%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET581+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 : n004.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 02:47:26 PM UTC 2026
% Result : Theorem 1.76s 1.27s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 17 unt; 1 def)
% Number of atoms : 75 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 65 ( 29 ~; 18 |; 13 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 39 !; 6 ?; 11 :)
% 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] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( ( member(X0,X2)
& member(X0,X1) )
=> not_equal(intersection(X1,X2),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th24) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( ( member(X0,X2)
& member(X0,X1) )
=> not_equal(intersection(X1,X2),empty_set) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( X0 != X1
=> not_equal(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f10,plain,
! [X0,X1] :
( X0 = X1
| not_equal(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f11,plain,
? [X0,X1,X2] :
( member(X0,X2)
& member(X0,X1)
& ~ not_equal(intersection(X1,X2),empty_set) ),
inference(ennf_transformation,[],[f8]) ).
fof(f12,plain,
? [X0,X1,X2] :
( member(X0,X2)
& member(X0,X1)
& ~ not_equal(intersection(X1,X2),empty_set) ),
inference(flattening,[],[f11]) ).
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(nnf_transformation,[],[f1]) ).
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(flattening,[],[f13]) ).
fof(f18,plain,
( member(sK1,sK3)
& member(sK1,sK2)
& ~ not_equal(intersection(sK2,sK3),empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f12]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f29,plain,
member(sK1,sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
member(sK1,sK2),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
~ not_equal(intersection(sK2,sK3),empty_set),
inference(cnf_transformation,[],[f18]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_52,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( not_equal(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_57,negated_conjecture,
~ not_equal(intersection(sK2,sK3),empty_set),
inference(cnf_transformation,[],[f31]) ).
tcf(c_58,negated_conjecture,
member(sK1,sK2),
inference(cnf_transformation,[],[f30]) ).
tcf(c_59,negated_conjecture,
member(sK1,sK3),
inference(cnf_transformation,[],[f29]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( X1 != empty_set )
| ( intersection(sK2,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_57]) ).
tcf(c_141,plain,
intersection(sK2,sK3) = empty_set,
inference(unflattening,[status(thm)],[c_140]) ).
tcf(c_211,definition,
iPr_def_10 = intersection(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_212,plain,
iPr_def_10 = empty_set,
inference(demodulation,[status(thm)],[c_141,c_211]) ).
tcf(c_213,negated_conjecture,
member(sK1,sK3),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_214,negated_conjecture,
member(sK1,sK2),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_344,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_52,c_212]) ).
tcf(c_365,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK3)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_211,c_49]) ).
tcf(c_368,plain,
! [X0: $i] :
( ~ member(X0,sK3)
| ~ member(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_365,c_344]) ).
tcf(c_429,plain,
~ member(sK1,sK3),
inference(superposition,[status(thm)],[c_214,c_368]) ).
tcf(c_430,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_429,c_213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:20:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 1.76/1.27 % SZS status Started for theBenchmark.p
% 1.76/1.27 % SZS status Theorem for theBenchmark.p
% 1.76/1.27
% 1.76/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.76/1.27
% 1.76/1.27 % ------ iProver source info
% 1.76/1.27
% 1.76/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.76/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.76/1.27 % git: non_committed_changes: false
% 1.76/1.27
% 1.76/1.27 % ------ Parsing...
% 1.76/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.76/1.27
% 1.76/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.76/1.27
% 1.76/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.76/1.27
% 1.76/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.76/1.27 % ------ Proving...
% 1.76/1.27 % ------ Problem Properties
% 1.76/1.27
% 1.76/1.27 %
% 1.76/1.27 % clauses 11
% 1.76/1.27 % conjectures 2
% 1.76/1.27 % EPR 4
% 1.76/1.27 % Horn 10
% 1.76/1.27 % unary 6
% 1.76/1.27 % binary 2
% 1.76/1.27 % lits 19
% 1.76/1.27 % lits eq 5
% 1.76/1.27 % fd_pure 0
% 1.76/1.27 % fd_pseudo 0
% 1.76/1.27 % fd_cond 0
% 1.76/1.27 % fd_pseudo_cond 2
% 1.76/1.27 % AC symbols 0
% 1.76/1.27
% 1.76/1.27 % ------ Schedule dynamic 5 is on
% 1.76/1.27
% 1.76/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.76/1.27
% 1.76/1.27
% 1.76/1.27 % ------
% 1.76/1.27 % Current options:
% 1.76/1.27 % ------
% 1.76/1.27
% 1.76/1.27
% 1.76/1.27 %
% 1.76/1.27
% 1.76/1.27 % ------ Proving...
% 1.76/1.27 %
% 1.76/1.27
% 1.76/1.27 % SZS status Theorem for theBenchmark.p
% 1.76/1.27
% 1.76/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.76/1.27
% 1.76/1.27
%------------------------------------------------------------------------------