%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 02:49:13 PM UTC 2026
% Result : Theorem 3.03s 1.30s
% Output : CNFRefutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 20 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 8 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 38 !; 4 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2,X3] : cartesian_product2(set_union2(X0,X1),set_union2(X2,X3)) = set_union2(set_union2(set_union2(cartesian_product2(X0,X2),cartesian_product2(X0,X3)),cartesian_product2(X1,X2)),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3] : cartesian_product2(set_union2(X0,X1),set_union2(X2,X3)) = set_union2(set_union2(set_union2(cartesian_product2(X0,X2),cartesian_product2(X0,X3)),cartesian_product2(X1,X2)),cartesian_product2(X1,X3)),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1,X2] : set_union2(set_union2(X0,X1),X2) = set_union2(X0,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
fof(f14,plain,
? [X0,X1,X2,X3] : cartesian_product2(set_union2(X0,X1),set_union2(X2,X3)) != set_union2(set_union2(set_union2(cartesian_product2(X0,X2),cartesian_product2(X0,X3)),cartesian_product2(X1,X2)),cartesian_product2(X1,X3)),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)) != set_union2(set_union2(set_union2(cartesian_product2(sK2,sK4),cartesian_product2(sK2,sK5)),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK5)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f14]) ).
fof(f18,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X2,X0,X1] : cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f25,plain,
! [X2,X0,X1] : cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f26,plain,
cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)) != set_union2(set_union2(set_union2(cartesian_product2(sK2,sK4),cartesian_product2(sK2,sK5)),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK5)),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X2,X0,X1] : set_union2(set_union2(X0,X1),X2) = set_union2(X0,set_union2(X1,X2)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_55,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,[],[f25]) ).
tcf(c_56,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,[],[f24]) ).
tcf(c_57,negated_conjecture,
set_union2(set_union2(set_union2(cartesian_product2(sK2,sK4),cartesian_product2(sK2,sK5)),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK5)) != cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(set_union2(X0,X1),X2) = set_union2(X0,set_union2(X1,X2)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_65,negated_conjecture,
set_union2(cartesian_product2(sK2,sK4),set_union2(cartesian_product2(sK2,sK5),set_union2(cartesian_product2(sK3,sK4),cartesian_product2(sK3,sK5)))) != cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)),
inference(theory_normalisation,[status(thm)],[c_57,c_58,c_49]) ).
tcf(c_96,plain,
set_union2(cartesian_product2(sK2,sK5),set_union2(cartesian_product2(sK3,sK5),cartesian_product2(set_union2(sK2,sK3),sK4))) != cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)),
inference(ac_demodulation,[status(thm)],[c_65,c_55,c_58,c_49]) ).
tcf(c_97,plain,
set_union2(cartesian_product2(set_union2(sK2,sK3),sK4),cartesian_product2(set_union2(sK2,sK3),sK5)) != cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)),
inference(ac_demodulation,[status(thm)],[c_96,c_55,c_58,c_49]) ).
tcf(c_98,plain,
$false,
inference(ac_demodulation,[status(thm)],[c_97,c_56,c_58,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:33:12 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 0.16/0.43
% 0.16/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.43
% 0.16/0.43 % Detected problem language: tptp
% 0.16/0.45 % Proving...
% 3.03/1.30 % SZS status Started for theBenchmark.p
% 3.03/1.30 % SZS status Theorem for theBenchmark.p
% 3.03/1.30
% 3.03/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.03/1.30
% 3.03/1.30 % ------ iProver source info
% 3.03/1.30
% 3.03/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.03/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.03/1.30 % git: non_committed_changes: false
% 3.03/1.30
% 3.03/1.30 % ------ Parsing...
% 3.03/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.03/1.30
% 3.03/1.30 % ------ Preprocessing...%
% 3.03/1.30
% 3.03/1.30 % SZS status Theorem for theBenchmark.p
% 3.03/1.30
% 3.03/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.03/1.30
% 3.03/1.30
%------------------------------------------------------------------------------