TSTP Solution File: SET979+1 by Etableau---0.67
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%------------------------------------------------------------------------------
% File : Etableau---0.67
% Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% Computer : n015.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 : 600s
% DateTime : Tue Jul 19 01:04:14 EDT 2022
% Result : Theorem 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 8 ~; 3 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% 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 : 24 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t132_zfmisc_1,conjecture,
! [X1,X2,X3] :
( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
& cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
fof(t41_enumset1,axiom,
! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_enumset1) ).
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/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
& cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
inference(assume_negation,[status(cth)],[t132_zfmisc_1]) ).
fof(c_0_4,negated_conjecture,
( cartesian_product2(unordered_pair(esk3_0,esk4_0),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0))
| cartesian_product2(esk5_0,unordered_pair(esk3_0,esk4_0)) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X21,X22] : unordered_pair(X21,X22) = set_union2(singleton(X21),singleton(X22)),
inference(variable_rename,[status(thm)],[t41_enumset1]) ).
cnf(c_0_6,negated_conjecture,
( cartesian_product2(unordered_pair(esk3_0,esk4_0),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0))
| cartesian_product2(esk5_0,unordered_pair(esk3_0,esk4_0)) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0))) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X15,X16,X17] :
( cartesian_product2(set_union2(X15,X16),X17) = set_union2(cartesian_product2(X15,X17),cartesian_product2(X16,X17))
& cartesian_product2(X17,set_union2(X15,X16)) = set_union2(cartesian_product2(X17,X15),cartesian_product2(X17,X16)) ),
inference(variable_rename,[status(thm)],[t120_zfmisc_1]) ).
cnf(c_0_9,negated_conjecture,
( cartesian_product2(esk5_0,set_union2(singleton(esk3_0),singleton(esk4_0))) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0)))
| cartesian_product2(set_union2(singleton(esk3_0),singleton(esk4_0)),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
cnf(c_0_10,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_8]) ).
cnf(c_0_11,negated_conjecture,
set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0)) != cartesian_product2(set_union2(singleton(esk3_0),singleton(esk4_0)),esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).
cnf(c_0_12,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_8]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 21:18:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.36 # No SInE strategy applied
% 0.19/0.36 # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 0.19/0.36 # and selection function SelectComplexExceptUniqMaxHorn.
% 0.19/0.36 #
% 0.19/0.36 # Presaturation interreduction done
% 0.19/0.36
% 0.19/0.36 # Proof found!
% 0.19/0.36 # SZS status Theorem
% 0.19/0.36 # SZS output start CNFRefutation
% See solution above
% 0.19/0.36 # Training examples: 0 positive, 0 negative
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