%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET617+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 05:08:08 PM UTC 2026
% Result : Theorem 1.24s 1.70s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 18 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th92,conjecture,
! [X1] :
( symmetric_difference(X1,empty_set) = X1
& symmetric_difference(empty_set,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th92) ).
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(no_difference_with_empty_set2,axiom,
! [X1] : difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
fof(no_difference_with_empty_set1,axiom,
! [X1] : difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).
fof(union_empty_set,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( symmetric_difference(X1,empty_set) = X1
& symmetric_difference(empty_set,X1) = X1 ),
inference(assume_negation,[status(cth)],[prove_th92]) ).
fof(c_0_7,negated_conjecture,
( symmetric_difference(esk4_0,empty_set) != esk4_0
| symmetric_difference(empty_set,esk4_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,
! [X26,X27] : symmetric_difference(X26,X27) = union(difference(X26,X27),difference(X27,X26)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_0_9,negated_conjecture,
( symmetric_difference(esk4_0,empty_set) != esk4_0
| symmetric_difference(empty_set,esk4_0) != esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X30] : difference(empty_set,X30) = empty_set,
inference(variable_rename,[status(thm)],[no_difference_with_empty_set2]) ).
cnf(c_0_12,negated_conjecture,
( union(difference(empty_set,esk4_0),difference(esk4_0,empty_set)) != esk4_0
| union(difference(esk4_0,empty_set),difference(empty_set,esk4_0)) != esk4_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_13,plain,
difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X29] : difference(X29,empty_set) = X29,
inference(variable_rename,[status(thm)],[no_difference_with_empty_set1]) ).
cnf(c_0_15,negated_conjecture,
( union(empty_set,difference(esk4_0,empty_set)) != esk4_0
| union(difference(esk4_0,empty_set),empty_set) != esk4_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_16,plain,
difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X28] : union(X28,empty_set) = X28,
inference(variable_rename,[status(thm)],[union_empty_set]) ).
fof(c_0_18,plain,
! [X34,X35] : union(X34,X35) = union(X35,X34),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_19,negated_conjecture,
( union(empty_set,esk4_0) != esk4_0
| union(esk4_0,empty_set) != esk4_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_20,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
union(empty_set,esk4_0) != esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_23,plain,
union(empty_set,X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET617+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
% 0.14/0.32 % Computer : n005.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:30:30 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.24/1.70 % Version : CSE_E---1.7
% 1.24/1.70 % Problem : theBenchmark.p
% 1.24/1.70 % SZS status Theorem for theBenchmark.p
% 1.24/1.70 % SZS output start CNFRefutation
% See solution above
% 1.24/1.70 % Total time : 1.367s
%------------------------------------------------------------------------------