%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET586+3 : 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 : n029.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 05:08:02 PM UTC 2026
% Result : Theorem 1.18s 1.97s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 63 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 56 ( 22 ~; 23 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 4 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_of_subset,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(intersection(X1,X3),intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_of_subset) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(intersection(X1,X3),intersection(X2,X3)) ),
inference(assume_negation,[status(cth)],[prove_intersection_of_subset]) ).
fof(c_0_5,plain,
! [X22,X23,X24,X25,X26] :
( ( ~ subset(X22,X23)
| ~ member(X24,X22)
| member(X24,X23) )
& ( member(esk1_2(X25,X26),X25)
| subset(X25,X26) )
& ( ~ member(esk1_2(X25,X26),X26)
| subset(X25,X26) ) ),
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_6,negated_conjecture,
( subset(esk3_0,esk4_0)
& ~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X19,X20,X21] :
( ( member(X21,X19)
| ~ member(X21,intersection(X19,X20)) )
& ( member(X21,X20)
| ~ member(X21,intersection(X19,X20)) )
& ( ~ member(X21,X19)
| ~ member(X21,X20)
| member(X21,intersection(X19,X20)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
! [X28,X29] : intersection(X28,X29) = intersection(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_17,negated_conjecture,
subset(intersection(esk3_0,X1),esk4_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
subset(intersection(X1,esk3_0),esk4_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,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_10,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,intersection(X2,esk3_0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_20]) ).
cnf(c_0_23,plain,
( subset(intersection(X1,X2),intersection(X3,X1))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( subset(intersection(X1,esk3_0),X2)
| member(esk1_2(intersection(X1,esk3_0),X2),esk4_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_25,negated_conjecture,
subset(intersection(X1,esk3_0),intersection(esk4_0,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
subset(intersection(esk3_0,X1),intersection(esk4_0,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.24 % Problem : SET586+3 : TPTP v9.2.1. Released v2.2.0.
% 0.03/0.24 % 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
% 0.12/0.50 % Computer : n029.cluster.edu
% 0.12/0.50 % Model : x86_64 x86_64
% 0.12/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.50 % Memory : 8042.1875MB
% 0.12/0.50 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.50 % CPULimit : 300
% 0.12/0.50 % WCLimit : 300
% 0.12/0.50 % DateTime : Tue May 5 02:28:44 EDT 2026
% 0.12/0.50 % CPUTime :
% 0.12/0.51 % start to proof: theBenchmark
% 1.18/1.97 % Version : CSE_E---1.7
% 1.18/1.97 % Problem : theBenchmark.p
% 1.18/1.97 % SZS status Theorem for theBenchmark.p
% 1.18/1.97 % SZS output start CNFRefutation
% See solution above
% 1.18/1.97 % Total time : 1.432s
%------------------------------------------------------------------------------