%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 02:45:59 PM UTC 2026
% Result : Theorem 0.61s 0.97s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 19 unt; 2 def)
% Number of atoms : 158 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 60 ~; 51 |; 21 &)
% ( 5 <=>; 1 =>; 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 84 !; 4 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f10,conjecture,
! [X0,X1] : intersection(difference(X0,X1),X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] : intersection(difference(X0,X1),X1) = empty_set,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f13,plain,
? [X0,X1] : empty_set != intersection(difference(X0,X1),X1),
inference(ennf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f18]) ).
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,[],[f12]) ).
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(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f21]) ).
fof(f26,plain,
empty_set != intersection(difference(sK2,sK3),sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
empty_set != intersection(difference(sK2,sK3),sK3),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f33]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_66,negated_conjecture,
intersection(difference(sK2,sK3),sK3) != empty_set,
inference(cnf_transformation,[],[f46]) ).
tcf(c_145,plain,
intersection(sK3,difference(sK2,sK3)) != empty_set,
inference(demodulation,[status(thm)],[c_66,c_59]) ).
tcf(c_340,definition,
iPr_def_10 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_341,definition,
iPr_def_11 = intersection(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_342,plain,
iPr_def_11 != empty_set,
inference(demodulation,[status(thm)],[c_145,c_340,c_341]) ).
tcf(c_554,plain,
intersection(iPr_def_10,sK3) = iPr_def_11,
inference(demodulation,[status(thm)],[c_341,c_59]) ).
tcf(c_582,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_554,c_50]) ).
tcf(c_597,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_554,c_51]) ).
tcf(c_629,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_61,c_582]) ).
tcf(c_637,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),sK3) ),
inference(superposition,[status(thm)],[c_61,c_597]) ).
tcf(c_640,plain,
( subset(iPr_def_11,empty_set)
| member(sK0(iPr_def_11,empty_set),sK3) ),
inference(instantiation,[status(thm)],[c_637]) ).
tcf(c_678,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_340,c_54]) ).
tcf(c_742,plain,
( ( iPr_def_11 = empty_set )
| ~ subset(iPr_def_11,empty_set)
| ~ subset(empty_set,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_746,plain,
( subset(empty_set,iPr_def_11)
| member(sK0(empty_set,iPr_def_11),empty_set) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_881,plain,
~ member(sK0(empty_set,iPr_def_11),empty_set),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_915,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| ~ member(sK0(iPr_def_11,X0),sK3) ),
inference(superposition,[status(thm)],[c_629,c_678]) ).
tcf(c_926,plain,
( subset(iPr_def_11,empty_set)
| ~ member(sK0(iPr_def_11,empty_set),sK3) ),
inference(instantiation,[status(thm)],[c_915]) ).
tcf(c_927,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_926,c_881,c_746,c_742,c_640,c_342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Thu Sep 24 09:03:52 UTC 2026
% 0.04/0.29 % CPUTime :
% 0.04/0.29 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.31 Running first-order theorem proving
% 0.04/0.31 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.32
% 0.04/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.32
% 0.04/0.32 % Detected problem language: tptp
% 0.04/0.32 % Proving...
% 0.61/0.97 % SZS status Started for theBenchmark.p
% 0.61/0.97 % SZS status Theorem for theBenchmark.p
% 0.61/0.97
% 0.61/0.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.61/0.97
% 0.61/0.97 % ------ iProver source info
% 0.61/0.97
% 0.61/0.97 % git: date: 2026-07-19 20:42:38 +0200
% 0.61/0.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.61/0.97 % git: non_committed_changes: false
% 0.61/0.97
% 0.61/0.97 % ------ Parsing...
% 0.61/0.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.61/0.97
% 0.61/0.97 % ------ Preprocessing... sup_sim: 1 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 %
% 0.61/0.97
% 0.61/0.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.61/0.97
% 0.61/0.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.61/0.97 % ------ Proving...
% 0.61/0.97 % ------ Problem Properties
% 0.61/0.97
% 0.61/0.97 %
% 0.61/0.97 % clauses 18
% 0.61/0.97 % conjectures 0
% 0.61/0.97 % EPR 5
% 0.61/0.97 % Horn 15
% 0.61/0.97 % unary 6
% 0.61/0.97 % binary 6
% 0.61/0.97 % lits 36
% 0.61/0.97 % lits eq 7
% 0.61/0.97 % fd_pure 0
% 0.61/0.97 % fd_pseudo 0
% 0.61/0.97 % fd_cond 0
% 0.61/0.97 % fd_pseudo_cond 3
% 0.61/0.97 % AC symbols 0
% 0.61/0.97
% 0.61/0.97 % ------ Schedule dynamic 5 is on
% 0.61/0.97
% 0.61/0.97 % ------ no conjectures: strip conj schedule
% 0.61/0.97
% 0.61/0.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.61/0.97
% 0.61/0.97
% 0.61/0.97 % ------
% 0.61/0.97 % Current options:
% 0.61/0.97 % ------
% 0.61/0.97
% 0.61/0.97
% 0.61/0.97 %
% 0.61/0.97
% 0.61/0.97 % ------ Proving...
% 0.61/0.97 %
% 0.61/0.97
% 0.61/0.97 % SZS status Theorem for theBenchmark.p
% 0.61/0.97
% 0.61/0.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.61/0.97
% 0.61/0.97
%------------------------------------------------------------------------------