%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET971+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 : n023.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 05:09:04 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 29 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 7 ~; 2 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t124_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_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(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(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(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
inference(assume_negation,[status(cth)],[t124_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
( subset(esk3_0,esk4_0)
& subset(esk5_0,esk6_0)
& set_intersection2(cartesian_product2(esk3_0,esk6_0),cartesian_product2(esk4_0,esk5_0)) != cartesian_product2(esk3_0,esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X29,X30,X31,X32] : cartesian_product2(set_intersection2(X29,X30),set_intersection2(X31,X32)) = set_intersection2(cartesian_product2(X29,X31),cartesian_product2(X30,X32)),
inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).
fof(c_0_7,plain,
! [X23,X24] : set_intersection2(X23,X24) = set_intersection2(X24,X23),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_8,plain,
! [X37,X38] :
( ~ subset(X37,X38)
| set_intersection2(X37,X38) = X37 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
cnf(c_0_9,negated_conjecture,
set_intersection2(cartesian_product2(esk3_0,esk6_0),cartesian_product2(esk4_0,esk5_0)) != cartesian_product2(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,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_6]) ).
cnf(c_0_11,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
cartesian_product2(set_intersection2(esk3_0,esk4_0),set_intersection2(esk5_0,esk6_0)) != cartesian_product2(esk3_0,esk5_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_15,negated_conjecture,
set_intersection2(esk5_0,esk6_0) = esk5_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
cartesian_product2(set_intersection2(esk3_0,esk4_0),esk5_0) != cartesian_product2(esk3_0,esk5_0),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
set_intersection2(esk3_0,esk4_0) = esk3_0,
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET971+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:41:24 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.372s
%------------------------------------------------------------------------------