%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET622+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 : n002.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 05:08:09 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th98,conjecture,
! [X1,X2,X3] : difference(X1,symmetric_difference(X2,X3)) = union(difference(X1,union(X2,X3)),intersection(intersection(X1,X2),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th98) ).
fof(symmetric_difference_and_difference,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(associativity_of_intersection,axiom,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(difference_difference_union2,axiom,
! [X1,X2,X3] : difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union2) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] : difference(X1,symmetric_difference(X2,X3)) = union(difference(X1,union(X2,X3)),intersection(intersection(X1,X2),X3)),
inference(assume_negation,[status(cth)],[prove_th98]) ).
fof(c_0_7,negated_conjecture,
difference(esk3_0,symmetric_difference(esk4_0,esk5_0)) != union(difference(esk3_0,union(esk4_0,esk5_0)),intersection(intersection(esk3_0,esk4_0),esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X47,X48] : symmetric_difference(X47,X48) = difference(union(X47,X48),intersection(X47,X48)),
inference(variable_rename,[status(thm)],[symmetric_difference_and_difference]) ).
cnf(c_0_9,negated_conjecture,
difference(esk3_0,symmetric_difference(esk4_0,esk5_0)) != union(difference(esk3_0,union(esk4_0,esk5_0)),intersection(intersection(esk3_0,esk4_0),esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X64,X65] : intersection(X64,X65) = intersection(X65,X64),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_12,negated_conjecture,
difference(esk3_0,difference(union(esk4_0,esk5_0),intersection(esk4_0,esk5_0))) != union(difference(esk3_0,union(esk4_0,esk5_0)),intersection(intersection(esk3_0,esk4_0),esk5_0)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X62,X63] : union(X62,X63) = union(X63,X62),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_15,plain,
! [X41,X42,X43] : intersection(intersection(X41,X42),X43) = intersection(X41,intersection(X42,X43)),
inference(variable_rename,[status(thm)],[associativity_of_intersection]) ).
cnf(c_0_16,negated_conjecture,
union(difference(esk3_0,union(esk4_0,esk5_0)),intersection(esk5_0,intersection(esk3_0,esk4_0))) != difference(esk3_0,difference(union(esk4_0,esk5_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X44,X45,X46] : difference(X44,difference(X45,X46)) = union(difference(X44,X45),intersection(X44,X46)),
inference(variable_rename,[status(thm)],[difference_difference_union2]) ).
cnf(c_0_20,negated_conjecture,
union(intersection(esk5_0,intersection(esk3_0,esk4_0)),difference(esk3_0,union(esk4_0,esk5_0))) != difference(esk3_0,difference(union(esk4_0,esk5_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
intersection(X1,intersection(X2,X3)) = intersection(X3,intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_22,plain,
difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
union(intersection(esk3_0,intersection(esk4_0,esk5_0)),difference(esk3_0,union(esk4_0,esk5_0))) != difference(esk3_0,difference(union(esk4_0,esk5_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
union(intersection(X1,X2),difference(X1,X3)) = difference(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET622+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
% 0.16/0.34 % Computer : n002.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:30:31 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.367s
%------------------------------------------------------------------------------