%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET386-6 : 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 : n020.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 08:36:16 AM UTC 2026
% Result : Unsatisfiable 3.83s 1.02s
% Output : CNFRefutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 17 unt; 0 def)
% Number of atoms : 31 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 2 con; 0-3 aty)
% Number of variables : 36 ( 1 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relation_property4_2,axiom,
~ subclass(x,cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_relation_property4_2) ).
cnf(c_36,plain,
~ subclass(x,cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_relation_property4_2]) ).
fof(prove_relation_property4_1,axiom,
restrict(x,universal_class,universal_class) = x,
file('theBenchmark.p',prove_relation_property4_1) ).
cnf(c_37,plain,
restrict(x,universal_class,universal_class) = x,
inference(clausify,[status(thm)],[prove_relation_property4_1]) ).
fof(restriction2,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(cross_product(VAR_0,VAR_1),VAR_2) = restrict(VAR_2,VAR_0,VAR_1),
file('theBenchmark.p',restriction2) ).
cnf(c_111,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_112,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_111]) ).
fof(restriction1,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(VAR_0,cross_product(VAR_1,VAR_2)) = restrict(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',restriction1) ).
cnf(c_113,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_2216,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_112,c_113]) ).
cnf(c_114,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_2216]) ).
fof(intersection2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection2) ).
cnf(c_122,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_143,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_144,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_2217,plain,
intersection(cross_product(universal_class,universal_class),x) = x,
inference(paramod,[status(thm)],[c_112,c_37]) ).
cnf(c_231,plain,
intersection(x,cross_product(universal_class,universal_class)) = x,
inference(paramod,[status(thm)],[c_114,c_2217]) ).
cnf(c_308,plain,
member(not_subclass_element(x,cross_product(universal_class,universal_class)),x),
inference(resolve,[status(thm)],[c_144,c_36]) ).
cnf(c_376,plain,
( member(A,cross_product(universal_class,universal_class))
| ~ member(A,x) ),
inference(paramod,[status(thm)],[c_231,c_122]) ).
cnf(c_920,plain,
member(not_subclass_element(x,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_376,c_308]) ).
cnf(c_2218,plain,
subclass(x,cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_920,c_143]) ).
cnf(c_2215,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_2218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET386-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 07:38:49 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 991512 was started by sandbox2 on n020,
% 0.18/0.45 % Sat Sep 26 07:38:49 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 3.83/1.02
% 3.83/1.02 % SZS status Unsatisfiable for theBenchmark
% 3.83/1.02
% 3.83/1.02 % Proof 1 at 0.41 (+ 0.12) seconds.
% 3.83/1.02 % Length of proof is 14.
% 3.83/1.02 % Level of proof is 6.
% 3.83/1.02 % Maximum clause weight is 11.000.
% 3.83/1.02 % Given clauses 346.
% 3.83/1.02
% 3.83/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------