%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET639+3 : 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 : n005.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 02:47:39 PM UTC 2026
% Result : Theorem 1.80s 1.17s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 18 unt; 1 def)
% Number of atoms : 45 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 3 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 18 !; 4 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> intersection(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_intersection) ).
fof(f6,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f10,conjecture,
! [X0,X1] :
( ( intersection(X1,X0) = empty_set
& subset(X0,X1) )
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th121) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( ( intersection(X1,X0) = empty_set
& subset(X0,X1) )
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| intersection(X0,X1) = X0 ),
inference(ennf_transformation,[],[f1]) ).
fof(f14,plain,
? [X0,X1] :
( intersection(X1,X0) = empty_set
& subset(X0,X1)
& empty_set != X0 ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0,X1] :
( intersection(X1,X0) = empty_set
& subset(X0,X1)
& empty_set != X0 ),
inference(flattening,[],[f14]) ).
fof(f26,plain,
( empty_set = intersection(sK3,sK2)
& subset(sK2,sK3)
& empty_set != sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f15]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| intersection(X0,X1) = X0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f38,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f44,plain,
empty_set = intersection(sK3,sK2),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = X0 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_64,negated_conjecture,
empty_set != sK2,
inference(cnf_transformation,[],[f46]) ).
tcf(c_65,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f45]) ).
tcf(c_66,negated_conjecture,
intersection(sK3,sK2) = empty_set,
inference(cnf_transformation,[],[f44]) ).
tcf(c_137,plain,
intersection(sK2,sK3) = empty_set,
inference(demodulation,[status(thm)],[c_66,c_60]) ).
tcf(c_308,definition,
iPr_def_10 = intersection(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_309,plain,
iPr_def_10 = empty_set,
inference(demodulation,[status(thm)],[c_137,c_308]) ).
tcf(c_310,negated_conjecture,
subset(sK2,sK3),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_311,negated_conjecture,
empty_set != sK2,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_510,plain,
sK2 != iPr_def_10,
inference(light_normalisation,[status(thm)],[c_311,c_309]) ).
tcf(c_547,plain,
intersection(sK2,sK3) = sK2,
inference(superposition,[status(thm)],[c_310,c_49]) ).
tcf(c_549,plain,
sK2 = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_547,c_308]) ).
tcf(c_550,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_549,c_510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET639+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:32:32 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...
% 1.80/1.17 % SZS status Started for theBenchmark.p
% 1.80/1.17 % SZS status Theorem for theBenchmark.p
% 1.80/1.17
% 1.80/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.80/1.17
% 1.80/1.17 % ------ iProver source info
% 1.80/1.17
% 1.80/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 1.80/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.80/1.17 % git: non_committed_changes: false
% 1.80/1.17
% 1.80/1.17 % ------ Parsing...
% 1.80/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.80/1.17
% 1.80/1.17 % ------ 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 %
% 1.80/1.17
% 1.80/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.80/1.17
% 1.80/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.80/1.17 % ------ Proving...
% 1.80/1.17 % ------ Problem Properties
% 1.80/1.17
% 1.80/1.17 %
% 1.80/1.17 % clauses 17
% 1.80/1.17 % conjectures 2
% 1.80/1.17 % EPR 7
% 1.80/1.17 % Horn 15
% 1.80/1.17 % unary 7
% 1.80/1.17 % binary 5
% 1.80/1.17 % lits 32
% 1.80/1.17 % lits eq 8
% 1.80/1.17 % fd_pure 0
% 1.80/1.17 % fd_pseudo 0
% 1.80/1.17 % fd_cond 0
% 1.80/1.17 % fd_pseudo_cond 3
% 1.80/1.17 % AC symbols 0
% 1.80/1.17
% 1.80/1.17 % ------ Schedule dynamic 5 is on
% 1.80/1.17
% 1.80/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.80/1.17
% 1.80/1.17
% 1.80/1.17 % ------
% 1.80/1.17 % Current options:
% 1.80/1.17 % ------
% 1.80/1.17
% 1.80/1.17
% 1.80/1.17 %
% 1.80/1.17
% 1.80/1.17 % ------ Proving...
% 1.80/1.17 %
% 1.80/1.17
% 1.80/1.17 % SZS status Theorem for theBenchmark.p
% 1.80/1.17
% 1.80/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.80/1.17
% 1.80/1.17
%------------------------------------------------------------------------------