%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET696+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 : n013.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 02:47:49 PM UTC 2026
% Result : Theorem 1.09s 1.20s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 7 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 130 ( 56 ~; 45 |; 20 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 75 !; 4 ?; 15 :)
% 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(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
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,X1] :
( subset(X0,X1)
=> equal_set(intersection(difference(X1,X0),X0),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI28) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> equal_set(intersection(difference(X1,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] :
( subset(X0,X1)
& ~ equal_set(intersection(difference(X1,X0),X0),empty_set) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
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,
( subset(sK0,sK1)
& ~ equal_set(intersection(difference(sK1,sK0),sK0),empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,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(f26,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,[],[f25]) ).
fof(f28,plain,
~ equal_set(intersection(difference(sK1,sK0),sK0),empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,negated_conjecture,
~ equal_set(intersection(difference(sK1,sK0),sK0),empty_set),
inference(cnf_transformation,[],[f28]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_124,plain,
( ~ subset(empty_set,intersection(difference(sK1,sK0),sK0))
| ~ subset(intersection(difference(sK1,sK0),sK0),empty_set) ),
inference(resolution,[status(thm)],[c_49,c_57]) ).
tcf(c_184,plain,
( subset(intersection(difference(sK1,sK0),sK0),empty_set)
| member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),intersection(difference(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_185,plain,
( subset(empty_set,intersection(difference(sK1,sK0),sK0))
| member(sK2(empty_set,intersection(difference(sK1,sK0),sK0)),empty_set) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_195,plain,
~ member(sK2(empty_set,intersection(difference(sK1,sK0),sK0)),empty_set),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_206,plain,
( member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),sK0)
| ~ member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),intersection(difference(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_207,plain,
( member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),difference(sK1,sK0))
| ~ member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),intersection(difference(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_212,plain,
! [X0: $i] :
( ~ member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),sK0)
| ~ member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),difference(X0,sK0)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_270,plain,
( ~ member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),sK0)
| ~ member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),difference(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_212]) ).
tcf(c_271,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_270,c_206,c_207,c_195,c_185,c_184,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET696+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 11:41:28 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...
% 1.09/1.20 % SZS status Started for theBenchmark.p
% 1.09/1.20 % SZS status Theorem for theBenchmark.p
% 1.09/1.20
% 1.09/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.09/1.20
% 1.09/1.20 % ------ iProver source info
% 1.09/1.20
% 1.09/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.09/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.09/1.20 % git: non_committed_changes: false
% 1.09/1.20
% 1.09/1.20 % ------ Parsing...
% 1.09/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.09/1.20
% 1.09/1.20 % ------ 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 %
% 1.09/1.20
% 1.09/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.09/1.20 % ------ Proving...
% 1.09/1.20 % ------ Problem Properties
% 1.09/1.20
% 1.09/1.20 %
% 1.09/1.20 % clauses 12
% 1.09/1.20 % conjectures 1
% 1.09/1.20 % EPR 3
% 1.09/1.20 % Horn 10
% 1.09/1.20 % unary 2
% 1.09/1.20 % binary 7
% 1.09/1.20 % lits 25
% 1.09/1.20 % lits eq 0
% 1.09/1.20 % fd_pure 0
% 1.09/1.20 % fd_pseudo 0
% 1.09/1.20 % fd_cond 0
% 1.09/1.20 % fd_pseudo_cond 0
% 1.09/1.20 % AC symbols 0
% 1.09/1.20
% 1.09/1.20 % ------ Schedule dynamic 5 is on
% 1.09/1.20
% 1.09/1.20 % ------ no equalities: superposition off
% 1.09/1.20
% 1.09/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.09/1.20
% 1.09/1.20
% 1.09/1.20 % ------
% 1.09/1.20 % Current options:
% 1.09/1.20 % ------
% 1.09/1.20
% 1.09/1.20
% 1.09/1.20 %
% 1.09/1.20
% 1.09/1.20 % ------ Proving...
% 1.09/1.20 %
% 1.09/1.20
% 1.09/1.20 % SZS status Theorem for theBenchmark.p
% 1.09/1.20
% 1.09/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.09/1.20
% 1.09/1.20
%------------------------------------------------------------------------------