%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET094+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 : n029.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 05:07:16 PM UTC 2026
% Result : Theorem 1.34s 1.75s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 37 ( 21 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 33 ( 11 ~; 11 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 17 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(property_of_singletons1_1,conjecture,
! [X1,X2] :
( ( singleton(member_of(X1)) = X1
& member(X2,X1) )
=> member_of(X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_singletons1_1) ).
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(member_of(X1)) = X1
& member(X2,X1) )
=> member_of(X1) = X2 ),
inference(assume_negation,[status(cth)],[property_of_singletons1_1]) ).
fof(c_0_4,negated_conjecture,
( singleton(member_of(esk8_0)) = esk8_0
& member(esk9_0,esk8_0)
& member_of(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,
! [X116] : singleton(X116) = unordered_pair(X116,X116),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_6,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_7,negated_conjecture,
singleton(member_of(esk8_0)) = esk8_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(member_of(esk8_0),member_of(esk8_0)) = esk8_0,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( X1 = member_of(esk8_0)
| ~ member(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,negated_conjecture,
member(esk9_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
member_of(esk8_0) != esk9_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET094+1 : TPTP v9.2.1. Bugfixed v7.3.0.
% 0.11/0.13 % 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
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:10:29 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.34/1.75 % Version : CSE_E---1.7
% 1.34/1.75 % Problem : theBenchmark.p
% 1.34/1.75 % SZS status Theorem for theBenchmark.p
% 1.34/1.75 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------