%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET079+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:35:39 AM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 28 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 4 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 6 sgn 7 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('theBenchmark.p',unordered_pair_defn) ).
fof(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('theBenchmark.p',singleton_set_defn) ).
fof(null_class_defn,axiom,
! [X] : ~ member(X,null_class),
file('theBenchmark.p',null_class_defn) ).
fof(corollary_to_set_in_its_singleton,conjecture,
! [X] :
( member(X,universal_class)
=> singleton(X) != null_class ),
file('theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(corollary_to_set_in_its_singleton_neg,negated_conjecture,
~ ! [X] :
( member(X,universal_class)
=> singleton(X) != null_class ),
inference(assume_negation,[status(cth)],[corollary_to_set_in_its_singleton]) ).
fof(nnf_42,plain,
? [X] :
( singleton(X) = null_class
& member(X,universal_class) ),
inference(fof_nnf,[status(thm)],[corollary_to_set_in_its_singleton_neg]) ).
fof(sk_corollary_to_set_in_its_singleton_neg,plain,
( singleton(sK0) = null_class
& member(sK0,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
singleton(sK0) = null_class,
inference(split_conjunct,[status(thm)],[sk_corollary_to_set_in_its_singleton_neg]) ).
cnf(c_65,negated_conjecture,
null_class = singleton(sK0),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_66,negated_conjecture,
member(sK0,universal_class),
inference(split_conjunct,[status(thm)],[sk_corollary_to_set_in_its_singleton_neg]) ).
cnf(c_115,plain,
~ member(A,null_class),
inference(clausify,[status(thm)],[null_class_defn]) ).
cnf(c_116,plain,
~ member(A,singleton(sK0)),
inference(paramod,[status(thm)],[c_65,c_115]) ).
cnf(c_135,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_137,plain,
( A != C
| ~ member(A,universal_class)
| member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_201,plain,
~ member(A,unordered_pair(sK0,sK0)),
inference(paramod,[status(thm)],[c_135,c_116]) ).
cnf(c_267,negated_conjecture,
( sK0 != B
| member(sK0,unordered_pair(A,B)) ),
inference(resolve,[status(thm)],[c_137,c_66]) ).
cnf(c_265,plain,
member(sK0,unordered_pair(A,sK0)),
inference(xxres,[status(thm)],[c_267]) ).
cnf(c_266,plain,
$false,
inference(resolve,[status(thm)],[c_265,c_201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET079+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:03:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1069069 was started by sandbox2 on n004,
% 0.12/0.36 % Sat Sep 26 07:03:36 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.41
% 0.12/0.41 % SZS status Theorem for theBenchmark
% 0.12/0.41
% 0.12/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.41 % Length of proof is 14.
% 0.12/0.41 % Level of proof is 5.
% 0.12/0.41 % Maximum clause weight is 21.000.
% 0.12/0.41 % Given clauses 34.
% 0.12/0.41
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------