%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET117-6 : 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 : n005.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 08:35:50 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.54s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 20 unt; 0 def)
% Number of atoms : 28 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 5 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_1_to_ordered_pairs_are_sets_2,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_corollary_1_to_ordered_pairs_are_sets_2) ).
cnf(c_34,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_corollary_1_to_ordered_pairs_are_sets_2]) ).
fof(prove_corollary_1_to_ordered_pairs_are_sets_1,axiom,
ordered_pair(first(x),second(x)) = x,
file('theBenchmark.p',prove_corollary_1_to_ordered_pairs_are_sets_1) ).
cnf(c_35,plain,
ordered_pair(first(x),second(x)) = x,
inference(clausify,[status(thm)],[prove_corollary_1_to_ordered_pairs_are_sets_1]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(singleton(VAR_0),unordered_pair(VAR_0,singleton(VAR_1))) = ordered_pair(VAR_0,VAR_1),
file('theBenchmark.p',ordered_pair) ).
cnf(c_107,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_108,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_107]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_109,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_110,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_109]) ).
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_111,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pairs_in_universal]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_118,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_121,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_326,plain,
unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))) = x,
inference(paramod,[status(thm)],[c_108,c_35]) ).
cnf(c_327,plain,
unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),singleton(second(x)))) = x,
inference(paramod,[status(thm)],[c_110,c_326]) ).
cnf(c_195,plain,
unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) = x,
inference(paramod,[status(thm)],[c_110,c_327]) ).
cnf(c_328,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_121,c_118]) ).
cnf(c_257,plain,
~ member(x,A),
inference(resolve,[status(thm)],[c_328,c_34]) ).
cnf(c_329,plain,
member(x,universal_class),
inference(paramod,[status(thm)],[c_195,c_111]) ).
cnf(c_325,plain,
$false,
inference(resolve,[status(thm)],[c_257,c_329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET117-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 07:09:48 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 1518117 was started by sandbox2 on n005,
% 0.18/0.44 % Sat Sep 26 07:09:48 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).
% 0.23/0.54
% 0.23/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.54
% 0.23/0.54 % Proof 1 at 0.07 (+ 0.01) seconds.
% 0.23/0.54 % Length of proof is 12.
% 0.23/0.54 % Level of proof is 3.
% 0.23/0.54 % Maximum clause weight is 16.000.
% 0.23/0.54 % Given clauses 96.
% 0.23/0.54
% 0.23/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------