%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET130-6 : 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 : n017.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 08:35:52 AM UTC 2026
% Result : Unsatisfiable 0.20s 5.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 27 unt; 0 def)
% Number of atoms : 47 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 23 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_member_of_triple1_2,axiom,
~ member(u,set_builder(u,set_builder(y,set_builder(z,null_class)))),
file('theBenchmark.p',prove_member_of_triple1_2) ).
cnf(c_34,plain,
~ member(u,set_builder(u,set_builder(y,set_builder(z,null_class)))),
inference(clausify,[status(thm)],[prove_member_of_triple1_2]) ).
fof(prove_member_of_triple1_1,axiom,
member(u,universal_class),
file('theBenchmark.p',prove_member_of_triple1_1) ).
cnf(c_35,plain,
member(u,universal_class),
inference(clausify,[status(thm)],[prove_member_of_triple1_1]) ).
fof(definition_of_set_builder,axiom,
! [VAR_0,VAR_1] : union(singleton(VAR_0),VAR_1) = set_builder(VAR_0,VAR_1),
file('theBenchmark.p',definition_of_set_builder) ).
cnf(c_36,plain,
union(singleton(A),B) = set_builder(A,B),
inference(clausify,[status(thm)],[definition_of_set_builder]) ).
cnf(c_37,plain,
set_builder(A,B) = union(singleton(A),B),
inference(copy,[status(thm)],[c_36]) ).
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_96,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_97,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_96]) ).
fof(complement2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,VAR_1)
| member(VAR_0,complement(VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',complement2) ).
cnf(c_98,plain,
( member(A,B)
| member(A,complement(B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[complement2]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_99,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_102,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_112,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_113,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_112]) ).
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_115,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
cnf(c_743,plain,
~ member(u,set_builder(u,set_builder(y,union(singleton(z),null_class)))),
inference(paramod,[status(thm)],[c_37,c_34]) ).
cnf(c_744,plain,
~ member(u,set_builder(u,set_builder(y,union(unordered_pair(z,z),null_class)))),
inference(paramod,[status(thm)],[c_113,c_743]) ).
cnf(c_745,plain,
~ member(u,set_builder(u,set_builder(y,complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))),
inference(paramod,[status(thm)],[c_97,c_744]) ).
cnf(c_746,plain,
~ member(u,set_builder(u,union(singleton(y),complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))),
inference(paramod,[status(thm)],[c_37,c_745]) ).
cnf(c_747,plain,
~ member(u,set_builder(u,union(unordered_pair(y,y),complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))),
inference(paramod,[status(thm)],[c_113,c_746]) ).
cnf(c_748,plain,
~ member(u,set_builder(u,complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))),
inference(paramod,[status(thm)],[c_97,c_747]) ).
cnf(c_749,plain,
~ member(u,union(singleton(u),complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))),
inference(paramod,[status(thm)],[c_37,c_748]) ).
cnf(c_750,plain,
~ member(u,union(unordered_pair(u,u),complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))),
inference(paramod,[status(thm)],[c_113,c_749]) ).
cnf(c_158,plain,
~ member(u,complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))),
inference(paramod,[status(thm)],[c_97,c_750]) ).
cnf(c_209,plain,
( member(u,A)
| member(u,complement(A)) ),
inference(resolve,[status(thm)],[c_98,c_35]) ).
cnf(c_233,plain,
member(u,unordered_pair(A,u)),
inference(resolve,[status(thm)],[c_115,c_35]) ).
cnf(c_395,plain,
~ member(u,complement(unordered_pair(A,u))),
inference(resolve,[status(thm)],[c_99,c_233]) ).
cnf(c_733,plain,
~ member(u,intersection(complement(unordered_pair(A,u)),B)),
inference(resolve,[status(thm)],[c_102,c_395]) ).
cnf(c_751,plain,
member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))),
inference(resolve,[status(thm)],[c_209,c_158]) ).
cnf(c_742,plain,
$false,
inference(resolve,[status(thm)],[c_733,c_751]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET130-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.42 % Computer : n017.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Sat Sep 26 07:07:24 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.43 % Process 116622 was started by sandbox on n017,
% 0.15/5.43 % Sat Sep 26 07:07:24 2026
% 0.15/5.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.44
% 0.15/5.44 % From the command line: assign(max_seconds, 300).
% 0.20/5.63
% 0.20/5.63 % SZS status Unsatisfiable for theBenchmark
% 0.20/5.63
% 0.20/5.63 % Proof 1 at 0.13 (+ 0.04) seconds.
% 0.20/5.63 % Length of proof is 18.
% 0.20/5.63 % Level of proof is 4.
% 0.20/5.63 % Maximum clause weight is 24.000.
% 0.20/5.63 % Given clauses 150.
% 0.20/5.63
% 0.20/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------