%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET252-6 : 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 : 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 08:36:06 AM UTC 2026
% Result : Unsatisfiable 5.71s 1.19s
% Output : CNFRefutation 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 27 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 35 ( 1 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_restriction_property3_1,axiom,
~ subclass(restrict(x,y,z),x),
file('theBenchmark.p',prove_restriction_property3_1) ).
cnf(c_36,plain,
~ subclass(restrict(x,y,z),x),
inference(clausify,[status(thm)],[prove_restriction_property3_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_110,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_111,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_110]) ).
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_112,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_5597,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_111,c_112]) ).
cnf(c_113,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_5597]) ).
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_122,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
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_142,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_143,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_5598,plain,
~ subclass(intersection(cross_product(y,z),x),x),
inference(paramod,[status(thm)],[c_111,c_36]) ).
cnf(c_230,plain,
~ subclass(intersection(x,cross_product(y,z)),x),
inference(paramod,[status(thm)],[c_113,c_5598]) ).
cnf(c_374,plain,
member(not_subclass_element(intersection(x,cross_product(y,z)),x),intersection(x,cross_product(y,z))),
inference(resolve,[status(thm)],[c_230,c_143]) ).
cnf(c_5570,plain,
member(not_subclass_element(intersection(x,cross_product(y,z)),x),x),
inference(resolve,[status(thm)],[c_374,c_122]) ).
cnf(c_5599,plain,
subclass(intersection(x,cross_product(y,z)),x),
inference(resolve,[status(thm)],[c_5570,c_142]) ).
cnf(c_5596,plain,
$false,
inference(resolve,[status(thm)],[c_230,c_5599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET252-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 07:22:08 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3119049 was started by sandbox2 on n007,
% 0.08/0.36 % Sat Sep 26 07:22:08 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 5.71/1.19
% 5.71/1.19 % given #500 (F,wt=29): 4670 intersection(cross_product(unordered_pair(A,A),universal_class),domain_of(flip(cross_product(intersection(cross_product(B,universal_class),C),universal_class)))) != null_class | -member(A,domain_of(domain_of(flip(cross_product(intersection(C,cross_product(B,universal_class)),universal_class))))). [para(361(a,1),225(b,2))].
% 5.71/1.19
% 5.71/1.19 % SZS status Unsatisfiable for theBenchmark
% 5.71/1.19
% 5.71/1.19 % Proof 1 at 0.67 (+ 0.13) seconds.
% 5.71/1.19 % Length of proof is 12.
% 5.71/1.19 % Level of proof is 6.
% 5.71/1.19 % Maximum clause weight is 13.000.
% 5.71/1.19 % Given clauses 549.
% 5.71/1.19
% 5.71/1.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------