%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC407+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 : n007.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 03:09:40 PM UTC 2026
% Result : Theorem 4.19s 1.28s
% Output : CNFRefutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 70 ( 18 unt; 0 def)
% Number of atoms : 288 ( 90 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 343 ( 125 ~; 139 |; 55 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 77 !; 20 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/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)
=> ( ~ memberP(X3,X5)
| cons(X5,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)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X5] :
( ssItem(X5)
=> ( ~ 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(f99,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
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)
& 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)
& memberP(X3,X5)
& cons(X5,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ~ memberP(X1,X4)
& memberP(X0,X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f235,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f235]) ).
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)
& 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(f305,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
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(f502,plain,
( nil = sK55
| memberP(sK56,sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil = sK55
| sK55 = cons(sK58,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( nil = sK56
| sK55 = cons(sK58,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
~ memberP(sK54,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
memberP(sK53,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
memberP(sK55,sK57),
inference(definition_unfolding,[],[f508,f509]) ).
fof(f512,plain,
~ memberP(sK56,sK57),
inference(definition_unfolding,[],[f507,f510]) ).
fof(f516,plain,
! [X2,X3,X1] :
( ~ ssList(app(X2,cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(app(X2,cons(X1,X3)),X1) ),
inference(equality_resolution,[],[f305]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f516]) ).
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,[],[f511]) ).
tcf(c_247,negated_conjecture,
~ memberP(sK56,sK57),
inference(cnf_transformation,[],[f512]) ).
tcf(c_248,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f506]) ).
tcf(c_249,negated_conjecture,
( ( nil = sK56 )
| ( cons(sK58,nil) = sK55 ) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_250,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK58,nil) = sK55 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_252,negated_conjecture,
( memberP(sK56,sK58)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_253,negated_conjecture,
( ssItem(sK58)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_254,negated_conjecture,
( ssItem(sK58)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_351,plain,
( ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ( nil != sK55 ) ),
inference(superposition,[status(thm)],[c_249,c_148]) ).
tcf(c_421,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( nil = sK56 )
| ( X0 = sK58 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_249,c_170]) ).
tcf(c_422,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_436,plain,
! [X0: $i] :
( memberP(app(X0,sK55),sK58)
| ( nil = sK55 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK58,nil))) ),
inference(superposition,[status(thm)],[c_250,c_54]) ).
tcf(c_491,plain,
( ( nil = sK56 )
| ( nil != sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_351,c_141,c_253,c_351]) ).
tcf(c_497,plain,
! [X0: $i] :
( ~ memberP(sK55,X0)
| ~ ssItem(X0)
| ( X0 = sK58 )
| ( nil = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_422,c_141,c_254,c_171,c_422]) ).
tcf(c_498,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( X0 = sK58 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(renaming,[status(thm)],[c_497]) ).
tcf(c_508,plain,
( ( sK57 = sK58 )
| ( nil = sK55 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_246,c_498]) ).
tcf(c_511,plain,
! [X0: $i] :
( ~ memberP(sK55,X0)
| ~ ssItem(X0)
| ( X0 = sK58 )
| ( nil = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_421,c_141,c_253,c_171,c_421]) ).
tcf(c_512,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( X0 = sK58 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(renaming,[status(thm)],[c_511]) ).
tcf(c_522,plain,
( ( sK57 = sK58 )
| ( nil = sK56 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_246,c_512]) ).
tcf(c_525,plain,
! [X0: $i] :
( memberP(app(X0,sK55),sK58)
| ( nil = sK55 )
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK58,nil))) ),
inference(global_subsumption_just,[status(thm)],[c_436,c_141,c_254,c_436]) ).
tcf(c_537,plain,
! [X0: $i] :
( memberP(app(X0,sK55),sK58)
| ( nil = sK55 )
| ~ ssList(X0)
| ~ ssList(app(X0,sK55)) ),
inference(superposition,[status(thm)],[c_250,c_525]) ).
tcf(c_670,plain,
( ( sK57 = sK58 )
| ( nil = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_508,c_248,c_508]) ).
tcf(c_683,plain,
( memberP(sK56,sK57)
| ( nil = sK55 ) ),
inference(superposition,[status(thm)],[c_670,c_252]) ).
tcf(c_766,plain,
nil = sK56,
inference(global_subsumption_just,[status(thm)],[c_522,c_247,c_491,c_683]) ).
tcf(c_769,plain,
~ memberP(nil,sK57),
inference(superposition,[status(thm)],[c_766,c_247]) ).
tcf(c_771,plain,
nil = sK55,
inference(global_subsumption_just,[status(thm)],[c_537,c_247,c_683]) ).
tcf(c_776,plain,
memberP(nil,sK57),
inference(superposition,[status(thm)],[c_771,c_246]) ).
tcf(c_778,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_776,c_769]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC407+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.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 18:03:22 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 4.19/1.28 % SZS status Started for theBenchmark.p
% 4.19/1.28 % SZS status Theorem for theBenchmark.p
% 4.19/1.28
% 4.19/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.19/1.28
% 4.19/1.28 % ------ iProver source info
% 4.19/1.28
% 4.19/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.19/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.19/1.28 % git: non_committed_changes: false
% 4.19/1.28
% 4.19/1.28 % ------ Parsing...
% 4.19/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.19/1.28 % ------ Proving...
% 4.19/1.28 % ------ Problem Properties
% 4.19/1.28
% 4.19/1.28 %
% 4.19/1.28 % clauses 210
% 4.19/1.28 % conjectures 13
% 4.19/1.28 % EPR 75
% 4.19/1.28 % Horn 133
% 4.19/1.28 % unary 19
% 4.19/1.28 % binary 59
% 4.19/1.28 % lits 689
% 4.19/1.28 % lits eq 89
% 4.19/1.28 % fd_pure 0
% 4.19/1.28 % fd_pseudo 0
% 4.19/1.28 % fd_cond 21
% 4.19/1.28 % fd_pseudo_cond 17
% 4.19/1.28 % AC symbols 0
% 4.19/1.28
% 4.19/1.28 % ------ Input Options Time Limit: Unbounded
% 4.19/1.28
% 4.19/1.28
% 4.19/1.28 % ------
% 4.19/1.28 % Current options:
% 4.19/1.28 % ------
% 4.19/1.28
% 4.19/1.28
% 4.19/1.28 %
% 4.19/1.28
% 4.19/1.28 % ------ Proving...
% 4.19/1.28 %
% 4.19/1.28
% 4.19/1.28 % SZS status Theorem for theBenchmark.p
% 4.19/1.28
% 4.19/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.19/1.28
% 4.19/1.28
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