%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET602+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 02:47:31 PM UTC 2026
% Result : Theorem 4.25s 1.31s
% Output : CNFRefutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 11 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 39 ~; 28 |; 9 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 53 !; 2 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f12,conjecture,
! [X0] : equal_set(difference(X0,X0),empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI29) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(difference(X0,X0),empty_set),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f16,plain,
? [X0] : ~ equal_set(difference(X0,X0),empty_set),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
~ equal_set(difference(sK0,sK0),empty_set),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( member(sK1(X0,X1),X0)
& ~ member(sK1(X0,X1),X1) )
| subset(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f24,plain,
~ equal_set(difference(sK0,sK0),empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,negated_conjecture,
~ equal_set(difference(sK0,sK0),empty_set),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f26]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_94,plain,
( ~ subset(empty_set,difference(sK0,sK0))
| ~ subset(difference(sK0,sK0),empty_set) ),
inference(resolution,[status(thm)],[c_49,c_50]) ).
tcf(c_132,plain,
( subset(difference(sK0,sK0),empty_set)
| member(sK1(difference(sK0,sK0),empty_set),difference(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_133,plain,
( subset(empty_set,difference(sK0,sK0))
| member(sK1(empty_set,difference(sK0,sK0)),empty_set) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_135,plain,
~ member(sK1(empty_set,difference(sK0,sK0)),empty_set),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_144,plain,
( member(sK1(difference(sK0,sK0),empty_set),sK0)
| ~ member(sK1(difference(sK0,sK0),empty_set),difference(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_145,plain,
! [X0: $i] :
( ~ member(sK1(difference(sK0,sK0),empty_set),sK0)
| ~ member(sK1(difference(sK0,sK0),empty_set),difference(X0,sK0)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_156,plain,
( ~ member(sK1(difference(sK0,sK0),empty_set),sK0)
| ~ member(sK1(difference(sK0,sK0),empty_set),difference(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_157,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_156,c_144,c_135,c_133,c_132,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET602+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 11:27:39 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 4.25/1.31 % SZS status Started for theBenchmark.p
% 4.25/1.31 % SZS status Theorem for theBenchmark.p
% 4.25/1.31
% 4.25/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.25/1.31
% 4.25/1.31 % ------ iProver source info
% 4.25/1.31
% 4.25/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.25/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.25/1.31 % git: non_committed_changes: false
% 4.25/1.31
% 4.25/1.31 % ------ Parsing...
% 4.25/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.25/1.31
% 4.25/1.31 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.25/1.31
% 4.25/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.25/1.31 % ------ Proving...
% 4.25/1.31 % ------ Problem Properties
% 4.25/1.31
% 4.25/1.31 %
% 4.25/1.31 % clauses 7
% 4.25/1.31 % conjectures 0
% 4.25/1.31 % EPR 1
% 4.25/1.31 % Horn 5
% 4.25/1.31 % unary 1
% 4.25/1.31 % binary 5
% 4.25/1.31 % lits 14
% 4.25/1.31 % lits eq 0
% 4.25/1.31 % fd_pure 0
% 4.25/1.31 % fd_pseudo 0
% 4.25/1.32 % fd_cond 0
% 4.25/1.32 % fd_pseudo_cond 0
% 4.25/1.32 % AC symbols 0
% 4.25/1.32
% 4.25/1.32 % ------ Schedule dynamic 5 is on
% 4.25/1.32
% 4.25/1.32 % ------ no conjectures: strip conj schedule
% 4.25/1.32
% 4.25/1.32 % ------ no equalities: superposition off
% 4.25/1.32
% 4.25/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.25/1.32
% 4.25/1.32
% 4.25/1.32 % ------
% 4.25/1.32 % Current options:
% 4.25/1.32 % ------
% 4.25/1.32
% 4.25/1.32
% 4.25/1.32 %
% 4.25/1.32
% 4.25/1.32 % ------ Proving...
% 4.25/1.32 %
% 4.25/1.32
% 4.25/1.32 % SZS status Theorem for theBenchmark.p
% 4.25/1.32
% 4.25/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.25/1.32
% 4.25/1.32
%------------------------------------------------------------------------------