%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET077+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 : n012.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 05:07:11 PM UTC 2026
% Result : Theorem 0.14s 1.53s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 3 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singletons_are_sets,conjecture,
! [X1] : member(singleton(X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletons_are_sets) ).
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(unordered_pair,axiom,
! [X1,X2] : member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] : member(singleton(X1),universal_class),
inference(assume_negation,[status(cth)],[singletons_are_sets]) ).
fof(c_0_4,negated_conjecture,
~ member(singleton(esk8_0),universal_class),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X111] : singleton(X111) = unordered_pair(X111,X111),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_6,negated_conjecture,
~ member(singleton(esk8_0),universal_class),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X109,X110] : member(unordered_pair(X109,X110),universal_class),
inference(variable_rename,[status(thm)],[unordered_pair]) ).
cnf(c_0_9,negated_conjecture,
~ member(unordered_pair(esk8_0,esk8_0),universal_class),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
member(unordered_pair(X1,X2),universal_class),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET077+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 0.00/0.07 % 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
% 0.07/0.26 % Computer : n012.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue May 5 02:09:16 EDT 2026
% 0.07/0.26 % CPUTime :
% 0.07/0.26 % start to proof: theBenchmark
% 0.14/1.53 % Version : CSE_E---1.7
% 0.14/1.53 % Problem : theBenchmark.p
% 0.14/1.53 % SZS status Theorem for theBenchmark.p
% 0.14/1.53 % SZS output start CNFRefutation
% See solution above
% 0.14/1.53 % Total time : 1.261s
%------------------------------------------------------------------------------