%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET104-7 : 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 : n002.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 08:35:47 AM UTC 2026
% Result : Unsatisfiable 0.19s 10.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 27 unt; 0 def)
% Number of atoms : 39 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_property_2_of_ordered_pair_3,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_property_2_of_ordered_pair_3) ).
cnf(c_33,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_property_2_of_ordered_pair_3]) ).
fof(prove_property_2_of_ordered_pair_2,axiom,
unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y),
file('theBenchmark.p',prove_property_2_of_ordered_pair_2) ).
cnf(c_34,plain,
unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y),
inference(clausify,[status(thm)],[prove_property_2_of_ordered_pair_2]) ).
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_38,plain,
unordered_pair(A,B) = union(singleton(A),singleton(B)),
inference(clausify,[status(thm)],[unordered_pairs_and_singletons]) ).
fof(singleton_is_null_class,axiom,
! [VAR_0] :
( singleton(VAR_0) = null_class
| member(VAR_0,universal_class) ),
file('theBenchmark.p',singleton_is_null_class) ).
cnf(c_61,plain,
( singleton(A) = null_class
| member(A,universal_class) ),
inference(clausify,[status(thm)],[singleton_is_null_class]) ).
fof(unordered_pair_equals_singleton2,axiom,
! [VAR_0,VAR_1] :
( unordered_pair(VAR_0,VAR_1) = singleton(VAR_1)
| member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair_equals_singleton2) ).
cnf(c_83,plain,
( unordered_pair(A,B) = singleton(B)
| member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair_equals_singleton2]) ).
cnf(c_84,plain,
( union(singleton(A),singleton(B)) = singleton(B)
| member(A,universal_class) ),
inference(paramod,[status(thm)],[c_38,c_83]) ).
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_166,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_167,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_166]) ).
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_180,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_790,plain,
unordered_pair(singleton(A),union(singleton(A),singleton(singleton(B)))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_38,c_180]) ).
cnf(c_791,plain,
unordered_pair(singleton(A),complement(intersection(complement(singleton(A)),complement(singleton(singleton(B)))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_167,c_790]) ).
cnf(c_792,plain,
union(singleton(singleton(A)),singleton(complement(intersection(complement(singleton(A)),complement(singleton(singleton(B))))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_38,c_791]) ).
cnf(c_793,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_167,c_792]) ).
cnf(c_181,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_793]) ).
cnf(c_794,plain,
union(singleton(null_class),singleton(singleton(singleton(y)))) != ordered_pair(x,y),
inference(paramod,[status(thm)],[c_38,c_34]) ).
cnf(c_795,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(singleton(y)))))) != ordered_pair(x,y),
inference(paramod,[status(thm)],[c_167,c_794]) ).
cnf(c_796,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(singleton(y)))))) != complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))))))),
inference(paramod,[status(thm)],[c_181,c_795]) ).
cnf(c_233,plain,
complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))))))) != complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(singleton(y)))))),
inference(copy,[status(thm)],[c_796]) ).
cnf(c_264,plain,
( complement(intersection(complement(singleton(A)),complement(singleton(B)))) = singleton(B)
| member(A,universal_class) ),
inference(paramod,[status(thm)],[c_167,c_84]) ).
cnf(c_326,plain,
singleton(x) = null_class,
inference(resolve,[status(thm)],[c_61,c_33]) ).
cnf(c_797,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))))))) != complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(singleton(y)))))),
inference(paramod,[status(thm)],[c_326,c_233]) ).
cnf(c_328,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y))))))))) != complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(singleton(y)))))),
inference(paramod,[status(thm)],[c_326,c_797]) ).
cnf(c_798,plain,
complement(intersection(complement(singleton(x)),complement(singleton(A)))) = singleton(A),
inference(resolve,[status(thm)],[c_264,c_33]) ).
cnf(c_788,plain,
complement(intersection(complement(null_class),complement(singleton(A)))) = singleton(A),
inference(paramod,[status(thm)],[c_326,c_798]) ).
cnf(c_799,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(singleton(y)))))) != complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(singleton(y)))))),
inference(paramod,[status(thm)],[c_788,c_328]) ).
cnf(c_789,plain,
$false,
inference(copy,[status(thm)],[c_799]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET104-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/10.43 % Computer : n002.cluster.edu
% 0.17/10.43 % Model : x86_64 x86_64
% 0.17/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.43 % Memory : 8046.5625MB
% 0.17/10.43 % OS : Linux 6.8.0-71-generic
% 0.17/10.43 % CPULimit : 300
% 0.17/10.43 % WCLimit : 300
% 0.17/10.43 % DateTime : Sat Sep 26 07:11:01 UTC 2026
% 0.17/10.43 % CPUTime :
% 0.17/10.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.43 % Process 1087830 was started by sandbox2 on n002,
% 0.17/10.43 % Sat Sep 26 07:11:01 2026
% 0.17/10.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/10.44
% 0.17/10.44 % From the command line: assign(max_seconds, 300).
% 0.19/10.57
% 0.19/10.57 % SZS status Unsatisfiable for theBenchmark
% 0.19/10.57
% 0.19/10.57 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.19/10.57 % Length of proof is 16.
% 0.19/10.57 % Level of proof is 5.
% 0.19/10.57 % Maximum clause weight is 28.000.
% 0.19/10.57 % Given clauses 119.
% 0.19/10.57
% 0.19/10.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------