%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET968+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:09:03 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 17 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% 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 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t121_zfmisc_1,conjecture,
! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t4_xboole_1,axiom,
! [X1,X2,X3] : set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
fof(t120_zfmisc_1,axiom,
! [X1,X2,X3] :
( cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
inference(assume_negation,[status(cth)],[t121_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0)),cartesian_product2(esk4_0,esk5_0)),cartesian_product2(esk4_0,esk6_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X25,X26] : set_union2(X25,X26) = set_union2(X26,X25),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_7,plain,
! [X41,X42,X43] : set_union2(set_union2(X41,X42),X43) = set_union2(X41,set_union2(X42,X43)),
inference(variable_rename,[status(thm)],[t4_xboole_1]) ).
cnf(c_0_8,negated_conjecture,
cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0)),cartesian_product2(esk4_0,esk5_0)),cartesian_product2(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X34,X35,X36] :
( cartesian_product2(set_union2(X34,X35),X36) = set_union2(cartesian_product2(X34,X36),cartesian_product2(X35,X36))
& cartesian_product2(X36,set_union2(X34,X35)) = set_union2(cartesian_product2(X36,X34),cartesian_product2(X36,X35)) ),
inference(variable_rename,[status(thm)],[t120_zfmisc_1]) ).
cnf(c_0_11,plain,
set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
set_union2(cartesian_product2(esk4_0,esk6_0),set_union2(cartesian_product2(esk4_0,esk5_0),set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0)))) != cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
cnf(c_0_13,plain,
cartesian_product2(X1,set_union2(X2,X3)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
set_union2(X1,set_union2(X2,X3)) = set_union2(X3,set_union2(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
set_union2(cartesian_product2(esk4_0,esk5_0),set_union2(cartesian_product2(esk4_0,esk6_0),cartesian_product2(esk3_0,set_union2(esk5_0,esk6_0)))) != cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_9]) ).
cnf(c_0_16,plain,
set_union2(cartesian_product2(X1,X2),set_union2(cartesian_product2(X1,X3),X4)) = set_union2(cartesian_product2(X1,set_union2(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_17,plain,
cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET968+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:40:32 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------