%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET635+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 : n005.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 05:08:12 PM UTC 2026
% Result : Theorem 1.33s 1.75s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 26 unt; 0 def)
% Number of atoms : 34 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_empty_set,axiom,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(difference_and_intersection_and_union,axiom,
! [X1,X2,X3] : difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).
fof(union_empty_set,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(prove_th117,conjecture,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th117) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(difference_and_intersection,axiom,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection) ).
fof(c_0_7,plain,
! [X42,X43] :
( ( difference(X42,X43) != empty_set
| subset(X42,X43) )
& ( ~ subset(X42,X43)
| difference(X42,X43) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_empty_set])]) ).
fof(c_0_8,plain,
! [X70] : subset(X70,X70),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
fof(c_0_9,plain,
! [X45,X46,X47] : difference(X45,intersection(X46,X47)) = union(difference(X45,X46),difference(X45,X47)),
inference(variable_rename,[status(thm)],[difference_and_intersection_and_union]) ).
cnf(c_0_10,plain,
( difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X44] : union(X44,empty_set) = X44,
inference(variable_rename,[status(thm)],[union_empty_set]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
inference(assume_negation,[status(cth)],[prove_th117]) ).
cnf(c_0_14,plain,
difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X62,X63] : intersection(X62,X63) = intersection(X63,X62),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_18,negated_conjecture,
intersection(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_19,plain,
! [X48,X49,X50] : intersection(X48,difference(X49,X50)) = difference(intersection(X48,X49),X50),
inference(variable_rename,[status(thm)],[difference_and_intersection]) ).
cnf(c_0_20,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
intersection(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
difference(X1,intersection(intersection(X2,X1),X3)) = difference(X1,intersection(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_20]),c_0_14]) ).
cnf(c_0_26,negated_conjecture,
intersection(esk4_0,difference(esk5_0,intersection(esk4_0,esk6_0))) != intersection(esk4_0,difference(esk5_0,esk6_0)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
intersection(X1,difference(X2,intersection(X1,X3))) = intersection(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_23]),c_0_25]) ).
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
% 0.00/0.12 % Problem : SET635+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
% 0.14/0.33 % Computer : n005.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 02:30:45 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.33/1.75 % Version : CSE_E---1.7
% 1.33/1.75 % Problem : theBenchmark.p
% 1.33/1.75 % SZS status Theorem for theBenchmark.p
% 1.33/1.75 % SZS output start CNFRefutation
% See solution above
% 1.33/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------