%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET073-6 : 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 : n007.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 08:35:38 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 17 unt; 0 def)
% Number of atoms : 66 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 28 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 40 ( 3 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_unordered_pair_axiom1_2,axiom,
unordered_pair(x,y) = null_class,
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom1_2) ).
cnf(c_34,plain,
unordered_pair(x,y) = null_class,
inference(clausify,[status(thm)],[prove_corollary_to_unordered_pair_axiom1_2]) ).
cnf(c_35,plain,
null_class = unordered_pair(x,y),
inference(copy,[status(thm)],[c_34]) ).
fof(prove_corollary_to_unordered_pair_axiom1_1,axiom,
member(x,universal_class),
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom1_1) ).
cnf(c_36,plain,
member(x,universal_class),
inference(clausify,[status(thm)],[prove_corollary_to_unordered_pair_axiom1_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_51,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_52,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_51]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_97,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_100,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(unordered_pair2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_0,VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair2) ).
cnf(c_114,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
fof(subclass_implies_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ subclass(VAR_1,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_implies_equal) ).
cnf(c_116,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
fof(equal_implies_subclass2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_1,VAR_0)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass2) ).
cnf(c_117,plain,
( subclass(B,A)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass2]) ).
fof(equal_implies_subclass1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass1) ).
cnf(c_118,plain,
( subclass(A,B)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass1]) ).
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_122,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_198,plain,
~ member(x,complement(universal_class)),
inference(resolve,[status(thm)],[c_97,c_36]) ).
cnf(c_215,plain,
( member(B,A)
| ~ member(B,null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_52,c_100]) ).
cnf(c_269,plain,
member(x,unordered_pair(x,A)),
inference(resolve,[status(thm)],[c_114,c_36]) ).
cnf(c_298,plain,
subclass(unordered_pair(x,y),null_class),
inference(resolve,[status(thm)],[c_117,c_35]) ).
cnf(c_911,plain,
unordered_pair(x,y) = null_class,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_319,plain,
subclass(null_class,unordered_pair(x,y)),
inference(resolve,[status(thm)],[c_117,c_911]) ).
cnf(c_912,plain,
( null_class = unordered_pair(x,y)
| ~ subclass(null_class,unordered_pair(x,y)) ),
inference(resolve,[status(thm)],[c_298,c_116]) ).
cnf(c_913,plain,
( unordered_pair(x,y) = null_class
| ~ subclass(null_class,unordered_pair(x,y)) ),
inference(copy,[status(thm)],[c_912]) ).
cnf(c_657,plain,
unordered_pair(x,y) = null_class,
inference(resolve,[status(thm)],[c_319,c_913]) ).
cnf(c_855,plain,
member(x,null_class),
inference(paramod,[status(thm)],[c_657,c_269]) ).
cnf(c_856,plain,
( member(x,A)
| null_class = A ),
inference(resolve,[status(thm)],[c_855,c_215]) ).
cnf(c_914,plain,
( member(x,A)
| ~ subclass(null_class,A) ),
inference(resolve,[status(thm)],[c_122,c_855]) ).
cnf(c_863,plain,
~ subclass(null_class,complement(universal_class)),
inference(resolve,[status(thm)],[c_914,c_198]) ).
cnf(c_866,plain,
null_class = complement(universal_class),
inference(resolve,[status(thm)],[c_856,c_198]) ).
cnf(c_915,plain,
null_class != complement(universal_class),
inference(resolve,[status(thm)],[c_118,c_863]) ).
cnf(c_916,plain,
complement(universal_class) != null_class,
inference(copy,[status(thm)],[c_915]) ).
cnf(c_910,plain,
$false,
inference(resolve,[status(thm)],[c_866,c_916]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET073-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 07:00:38 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 3069646 was started by sandbox on n007,
% 0.08/0.34 % Sat Sep 26 07:00:38 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.45
% 0.12/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.45
% 0.12/0.45 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.12/0.45 % Length of proof is 23.
% 0.12/0.45 % Level of proof is 7.
% 0.12/0.45 % Maximum clause weight is 24.000.
% 0.12/0.45 % Given clauses 167.
% 0.12/0.45
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------