%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 08:35:48 AM UTC 2026
% Result : Unsatisfiable 38.84s 11.80s
% Output : CNFRefutation 38.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 47 unt; 0 def)
% Number of atoms : 59 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 18 ~; 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 : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_property_3_of_ordered_pair_3,axiom,
~ member(y,universal_class),
file('theBenchmark.p',prove_property_3_of_ordered_pair_3) ).
cnf(c_33,plain,
~ member(y,universal_class),
inference(clausify,[status(thm)],[prove_property_3_of_ordered_pair_3]) ).
fof(prove_property_3_of_ordered_pair_2,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_property_3_of_ordered_pair_2) ).
cnf(c_34,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_property_3_of_ordered_pair_2]) ).
fof(prove_property_3_of_ordered_pair_1,axiom,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
file('theBenchmark.p',prove_property_3_of_ordered_pair_1) ).
cnf(c_35,plain,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
inference(clausify,[status(thm)],[prove_property_3_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_39,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_62,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_84,plain,
( unordered_pair(A,B) = singleton(B)
| member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair_equals_singleton2]) ).
cnf(c_85,plain,
( union(singleton(A),singleton(B)) = singleton(B)
| member(A,universal_class) ),
inference(paramod,[status(thm)],[c_39,c_84]) ).
fof(commutativity_of_unordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(VAR_0,VAR_1) = unordered_pair(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_unordered_pair) ).
cnf(c_92,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_of_unordered_pair]) ).
cnf(c_21371,plain,
union(singleton(A),singleton(B)) = unordered_pair(B,A),
inference(paramod,[status(thm)],[c_39,c_92]) ).
cnf(c_93,plain,
union(singleton(A),singleton(B)) = union(singleton(B),singleton(A)),
inference(paramod,[status(thm)],[c_39,c_21371]) ).
fof(successor,axiom,
! [VAR_0] : union(VAR_0,singleton(VAR_0)) = successor(VAR_0),
file('theBenchmark.p',successor) ).
cnf(c_144,plain,
union(A,singleton(A)) = successor(A),
inference(clausify,[status(thm)],[successor]) ).
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_167,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_168,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_167]) ).
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_181,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_21372,plain,
unordered_pair(singleton(A),union(singleton(A),singleton(singleton(B)))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_39,c_181]) ).
cnf(c_21373,plain,
unordered_pair(singleton(A),complement(intersection(complement(singleton(A)),complement(singleton(singleton(B)))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_168,c_21372]) ).
cnf(c_21374,plain,
union(singleton(singleton(A)),singleton(complement(intersection(complement(singleton(A)),complement(singleton(singleton(B))))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_39,c_21373]) ).
cnf(c_21375,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_168,c_21374]) ).
cnf(c_182,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_21375]) ).
cnf(c_21376,plain,
union(singleton(null_class),singleton(singleton(null_class))) != ordered_pair(x,y),
inference(paramod,[status(thm)],[c_39,c_35]) ).
cnf(c_21377,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(null_class))))) != ordered_pair(x,y),
inference(paramod,[status(thm)],[c_168,c_21376]) ).
cnf(c_21378,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(null_class))))) != complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))))))),
inference(paramod,[status(thm)],[c_182,c_21377]) ).
cnf(c_234,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(null_class))))),
inference(copy,[status(thm)],[c_21378]) ).
cnf(c_258,plain,
complement(intersection(complement(A),complement(singleton(A)))) = successor(A),
inference(paramod,[status(thm)],[c_168,c_144]) ).
cnf(c_21379,plain,
complement(intersection(complement(singleton(A)),complement(singleton(B)))) = union(singleton(B),singleton(A)),
inference(paramod,[status(thm)],[c_168,c_93]) ).
cnf(c_261,plain,
complement(intersection(complement(singleton(A)),complement(singleton(B)))) = complement(intersection(complement(singleton(B)),complement(singleton(A)))),
inference(paramod,[status(thm)],[c_168,c_21379]) ).
cnf(c_265,plain,
( complement(intersection(complement(singleton(A)),complement(singleton(B)))) = singleton(B)
| member(A,universal_class) ),
inference(paramod,[status(thm)],[c_168,c_85]) ).
cnf(c_297,plain,
complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))))))) != successor(singleton(null_class)),
inference(paramod,[status(thm)],[c_258,c_234]) ).
cnf(c_328,plain,
singleton(x) = null_class,
inference(resolve,[status(thm)],[c_62,c_34]) ).
cnf(c_329,plain,
singleton(y) = null_class,
inference(resolve,[status(thm)],[c_62,c_33]) ).
cnf(c_21380,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))))))) != successor(singleton(null_class)),
inference(paramod,[status(thm)],[c_328,c_297]) ).
cnf(c_21381,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y))))))))) != successor(singleton(null_class)),
inference(paramod,[status(thm)],[c_328,c_21380]) ).
cnf(c_21382,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(null_class)))))))) != successor(singleton(null_class)),
inference(paramod,[status(thm)],[c_329,c_21381]) ).
cnf(c_331,plain,
complement(intersection(complement(singleton(null_class)),complement(singleton(successor(null_class))))) != successor(singleton(null_class)),
inference(paramod,[status(thm)],[c_258,c_21382]) ).
cnf(c_719,plain,
complement(intersection(complement(singleton(singleton(A))),complement(singleton(A)))) = successor(singleton(A)),
inference(paramod,[status(thm)],[c_261,c_258]) ).
cnf(c_21383,plain,
complement(intersection(complement(singleton(x)),complement(singleton(A)))) = singleton(A),
inference(resolve,[status(thm)],[c_265,c_34]) ).
cnf(c_791,plain,
complement(intersection(complement(null_class),complement(singleton(A)))) = singleton(A),
inference(paramod,[status(thm)],[c_328,c_21383]) ).
cnf(c_1490,plain,
complement(intersection(complement(singleton(successor(null_class))),complement(singleton(null_class)))) != successor(singleton(null_class)),
inference(paramod,[status(thm)],[c_261,c_331]) ).
cnf(c_21384,plain,
singleton(null_class) = successor(null_class),
inference(paramod,[status(thm)],[c_791,c_258]) ).
cnf(c_21297,plain,
successor(null_class) = singleton(null_class),
inference(copy,[status(thm)],[c_21384]) ).
cnf(c_21385,plain,
complement(intersection(complement(singleton(singleton(null_class))),complement(singleton(null_class)))) != successor(singleton(null_class)),
inference(paramod,[status(thm)],[c_21297,c_1490]) ).
cnf(c_21386,plain,
successor(singleton(null_class)) != successor(singleton(null_class)),
inference(paramod,[status(thm)],[c_719,c_21385]) ).
cnf(c_21370,plain,
$false,
inference(copy,[status(thm)],[c_21386]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:13:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1209082 was started by sandbox on n001,
% 0.09/0.35 % Sat Sep 26 07:13:57 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 38.84/11.80
% 38.84/11.80 % given #500 (T,wt=8): 2599 member(null_class,intersection(universal_class,intersection(universal_class,successor(null_class)))). [resolve(2581,a,441,a)].
% 38.84/11.80
% 38.84/11.80 % given #1000 (T,wt=9): 3567 member(null_class,intersection(intersection(singleton(null_class),singleton(null_class)),omega)). [resolve(463,a,970,a)].
% 38.84/11.80
% 38.84/11.80 % given #1500 (T,wt=9): 10735 singleton(universal_class) != universal_class | not_subclass_element(omega,null_class) = universal_class. [resolve(10693,a,49,b),rewrite([1531(2),1531(6)]),flip(b)].
% 38.84/11.80
% 38.84/11.80 % SZS status Unsatisfiable for theBenchmark
% 38.84/11.80
% 38.84/11.80 % Proof 1 at 4.50 (+ 0.81) seconds.
% 38.84/11.80 % Length of proof is 27.
% 38.84/11.80 % Level of proof is 7.
% 38.84/11.80 % Maximum clause weight is 27.000.
% 38.84/11.80 % Given clauses 1723.
% 38.84/11.80
% 38.84/11.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------