%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET984+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 05:09:05 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 19 unt; 0 def)
% Number of atoms : 113 ( 91 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 94 ( 27 ~; 54 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 96 ( 14 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t138_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(t134_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(t123_zfmisc_1,axiom,
! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(t28_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(t17_xboole_1,axiom,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t113_zfmisc_1,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ) ),
inference(assume_negation,[status(cth)],[t138_zfmisc_1]) ).
fof(c_0_8,plain,
! [X43,X44,X45,X46] :
( ( X43 = X45
| X43 = empty_set
| X44 = empty_set
| cartesian_product2(X43,X44) != cartesian_product2(X45,X46) )
& ( X44 = X46
| X43 = empty_set
| X44 = empty_set
| cartesian_product2(X43,X44) != cartesian_product2(X45,X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t134_zfmisc_1])])]) ).
fof(c_0_9,plain,
! [X39,X40,X41,X42] : cartesian_product2(set_intersection2(X39,X40),set_intersection2(X41,X42)) = set_intersection2(cartesian_product2(X39,X41),cartesian_product2(X40,X42)),
inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).
fof(c_0_10,plain,
! [X53,X54] :
( ~ subset(X53,X54)
| set_intersection2(X53,X54) = X53 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_11,negated_conjecture,
( subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
& cartesian_product2(esk3_0,esk4_0) != empty_set
& ( ~ subset(esk3_0,esk5_0)
| ~ subset(esk4_0,esk6_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( X1 = X2
| X3 = empty_set
| X1 = empty_set
| cartesian_product2(X3,X1) != cartesian_product2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X51,X52] : subset(set_intersection2(X51,X52),X51),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(c_0_17,plain,
! [X31,X32] : set_intersection2(X31,X32) = set_intersection2(X32,X31),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_18,plain,
( X1 = set_intersection2(X2,X3)
| X1 = empty_set
| X4 = empty_set
| cartesian_product2(X4,X1) != set_intersection2(cartesian_product2(X5,X2),cartesian_product2(X6,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
set_intersection2(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) = cartesian_product2(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( X1 = X2
| X1 = empty_set
| X3 = empty_set
| cartesian_product2(X1,X3) != cartesian_product2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( X1 = set_intersection2(esk4_0,esk6_0)
| X2 = empty_set
| X1 = empty_set
| cartesian_product2(X2,X1) != cartesian_product2(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X37,X38] :
( ( cartesian_product2(X37,X38) != empty_set
| X37 = empty_set
| X38 = empty_set )
& ( X37 != empty_set
| cartesian_product2(X37,X38) = empty_set )
& ( X38 != empty_set
| cartesian_product2(X37,X38) = empty_set ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])]) ).
cnf(c_0_25,plain,
( X1 = set_intersection2(X2,X3)
| X1 = empty_set
| X4 = empty_set
| cartesian_product2(X1,X4) != set_intersection2(cartesian_product2(X2,X5),cartesian_product2(X3,X6)) ),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_26,plain,
subset(set_intersection2(X1,X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( set_intersection2(esk4_0,esk6_0) = esk4_0
| esk4_0 = empty_set
| esk3_0 = empty_set ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( set_intersection2(X1,X2) = empty_set
| set_intersection2(X3,X4) = empty_set
| set_intersection2(X1,X2) = X5
| set_intersection2(cartesian_product2(X3,X1),cartesian_product2(X4,X2)) != cartesian_product2(X6,X5) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_29,negated_conjecture,
set_intersection2(cartesian_product2(X1,cartesian_product2(esk3_0,esk4_0)),cartesian_product2(X2,cartesian_product2(esk5_0,esk6_0))) = cartesian_product2(set_intersection2(X1,X2),cartesian_product2(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_30,negated_conjecture,
cartesian_product2(esk3_0,esk4_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,plain,
( cartesian_product2(X2,X1) = empty_set
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( X1 = set_intersection2(esk3_0,esk5_0)
| X2 = empty_set
| X1 = empty_set
| cartesian_product2(X1,X2) != cartesian_product2(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_33,negated_conjecture,
( ~ subset(esk3_0,esk5_0)
| ~ subset(esk4_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,negated_conjecture,
( esk3_0 = empty_set
| esk4_0 = empty_set
| subset(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( cartesian_product2(esk3_0,esk4_0) = X1
| set_intersection2(X2,X3) = empty_set
| cartesian_product2(set_intersection2(X2,X3),cartesian_product2(esk3_0,esk4_0)) != cartesian_product2(X4,X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_19]),c_0_19]),c_0_30]) ).
cnf(c_0_36,plain,
cartesian_product2(X1,empty_set) = empty_set,
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( set_intersection2(esk3_0,esk5_0) = esk3_0
| esk3_0 = empty_set
| esk4_0 = empty_set ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( esk4_0 = empty_set
| esk3_0 = empty_set
| ~ subset(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( set_intersection2(X1,X2) = empty_set
| cartesian_product2(set_intersection2(X1,X2),cartesian_product2(esk3_0,esk4_0)) != empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_30]) ).
cnf(c_0_40,negated_conjecture,
( esk4_0 = empty_set
| esk3_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_38]) ).
cnf(c_0_41,plain,
( cartesian_product2(X1,X2) = empty_set
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_42,negated_conjecture,
cartesian_product2(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk3_0,esk4_0)) != empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_19]),c_0_30]) ).
cnf(c_0_43,negated_conjecture,
esk3_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_40]),c_0_36])]) ).
cnf(c_0_44,plain,
cartesian_product2(empty_set,X1) = empty_set,
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_43]),c_0_44]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET984+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n017.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:39:42 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------