%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET082-6 : 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 : n008.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 08:35:41 AM UTC 2026
% Result : Unsatisfiable 3.64s 0.97s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 53 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 14 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 4 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_singleton_is_null_class_2,axiom,
singleton(x) != null_class,
file('theBenchmark.p',prove_singleton_is_null_class_2) ).
cnf(c_34,plain,
singleton(x) != null_class,
inference(clausify,[status(thm)],[prove_singleton_is_null_class_2]) ).
fof(prove_singleton_is_null_class_1,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_singleton_is_null_class_1) ).
cnf(c_35,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_singleton_is_null_class_1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_52,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_53,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_52]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_109,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_110,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_109]) ).
fof(unordered_pair_member,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_member) ).
cnf(c_114,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_118,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_121,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_196,plain,
unordered_pair(x,x) != null_class,
inference(paramod,[status(thm)],[c_110,c_34]) ).
cnf(c_1770,plain,
( null_class = unordered_pair(A,B)
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(resolve,[status(thm)],[c_114,c_53]) ).
cnf(c_230,plain,
( unordered_pair(A,B) = null_class
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_1770]) ).
cnf(c_231,plain,
( unordered_pair(A,A) = null_class
| regular(unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_230]) ).
cnf(c_252,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_121,c_118]) ).
cnf(c_1771,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_121,c_118]) ).
cnf(c_262,plain,
~ member(x,A),
inference(resolve,[status(thm)],[c_1771,c_35]) ).
cnf(c_393,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_252,c_53]) ).
cnf(c_1772,plain,
( null_class = unordered_pair(A,A)
| member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(paramod,[status(thm)],[c_231,c_393]) ).
cnf(c_1773,plain,
( unordered_pair(A,A) = null_class
| member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_1772]) ).
cnf(c_1027,plain,
( member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_1773]) ).
cnf(c_1774,plain,
unordered_pair(x,x) = null_class,
inference(resolve,[status(thm)],[c_1027,c_262]) ).
cnf(c_1769,plain,
$false,
inference(resolve,[status(thm)],[c_196,c_1774]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET082-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n008.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 07:04:54 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3031964 was started by sandbox2 on n008,
% 0.17/0.44 % Sat Sep 26 07:04:54 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 3.64/0.97
% 3.64/0.97 % SZS status Unsatisfiable for theBenchmark
% 3.64/0.97
% 3.64/0.97 % Proof 1 at 0.41 (+ 0.09) seconds.
% 3.64/0.97 % Length of proof is 17.
% 3.64/0.97 % Level of proof is 5.
% 3.64/0.97 % Maximum clause weight is 32.000.
% 3.64/0.97 % Given clauses 302.
% 3.64/0.97
% 3.64/0.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------