%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET183+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n024.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 05:07:32 PM UTC 2026
% Result : Theorem 1.10s 1.62s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 68 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 25 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 1 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(prove_subset_intersection,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_intersection) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(intersection_is_subset,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(c_0_6,plain,
! [X27,X28,X29,X30,X31] :
( ( ~ subset(X27,X28)
| ~ member(X29,X27)
| member(X29,X28) )
& ( member(esk1_2(X30,X31),X30)
| subset(X30,X31) )
& ( ~ member(esk1_2(X30,X31),X31)
| subset(X30,X31) ) ),
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_defn])])])])])]) ).
fof(c_0_7,plain,
! [X22,X23,X24] :
( ( member(X24,X22)
| ~ member(X24,intersection(X22,X23)) )
& ( member(X24,X23)
| ~ member(X24,intersection(X22,X23)) )
& ( ~ member(X24,X22)
| ~ member(X24,X23)
| member(X24,intersection(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[prove_subset_intersection]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( subset(esk3_0,esk4_0)
& intersection(esk3_0,esk4_0) != esk3_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_12,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X35,X36] : intersection(X35,X36) = intersection(X36,X35),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_19,plain,
! [X33,X34] :
( ( subset(X33,X34)
| X33 != X34 )
& ( subset(X34,X33)
| X33 != X34 )
& ( ~ subset(X33,X34)
| ~ subset(X34,X33)
| X33 = X34 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_20,negated_conjecture,
( subset(X1,intersection(esk4_0,X1))
| ~ member(esk1_2(X1,intersection(esk4_0,X1)),esk3_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X25,X26] : subset(intersection(X25,X26),X25),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
subset(esk3_0,intersection(esk3_0,esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_21]) ).
cnf(c_0_25,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
intersection(esk3_0,esk4_0) != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SET183+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.06 % 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
% 0.05/0.25 % Computer : n024.cluster.edu
% 0.05/0.25 % Model : x86_64 x86_64
% 0.05/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.25 % Memory : 8042.1875MB
% 0.05/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.05/0.25 % CPULimit : 300
% 0.05/0.25 % WCLimit : 300
% 0.05/0.25 % DateTime : Mon May 4 21:13:56 EDT 2026
% 0.05/0.25 % CPUTime :
% 0.05/0.25 % start to proof: theBenchmark
% 1.10/1.62 % Version : CSE_E---1.7
% 1.10/1.62 % Problem : theBenchmark.p
% 1.10/1.62 % SZS status Theorem for theBenchmark.p
% 1.10/1.62 % SZS output start CNFRefutation
% See solution above
% 1.10/1.62 % Total time : 1.362s
%------------------------------------------------------------------------------