%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU167+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 02:55:43 PM UTC 2026
% Result : Theorem 1.64s 6.48s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 12 unt; 2 def)
% Number of atoms : 75 ( 2 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 60 ( 26 ~; 19 |; 11 &)
% ( 0 <=>; 4 =>; 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; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 45 !; 8 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f4,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f8,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f9,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f10,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
( subset(sK2,sK3)
& subset(sK0,sK1)
& ~ subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f10]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f16,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f17,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f13]) ).
fof(f18,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
~ subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK3)),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_52,negated_conjecture,
~ subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK3)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_53,negated_conjecture,
subset(sK0,sK1),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f17]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_80,definition,
iPr_def_10 = cartesian_product2(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_81,definition,
iPr_def_11 = cartesian_product2(sK1,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_82,negated_conjecture,
subset(sK2,sK3),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_83,negated_conjecture,
subset(sK0,sK1),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_84,negated_conjecture,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_52,c_81,c_80]) ).
tcf(c_193,plain,
! [X0: $i] :
( subset(iPr_def_10,cartesian_product2(X0,sK2))
| ~ subset(sK0,X0) ),
inference(superposition,[status(thm)],[c_80,c_50]) ).
tcf(c_226,plain,
! [X0: $i] :
( subset(cartesian_product2(sK1,X0),iPr_def_11)
| ~ subset(X0,sK3) ),
inference(superposition,[status(thm)],[c_81,c_51]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_10,X1)
| ~ subset(sK0,X0)
| ~ subset(cartesian_product2(X0,sK2),X1) ),
inference(superposition,[status(thm)],[c_193,c_55]) ).
tcf(c_366,plain,
( subset(iPr_def_10,iPr_def_11)
| ~ subset(sK2,sK3)
| ~ subset(sK0,sK1) ),
inference(superposition,[status(thm)],[c_226,c_250]) ).
tcf(c_368,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_366,c_84,c_82,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU167+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.57 % Computer : n010.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Thu Sep 24 13:01:41 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.09/5.57 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.61 Running first-order theorem proving
% 0.12/5.61 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
% 0.12/5.62
% 0.12/5.62 % ======== iProver multi-core TPTP/SMT =========
% 0.12/5.62
% 0.12/5.62 % Detected problem language: tptp
% 0.12/5.64 % Proving...
% 1.64/6.48 % SZS status Started for theBenchmark.p
% 1.64/6.48 % SZS status Theorem for theBenchmark.p
% 1.64/6.48
% 1.64/6.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.64/6.48
% 1.64/6.48 % ------ iProver source info
% 1.64/6.48
% 1.64/6.48 % git: date: 2026-07-19 20:42:38 +0200
% 1.64/6.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.64/6.48 % git: non_committed_changes: false
% 1.64/6.48
% 1.64/6.48 % ------ Parsing...
% 1.64/6.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.64/6.48
% 1.64/6.48 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.64/6.48
% 1.64/6.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.64/6.48
% 1.64/6.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.64/6.48 % ------ Proving...
% 1.64/6.48 % ------ Problem Properties
% 1.64/6.48
% 1.64/6.48 %
% 1.64/6.48 % clauses 9
% 1.64/6.48 % conjectures 3
% 1.64/6.48 % EPR 5
% 1.64/6.48 % Horn 9
% 1.64/6.48 % unary 6
% 1.64/6.48 % binary 2
% 1.64/6.48 % lits 13
% 1.64/6.48 % lits eq 2
% 1.64/6.48 % fd_pure 0
% 1.64/6.48 % fd_pseudo 0
% 1.64/6.48 % fd_cond 0
% 1.64/6.48 % fd_pseudo_cond 0
% 1.64/6.48 % AC symbols 0
% 1.64/6.48
% 1.64/6.48 % ------ Schedule dynamic 5 is on
% 1.64/6.48
% 1.64/6.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.64/6.48
% 1.64/6.48
% 1.64/6.48 % ------
% 1.64/6.48 % Current options:
% 1.64/6.48 % ------
% 1.64/6.48
% 1.64/6.48
% 1.64/6.48 %
% 1.64/6.48
% 1.64/6.48 % ------ Proving...
% 1.64/6.48 %
% 1.64/6.48
% 1.64/6.48 % SZS status Theorem for theBenchmark.p
% 1.64/6.48
% 1.64/6.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.64/6.48
% 1.64/6.48
%------------------------------------------------------------------------------