%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET090+1 : TPTP v9.2.1. Bugfixed v7.3.0.
% 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 : n019.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 05:07:15 PM UTC 2026
% Result : Theorem 1.17s 1.88s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 61 ( 27 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 53 ( 20 ~; 20 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_of_singleton,conjecture,
! [X1,X3] :
( ( member(X3,universal_class)
& X1 = singleton(X3) )
=> member_of(X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_singleton) ).
fof(member_singleton_singleton,axiom,
! [X2] :
( member(X2,universal_class)
=> singleton(member_of(singleton(X2))) = singleton(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_singleton_singleton) ).
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(member_singleton_universal,axiom,
! [X2] :
( member(X2,universal_class)
=> member(member_of(singleton(X2)),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_singleton_universal) ).
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_5,negated_conjecture,
~ ! [X1,X3] :
( ( member(X3,universal_class)
& X1 = singleton(X3) )
=> member_of(X1) = X3 ),
inference(assume_negation,[status(cth)],[member_of_singleton]) ).
fof(c_0_6,plain,
! [X200] :
( ~ member(X200,universal_class)
| singleton(member_of(singleton(X200))) = singleton(X200) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_singleton_singleton])]) ).
fof(c_0_7,plain,
! [X116] : singleton(X116) = unordered_pair(X116,X116),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_8,negated_conjecture,
( member(esk9_0,universal_class)
& esk8_0 = singleton(esk9_0)
& member_of(esk8_0) != esk9_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,plain,
! [X199] :
( ~ member(X199,universal_class)
| member(member_of(singleton(X199)),universal_class) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_singleton_universal])]) ).
fof(c_0_10,plain,
! [X111,X112,X113] :
( ( member(X111,universal_class)
| ~ member(X111,unordered_pair(X112,X113)) )
& ( X111 = X112
| X111 = X113
| ~ member(X111,unordered_pair(X112,X113)) )
& ( X111 != X112
| ~ member(X111,universal_class)
| member(X111,unordered_pair(X112,X113)) )
& ( X111 != X113
| ~ member(X111,universal_class)
| member(X111,unordered_pair(X112,X113)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])]) ).
cnf(c_0_11,plain,
( singleton(member_of(singleton(X1))) = singleton(X1)
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
esk8_0 = singleton(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( member(member_of(singleton(X1)),universal_class)
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( unordered_pair(member_of(unordered_pair(X1,X1)),member_of(unordered_pair(X1,X1))) = unordered_pair(X1,X1)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_17,negated_conjecture,
esk8_0 = unordered_pair(esk9_0,esk9_0),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
( member(member_of(unordered_pair(X1,X1)),universal_class)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_20,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
unordered_pair(member_of(esk8_0),member_of(esk8_0)) = esk8_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
member(member_of(esk8_0),universal_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_18])]) ).
cnf(c_0_24,negated_conjecture,
( X1 = esk9_0
| ~ member(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
member(member_of(esk8_0),esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
member_of(esk8_0) != esk9_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.22 % Problem : SET090+1 : TPTP v9.2.1. Bugfixed v7.3.0.
% 0.04/0.22 % 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
% 0.13/0.45 % Computer : n019.cluster.edu
% 0.13/0.45 % Model : x86_64 x86_64
% 0.13/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.45 % Memory : 8042.1875MB
% 0.13/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.45 % CPULimit : 300
% 0.13/0.45 % WCLimit : 300
% 0.13/0.45 % DateTime : Tue May 5 02:09:44 EDT 2026
% 0.13/0.46 % CPUTime :
% 0.15/0.47 % start to proof: theBenchmark
% 1.17/1.88 % Version : CSE_E---1.7
% 1.17/1.88 % Problem : theBenchmark.p
% 1.17/1.88 % SZS status Theorem for theBenchmark.p
% 1.17/1.88 % SZS output start CNFRefutation
% See solution above
% 1.17/1.88 % Total time : 1.381s
%------------------------------------------------------------------------------