%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET183+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 : n011.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 02:46:51 PM UTC 2026
% Result : Theorem 0.68s 16.06s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 13 unt; 1 def)
% Number of atoms : 178 ( 34 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 165 ( 66 ~; 69 |; 22 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 75 !; 6 ?; 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(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f8,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> intersection(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_intersection) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> intersection(X0,X1) = X0 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
? [X0,X1] :
( subset(X0,X1)
& intersection(X0,X1) != X0 ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,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(f13,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,[],[f12]) ).
fof(f14,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,[],[f10]) ).
fof(f15,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,[],[f14]) ).
fof(f16,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))],[f15]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) )
& ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f20]) ).
fof(f22,plain,
( subset(sK2,sK3)
& sK2 != intersection(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f11]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
sK2 != intersection(sK2,sK3),
inference(cnf_transformation,[],[f22]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_63,negated_conjecture,
intersection(sK2,sK3) != sK2,
inference(cnf_transformation,[],[f40]) ).
tcf(c_64,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f39]) ).
tcf(c_285,definition,
iPr_def_10 = intersection(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_286,negated_conjecture,
subset(sK2,sK3),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_287,negated_conjecture,
iPr_def_10 != sK2,
inference(demodulation,[status(thm)],[c_63,c_285]) ).
tcf(c_288,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_489,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_285,c_50]) ).
tcf(c_621,plain,
! [X0: $i] :
( ( iPr_def_10 = sK2 )
| ( iPr_def_10 != X0 )
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_290]) ).
tcf(c_703,plain,
( ( iPr_def_10 = sK2 )
| ( iPr_def_10 != iPr_def_10 )
| ( sK2 != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_621]) ).
tcf(c_704,plain,
iPr_def_10 = iPr_def_10,
inference(instantiation,[status(thm)],[c_288]) ).
tcf(c_715,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK3)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_285,c_49]) ).
tcf(c_745,plain,
! [X0: $i] :
( member(sK1(X0,iPr_def_10),sK2)
| member(sK1(X0,iPr_def_10),X0)
| ( X0 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_62,c_489]) ).
tcf(c_786,plain,
( member(sK1(sK2,iPr_def_10),sK2)
| ( sK2 = iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_745]) ).
tcf(c_815,plain,
( ( sK2 = iPr_def_10 )
| ~ member(sK1(sK2,iPr_def_10),iPr_def_10)
| ~ member(sK1(sK2,iPr_def_10),sK2) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_1590,plain,
( member(sK1(sK2,iPr_def_10),sK2)
| ( sK2 = iPr_def_10 ) ),
inference(equality_factoring,[status(thm)],[c_745]) ).
tcf(c_1628,plain,
member(sK1(sK2,iPr_def_10),sK2),
inference(global_subsumption_just,[status(thm)],[c_1590,c_287,c_703,c_704,c_786]) ).
tcf(c_1630,plain,
! [X0: $i] :
( member(sK1(sK2,iPr_def_10),X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_1628,c_55]) ).
tcf(c_1632,plain,
( member(sK1(sK2,iPr_def_10),iPr_def_10)
| ~ member(sK1(sK2,iPr_def_10),sK3) ),
inference(superposition,[status(thm)],[c_1628,c_715]) ).
tcf(c_1955,plain,
~ member(sK1(sK2,iPr_def_10),sK3),
inference(global_subsumption_just,[status(thm)],[c_1632,c_287,c_703,c_704,c_786,c_815,c_1632]) ).
tcf(c_1958,plain,
~ subset(sK2,sK3),
inference(superposition,[status(thm)],[c_1630,c_1955]) ).
tcf(c_1959,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1958,c_286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET183+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.03/15.41 % CPULimit : 300
% 0.03/15.41 % WCLimit : 300
% 0.03/15.41 % DateTime : Thu Sep 24 10:10:12 UTC 2026
% 0.03/15.41 % CPUTime :
% 0.03/15.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/15.43 Running first-order theorem proving
% 0.03/15.43 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
% 0.03/15.43
% 0.03/15.43 % ======== iProver multi-core TPTP/SMT =========
% 0.03/15.43
% 0.03/15.43 % Detected problem language: tptp
% 0.03/15.44 % Proving...
% 0.68/16.06 % SZS status Started for theBenchmark.p
% 0.68/16.06 % SZS status Theorem for theBenchmark.p
% 0.68/16.06
% 0.68/16.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.68/16.06
% 0.68/16.06 % ------ iProver source info
% 0.68/16.06
% 0.68/16.06 % git: date: 2026-07-19 20:42:38 +0200
% 0.68/16.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.68/16.06 % git: non_committed_changes: false
% 0.68/16.06
% 0.68/16.06 % ------ Parsing...
% 0.68/16.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.68/16.06
% 0.68/16.06 % ------ 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 %
% 0.68/16.06
% 0.68/16.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.68/16.06
% 0.68/16.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.68/16.06 % ------ Proving...
% 0.68/16.06 % ------ Problem Properties
% 0.68/16.06
% 0.68/16.06 %
% 0.68/16.06 % clauses 15
% 0.68/16.06 % conjectures 2
% 0.68/16.06 % EPR 5
% 0.68/16.06 % Horn 13
% 0.68/16.06 % unary 6
% 0.68/16.06 % binary 4
% 0.68/16.06 % lits 29
% 0.68/16.06 % lits eq 6
% 0.68/16.06 % fd_pure 0
% 0.68/16.06 % fd_pseudo 0
% 0.68/16.06 % fd_cond 0
% 0.68/16.06 % fd_pseudo_cond 3
% 0.68/16.06 % AC symbols 0
% 0.68/16.06
% 0.68/16.06 % ------ Schedule dynamic 5 is on
% 0.68/16.06
% 0.68/16.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.68/16.06
% 0.68/16.06
% 0.68/16.06 % ------
% 0.68/16.06 % Current options:
% 0.68/16.06 % ------
% 0.68/16.06
% 0.68/16.06
% 0.68/16.06 %
% 0.68/16.06
% 0.68/16.06 % ------ Proving...
% 0.68/16.06 %
% 0.68/16.06
% 0.68/16.06 % SZS status Theorem for theBenchmark.p
% 0.68/16.06
% 0.68/16.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.68/16.06
% 0.68/16.06
%------------------------------------------------------------------------------