%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET084+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 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 : n031.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 05:07:13 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 42 ( 22 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 39 ( 14 ~; 14 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singleton_identified_by_element2,conjecture,
! [X1,X2] :
( ( singleton(X1) = singleton(X2)
& member(X2,universal_class) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element2) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( member(X3,universal_class)
& ( X3 = X1
| X3 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( ( singleton(X1) = singleton(X2)
& member(X2,universal_class) )
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[singleton_identified_by_element2]) ).
fof(c_0_4,negated_conjecture,
( singleton(esk8_0) = singleton(esk9_0)
& member(esk9_0,universal_class)
& esk8_0 != esk9_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X112] : singleton(X112) = unordered_pair(X112,X112),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_6,plain,
! [X107,X108,X109] :
( ( member(X107,universal_class)
| ~ member(X107,unordered_pair(X108,X109)) )
& ( X107 = X108
| X107 = X109
| ~ member(X107,unordered_pair(X108,X109)) )
& ( X107 != X108
| ~ member(X107,universal_class)
| member(X107,unordered_pair(X108,X109)) )
& ( X107 != X109
| ~ member(X107,universal_class)
| member(X107,unordered_pair(X108,X109)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])]) ).
cnf(c_0_7,negated_conjecture,
singleton(esk8_0) = singleton(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
unordered_pair(esk9_0,esk9_0) = unordered_pair(esk8_0,esk8_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( X1 = esk8_0
| ~ member(X1,unordered_pair(esk9_0,esk9_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,negated_conjecture,
esk8_0 != esk9_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET084+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 0.00/0.11 % 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 : n031.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 02:11:53 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % 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 : 1.371s
%------------------------------------------------------------------------------