%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET103-6 : 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 : 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 08:35:47 AM UTC 2026
% Result : Unsatisfiable 2.55s 0.73s
% Output : CNFRefutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 25 unt; 0 def)
% Number of atoms : 71 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 8 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_property_1_of_ordered_pair_2,axiom,
~ member(y,universal_class),
file('theBenchmark.p',prove_property_1_of_ordered_pair_2) ).
cnf(c_34,plain,
~ member(y,universal_class),
inference(clausify,[status(thm)],[prove_property_1_of_ordered_pair_2]) ).
fof(prove_property_1_of_ordered_pair_1,axiom,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
file('theBenchmark.p',prove_property_1_of_ordered_pair_1) ).
cnf(c_35,plain,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
inference(clausify,[status(thm)],[prove_property_1_of_ordered_pair_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(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_107,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_108,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_107]) ).
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_pairs_in_universal,axiom,
! [VAR_0,VAR_1] : member(unordered_pair(VAR_0,VAR_1),universal_class),
file('theBenchmark.p',unordered_pairs_in_universal) ).
cnf(c_111,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pairs_in_universal]) ).
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_112,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
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_1771,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != ordered_pair(x,y),
inference(paramod,[status(thm)],[c_110,c_35]) ).
cnf(c_1772,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(singleton(x),unordered_pair(x,singleton(y))),
inference(paramod,[status(thm)],[c_108,c_1771]) ).
cnf(c_1773,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,singleton(y))),
inference(paramod,[status(thm)],[c_110,c_1772]) ).
cnf(c_1774,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(paramod,[status(thm)],[c_110,c_1773]) ).
cnf(c_195,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),
inference(copy,[status(thm)],[c_1774]) ).
cnf(c_224,plain,
member(unordered_pair(A,B),unordered_pair(C,unordered_pair(A,B))),
inference(resolve,[status(thm)],[c_112,c_111]) ).
cnf(c_1775,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_1775]) ).
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_1776,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_121,c_118]) ).
cnf(c_262,plain,
~ member(y,A),
inference(resolve,[status(thm)],[c_1776,c_34]) ).
cnf(c_1777,plain,
( unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))) = A
| ~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),unordered_pair(unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),A)) ),
inference(resolve,[status(thm)],[c_114,c_195]) ).
cnf(c_351,plain,
~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),unordered_pair(unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)))),
inference(resolve,[status(thm)],[c_1777,c_195]) ).
cnf(c_392,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_252,c_53]) ).
cnf(c_1778,plain,
( null_class = unordered_pair(A,A)
| member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(paramod,[status(thm)],[c_231,c_392]) ).
cnf(c_1779,plain,
( unordered_pair(A,A) = null_class
| member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_1778]) ).
cnf(c_1016,plain,
( member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_1779]) ).
cnf(c_1745,plain,
unordered_pair(y,y) = null_class,
inference(resolve,[status(thm)],[c_1016,c_262]) ).
cnf(c_1780,plain,
~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),unordered_pair(unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)))),
inference(paramod,[status(thm)],[c_1745,c_351]) ).
cnf(c_1770,plain,
$false,
inference(resolve,[status(thm)],[c_224,c_1780]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET103-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 07:13:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1208292 was started by sandbox2 on n001,
% 0.10/0.36 % Sat Sep 26 07:13:42 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 2.55/0.73
% 2.55/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.55/0.73
% 2.55/0.73 % Proof 1 at 0.28 (+ 0.07) seconds.
% 2.55/0.73 % Length of proof is 24.
% 2.55/0.73 % Level of proof is 6.
% 2.55/0.73 % Maximum clause weight is 90.000.
% 2.55/0.73 % Given clauses 302.
% 2.55/0.73
% 2.55/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------