%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET052-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 02:41:44 PM UTC 2026
% Result : Unsatisfiable 8.91s 1.52s
% Output : Proof 8.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 36 unt; 0 def)
% Number of atoms : 72 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 34 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 74 ( 17 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/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(t85,plain,
ifeq(subclass(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t144,plain,
ifeq(subclass(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t85]) ).
cnf(f92,negated_conjecture,
~ member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_cartesian_product_2) ).
fof(f92_nnf,plain,
~ member(u,universal_class),
inference(nnf_transformation,[status(thm)],[f92]) ).
fof(f92_sk,plain,
~ member(u,universal_class),
inference(skolemisation,[status(esa)],[f92_nnf]) ).
cnf(c92,plain,
~ member(u,universal_class),
inference(cnf_transformation,[status(esa)],[f92_sk]) ).
cnf(t6,plain,
member(u,universal_class) = false,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t329,plain,
member(u,universal_class) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t331,plain,
true = ifeq(subclass(X1,universal_class),true,ifeq(member(u,X1),true,false,true),true),
inference(cp,[status(thm)],[t144,t329]) ).
cnf(f3,axiom,
subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f3_nnf,plain,
! [X] : subclass(X,universal_class),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : subclass(X,universal_class),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t11,plain,
subclass(X1,universal_class) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t243,plain,
subclass(X1,universal_class) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t1547,plain,
true = ifeq(true,true,ifeq(member(u,X1),true,false,true),true),
inference(step,[status(thm)],[t331,t243]) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t106,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t1548,plain,
true = ifeq(member(u,X1),true,false,true),
inference(step,[status(thm)],[t1547,t106]) ).
cnf(t1443,plain,
ifeq(member(u,X1),true,false,true) = true,
inference(orient,[status(thm)],[t1548]) ).
cnf(f13,axiom,
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f13_nnf,plain,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t74,plain,
ifeq(member(ordered_pair(X1,X2),cross_product(X3,X4)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t132,plain,
ifeq(member(ordered_pair(X1,X2),cross_product(X3,X4)),true,member(X1,X3),true) = true,
inference(orient,[status(thm)],[t74]) ).
cnf(f91,negated_conjecture,
member(ordered_pair(u,v),cross_product(x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_cartesian_product_1) ).
fof(f91_nnf,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(t31,plain,
member(ordered_pair(u,v),cross_product(x,y)) = true,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(t178,plain,
member(ordered_pair(u,v),cross_product(x,y)) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t183,plain,
true = ifeq(true,true,member(u,x),true),
inference(cp,[status(thm)],[t132,t178]) ).
cnf(t1476,plain,
true = member(u,x),
inference(step,[status(thm)],[t183,t106]) ).
cnf(t499,plain,
member(u,x) = true,
inference(orient,[status(thm)],[t1476]) ).
cnf(t1444,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t1443,t499]) ).
cnf(t1549,plain,
true = false,
inference(step,[status(thm)],[t1444,t106]) ).
cnf(t1447,plain,
false = true,
inference(orient,[status(thm)],[t1549]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c92]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1447]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET052-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Thu Sep 24 09:26:36 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.91/1.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.91/1.52 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------