%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC398+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 : n008.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 4.44s 11.47s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 18 unt; 0 def)
% Number of atoms : 163 ( 39 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 198 ( 67 ~; 61 |; 53 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 41 !; 18 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssItem(X8)
=> ( memberP(X1,X8)
| ~ memberP(X0,X8) ) )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| 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 )
| ! [X8] :
( ssItem(X8)
=> ( memberP(X1,X8)
| ~ memberP(X0,X8) ) )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| 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 )
& ? [X8] :
( ssItem(X8)
& ~ memberP(X1,X8)
& memberP(X0,X8) )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& 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 )
& ? [X8] :
( ssItem(X8)
& ~ memberP(X1,X8)
& memberP(X0,X8) )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f120,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(f125,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( nil != sK2
| nil = sK3 )
& ssItem(sK5)
& ~ memberP(sK1,sK5)
& memberP(sK0,sK5)
& ssList(sK4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK2)
& sK3 = app(sK2,sK4)
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X8,sK5)],[f99]) ).
fof(f132,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,[],[f120]) ).
fof(f133,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,[],[f132]) ).
fof(f140,plain,
ssList(sK0),
inference(cnf_transformation,[],[f125]) ).
fof(f145,plain,
ssItem(sK5),
inference(cnf_transformation,[],[f125]) ).
fof(f146,plain,
~ memberP(sK1,sK5),
inference(cnf_transformation,[],[f125]) ).
fof(f147,plain,
memberP(sK0,sK5),
inference(cnf_transformation,[],[f125]) ).
fof(f148,plain,
ssList(sK4),
inference(cnf_transformation,[],[f125]) ).
fof(f151,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f125]) ).
fof(f152,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f125]) ).
fof(f153,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f125]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f197,plain,
memberP(sK2,sK5),
inference(definition_unfolding,[],[f147,f152]) ).
fof(f198,plain,
~ memberP(sK3,sK5),
inference(definition_unfolding,[],[f146,f153]) ).
fof(f200,plain,
ssList(sK2),
inference(definition_unfolding,[],[f140,f152]) ).
tcf(c_49,negated_conjecture,
app(sK2,sK4) = sK3,
inference(cnf_transformation,[],[f151]) ).
tcf(c_52,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f148]) ).
tcf(c_53,negated_conjecture,
memberP(sK2,sK5),
inference(cnf_transformation,[],[f197]) ).
tcf(c_54,negated_conjecture,
~ memberP(sK3,sK5),
inference(cnf_transformation,[],[f198]) ).
tcf(c_55,negated_conjecture,
ssItem(sK5),
inference(cnf_transformation,[],[f145]) ).
tcf(c_60,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f200]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_3456,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK4)
| ~ ssList(sK2)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_49,c_88]) ).
tcf(c_3468,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3456,c_52,c_60]) ).
tcf(c_3516,plain,
( memberP(sK3,sK5)
| ~ ssItem(sK5) ),
inference(superposition,[status(thm)],[c_53,c_3468]) ).
tcf(c_3517,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3516,c_54,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC398+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/10.39 % Computer : n008.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Thu Sep 24 18:03:24 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.45 Running first-order theorem proving
% 0.15/10.45 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
% 0.15/10.47
% 0.15/10.47 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.47
% 0.15/10.47 % Detected problem language: tptp
% 0.15/10.49 % Proving...
% 4.44/11.47 % SZS status Started for theBenchmark.p
% 4.44/11.47 % SZS status Theorem for theBenchmark.p
% 4.44/11.47
% 4.44/11.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.44/11.47
% 4.44/11.47 % ------ iProver source info
% 4.44/11.47
% 4.44/11.47 % git: date: 2026-07-19 20:42:38 +0200
% 4.44/11.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.44/11.47 % git: non_committed_changes: false
% 4.44/11.47
% 4.44/11.47 % ------ Parsing...
% 4.44/11.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.44/11.47
% 4.44/11.47 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.44/11.47
% 4.44/11.47 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.44/11.47
% 4.44/11.47 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.44/11.47 % ------ Proving...
% 4.44/11.47 % ------ Problem Properties
% 4.44/11.47
% 4.44/11.47 %
% 4.44/11.47 % clauses 53
% 4.44/11.47 % conjectures 10
% 4.44/11.47 % EPR 14
% 4.44/11.47 % Horn 43
% 4.44/11.47 % unary 14
% 4.44/11.47 % binary 5
% 4.44/11.47 % lits 163
% 4.44/11.47 % lits eq 35
% 4.44/11.47 % fd_pure 0
% 4.44/11.47 % fd_pseudo 0
% 4.44/11.47 % fd_cond 4
% 4.44/11.47 % fd_pseudo_cond 6
% 4.44/11.47 % AC symbols 0
% 4.44/11.47
% 4.44/11.47 % ------ Schedule dynamic 5 is on
% 4.44/11.47
% 4.44/11.47 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.44/11.47
% 4.44/11.47
% 4.44/11.47 % ------
% 4.44/11.47 % Current options:
% 4.44/11.47 % ------
% 4.44/11.47
% 4.44/11.47
% 4.44/11.47 %
% 4.44/11.47
% 4.44/11.47 % ------ Proving...
% 4.44/11.47 %
% 4.44/11.47
% 4.44/11.47 % SZS status Theorem for theBenchmark.p
% 4.44/11.47
% 4.44/11.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.44/11.47
% 4.44/11.47
%------------------------------------------------------------------------------