%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET702+4 : TPTP v9.2.1. Released v2.2.0.
% 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 : n021.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 05:08:21 PM UTC 2026
% Result : Theorem 1.48s 1.78s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 55 ( 21 ~; 22 |; 7 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI36,conjecture,
! [X1,X2] : subset(intersection(product(X1),product(X2)),product(intersection(X1,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI36) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(product,axiom,
! [X3,X1] :
( member(X3,product(X1))
<=> ! [X5] :
( member(X5,X1)
=> member(X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',product) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] : subset(intersection(product(X1),product(X2)),product(intersection(X1,X2))),
inference(assume_negation,[status(cth)],[thI36]) ).
fof(c_0_5,negated_conjecture,
~ subset(intersection(product(esk4_0),product(esk5_0)),product(intersection(esk4_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,
! [X36,X37,X38,X39,X40] :
( ( ~ subset(X36,X37)
| ~ member(X38,X36)
| member(X38,X37) )
& ( member(esk1_2(X39,X40),X39)
| subset(X39,X40) )
& ( ~ member(esk1_2(X39,X40),X40)
| subset(X39,X40) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])]) ).
fof(c_0_7,plain,
! [X46,X47,X48] :
( ( member(X46,X47)
| ~ member(X46,intersection(X47,X48)) )
& ( member(X46,X48)
| ~ member(X46,intersection(X47,X48)) )
& ( ~ member(X46,X47)
| ~ member(X46,X48)
| member(X46,intersection(X47,X48)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
cnf(c_0_8,negated_conjecture,
~ subset(intersection(product(esk4_0),product(esk5_0)),product(intersection(esk4_0,esk5_0))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X67,X68,X69,X70,X71] :
( ( ~ member(X67,product(X68))
| ~ member(X69,X68)
| member(X67,X69) )
& ( member(esk3_2(X70,X71),X71)
| member(X70,product(X71)) )
& ( ~ member(X70,esk3_2(X70,X71))
| member(X70,product(X71)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[product])])])])])]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
member(esk1_2(intersection(product(esk4_0),product(esk5_0)),product(intersection(esk4_0,esk5_0))),intersection(product(esk4_0),product(esk5_0))),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( member(X1,X3)
| ~ member(X1,product(X2))
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
member(esk1_2(intersection(product(esk4_0),product(esk5_0)),product(intersection(esk4_0,esk5_0))),product(esk5_0)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( member(X1,product(X2))
| ~ member(X1,esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( member(esk1_2(intersection(product(esk4_0),product(esk5_0)),product(intersection(esk4_0,esk5_0))),X1)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( member(esk3_2(X1,X2),X2)
| member(X1,product(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( member(esk1_2(intersection(product(esk4_0),product(esk5_0)),product(intersection(esk4_0,esk5_0))),product(X1))
| ~ member(esk3_2(esk1_2(intersection(product(esk4_0),product(esk5_0)),product(intersection(esk4_0,esk5_0))),X1),esk5_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( member(esk3_2(X1,intersection(X2,X3)),X3)
| member(X1,product(intersection(X2,X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
~ member(esk1_2(intersection(product(esk4_0),product(esk5_0)),product(intersection(esk4_0,esk5_0))),product(intersection(esk4_0,esk5_0))),
inference(spm,[status(thm)],[c_0_8,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
member(esk1_2(intersection(product(esk4_0),product(esk5_0)),product(intersection(esk4_0,esk5_0))),product(intersection(X1,esk5_0))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET702+4 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n021.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:33:10 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.48/1.78 % Version : CSE_E---1.7
% 1.48/1.78 % Problem : theBenchmark.p
% 1.48/1.78 % SZS status Theorem for theBenchmark.p
% 1.48/1.78 % SZS output start CNFRefutation
% See solution above
% 1.48/1.79 % Total time : 1.370s
%------------------------------------------------------------------------------