%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET621+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 : 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 : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th97,conjecture,
! [X1,X2,X3] : difference(symmetric_difference(X1,X2),X3) = union(difference(X1,union(X2,X3)),difference(X2,union(X1,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th97) ).
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(difference_difference_union,axiom,
! [X1,X2,X3] : difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_difference_union) ).
fof(difference_distributes_over_union,axiom,
! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] : difference(symmetric_difference(X1,X2),X3) = union(difference(X1,union(X2,X3)),difference(X2,union(X1,X3))),
inference(assume_negation,[status(cth)],[prove_th97]) ).
fof(c_0_5,negated_conjecture,
difference(symmetric_difference(esk3_0,esk4_0),esk5_0) != union(difference(esk3_0,union(esk4_0,esk5_0)),difference(esk4_0,union(esk3_0,esk5_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X34,X35] : symmetric_difference(X34,X35) = union(difference(X34,X35),difference(X35,X34)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_0_7,negated_conjecture,
difference(symmetric_difference(esk3_0,esk4_0),esk5_0) != union(difference(esk3_0,union(esk4_0,esk5_0)),difference(esk4_0,union(esk3_0,esk5_0))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X36,X37,X38] : difference(difference(X36,X37),X38) = difference(X36,union(X37,X38)),
inference(variable_rename,[status(thm)],[difference_difference_union]) ).
cnf(c_0_10,negated_conjecture,
difference(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),esk5_0) != union(difference(esk3_0,union(esk4_0,esk5_0)),difference(esk4_0,union(esk3_0,esk5_0))),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X39,X40,X41] : difference(union(X39,X40),X41) = union(difference(X39,X41),difference(X40,X41)),
inference(variable_rename,[status(thm)],[difference_distributes_over_union]) ).
cnf(c_0_13,negated_conjecture,
union(difference(difference(esk3_0,esk4_0),esk5_0),difference(difference(esk4_0,esk3_0),esk5_0)) != difference(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),esk5_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_14,plain,
difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET621+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 : n002.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 02:30:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % 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
% 1.27/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------