%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC403+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 : n010.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 03:09:39 PM UTC 2026
% Result : Theorem 25.95s 5.79s
% Output : CNFRefutation 25.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 59 ( 20 unt; 0 def)
% Number of atoms : 282 ( 24 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 373 ( 150 ~; 144 |; 58 &)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 82 !; 20 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
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] :
( ssList(X3)
=> ( ! [X5] :
( ssItem(X5)
=> ( memberP(X1,X5)
| ~ memberP(X0,X5) ) )
| ? [X4] :
( strictorderedP(X4)
& segmentP(X4,X2)
& segmentP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| ~ strictorderedP(X2)
| ~ segmentP(X3,X2)
| 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)
=> ( ! [X5] :
( ssItem(X5)
=> ( memberP(X1,X5)
| ~ memberP(X0,X5) ) )
| ? [X4] :
( strictorderedP(X4)
& segmentP(X4,X2)
& segmentP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| ~ strictorderedP(X2)
| ~ segmentP(X3,X2)
| 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)
& ? [X5] :
( ssItem(X5)
& ~ memberP(X1,X5)
& memberP(X0,X5) )
& ! [X4] :
( ~ strictorderedP(X4)
| ~ segmentP(X4,X2)
| ~ segmentP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& strictorderedP(X2)
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X5] :
( ssItem(X5)
& ~ memberP(X1,X5)
& memberP(X0,X5) )
& ! [X4] :
( ~ strictorderedP(X4)
| ~ segmentP(X4,X2)
| ~ segmentP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& strictorderedP(X2)
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f104,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(f115,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f137,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f171,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ssItem(sK4)
& ~ memberP(sK1,sK4)
& memberP(sK0,sK4)
& ! [X4] :
( ~ strictorderedP(X4)
| ~ segmentP(X4,sK2)
| ~ segmentP(sK3,X4)
| ~ neq(sK2,X4)
| ~ ssList(X4) )
& strictorderedP(sK2)
& segmentP(sK3,sK2)
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4)],[f99]) ).
fof(f177,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,[],[f104]) ).
fof(f178,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,[],[f177]) ).
fof(f183,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f115]) ).
fof(f184,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(rectify,[],[f183]) ).
fof(f185,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0
& ssList(sK10(X0,X1))
& ssList(sK9(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f184]) ).
fof(f198,plain,
ssList(sK0),
inference(cnf_transformation,[],[f171]) ).
fof(f199,plain,
ssList(sK1),
inference(cnf_transformation,[],[f171]) ).
fof(f202,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f171]) ).
fof(f203,plain,
~ memberP(sK1,sK4),
inference(cnf_transformation,[],[f171]) ).
fof(f204,plain,
memberP(sK0,sK4),
inference(cnf_transformation,[],[f171]) ).
fof(f207,plain,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f171]) ).
fof(f208,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f171]) ).
fof(f209,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f171]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f235,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f185]) ).
fof(f236,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ssList(sK10(X0,X1)) ),
inference(cnf_transformation,[],[f185]) ).
fof(f237,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ssList(sK9(X0,X1)) ),
inference(cnf_transformation,[],[f185]) ).
fof(f273,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f297,plain,
memberP(sK2,sK4),
inference(definition_unfolding,[],[f204,f208]) ).
fof(f298,plain,
~ memberP(sK3,sK4),
inference(definition_unfolding,[],[f203,f209]) ).
fof(f299,plain,
ssList(sK3),
inference(definition_unfolding,[],[f199,f209]) ).
fof(f300,plain,
ssList(sK2),
inference(definition_unfolding,[],[f198,f208]) ).
tcf(c_49,negated_conjecture,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f207]) ).
tcf(c_52,negated_conjecture,
memberP(sK2,sK4),
inference(cnf_transformation,[],[f297]) ).
tcf(c_53,negated_conjecture,
~ memberP(sK3,sK4),
inference(cnf_transformation,[],[f298]) ).
tcf(c_54,negated_conjecture,
ssItem(sK4),
inference(cnf_transformation,[],[f202]) ).
tcf(c_57,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f299]) ).
tcf(c_58,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f300]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ssList(sK9(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ssList(sK10(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ( app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_8679,plain,
( ( app(app(sK9(sK3,sK2),sK2),sK10(sK3,sK2)) = sK3 )
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_49,c_87]) ).
tcf(c_8689,plain,
app(app(sK9(sK3,sK2),sK2),sK10(sK3,sK2)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_8679,c_58,c_57]) ).
tcf(c_8799,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ ssList(sK10(sK3,sK2))
| ~ ssList(app(sK9(sK3,sK2),sK2))
| ~ memberP(app(sK9(sK3,sK2),sK2),X0) ),
inference(superposition,[status(thm)],[c_8689,c_70]) ).
tcf(c_23929,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK2)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK10(sK3,sK2))
| ~ ssList(sK9(sK3,sK2))
| ~ ssList(app(sK9(sK3,sK2),sK2)) ),
inference(superposition,[status(thm)],[c_71,c_8799]) ).
tcf(c_23930,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK10(sK3,sK2))
| ~ ssList(sK9(sK3,sK2))
| ~ ssList(app(sK9(sK3,sK2),sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23929,c_58]) ).
tcf(c_77888,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK2)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK10(sK3,sK2))
| ~ ssList(sK9(sK3,sK2)) ),
inference(superposition,[status(thm)],[c_121,c_23930]) ).
tcf(c_77889,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK10(sK3,sK2))
| ~ ssList(sK9(sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_77888,c_58]) ).
tcf(c_77911,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK2)
| ~ ssList(sK3)
| ~ ssItem(X0)
| ~ segmentP(sK3,sK2)
| ~ memberP(sK2,X0)
| ~ ssList(sK9(sK3,sK2)) ),
inference(superposition,[status(thm)],[c_86,c_77889]) ).
tcf(c_77912,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK9(sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_77911,c_58,c_57,c_49]) ).
tcf(c_77930,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK2)
| ~ ssList(sK3)
| ~ ssItem(X0)
| ~ segmentP(sK3,sK2)
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_85,c_77912]) ).
tcf(c_77931,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_77930,c_58,c_57,c_49]) ).
tcf(c_77945,plain,
( memberP(sK3,sK4)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_52,c_77931]) ).
tcf(c_77946,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_77945,c_53,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC403+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n010.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 18:04:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 25.95/5.79 % SZS status Started for theBenchmark.p
% 25.95/5.79 % SZS status Theorem for theBenchmark.p
% 25.95/5.79
% 25.95/5.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.95/5.79
% 25.95/5.79 % ------ iProver source info
% 25.95/5.79
% 25.95/5.79 % git: date: 2026-07-19 20:42:38 +0200
% 25.95/5.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.95/5.79 % git: non_committed_changes: false
% 25.95/5.79
% 25.95/5.79 % ------ Parsing...
% 25.95/5.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.95/5.79
% 25.95/5.79 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 25.95/5.79
% 25.95/5.79 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 25.95/5.79
% 25.95/5.79 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.95/5.79 % ------ Proving...
% 25.95/5.79 % ------ Problem Properties
% 25.95/5.79
% 25.95/5.79 %
% 25.95/5.79 % clauses 87
% 25.95/5.79 % conjectures 7
% 25.95/5.79 % EPR 29
% 25.95/5.79 % Horn 62
% 25.95/5.79 % unary 14
% 25.95/5.79 % binary 8
% 25.95/5.79 % lits 304
% 25.95/5.79 % lits eq 58
% 25.95/5.79 % fd_pure 0
% 25.95/5.79 % fd_pseudo 0
% 25.95/5.79 % fd_cond 17
% 25.95/5.79 % fd_pseudo_cond 9
% 25.95/5.79 % AC symbols 0
% 25.95/5.79
% 25.95/5.79 % ------ Schedule dynamic 5 is on
% 25.95/5.79
% 25.95/5.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 25.95/5.79
% 25.95/5.79
% 25.95/5.79 % ------
% 25.95/5.79 % Current options:
% 25.95/5.79 % ------
% 25.95/5.79
% 25.95/5.79
% 25.95/5.79 %
% 25.95/5.79
% 25.95/5.79 % ------ Proving...
% 25.95/5.79 %
% 25.95/5.79
% 25.95/5.79 % SZS status Theorem for theBenchmark.p
% 25.95/5.79
% 25.95/5.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.95/5.79
%------------------------------------------------------------------------------