%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC200+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 : n015.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 03:08:50 PM UTC 2026
% Result : Theorem 1.40s 1.76s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 65 ( 16 unt; 0 def)
% Number of atoms : 232 ( 56 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 275 ( 108 ~; 103 |; 45 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 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; 7 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 65 !; 18 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax2) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
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)
=> ( ? [X4] :
( ! [X5] :
( ssItem(X5)
=> ( X4 = X5
| ~ memberP(X0,X5) ) )
& ssItem(X4) )
| ~ singletonP(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)
=> ( ? [X4] :
( ! [X5] :
( ssItem(X5)
=> ( X4 = X5
| ~ memberP(X0,X5) ) )
& ssItem(X4) )
| ~ singletonP(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)
& ! [X4] :
( ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X0,X5) )
| ~ ssItem(X4) )
& singletonP(X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ! [X4] :
( ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X0,X5) )
| ~ ssItem(X4) )
& singletonP(X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f101,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(f104,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f123,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ! [X4] :
( ( ssItem(sK4(X4))
& sK4(X4) != X4
& memberP(sK0,sK4(X4)) )
| ~ ssItem(X4) )
& singletonP(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(X4))],[f99]) ).
fof(f124,plain,
( sK5 != sK6
& ssItem(sK6)
& ssItem(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f2]) ).
fof(f125,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,[],[f101]) ).
fof(f126,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,[],[f125]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f133,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f132]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK9(X0),nil) = X0
& ssItem(sK9(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0))],[f133]) ).
fof(f138,plain,
ssList(sK0),
inference(cnf_transformation,[],[f123]) ).
fof(f142,plain,
! [X4] :
( ssItem(sK4(X4))
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f123]) ).
fof(f143,plain,
! [X4] :
( sK4(X4) != X4
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f123]) ).
fof(f144,plain,
! [X4] :
( memberP(sK0,sK4(X4))
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f123]) ).
fof(f145,plain,
singletonP(sK2),
inference(cnf_transformation,[],[f123]) ).
fof(f146,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f123]) ).
fof(f150,plain,
ssItem(sK5),
inference(cnf_transformation,[],[f124]) ).
fof(f151,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f126]) ).
fof(f163,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| cons(sK9(X0),nil) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f164,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| ssItem(sK9(X0)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f170,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f186,plain,
! [X4] :
( memberP(sK2,sK4(X4))
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f144,f146]) ).
fof(f188,plain,
ssList(sK2),
inference(definition_unfolding,[],[f138,f146]) ).
tcf(c_49,negated_conjecture,
singletonP(sK2),
inference(cnf_transformation,[],[f145]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( memberP(sK2,sK4(X0))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( ~ ssItem(X0)
| ( sK4(X0) != X0 ) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( ssItem(sK4(X0))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_56,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f188]) ).
tcf(c_57,plain,
ssItem(sK5),
inference(cnf_transformation,[],[f150]) ).
tcf(c_60,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_63,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,[],[f152]) ).
tcf(c_73,plain,
! [X0: $i] :
( ssItem(sK9(X0))
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_74,plain,
! [X0: $i] :
( ( cons(sK9(X0),nil) = X0 )
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_79,plain,
ssList(nil),
inference(cnf_transformation,[],[f170]) ).
tcf(c_675,plain,
! [X0: $i] :
( ssItem(sK9(X0))
| ~ ssList(X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_73]) ).
tcf(c_676,plain,
( ssItem(sK9(sK2))
| ~ ssList(sK2) ),
inference(unflattening,[status(thm)],[c_675]) ).
tcf(c_2143,plain,
( ( cons(sK9(sK2),nil) = sK2 )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_49,c_74]) ).
tcf(c_2144,plain,
cons(sK9(sK2),nil) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_2143,c_56]) ).
tcf(c_2380,plain,
( ssItem(sK4(sK5))
| ~ ssItem(sK5) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_3033,plain,
( ~ ssItem(sK4(sK5))
| ( sK4(sK4(sK5)) != sK4(sK5) ) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_3070,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK9(sK2) = X0 )
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK9(sK2))
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_2144,c_63]) ).
tcf(c_3073,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK9(sK2) = X0 )
| ~ ssItem(X0)
| ~ ssItem(sK9(sK2))
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3070,c_79]) ).
tcf(c_18669,plain,
( ( cons(sK9(sK2),nil) = sK2 )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_49,c_74]) ).
tcf(c_18670,plain,
cons(sK9(sK2),nil) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_18669,c_56]) ).
tcf(c_20338,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK9(sK2) = X0 )
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK9(sK2))
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_18670,c_63]) ).
tcf(c_20340,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK9(sK2) = X0 )
| ~ ssItem(X0)
| ~ ssItem(sK9(sK2))
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20338,c_79]) ).
tcf(c_20633,plain,
! [X0: $i] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0)
| ( sK9(sK2) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_20340,c_56,c_60,c_676,c_3073]) ).
tcf(c_20634,plain,
! [X0: $i] :
( ( sK9(sK2) = X0 )
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(renaming,[status(thm)],[c_20633]) ).
tcf(c_20642,plain,
! [X0: $i] :
( ( sK4(X0) = sK9(sK2) )
| ~ ssItem(X0)
| ~ ssItem(sK4(X0)) ),
inference(superposition,[status(thm)],[c_50,c_20634]) ).
tcf(c_20679,plain,
! [X0: $i] :
( ( sK4(X0) = sK9(sK2) )
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_20642,c_52,c_20642]) ).
tcf(c_20686,plain,
! [X0: $i] :
( ( sK4(sK4(X0)) = sK9(sK2) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_52,c_20679]) ).
tcf(c_20687,plain,
sK4(sK5) = sK9(sK2),
inference(superposition,[status(thm)],[c_57,c_20679]) ).
tcf(c_20724,plain,
! [X0: $i] :
( ( sK4(sK4(X0)) = sK4(sK5) )
| ~ ssItem(X0) ),
inference(light_normalisation,[status(thm)],[c_20686,c_20687]) ).
tcf(c_20732,plain,
sK4(sK4(sK5)) = sK4(sK5),
inference(superposition,[status(thm)],[c_57,c_20724]) ).
tcf(c_20744,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20732,c_3033,c_2380,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC200+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 16:59:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.40/1.76 % SZS status Started for theBenchmark.p
% 1.40/1.76 % SZS status Theorem for theBenchmark.p
% 1.40/1.76
% 1.40/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.40/1.76
% 1.40/1.76 % ------ iProver source info
% 1.40/1.76
% 1.40/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 1.40/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.40/1.76 % git: non_committed_changes: false
% 1.40/1.76
% 1.40/1.76 % ------ Parsing...
% 1.40/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.40/1.76
% 1.40/1.76 % ------ 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 %
% 1.40/1.76
% 1.40/1.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.40/1.76
% 1.40/1.76 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.40/1.76 % ------ Proving...
% 1.40/1.76 % ------ Problem Properties
% 1.40/1.76
% 1.40/1.76 %
% 1.40/1.76 % clauses 44
% 1.40/1.76 % conjectures 6
% 1.40/1.76 % EPR 9
% 1.40/1.76 % Horn 39
% 1.40/1.76 % unary 9
% 1.40/1.76 % binary 6
% 1.40/1.76 % lits 139
% 1.40/1.76 % lits eq 29
% 1.40/1.76 % fd_pure 0
% 1.40/1.76 % fd_pseudo 0
% 1.40/1.76 % fd_cond 4
% 1.40/1.76 % fd_pseudo_cond 5
% 1.40/1.76 % AC symbols 0
% 1.40/1.76
% 1.40/1.76 % ------ Schedule dynamic 5 is on
% 1.40/1.76
% 1.40/1.76 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.40/1.76
% 1.40/1.76
% 1.40/1.76 % ------
% 1.40/1.76 % Current options:
% 1.40/1.76 % ------
% 1.40/1.76
% 1.40/1.76
% 1.40/1.76 %
% 1.40/1.76
% 1.40/1.76 % ------ Proving...
% 1.40/1.76 %
% 1.40/1.76
% 1.40/1.76 % SZS status Theorem for theBenchmark.p
% 1.40/1.76
% 1.40/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.40/1.76
% 1.40/1.76
%------------------------------------------------------------------------------