%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET630+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 : n009.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 05:08:11 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 44 ( 6 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 11 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_and_symmetric_difference_disjoint,conjecture,
! [X1,X2] : disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(intersection_and_union_disjoint,axiom,
! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_and_union_disjoint) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(intersect_with_union,axiom,
! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X2)
| intersect(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_with_union) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] : disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
inference(assume_negation,[status(cth)],[prove_intersection_and_symmetric_difference_disjoint]) ).
fof(c_0_7,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),symmetric_difference(esk3_0,esk4_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X32,X33] : symmetric_difference(X32,X33) = union(difference(X32,X33),difference(X33,X32)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
fof(c_0_9,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
fof(c_0_10,plain,
! [X37,X38] : disjoint(intersection(X37,X38),difference(X37,X38)),
inference(variable_rename,[status(thm)],[intersection_and_union_disjoint]) ).
fof(c_0_11,plain,
! [X52,X53] : intersection(X52,X53) = intersection(X53,X52),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_12,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),symmetric_difference(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X48,X49] :
( ( ~ disjoint(X48,X49)
| ~ intersect(X48,X49) )
& ( intersect(X48,X49)
| disjoint(X48,X49) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
cnf(c_0_15,plain,
disjoint(intersection(X1,X2),difference(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X34,X35,X36] :
( ( ~ intersect(X34,union(X35,X36))
| intersect(X34,X35)
| intersect(X34,X36) )
& ( ~ intersect(X34,X35)
| intersect(X34,union(X35,X36)) )
& ( ~ intersect(X34,X36)
| intersect(X34,union(X35,X36)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersect_with_union])])]) ).
cnf(c_0_18,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( intersect(X1,X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ disjoint(X1,X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
disjoint(intersection(X1,X2),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( intersect(X1,X2)
| intersect(X1,X3)
| ~ intersect(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
intersect(intersection(esk3_0,esk4_0),union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
~ intersect(intersection(X1,X2),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
~ intersect(intersection(X1,X2),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET630+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 : n009.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 02:29:41 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------