%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET078-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Unsatisfiable 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 11 unt; 0 def)
% Number of atoms : 15 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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; 0-2 aty)
% Number of variables : 14 ( 4 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_1_to_singletons_are_sets_1,axiom,
~ member(singleton(y),unordered_pair(x,singleton(y))),
file('theBenchmark.p',prove_corollary_1_to_singletons_are_sets_1) ).
cnf(c_33,plain,
~ member(singleton(y),unordered_pair(x,singleton(y))),
inference(clausify,[status(thm)],[prove_corollary_1_to_singletons_are_sets_1]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_138,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_139,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_138]) ).
fof(unordered_pairs_in_universal,axiom,
! [VAR_0,VAR_1] : member(unordered_pair(VAR_0,VAR_1),universal_class),
file('theBenchmark.p',unordered_pairs_in_universal) ).
cnf(c_140,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pairs_in_universal]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_141,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
cnf(c_327,plain,
~ member(unordered_pair(y,y),unordered_pair(x,singleton(y))),
inference(paramod,[status(thm)],[c_139,c_33]) ).
cnf(c_238,plain,
~ member(unordered_pair(y,y),unordered_pair(x,unordered_pair(y,y))),
inference(paramod,[status(thm)],[c_139,c_327]) ).
cnf(c_325,plain,
member(unordered_pair(A,B),unordered_pair(C,unordered_pair(A,B))),
inference(resolve,[status(thm)],[c_141,c_140]) ).
cnf(c_326,plain,
$false,
inference(resolve,[status(thm)],[c_325,c_238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET078-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n009.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 07:03:44 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3631792 was started by sandbox2 on n009,
% 0.18/0.44 % Sat Sep 26 07:03:44 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.50
% 0.18/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.50
% 0.18/0.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.18/0.50 % Length of proof is 8.
% 0.18/0.50 % Level of proof is 3.
% 0.18/0.50 % Maximum clause weight is 9.000.
% 0.18/0.50 % Given clauses 42.
% 0.18/0.50
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------