%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET454-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 02:43:16 PM UTC 2026
% Result : Unsatisfiable 8.09s 11.53s
% Output : Proof 8.09s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t110,axiom,
sF2 = ifeq(subclass(identity_relation,cross_product(universal_class,universal_class)),true,false,true),
introduced(definition) ).
cnf(t108,axiom,
sF0 = cross_product(universal_class,universal_class),
introduced(definition) ).
cnf(t122,plain,
cross_product(universal_class,universal_class) = sF0,
inference(orient,[status(thm)],[t108]) ).
cnf(t1884,plain,
sF2 = ifeq(subclass(identity_relation,sF0),true,false,true),
inference(step,[status(thm)],[t110,t122]) ).
cnf(f112,negated_conjecture,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_identity_alternate_defn1_1) ).
fof(f112_nnf,plain,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(t15,plain,
subclass(identity_relation,cross_product(universal_class,universal_class)) = false,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t1859,plain,
subclass(identity_relation,sF0) = false,
inference(step,[status(thm)],[t15,t122]) ).
cnf(t127,plain,
subclass(identity_relation,sF0) = false,
inference(orient,[status(thm)],[t1859]) ).
cnf(t109,axiom,
sF1 = subclass(identity_relation,cross_product(universal_class,universal_class)),
introduced(definition) ).
cnf(t1861,plain,
sF1 = subclass(identity_relation,sF0),
inference(step,[status(thm)],[t109,t122]) ).
cnf(t1862,plain,
sF1 = false,
inference(step,[status(thm)],[t1861,t127]) ).
cnf(t129,plain,
false = sF1,
inference(orient,[status(thm)],[t1862]) ).
cnf(t1868,plain,
subclass(identity_relation,sF0) = sF1,
inference(step,[status(thm)],[t127,t129]) ).
cnf(t135,plain,
subclass(identity_relation,sF0) = sF1,
inference(orient,[status(thm)],[t1868]) ).
cnf(t1885,plain,
sF2 = ifeq(sF1,true,false,true),
inference(step,[status(thm)],[t1884,t135]) ).
cnf(t1886,plain,
sF2 = ifeq(sF1,true,sF1,true),
inference(step,[status(thm)],[t1885,t129]) ).
cnf(t39,plain,
ifeq(subclass(identity_relation,cross_product(universal_class,universal_class)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t1879,plain,
ifeq(subclass(identity_relation,sF0),true,false,true) = true,
inference(step,[status(thm)],[t39,t122]) ).
cnf(t1880,plain,
ifeq(sF1,true,false,true) = true,
inference(step,[status(thm)],[t1879,t135]) ).
cnf(t1881,plain,
ifeq(sF1,true,sF1,true) = true,
inference(step,[status(thm)],[t1880,t129]) ).
cnf(t222,plain,
ifeq(sF1,true,sF1,true) = true,
inference(orient,[status(thm)],[t1881]) ).
cnf(t1887,plain,
sF2 = true,
inference(step,[status(thm)],[t1886,t222]) ).
cnf(t229,plain,
true = sF2,
inference(orient,[status(thm)],[t1887]) ).
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(t50,plain,
ifeq(member(not_subclass_element(X1,X2),X2),true,subclass(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t2018,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),true) = true,
inference(step,[status(thm)],[t50,t229]) ).
cnf(t2019,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),sF2) = true,
inference(step,[status(thm)],[t2018,t229]) ).
cnf(t2020,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),sF2) = sF2,
inference(step,[status(thm)],[t2019,t229]) ).
cnf(t470,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),sF2) = sF2,
inference(orient,[status(thm)],[t2020]) ).
cnf(f20,axiom,
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f20_nnf,plain,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t46,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t1980,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X2),true) = true,
inference(step,[status(thm)],[t46,t229]) ).
cnf(t1981,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X2),sF2) = true,
inference(step,[status(thm)],[t1980,t229]) ).
cnf(t1982,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X2),sF2) = sF2,
inference(step,[status(thm)],[t1981,t229]) ).
cnf(t395,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X2),sF2) = sF2,
inference(orient,[status(thm)],[t1982]) ).
cnf(f73,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).
fof(f73_nnf,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(nnf_transformation,[status(thm)],[f73]) ).
cnf(c73,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(cnf_transformation,[status(esa)],[f73_nnf]) ).
cnf(u45,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(f37,axiom,
domain_of(flip(cross_product(Y,universal_class))) = inverse(Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f37_nnf,plain,
! [Y] : domain_of(flip(cross_product(Y,universal_class))) = inverse(Y),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [Y] : domain_of(flip(cross_product(Y,universal_class))) = inverse(Y),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(d5,axiom,
domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t73,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = subset_relation,
inference(definition_unfolding,[status(thm)],[u45,d5]) ).
cnf(t2284,plain,
intersection(sF0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = subset_relation,
inference(step,[status(thm)],[t73,t122]) ).
cnf(t2285,plain,
intersection(sF0,intersection(sF0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = subset_relation,
inference(step,[status(thm)],[t2284,t122]) ).
cnf(t1392,plain,
intersection(sF0,intersection(sF0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = subset_relation,
inference(orient,[status(thm)],[t2285]) ).
cnf(t1393,plain,
sF2 = ifeq(member(X1,subset_relation),sF2,member(X1,sF0),sF2),
inference(cp,[status(thm)],[t395,t1392]) ).
cnf(t1523,plain,
ifeq(member(X1,subset_relation),sF2,member(X1,sF0),sF2) = sF2,
inference(orient,[status(thm)],[t1393]) ).
cnf(f21,axiom,
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f21_nnf,plain,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t47,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t1989,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),true) = true,
inference(step,[status(thm)],[t47,t229]) ).
cnf(t1990,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = true,
inference(step,[status(thm)],[t1989,t229]) ).
cnf(t1991,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = sF2,
inference(step,[status(thm)],[t1990,t229]) ).
cnf(t416,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = sF2,
inference(orient,[status(thm)],[t1991]) ).
cnf(f74,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
fof(f74_nnf,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(nnf_transformation,[status(thm)],[f74]) ).
cnf(c74,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(cnf_transformation,[status(esa)],[f74_nnf]) ).
cnf(u46,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t25,plain,
intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = identity_relation,
inference(definition_unfolding,[status(thm)],[u46,d5]) ).
cnf(t180,plain,
intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = identity_relation,
inference(orient,[status(thm)],[t25]) ).
cnf(t420,plain,
sF2 = ifeq(member(X1,identity_relation),sF2,member(X1,subset_relation),sF2),
inference(cp,[status(thm)],[t416,t180]) ).
cnf(t487,plain,
ifeq(member(X1,identity_relation),sF2,member(X1,subset_relation),sF2) = sF2,
inference(orient,[status(thm)],[t420]) ).
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(t41,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t223,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t224,plain,
true = or(member(not_subclass_element(identity_relation,sF0),identity_relation),sF1),
inference(cp,[status(thm)],[t223,t135]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t117,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t1866,plain,
or(X1,sF1) = X1,
inference(step,[status(thm)],[t117,t129]) ).
cnf(t133,plain,
or(X1,sF1) = X1,
inference(rw,[status(thm)],[t1866]) ).
cnf(t138,plain,
or(X1,sF1) = X1,
inference(orient,[status(thm)],[t133]) ).
cnf(t1882,plain,
true = member(not_subclass_element(identity_relation,sF0),identity_relation),
inference(step,[status(thm)],[t224,t138]) ).
cnf(t227,plain,
member(not_subclass_element(identity_relation,sF0),identity_relation) = true,
inference(orient,[status(thm)],[t1882]) ).
cnf(t1934,plain,
member(not_subclass_element(identity_relation,sF0),identity_relation) = sF2,
inference(step,[status(thm)],[t227,t229]) ).
cnf(t315,plain,
member(not_subclass_element(identity_relation,sF0),identity_relation) = sF2,
inference(orient,[status(thm)],[t1934]) ).
cnf(t488,plain,
sF2 = ifeq(sF2,sF2,member(not_subclass_element(identity_relation,sF0),subset_relation),sF2),
inference(cp,[status(thm)],[t487,t315]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t123,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t2021,plain,
sF2 = member(not_subclass_element(identity_relation,sF0),subset_relation),
inference(step,[status(thm)],[t488,t123]) ).
cnf(t489,plain,
member(not_subclass_element(identity_relation,sF0),subset_relation) = sF2,
inference(orient,[status(thm)],[t2021]) ).
cnf(t1524,plain,
sF2 = ifeq(sF2,sF2,member(not_subclass_element(identity_relation,sF0),sF0),sF2),
inference(cp,[status(thm)],[t1523,t489]) ).
cnf(t2323,plain,
sF2 = member(not_subclass_element(identity_relation,sF0),sF0),
inference(step,[status(thm)],[t1524,t123]) ).
cnf(t1534,plain,
member(not_subclass_element(identity_relation,sF0),sF0) = sF2,
inference(orient,[status(thm)],[t2323]) ).
cnf(t1537,plain,
sF2 = ifeq(sF2,sF2,subclass(identity_relation,sF0),sF2),
inference(cp,[status(thm)],[t470,t1534]) ).
cnf(t2324,plain,
sF2 = subclass(identity_relation,sF0),
inference(step,[status(thm)],[t1537,t123]) ).
cnf(t2325,plain,
sF2 = sF1,
inference(step,[status(thm)],[t2324,t135]) ).
cnf(t1543,plain,
sF2 = sF1,
inference(orient,[status(thm)],[t2325]) ).
cnf(t2368,plain,
true = sF1,
inference(step,[status(thm)],[t229,t1543]) ).
cnf(t1586,plain,
true = sF1,
inference(orient,[status(thm)],[t2368]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/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/sandbox2/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,c112]) ).
cnf(g0_0,plain,
sF1 != false,
inference(rw,[status(thm)],[goal_0,t1586]) ).
cnf(g0_1,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_0,t129]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET454-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.39 % Computer : n013.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Thu Sep 24 10:58:50 UTC 2026
% 0.16/10.40 % CPUTime :
% 0.16/10.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.09/11.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.09/11.53 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------