%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:49:15 PM UTC 2026
% Result : Theorem 1.18s 1.27s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 5 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 25 !; 3 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2] :
( cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
& cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
& cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,axiom,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
fof(f15,plain,
? [X0,X1,X2] :
( cartesian_product2(X2,unordered_pair(X0,X1)) != set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
| cartesian_product2(unordered_pair(X0,X1),X2) != set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f18,plain,
( cartesian_product2(sK4,unordered_pair(sK2,sK3)) != set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3)))
| cartesian_product2(unordered_pair(sK2,sK3),sK4) != set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f15]) ).
fof(f26,plain,
! [X2,X0,X1] : cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X2,X0,X1] : cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f28,plain,
( cartesian_product2(sK4,unordered_pair(sK2,sK3)) != set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3)))
| cartesian_product2(unordered_pair(sK2,sK3),sK4) != set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f31,plain,
( set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))) != cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3)))
| set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)) != cartesian_product2(set_union2(singleton(sK2),singleton(sK3)),sK4) ),
inference(definition_unfolding,[],[f28,f29,f29]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(cartesian_product2(X0,X1),cartesian_product2(X2,X1)) = cartesian_product2(set_union2(X0,X2),X1),
inference(cnf_transformation,[],[f27]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) = cartesian_product2(X0,set_union2(X1,X2)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_58,negated_conjecture,
( ( set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))) != cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3))) )
| ( set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)) != cartesian_product2(set_union2(singleton(sK2),singleton(sK3)),sK4) ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_75,plain,
set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))) != cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3))),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_56]) ).
tcf(c_78,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_75,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:32:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 1.18/1.27 % SZS status Started for theBenchmark.p
% 1.18/1.27 % SZS status Theorem for theBenchmark.p
% 1.18/1.27
% 1.18/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.18/1.27
% 1.18/1.27 % ------ iProver source info
% 1.18/1.27
% 1.18/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.18/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.18/1.27 % git: non_committed_changes: false
% 1.18/1.27
% 1.18/1.27 % ------ Parsing...
% 1.18/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.18/1.27
% 1.18/1.27 % ------ Preprocessing...%
% 1.18/1.27
% 1.18/1.27 % SZS status Theorem for theBenchmark.p
% 1.18/1.27
% 1.18/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.18/1.27
% 1.18/1.27
%------------------------------------------------------------------------------