%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET231-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 : Fri Sep 25 02:42:55 PM UTC 2026
% Result : Unsatisfiable 116.92s 17.45s
% Output : Proof 116.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 28 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 4 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f16,axiom,
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f16_nnf,plain,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(f1,axiom,
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f1_nnf,plain,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p207,plain,
( subclass(cross_product(X0,X1),X2)
| ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) = not_subclass_element(cross_product(X0,X1),X2) ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(f113,negated_conjecture,
ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) != not_subclass_element(cross_product(x,y),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property6_2) ).
fof(f113_nnf,plain,
ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) != not_subclass_element(cross_product(x,y),z),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) != not_subclass_element(cross_product(x,y),z),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) != not_subclass_element(cross_product(x,y),z),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(p12918,plain,
subclass(cross_product(x,y),z),
inference(resolution,[status(thm)],[p207,c113]) ).
cnf(f112,negated_conjecture,
~ subclass(cross_product(x,y),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property6_1) ).
fof(f112_nnf,plain,
~ subclass(cross_product(x,y),z),
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
~ subclass(cross_product(x,y),z),
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
~ subclass(cross_product(x,y),z),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(p12963,plain,
$false,
inference(resolution,[status(thm)],[p12918,c112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET231-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 10:19:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 116.92/17.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 116.92/17.45 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------