%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET091+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 : n019.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 08:35:43 AM UTC 2026
% Result : Theorem 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 5 unt; 0 def)
% Number of atoms : 35 ( 27 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 33 ( 14 ~; 9 |; 8 &)
% ( 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 : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_universal_self,axiom,
! [X] :
( member_of(X) = X
| member(member_of(X),universal_class) ),
file('theBenchmark.p',member_universal_self) ).
fof(singleton_self,axiom,
! [X] :
( member_of(X) = X
| singleton(member_of(X)) = X ),
file('theBenchmark.p',singleton_self) ).
fof(member_when_not_a_singleton,conjecture,
! [X,U] :
( ( X = U
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
=> member_of(X) = U ),
file('theBenchmark.p',member_when_not_a_singleton) ).
fof(member_when_not_a_singleton_neg,negated_conjecture,
~ ! [X,U] :
( ( X = U
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
=> member_of(X) = U ),
inference(assume_negation,[status(cth)],[member_when_not_a_singleton]) ).
fof(nnf_46,plain,
? [X,U] :
( member_of(X) != U
& U = X
& ! [Y] :
( singleton(Y) != X
| ~ member(Y,universal_class) ) ),
inference(fof_nnf,[status(thm)],[member_when_not_a_singleton_neg]) ).
fof(sk_member_when_not_a_singleton_neg,plain,
( member_of(sK0) != sK1
& sK1 = sK0
& ! [Y] :
( singleton(Y) != sK0
| ~ member(Y,universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(U,sK1)],[nnf_46]) ).
cnf(c_68,negated_conjecture,
member_of(sK0) != sK1,
inference(split_conjunct,[status(thm)],[sk_member_when_not_a_singleton_neg]) ).
cnf(c_69,negated_conjecture,
sK1 = sK0,
inference(split_conjunct,[status(thm)],[sk_member_when_not_a_singleton_neg]) ).
cnf(c_70,negated_conjecture,
( singleton(A) != sK0
| ~ member(A,universal_class) ),
inference(split_conjunct,[status(thm)],[sk_member_when_not_a_singleton_neg]) ).
cnf(c_71,plain,
( member_of(A) = A
| singleton(member_of(A)) = A ),
inference(clausify,[status(thm)],[singleton_self]) ).
cnf(c_72,plain,
( member_of(A) = A
| member(member_of(A),universal_class) ),
inference(clausify,[status(thm)],[member_universal_self]) ).
cnf(c_170,plain,
member_of(sK0) != sK0,
inference(paramod,[status(thm)],[c_69,c_68]) ).
cnf(c_171,plain,
( singleton(member_of(A)) != sK0
| member_of(A) = A ),
inference(resolve,[status(thm)],[c_72,c_70]) ).
cnf(c_739,plain,
( member_of(sK0) = sK0
| member_of(sK0) = sK0 ),
inference(resolve,[status(thm)],[c_171,c_71]) ).
cnf(c_740,plain,
member_of(sK0) = sK0,
inference(copy,[status(thm)],[c_739]) ).
cnf(c_738,plain,
$false,
inference(resolve,[status(thm)],[c_170,c_740]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET091+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 07:05:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 669521 was started by sandbox on n019,
% 0.08/0.35 % Sat Sep 26 07:05:20 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.42
% 0.12/0.42 % SZS status Theorem for theBenchmark
% 0.12/0.42
% 0.12/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.12/0.42 % Length of proof is 11.
% 0.12/0.42 % Level of proof is 3.
% 0.12/0.42 % Maximum clause weight is 24.000.
% 0.12/0.42 % Given clauses 130.
% 0.12/0.42
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------