%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET093+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 08:35:44 AM UTC 2026
% Result : Theorem 0.12s 0.61s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 28 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 3 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 5 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(class_elements_are_sets,axiom,
! [X] : subclass(X,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
fof(unordered_pair,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('theBenchmark.p',unordered_pair) ).
fof(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('theBenchmark.p',singleton_set_defn) ).
fof(corollary_2_to_singletons_are_sets,conjecture,
! [X] :
( singleton(member_of(X)) = X
=> member(X,universal_class) ),
file('theBenchmark.p',corollary_2_to_singletons_are_sets) ).
fof(corollary_2_to_singletons_are_sets_neg,negated_conjecture,
~ ! [X] :
( singleton(member_of(X)) = X
=> member(X,universal_class) ),
inference(assume_negation,[status(cth)],[corollary_2_to_singletons_are_sets]) ).
fof(nnf_46,plain,
? [X] :
( ~ member(X,universal_class)
& singleton(member_of(X)) = X ),
inference(fof_nnf,[status(thm)],[corollary_2_to_singletons_are_sets_neg]) ).
fof(sk_corollary_2_to_singletons_are_sets_neg,plain,
( ~ member(sK0,universal_class)
& singleton(member_of(sK0)) = sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_46]) ).
cnf(c_68,negated_conjecture,
~ member(sK0,universal_class),
inference(split_conjunct,[status(thm)],[sk_corollary_2_to_singletons_are_sets_neg]) ).
cnf(c_69,negated_conjecture,
singleton(member_of(sK0)) = sK0,
inference(split_conjunct,[status(thm)],[sk_corollary_2_to_singletons_are_sets_neg]) ).
cnf(c_136,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_137,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pair]) ).
cnf(c_145,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
cnf(c_148,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_defn]) ).
cnf(c_204,negated_conjecture,
unordered_pair(member_of(sK0),member_of(sK0)) = sK0,
inference(paramod,[status(thm)],[c_136,c_69]) ).
cnf(c_512,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_148,c_145]) ).
cnf(c_346,negated_conjecture,
~ member(sK0,A),
inference(resolve,[status(thm)],[c_512,c_68]) ).
cnf(c_513,plain,
member(sK0,universal_class),
inference(paramod,[status(thm)],[c_204,c_137]) ).
cnf(c_511,plain,
$false,
inference(resolve,[status(thm)],[c_346,c_513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET093+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.43 % Computer : n007.cluster.edu
% 0.09/0.43 % Model : x86_64 x86_64
% 0.09/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.43 % Memory : 8046.5625MB
% 0.09/0.43 % OS : Linux 6.8.0-71-generic
% 0.09/0.43 % CPULimit : 300
% 0.09/0.43 % WCLimit : 300
% 0.09/0.43 % DateTime : Sat Sep 26 07:03:53 UTC 2026
% 0.09/0.44 % CPUTime :
% 0.09/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.44 % Process 3076986 was started by sandbox on n007,
% 0.09/0.44 % Sat Sep 26 07:03:53 2026
% 0.09/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.45
% 0.09/0.45 % From the command line: assign(max_seconds, 300).
% 0.12/0.61
% 0.12/0.61 % SZS status Theorem for theBenchmark
% 0.12/0.61
% 0.12/0.61 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.12/0.61 % Length of proof is 14.
% 0.12/0.61 % Level of proof is 3.
% 0.12/0.61 % Maximum clause weight is 9.000.
% 0.12/0.61 % Given clauses 101.
% 0.12/0.61
% 0.12/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------