%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC399+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 : n009.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 4.40s 1.30s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 20 unt; 0 def)
% Number of atoms : 211 ( 40 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 273 ( 105 ~; 101 |; 52 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 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 : 83 ( 0 sgn 64 !; 19 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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] :
( ( nil = X2
& nil != X3 )
| ! [X12] :
( memberP(X1,X12)
| ~ memberP(X0,X12)
| ~ ssItem(X12) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X5
& ssList(X10) )
& ssItem(X9) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( app(cons(X6,nil),X8) = X2
& ssList(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(app(X4,X2),X5) != X3
| ~ ssList(X5) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( nil = X2
& nil != X3 )
| ! [X12] :
( memberP(X1,X12)
| ~ memberP(X0,X12)
| ~ ssItem(X12) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X5
& ssList(X10) )
& ssItem(X9) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( app(cons(X6,nil),X8) = X2
& ssList(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(app(X4,X2),X5) != X3
| ~ ssList(X5) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X12] :
( ~ memberP(X1,X12)
& memberP(X0,X12)
& ssItem(X12) )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(X11,cons(X9,nil)) != X2
| ~ ssList(X11) )
| app(cons(X9,nil),X10) != X5
| ~ ssList(X10) )
| ~ ssItem(X9) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( app(cons(X6,nil),X8) != X2
| ~ ssList(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f119,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(f124,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ( nil != sK2
| nil = sK3 )
& ~ memberP(sK1,sK6)
& memberP(sK0,sK6)
& ssItem(sK6)
& ssList(sK4)
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(X11,cons(X9,nil)) != sK2
| ~ ssList(X11) )
| app(cons(X9,nil),X10) != sK5
| ~ ssList(X10) )
| ~ ssItem(X9) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( app(cons(X6,nil),X8) != sK2
| ~ ssList(X8) )
| app(X7,cons(X6,nil)) != sK4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK2)
& sK3 = app(app(sK4,sK2),sK5)
& ssList(sK5)
& sK0 = sK2
& sK1 = sK3
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X12,sK6)],[f98]) ).
fof(f131,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,[],[f119]) ).
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(flattening,[],[f131]) ).
fof(f139,plain,
ssList(sK0),
inference(cnf_transformation,[],[f124]) ).
fof(f143,plain,
~ memberP(sK1,sK6),
inference(cnf_transformation,[],[f124]) ).
fof(f144,plain,
memberP(sK0,sK6),
inference(cnf_transformation,[],[f124]) ).
fof(f145,plain,
ssItem(sK6),
inference(cnf_transformation,[],[f124]) ).
fof(f146,plain,
ssList(sK4),
inference(cnf_transformation,[],[f124]) ).
fof(f150,plain,
sK3 = app(app(sK4,sK2),sK5),
inference(cnf_transformation,[],[f124]) ).
fof(f151,plain,
ssList(sK5),
inference(cnf_transformation,[],[f124]) ).
fof(f152,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f124]) ).
fof(f153,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f124]) ).
fof(f176,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f198,plain,
memberP(sK2,sK6),
inference(definition_unfolding,[],[f144,f152]) ).
fof(f199,plain,
~ memberP(sK3,sK6),
inference(definition_unfolding,[],[f143,f153]) ).
fof(f201,plain,
ssList(sK2),
inference(definition_unfolding,[],[f139,f152]) ).
tcf(c_50,negated_conjecture,
ssList(sK5),
inference(cnf_transformation,[],[f151]) ).
tcf(c_51,negated_conjecture,
app(app(sK4,sK2),sK5) = sK3,
inference(cnf_transformation,[],[f150]) ).
tcf(c_55,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f146]) ).
tcf(c_56,negated_conjecture,
ssItem(sK6),
inference(cnf_transformation,[],[f145]) ).
tcf(c_57,negated_conjecture,
memberP(sK2,sK6),
inference(cnf_transformation,[],[f198]) ).
tcf(c_58,negated_conjecture,
~ memberP(sK3,sK6),
inference(cnf_transformation,[],[f199]) ).
tcf(c_62,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f201]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_3487,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK5)
| ~ ssItem(X0)
| ~ ssList(app(sK4,sK2))
| ~ memberP(app(sK4,sK2),X0) ),
inference(superposition,[status(thm)],[c_51,c_90]) ).
tcf(c_3499,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sK4,sK2))
| ~ memberP(app(sK4,sK2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3487,c_50]) ).
tcf(c_7267,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK2)
| ~ ssList(sK4)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(app(sK4,sK2)) ),
inference(superposition,[status(thm)],[c_91,c_3499]) ).
tcf(c_7268,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(app(sK4,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7267,c_62,c_55]) ).
tcf(c_7537,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK2)
| ~ ssList(sK4)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_84,c_7268]) ).
tcf(c_7538,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7537,c_62,c_55]) ).
tcf(c_7552,plain,
( memberP(sK3,sK6)
| ~ ssItem(sK6) ),
inference(superposition,[status(thm)],[c_57,c_7538]) ).
tcf(c_7553,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7552,c_58,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC399+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 18:02:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 4.40/1.30 % SZS status Started for theBenchmark.p
% 4.40/1.30 % SZS status Theorem for theBenchmark.p
% 4.40/1.30
% 4.40/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.40/1.30
% 4.40/1.30 % ------ iProver source info
% 4.40/1.30
% 4.40/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.40/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.40/1.30 % git: non_committed_changes: false
% 4.40/1.30
% 4.40/1.30 % ------ Parsing...
% 4.40/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.40/1.30
% 4.40/1.30 % ------ 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 %
% 4.40/1.30
% 4.40/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.40/1.30
% 4.40/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.40/1.30 % ------ Proving...
% 4.40/1.30 % ------ Problem Properties
% 4.40/1.30
% 4.40/1.30 %
% 4.40/1.30 % clauses 55
% 4.40/1.30 % conjectures 12
% 4.40/1.30 % EPR 15
% 4.40/1.30 % Horn 45
% 4.40/1.30 % unary 15
% 4.40/1.30 % binary 5
% 4.40/1.30 % lits 169
% 4.40/1.30 % lits eq 37
% 4.40/1.30 % fd_pure 0
% 4.40/1.30 % fd_pseudo 0
% 4.40/1.30 % fd_cond 4
% 4.40/1.30 % fd_pseudo_cond 6
% 4.40/1.30 % AC symbols 0
% 4.40/1.30
% 4.40/1.30 % ------ Schedule dynamic 5 is on
% 4.40/1.30
% 4.40/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.40/1.30
% 4.40/1.30
% 4.40/1.30 % ------
% 4.40/1.30 % Current options:
% 4.40/1.30 % ------
% 4.40/1.30
% 4.40/1.30
% 4.40/1.30 %
% 4.40/1.30
% 4.40/1.30 % ------ Proving...
% 4.40/1.30 %
% 4.40/1.30
% 4.40/1.30 % SZS status Theorem for theBenchmark.p
% 4.40/1.30
% 4.40/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.40/1.30
% 4.40/1.30
%------------------------------------------------------------------------------