%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET108-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 02:42:19 PM UTC 2026
% Result : Unsatisfiable 22.79s 3.72s
% Output : Proof 22.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 18 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 4 sgn 6 !; 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(f152,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_1) ).
fof(f152_nnf,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f152]) ).
cnf(c152,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f152_nnf]) ).
cnf(p256,plain,
ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))) = ordered_pair(y,z),
inference(resolution,[status(thm)],[c16,c152]) ).
cnf(f153,negated_conjecture,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_2) ).
fof(f153_nnf,plain,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f153]) ).
fof(f153_sk,plain,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(skolemisation,[status(esa)],[f153_nnf]) ).
cnf(c153,plain,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f153_sk]) ).
cnf(p257,plain,
~ member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(demodulation,[status(thm)],[p256,c153]) ).
cnf(p263,plain,
$false,
inference(resolution,[status(thm)],[p257,c152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET108-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 09:51:32 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.79/3.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.79/3.72 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------