%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET236-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 02:42:56 PM UTC 2026
% Result : Unsatisfiable 30.15s 10.04s
% Output : Proof 30.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 58 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 21 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 43 ( 4 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f16,axiom,
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f112,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property11_1) ).
fof(f112_nnf,plain,
subclass(x,cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
subclass(x,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(f0,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f0_nnf,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p116,plain,
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[c112,c0]) ).
cnf(p117,plain,
( member(not_subclass_element(x,X0),cross_product(universal_class,universal_class))
| subclass(x,X0) ),
inference(resolution,[status(thm)],[c1,p116]) ).
cnf(p215,plain,
( subclass(x,X0)
| ordered_pair(first(not_subclass_element(x,X0)),second(not_subclass_element(x,X0))) = not_subclass_element(x,X0) ),
inference(resolution,[status(thm)],[c16,p117]) ).
cnf(f113,negated_conjecture,
member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property11_2) ).
fof(f113_nnf,plain,
member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),y),
inference(nnf_transformation,[status(thm)],[f113]) ).
cnf(c113,plain,
member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),y),
inference(cnf_transformation,[status(esa)],[f113_nnf]) ).
cnf(p239,plain,
( member(not_subclass_element(x,y),y)
| subclass(x,y) ),
inference(superposition,[status(thm)],[p215,c113]) ).
cnf(f2,axiom,
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f2_nnf,plain,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p262,plain,
( subclass(x,y)
| subclass(x,y) ),
inference(resolution,[status(thm)],[p239,c2]) ).
cnf(p265,plain,
subclass(x,y),
inference(factoring,[status(thm)],[p262]) ).
cnf(f114,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property11_3) ).
fof(f114_nnf,plain,
~ subclass(x,y),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
~ subclass(x,y),
inference(skolemisation,[status(esa)],[f114_nnf]) ).
cnf(c114,plain,
~ subclass(x,y),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(p268,plain,
$false,
inference(resolution,[status(thm)],[p265,c114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET236-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.37 % Computer : n016.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Thu Sep 24 10:25:17 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 30.15/10.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.15/10.04 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------