%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET024+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:35:22 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 24 ( 6 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 1 sgn 6 !; 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(set_in_its_singleton,conjecture,
! [X] :
( member(X,universal_class)
=> member(X,singleton(X)) ),
file('theBenchmark.p',set_in_its_singleton) ).
fof(set_in_its_singleton_neg,negated_conjecture,
~ ! [X] :
( member(X,universal_class)
=> member(X,singleton(X)) ),
inference(assume_negation,[status(cth)],[set_in_its_singleton]) ).
fof(nnf_42,plain,
? [X] :
( ~ member(X,singleton(X))
& member(X,universal_class) ),
inference(fof_nnf,[status(thm)],[set_in_its_singleton_neg]) ).
fof(sk_set_in_its_singleton_neg,plain,
( ~ member(sK0,singleton(sK0))
& member(sK0,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
~ member(sK0,singleton(sK0)),
inference(split_conjunct,[status(thm)],[sk_set_in_its_singleton_neg]) ).
cnf(c_65,negated_conjecture,
member(sK0,universal_class),
inference(split_conjunct,[status(thm)],[sk_set_in_its_singleton_neg]) ).
cnf(c_128,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_131,plain,
( A != B
| ~ member(A,universal_class)
| member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_193,negated_conjecture,
~ member(sK0,unordered_pair(sK0,sK0)),
inference(paramod,[status(thm)],[c_128,c_64]) ).
cnf(c_448,negated_conjecture,
( sK0 != sK0
| ~ member(sK0,universal_class) ),
inference(resolve,[status(thm)],[c_131,c_193]) ).
cnf(c_449,plain,
~ member(sK0,universal_class),
inference(xxres,[status(thm)],[c_448]) ).
cnf(c_447,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_65,c_449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET024+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.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 06:53:34 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 2432702 was started by sandbox on n014,
% 0.10/0.37 % Sat Sep 26 06:53:34 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.45
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45
% 0.10/0.45 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.10/0.45 % Length of proof is 9.
% 0.10/0.45 % Level of proof is 3.
% 0.10/0.45 % Maximum clause weight is 11.000.
% 0.10/0.45 % Given clauses 97.
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------