%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET619+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th95,conjecture,
! [X1,X2] : union(X1,X2) = union(symmetric_difference(X1,X2),intersection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th95) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(associativity_of_union,axiom,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_union) ).
fof(union_intersection,axiom,
! [X1,X2] : union(X1,intersection(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection) ).
fof(union_intersection_difference,axiom,
! [X1,X2] : union(intersection(X1,X2),difference(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection_difference) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] : union(X1,X2) = union(symmetric_difference(X1,X2),intersection(X1,X2)),
inference(assume_negation,[status(cth)],[prove_th95]) ).
fof(c_0_8,negated_conjecture,
union(esk3_0,esk4_0) != union(symmetric_difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_9,plain,
! [X36,X37] : symmetric_difference(X36,X37) = union(difference(X36,X37),difference(X37,X36)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
fof(c_0_10,plain,
! [X38,X39,X40] : union(union(X38,X39),X40) = union(X38,union(X39,X40)),
inference(variable_rename,[status(thm)],[associativity_of_union]) ).
fof(c_0_11,plain,
! [X41,X42] : union(X41,intersection(X41,X42)) = X41,
inference(variable_rename,[status(thm)],[union_intersection]) ).
fof(c_0_12,plain,
! [X43,X44] : union(intersection(X43,X44),difference(X43,X44)) = X43,
inference(variable_rename,[status(thm)],[union_intersection_difference]) ).
fof(c_0_13,plain,
! [X55,X56] : intersection(X55,X56) = intersection(X56,X55),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_14,negated_conjecture,
union(esk3_0,esk4_0) != union(symmetric_difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,plain,
! [X53,X54] : union(X53,X54) = union(X54,X53),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_17,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
union(X1,intersection(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
union(esk3_0,esk4_0) != union(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),intersection(esk3_0,esk4_0)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
union(X1,union(intersection(X1,X2),X3)) = union(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
union(intersection(X1,X2),difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
union(intersection(esk3_0,esk4_0),union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) != union(esk3_0,esk4_0),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
union(intersection(X1,X2),union(difference(X1,X2),X3)) = union(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_27,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET619+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n004.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 02:30:17 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------