%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET204-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 02:42:53 PM UTC 2026
% Result : Unsatisfiable 9.13s 6.62s
% Output : Proof 9.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 30 unt; 0 def)
% Number of atoms : 74 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 38 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 91 ( 12 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(hi11,axiom,
ifeq(member(ordered_pair(X0,X1),cross_product(X2,X3)),true,member(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f112,negated_conjecture,
member(ordered_pair(u,v),cross_product(x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property2_1) ).
fof(f112_nnf,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(hi102,negated_conjecture,
member(ordered_pair(u,v),cross_product(x,y)) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(f12,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f12_nnf,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f11_nnf,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi13,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h92,plain,
member(u,x) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi102,hi12,hi13]) ).
cnf(f14,axiom,
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f14_nnf,plain,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(member(ordered_pair(X0,X1),cross_product(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h91,plain,
member(v,y) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi102,hi12,hi13]) ).
cnf(f15,axiom,
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f15_nnf,plain,
! [U,X,V,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [U,X,V,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(member(X0,X1),true,ifeq(member(X2,X3),true,member(ordered_pair(X0,X2),cross_product(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h144,plain,
member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(u,u))),cross_product(y,x)) = true,
inference(hyper_resolution,[status(thm)],[hi15,h91,h92,hi12,hi13]) ).
cnf(f113,negated_conjecture,
~ member(ordered_pair(v,u),cross_product(y,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property2_2) ).
fof(f113_nnf,plain,
~ member(ordered_pair(v,u),cross_product(y,x)),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
~ member(ordered_pair(v,u),cross_product(y,x)),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
~ member(ordered_pair(v,u),cross_product(y,x)),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(hi105,negated_conjecture,
ifeq(member(ordered_pair(v,u),cross_product(y,x)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi105,h144,hi12,hi13]) ).
cnf(t711,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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,c113]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t711]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET204-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n010.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 10:15:04 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.13/6.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.13/6.62 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------