%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET101-7 : 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 08:35:46 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 19 unt; 0 def)
% Number of atoms : 27 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 5 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_singleton_member_of_ordered_pair_1,axiom,
~ member(singleton(x),ordered_pair(x,y)),
file('theBenchmark.p',prove_singleton_member_of_ordered_pair_1) ).
cnf(c_33,plain,
~ member(singleton(x),ordered_pair(x,y)),
inference(clausify,[status(thm)],[prove_singleton_member_of_ordered_pair_1]) ).
fof(unordered_pairs_and_singletons,axiom,
! [VAR_0,VAR_1] : unordered_pair(VAR_0,VAR_1) = union(singleton(VAR_0),singleton(VAR_1)),
file('theBenchmark.p',unordered_pairs_and_singletons) ).
cnf(c_35,plain,
unordered_pair(A,B) = union(singleton(A),singleton(B)),
inference(clausify,[status(thm)],[unordered_pairs_and_singletons]) ).
fof(singletons_are_sets,axiom,
! [VAR_0] : member(singleton(VAR_0),universal_class),
file('theBenchmark.p',singletons_are_sets) ).
cnf(c_65,plain,
member(singleton(A),universal_class),
inference(clausify,[status(thm)],[singletons_are_sets]) ).
fof(union,axiom,
! [VAR_0,VAR_1] : complement(intersection(complement(VAR_0),complement(VAR_1))) = union(VAR_0,VAR_1),
file('theBenchmark.p',union) ).
cnf(c_163,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_164,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_163]) ).
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_177,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_507,plain,
unordered_pair(singleton(A),union(singleton(A),singleton(singleton(B)))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_35,c_177]) ).
cnf(c_508,plain,
unordered_pair(singleton(A),complement(intersection(complement(singleton(A)),complement(singleton(singleton(B)))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_164,c_507]) ).
cnf(c_509,plain,
union(singleton(singleton(A)),singleton(complement(intersection(complement(singleton(A)),complement(singleton(singleton(B))))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_35,c_508]) ).
cnf(c_510,plain,
complement(intersection(complement(singleton(singleton(A))),complement(singleton(complement(intersection(complement(singleton(A)),complement(singleton(singleton(B))))))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_164,c_509]) ).
cnf(c_178,plain,
ordered_pair(A,B) = complement(intersection(complement(singleton(singleton(A))),complement(singleton(complement(intersection(complement(singleton(A)),complement(singleton(singleton(B))))))))),
inference(copy,[status(thm)],[c_510]) ).
fof(unordered_pair2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_0,VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair2) ).
cnf(c_185,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
cnf(c_511,plain,
( member(A,union(singleton(A),singleton(B)))
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_35,c_185]) ).
cnf(c_186,plain,
( member(A,complement(intersection(complement(singleton(A)),complement(singleton(B)))))
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_164,c_511]) ).
cnf(c_286,plain,
~ member(singleton(x),complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y)))))))))),
inference(paramod,[status(thm)],[c_178,c_33]) ).
cnf(c_505,plain,
member(singleton(A),complement(intersection(complement(singleton(singleton(A))),complement(singleton(B))))),
inference(resolve,[status(thm)],[c_186,c_65]) ).
cnf(c_506,plain,
$false,
inference(resolve,[status(thm)],[c_505,c_286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET101-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n009.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sat Sep 26 07:07:25 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.38 % Process 3642513 was started by sandbox2 on n009,
% 0.09/10.38 % Sat Sep 26 07:07:25 2026
% 0.09/10.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/10.39
% 0.09/10.39 % From the command line: assign(max_seconds, 300).
% 0.14/10.44
% 0.14/10.44 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.44
% 0.14/10.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/10.44 % Length of proof is 12.
% 0.14/10.44 % Level of proof is 4.
% 0.14/10.44 % Maximum clause weight is 21.000.
% 0.14/10.44 % Given clauses 62.
% 0.14/10.44
% 0.14/10.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------