%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET201+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 : n006.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 05:07:35 PM UTC 2026
% Result : Theorem 2.18s 2.00s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 70 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 25 ~; 26 |; 9 &)
% ( 2 <=>; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 4 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th41,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(intersection(X1,X3),intersection(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th41) ).
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,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(intersection(X1,X3),intersection(X2,X4)) ),
inference(assume_negation,[status(cth)],[prove_th41]) ).
fof(c_0_5,plain,
! [X24,X25,X26,X27,X28] :
( ( ~ subset(X24,X25)
| ~ member(X26,X24)
| member(X26,X25) )
& ( member(esk1_2(X27,X28),X27)
| subset(X27,X28) )
& ( ~ member(esk1_2(X27,X28),X28)
| subset(X27,X28) ) ),
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(esk5_0,esk6_0)
& ~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk6_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,
! [X21,X22,X23] :
( ( member(X23,X21)
| ~ member(X23,intersection(X21,X22)) )
& ( member(X23,X22)
| ~ member(X23,intersection(X21,X22)) )
& ( ~ member(X23,X21)
| ~ member(X23,X22)
| member(X23,intersection(X21,X22)) ) ),
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,
! [X30,X31] : intersection(X30,X31) = intersection(X31,X30),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_17,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
subset(intersection(esk3_0,X1),esk4_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
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_17]) ).
cnf(c_0_22,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
subset(intersection(X1,esk3_0),esk4_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( subset(X1,intersection(X2,esk6_0))
| ~ member(esk1_2(X1,intersection(X2,esk6_0)),esk5_0)
| ~ member(esk1_2(X1,intersection(X2,esk6_0)),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,intersection(X2,esk3_0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( subset(intersection(esk5_0,X1),intersection(X2,esk6_0))
| ~ member(esk1_2(intersection(esk5_0,X1),intersection(X2,esk6_0)),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_27,negated_conjecture,
( subset(intersection(X1,esk3_0),X2)
| member(esk1_2(intersection(X1,esk3_0),X2),esk4_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_28,negated_conjecture,
~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_20]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET201+3 : 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
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:15:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.18/2.00 % Version : CSE_E---1.7
% 2.18/2.00 % Problem : theBenchmark.p
% 2.18/2.00 % SZS status Theorem for theBenchmark.p
% 2.18/2.00 % SZS output start CNFRefutation
% See solution above
% 2.18/2.01 % Total time : 1.368s
%------------------------------------------------------------------------------