%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET124-6 : 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 : 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 0.13s 0.55s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 21 unt; 0 def)
% Number of atoms : 41 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 17 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 38 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_set_builder_alternate_defn2_2,axiom,
~ member(x,set_builder(x,z)),
file('theBenchmark.p',prove_set_builder_alternate_defn2_2) ).
cnf(c_34,plain,
~ member(x,set_builder(x,z)),
inference(clausify,[status(thm)],[prove_set_builder_alternate_defn2_2]) ).
fof(prove_set_builder_alternate_defn2_1,axiom,
member(x,universal_class),
file('theBenchmark.p',prove_set_builder_alternate_defn2_1) ).
cnf(c_35,plain,
member(x,universal_class),
inference(clausify,[status(thm)],[prove_set_builder_alternate_defn2_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(x,union(singleton(x),z)),
inference(paramod,[status(thm)],[c_37,c_34]) ).
cnf(c_744,plain,
~ member(x,union(unordered_pair(x,x),z)),
inference(paramod,[status(thm)],[c_113,c_743]) ).
cnf(c_158,plain,
~ member(x,complement(intersection(complement(unordered_pair(x,x)),complement(z)))),
inference(paramod,[status(thm)],[c_97,c_744]) ).
cnf(c_209,plain,
( member(x,A)
| member(x,complement(A)) ),
inference(resolve,[status(thm)],[c_98,c_35]) ).
cnf(c_233,plain,
member(x,unordered_pair(A,x)),
inference(resolve,[status(thm)],[c_115,c_35]) ).
cnf(c_395,plain,
~ member(x,complement(unordered_pair(A,x))),
inference(resolve,[status(thm)],[c_99,c_233]) ).
cnf(c_733,plain,
~ member(x,intersection(complement(unordered_pair(A,x)),B)),
inference(resolve,[status(thm)],[c_102,c_395]) ).
cnf(c_745,plain,
member(x,intersection(complement(unordered_pair(x,x)),complement(z))),
inference(resolve,[status(thm)],[c_209,c_158]) ).
cnf(c_742,plain,
$false,
inference(resolve,[status(thm)],[c_733,c_745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET124-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.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 07:06:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 115004 was started by sandbox2 on n017,
% 0.09/0.36 % Sat Sep 26 07:06:50 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.55
% 0.13/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.55
% 0.13/0.55 % Proof 1 at 0.13 (+ 0.04) seconds.
% 0.13/0.55 % Length of proof is 18.
% 0.13/0.55 % Level of proof is 4.
% 0.13/0.55 % Maximum clause weight is 10.000.
% 0.13/0.55 % Given clauses 150.
% 0.13/0.55
% 0.13/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------