%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET091+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 : n017.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 1.40s 1.80s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 41 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 14 ~; 12 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 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 : 21 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_when_not_a_singleton,conjecture,
! [X1,X3] :
( ( ~ ? [X2] :
( member(X2,universal_class)
& X1 = singleton(X2) )
& X1 = X3 )
=> member_of(X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_when_not_a_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_universal_self,axiom,
! [X1] :
( member(member_of(X1),universal_class)
| member_of(X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_universal_self) ).
fof(singleton_self,axiom,
! [X1] :
( singleton(member_of(X1)) = X1
| member_of(X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_self) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X3] :
( ( ~ ? [X2] :
( member(X2,universal_class)
& X1 = singleton(X2) )
& X1 = X3 )
=> member_of(X1) = X3 ),
inference(assume_negation,[status(cth)],[member_when_not_a_singleton]) ).
fof(c_0_5,negated_conjecture,
! [X206] :
( ( ~ member(X206,universal_class)
| esk8_0 != singleton(X206) )
& esk8_0 = esk9_0
& member_of(esk8_0) != esk9_0 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X117] : singleton(X117) = unordered_pair(X117,X117),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_7,negated_conjecture,
( ~ member(X1,universal_class)
| esk8_0 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X202] :
( member(member_of(X202),universal_class)
| member_of(X202) = X202 ),
inference(variable_rename,[status(thm)],[member_universal_self]) ).
fof(c_0_10,plain,
! [X203] :
( singleton(member_of(X203)) = X203
| member_of(X203) = X203 ),
inference(variable_rename,[status(thm)],[singleton_self]) ).
cnf(c_0_11,negated_conjecture,
( esk8_0 != unordered_pair(X1,X1)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( member(member_of(X1),universal_class)
| member_of(X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( singleton(member_of(X1)) = X1
| member_of(X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
member_of(esk8_0) != esk9_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
esk8_0 = esk9_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
( member_of(X1) = X1
| unordered_pair(member_of(X1),member_of(X1)) != esk8_0 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( member_of(X1) = X1
| unordered_pair(member_of(X1),member_of(X1)) = X1 ),
inference(rw,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
member_of(esk8_0) != esk8_0,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( member_of(X1) = X1
| X1 != esk8_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_18,c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET091+1 : TPTP v9.2.1. Bugfixed v7.3.0.
% 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
% 0.16/0.33 % Computer : n017.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 02:07:58 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.40/1.80 % Version : CSE_E---1.7
% 1.40/1.80 % Problem : theBenchmark.p
% 1.40/1.80 % SZS status Theorem for theBenchmark.p
% 1.40/1.80 % SZS output start CNFRefutation
% See solution above
% 1.40/1.80 % Total time : 1.424s
%------------------------------------------------------------------------------