X5] :
( ssItem(X5)
=> ( ? [X6] :
( leq(X6,X5)
& memberP(X3,X6)
& X5 != X6
& ssItem(X6) )
| ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,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] :
( leq(X6,X5)
& memberP(X3,X6)
& X5 != X6
& ssItem(X6) )
| ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
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(f148,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ~ leq(X6,X5)
| ~ memberP(X3,X6)
| X5 = X6
| ~ ssItem(X6) )
& memberP(X3,X5)
& cons(X5,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)
& ( ( nil = X2
& nil = X3 )
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ~ leq(X6,X5)
| ~ memberP(X3,X6)
| X5 = X6
| ~ ssItem(X6) )
& memberP(X3,X5)
& cons(X5,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ~ memberP(X1,X4)
& memberP(X0,X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
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)
& ( ( nil = sK55
& nil = sK56 )
| ( ssItem(sK58)
& ! [X6] :
( ~ leq(X6,sK58)
| ~ memberP(sK56,X6)
| sK58 = X6
| ~ ssItem(X6) )
& memberP(sK56,sK58)
& sK55 = cons(sK58,nil) ) )
& 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]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58)],[f222]) ).
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(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(f419,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f500,plain,
( nil = sK55
| ssItem(sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil = sK56
| ssItem(sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil = sK55
| memberP(sK56,sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( nil = sK55
| sK55 = cons(sK58,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( nil = sK56
| sK55 = cons(sK58,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
~ memberP(sK54,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
memberP(sK53,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
memberP(sK55,sK57),
inference(definition_unfolding,[],[f510,f511]) ).
fof(f514,plain,
~ memberP(sK56,sK57),
inference(definition_unfolding,[],[f509,f512]) ).
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_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_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_246,negated_conjecture,
memberP(sK55,sK57),
inference(cnf_transformation,[],[f513]) ).
tcf(c_247,negated_conjecture,
~ memberP(sK56,sK57),
inference(cnf_transformation,[],[f514]) ).
tcf(c_248,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f508]) ).
tcf(c_249,negated_conjecture,
( ( nil = sK56 )
| ( cons(sK58,nil) = sK55 ) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_250,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK58,nil) = sK55 ) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_252,negated_conjecture,
( memberP(sK56,sK58)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_255,negated_conjecture,
( ssItem(sK58)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_256,negated_conjecture,
( ssItem(sK58)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_363,plain,
( ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ( nil != sK55 ) ),
inference(superposition,[status(thm)],[c_249,c_148]) ).
tcf(c_480,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( nil = sK55 )
| ( X0 = sK58 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_250,c_170]) ).
tcf(c_549,plain,
( ( nil = sK56 )
| ( nil != sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_363,c_141,c_255,c_363]) ).
tcf(c_555,plain,
! [X0: $i] :
( ~ memberP(sK55,X0)
| ~ ssItem(X0)
| ( X0 = sK58 )
| ( nil = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_480,c_141,c_256,c_171,c_480]) ).
tcf(c_556,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( X0 = sK58 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(renaming,[status(thm)],[c_555]) ).
tcf(c_566,plain,
( ( sK57 = sK58 )
| ( nil = sK55 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_246,c_556]) ).
tcf(c_686,plain,
( ( sK57 = sK58 )
| ( nil = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_566,c_248,c_566]) ).
tcf(c_701,plain,
( memberP(sK56,sK57)
| ( nil = sK55 ) ),
inference(superposition,[status(thm)],[c_686,c_252]) ).
tcf(c_707,negated_conjecture,
nil = sK55,
inference(global_subsumption_just,[status(thm)],[c_256,c_247,c_701]) ).
tcf(c_709,plain,
memberP(nil,sK57),
inference(superposition,[status(thm)],[c_707,c_246]) ).
tcf(c_711,negated_conjecture,
nil = sK56,
inference(global_subsumption_just,[status(thm)],[c_255,c_247,c_549,c_701]) ).
tcf(c_713,plain,
~ memberP(nil,sK57),
inference(superposition,[status(thm)],[c_711,c_247]) ).
tcf(c_715,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_713,c_709]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC392+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 18:02:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.09/1.20 % SZS status Started for theBenchmark.p
% 1.09/1.20 % SZS status Theorem for theBenchmark.p
% 1.09/1.20
% 1.09/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.09/1.20
% 1.09/1.20 % ------ iProver source info
% 1.09/1.20
% 1.09/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.09/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.09/1.20 % git: non_committed_changes: false
% 1.09/1.20
% 1.09/1.20 % ------ Parsing...
% 1.09/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.09/1.20 % ------ Proving...
% 1.09/1.20 % ------ Problem Properties
% 1.09/1.20
% 1.09/1.20 %
% 1.09/1.20 % clauses 212
% 1.09/1.20 % conjectures 15
% 1.09/1.20 % EPR 77
% 1.09/1.20 % Horn 133
% 1.09/1.20 % unary 19
% 1.09/1.20 % binary 59
% 1.09/1.20 % lits 699
% 1.09/1.20 % lits eq 93
% 1.09/1.20 % fd_pure 0
% 1.09/1.20 % fd_pseudo 0
% 1.09/1.20 % fd_cond 23
% 1.09/1.20 % fd_pseudo_cond 17
% 1.09/1.20 % AC symbols 0
% 1.09/1.20
% 1.09/1.20 % ------ Input Options Time Limit: Unbounded
% 1.09/1.20
% 1.09/1.20
% 1.09/1.20 % ------
% 1.09/1.20 % Current options:
% 1.09/1.20 % ------
% 1.09/1.20
% 1.09/1.20
% 1.09/1.20 %
% 1.09/1.20
% 1.09/1.20 % ------ Proving...
% 1.09/1.20 %
% 1.09/1.20
% 1.09/1.20 % SZS status Theorem for theBenchmark.p
% 1.09/1.20
% 1.09/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.09/1.20
% 1.09/1.20
%------------------------------------------------------------------------------