%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET096+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 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 : n018.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 05:07:17 PM UTC 2026
% Result : Theorem 1.37s 1.76s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 92 ( 35 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 88 ( 30 ~; 36 |; 15 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(two_subsets_of_singleton,conjecture,
! [X1,X2] :
( subclass(X1,singleton(X2))
=> ( X1 = null_class
| singleton(X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',subclass_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/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( member(X3,universal_class)
& member(X3,X1)
& disjoint(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(extensionality,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subclass(X1,X2)
& subclass(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',extensionality) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subclass(X1,singleton(X2))
=> ( X1 = null_class
| singleton(X2) = X1 ) ),
inference(assume_negation,[status(cth)],[two_subsets_of_singleton]) ).
fof(c_0_7,negated_conjecture,
( subclass(esk8_0,singleton(esk9_0))
& esk8_0 != null_class
& singleton(esk9_0) != esk8_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X112] : singleton(X112) = unordered_pair(X112,X112),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_9,plain,
! [X98,X99,X100,X101,X102] :
( ( ~ subclass(X98,X99)
| ~ member(X100,X98)
| member(X100,X99) )
& ( member(esk1_2(X101,X102),X101)
| subclass(X101,X102) )
& ( ~ member(esk1_2(X101,X102),X102)
| subclass(X101,X102) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subclass_defn])])])])])]) ).
cnf(c_0_10,negated_conjecture,
subclass(esk8_0,singleton(esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,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_13,plain,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
subclass(esk8_0,unordered_pair(esk9_0,esk9_0)),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( member(esk1_2(X1,X2),X1)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
( member(X1,unordered_pair(esk9_0,esk9_0))
| ~ member(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,plain,
! [X189] :
( ( member(esk6_1(X189),universal_class)
| X189 = null_class )
& ( member(esk6_1(X189),X189)
| X189 = null_class )
& ( disjoint(esk6_1(X189),X189)
| X189 = null_class ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[regularity])])])]) ).
fof(c_0_19,plain,
! [X105,X106] :
( ( subclass(X105,X106)
| X105 != X106 )
& ( subclass(X106,X105)
| X105 != X106 )
& ( ~ subclass(X105,X106)
| ~ subclass(X106,X105)
| X105 = X106 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[extensionality])])]) ).
cnf(c_0_20,negated_conjecture,
singleton(esk9_0) != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X1
| esk1_2(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( X1 = esk9_0
| ~ member(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_23,plain,
( member(esk6_1(X1),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
esk8_0 != null_class,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
unordered_pair(esk9_0,esk9_0) != esk8_0,
inference(rw,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_27,plain,
( subclass(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,plain,
( esk1_2(unordered_pair(X1,X1),X2) = X1
| subclass(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_21])]) ).
cnf(c_0_29,negated_conjecture,
esk6_1(esk8_0) = esk9_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
~ subclass(unordered_pair(esk9_0,esk9_0),esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_14]),c_0_26]) ).
cnf(c_0_31,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
member(esk9_0,esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_24]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET096+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 0.00/0.14 % 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
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue May 5 02:10:17 EDT 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % start to proof: theBenchmark
% 1.37/1.76 % Version : CSE_E---1.7
% 1.37/1.76 % Problem : theBenchmark.p
% 1.37/1.76 % SZS status Theorem for theBenchmark.p
% 1.37/1.76 % SZS output start CNFRefutation
% See solution above
% 1.37/1.76 % Total time : 1.371s
%------------------------------------------------------------------------------