%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET086+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 : 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 08:35:42 AM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 40 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 46 ( 20 ~; 14 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 7 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_of_substitution,conjecture,
! [X] :
? [U] :
( ( U = X
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
| ( X = singleton(U)
& member(U,universal_class) ) ),
file('theBenchmark.p',member_of_substitution) ).
fof(member_of_substitution_neg,negated_conjecture,
~ ! [X] :
? [U] :
( ( U = X
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
| ( X = singleton(U)
& member(U,universal_class) ) ),
inference(assume_negation,[status(cth)],[member_of_substitution]) ).
fof(nnf_42,plain,
? [X] :
! [U] :
( ( U != X
| ? [Y] :
( singleton(Y) = X
& member(Y,universal_class) ) )
& ( singleton(U) != X
| ~ member(U,universal_class) ) ),
inference(fof_nnf,[status(thm)],[member_of_substitution_neg]) ).
fof(sk_member_of_substitution_neg_sk,plain,
! [U] :
( ( U != sK1
| ( singleton(sK0(U)) = sK1
& member(sK0(U),universal_class) ) )
& ( singleton(U) != sK1
| ~ member(U,universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X,sK1),skolemize(Y,sK0(U))],[nnf_42]) ).
fof(sk_member_of_substitution_neg,plain,
( ! [VAR_0] :
( VAR_0 != sK1
| singleton(sK0(VAR_0)) = sK1 )
& ! [VAR_0] :
( VAR_0 != sK1
| member(sK0(VAR_0),universal_class) )
& ! [VAR_0] :
( singleton(VAR_0) != sK1
| ~ member(VAR_0,universal_class) ) ),
inference(cnf_transformation,[status(thm)],[sk_member_of_substitution_neg_sk]) ).
cnf(c_64,negated_conjecture,
( A != sK1
| singleton(sK0(A)) = sK1 ),
inference(split_conjunct,[status(thm)],[sk_member_of_substitution_neg]) ).
cnf(c_65,negated_conjecture,
( sK1 != A
| singleton(sK0(A)) = sK1 ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_66,negated_conjecture,
( A != sK1
| member(sK0(A),universal_class) ),
inference(split_conjunct,[status(thm)],[sk_member_of_substitution_neg]) ).
cnf(c_67,negated_conjecture,
( sK1 != A
| member(sK0(A),universal_class) ),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_68,negated_conjecture,
( singleton(A) != sK1
| ~ member(A,universal_class) ),
inference(split_conjunct,[status(thm)],[sk_member_of_substitution_neg]) ).
cnf(c_164,plain,
singleton(sK0(sK1)) = sK1,
inference(xxres,[status(thm)],[c_65]) ).
cnf(c_165,plain,
member(sK0(sK1),universal_class),
inference(xxres,[status(thm)],[c_67]) ).
cnf(c_638,negated_conjecture,
singleton(sK0(sK1)) != sK1,
inference(resolve,[status(thm)],[c_165,c_68]) ).
cnf(c_637,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_164,c_638]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET086+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 07:02:23 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3073104 was started by sandbox2 on n007,
% 0.10/0.37 % Sat Sep 26 07:02:23 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.40
% 0.15/0.40 % From the command line: assign(max_seconds, 300).
% 0.15/0.46
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46
% 0.15/0.46 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.15/0.46 % Length of proof is 9.
% 0.15/0.46 % Level of proof is 4.
% 0.15/0.46 % Maximum clause weight is 23.000.
% 0.15/0.46 % Given clauses 120.
% 0.15/0.46
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------