%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET553-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 02:43:24 PM UTC 2026
% Result : Unsatisfiable 11.94s 2.07s
% Output : Proof 11.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 19
% Syntax : Number of formulae : 112 ( 92 unt; 0 def)
% Number of atoms : 132 ( 91 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 50 ( 30 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 15 con; 0-4 aty)
% Number of variables : 82 ( 6 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox/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(t48,plain,
ifeq(member(not_subclass_element(X1,X2),X2),true,subclass(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t362,plain,
ifeq(member(not_subclass_element(X1,X2),X2),true,subclass(X1,X2),true) = true,
inference(orient,[status(thm)],[t48]) ).
cnf(f20,axiom,
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/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(t44,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t284,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(f1,axiom,
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox/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(t39,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t222,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(f112,negated_conjecture,
~ subclass(cantor(x),domain_of(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cantor_class_alternate_defn_1) ).
fof(f112_nnf,plain,
~ subclass(cantor(x),domain_of(x)),
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
~ subclass(cantor(x),domain_of(x)),
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
~ subclass(cantor(x),domain_of(x)),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(u63,axiom,
subclass(cantor(x),domain_of(x)) = false,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(f76,axiom,
intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))) = cantor(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cantor_class) ).
fof(f76_nnf,plain,
! [X] : intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))) = cantor(X),
inference(nnf_transformation,[status(thm)],[f76]) ).
fof(f76_sk,plain,
! [X] : intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))) = cantor(X),
inference(skolemisation,[status(esa)],[f76_nnf]) ).
cnf(c76,plain,
intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
inference(cnf_transformation,[status(esa)],[f76_sk]) ).
cnf(u47,axiom,
intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
inference(equality_encoding,[status(esa)],[c76]) ).
cnf(f37,axiom,
domain_of(flip(cross_product(Y,universal_class))) = inverse(Y),
file('/export/starexec/sandbox/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(f75,axiom,
complement(domain_of(intersection(Xr,identity_relation))) = diagonalise(Xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonalisation) ).
fof(f75_nnf,plain,
! [Xr] : complement(domain_of(intersection(Xr,identity_relation))) = diagonalise(Xr),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
! [Xr] : complement(domain_of(intersection(Xr,identity_relation))) = diagonalise(Xr),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
complement(domain_of(intersection(X0,identity_relation))) = diagonalise(X0),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(d13,axiom,
complement(domain_of(intersection(X0,identity_relation))) = diagonalise(X0),
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(d14,axiom,
intersection(domain_of(X0),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),X0),identity_relation)))) = cantor(X0),
inference(definition_unfolding,[status(thm)],[u47,d5,d13]) ).
cnf(t72,plain,
subclass(intersection(domain_of(x),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)))),domain_of(x)) = false,
inference(definition_unfolding,[status(thm)],[u63,d14]) ).
cnf(t108,axiom,
sF0 = domain_of(x),
introduced(definition) ).
cnf(t123,plain,
domain_of(x) = sF0,
inference(orient,[status(thm)],[t108]) ).
cnf(t1720,plain,
subclass(intersection(sF0,complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)))),domain_of(x)) = false,
inference(step,[status(thm)],[t72,t123]) ).
cnf(t109,axiom,
sF1 = cross_product(element_relation,universal_class),
introduced(definition) ).
cnf(t131,plain,
cross_product(element_relation,universal_class) = sF1,
inference(orient,[status(thm)],[t109]) ).
cnf(t1721,plain,
subclass(intersection(sF0,complement(domain_of(intersection(compose(domain_of(flip(sF1)),x),identity_relation)))),domain_of(x)) = false,
inference(step,[status(thm)],[t1720,t131]) ).
cnf(t110,axiom,
sF2 = flip(cross_product(element_relation,universal_class)),
introduced(definition) ).
cnf(t1459,plain,
sF2 = flip(sF1),
inference(step,[status(thm)],[t110,t131]) ).
cnf(t132,plain,
flip(sF1) = sF2,
inference(orient,[status(thm)],[t1459]) ).
cnf(t1722,plain,
subclass(intersection(sF0,complement(domain_of(intersection(compose(domain_of(sF2),x),identity_relation)))),domain_of(x)) = false,
inference(step,[status(thm)],[t1721,t132]) ).
cnf(t111,axiom,
sF3 = domain_of(flip(cross_product(element_relation,universal_class))),
introduced(definition) ).
cnf(t1460,plain,
sF3 = domain_of(flip(sF1)),
inference(step,[status(thm)],[t111,t131]) ).
cnf(t1461,plain,
sF3 = domain_of(sF2),
inference(step,[status(thm)],[t1460,t132]) ).
cnf(t138,plain,
domain_of(sF2) = sF3,
inference(orient,[status(thm)],[t1461]) ).
cnf(t1723,plain,
subclass(intersection(sF0,complement(domain_of(intersection(compose(sF3,x),identity_relation)))),domain_of(x)) = false,
inference(step,[status(thm)],[t1722,t138]) ).
cnf(t112,axiom,
sF4 = compose(domain_of(flip(cross_product(element_relation,universal_class))),x),
introduced(definition) ).
cnf(t1462,plain,
sF4 = compose(domain_of(flip(sF1)),x),
inference(step,[status(thm)],[t112,t131]) ).
cnf(t1463,plain,
sF4 = compose(domain_of(sF2),x),
inference(step,[status(thm)],[t1462,t132]) ).
cnf(t1464,plain,
sF4 = compose(sF3,x),
inference(step,[status(thm)],[t1463,t138]) ).
cnf(t177,plain,
compose(sF3,x) = sF4,
inference(orient,[status(thm)],[t1464]) ).
cnf(t1724,plain,
subclass(intersection(sF0,complement(domain_of(intersection(sF4,identity_relation)))),domain_of(x)) = false,
inference(step,[status(thm)],[t1723,t177]) ).
cnf(t113,axiom,
sF5 = intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation),
introduced(definition) ).
cnf(t1466,plain,
sF5 = intersection(compose(domain_of(flip(sF1)),x),identity_relation),
inference(step,[status(thm)],[t113,t131]) ).
cnf(t1467,plain,
sF5 = intersection(compose(domain_of(sF2),x),identity_relation),
inference(step,[status(thm)],[t1466,t132]) ).
cnf(t1468,plain,
sF5 = intersection(compose(sF3,x),identity_relation),
inference(step,[status(thm)],[t1467,t138]) ).
cnf(t1469,plain,
sF5 = intersection(sF4,identity_relation),
inference(step,[status(thm)],[t1468,t177]) ).
cnf(t223,plain,
intersection(sF4,identity_relation) = sF5,
inference(orient,[status(thm)],[t1469]) ).
cnf(t1725,plain,
subclass(intersection(sF0,complement(domain_of(sF5))),domain_of(x)) = false,
inference(step,[status(thm)],[t1724,t223]) ).
cnf(t114,axiom,
sF6 = domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)),
introduced(definition) ).
cnf(t1481,plain,
sF6 = domain_of(intersection(compose(domain_of(flip(sF1)),x),identity_relation)),
inference(step,[status(thm)],[t114,t131]) ).
cnf(t1482,plain,
sF6 = domain_of(intersection(compose(domain_of(sF2),x),identity_relation)),
inference(step,[status(thm)],[t1481,t132]) ).
cnf(t1483,plain,
sF6 = domain_of(intersection(compose(sF3,x),identity_relation)),
inference(step,[status(thm)],[t1482,t138]) ).
cnf(t1484,plain,
sF6 = domain_of(intersection(sF4,identity_relation)),
inference(step,[status(thm)],[t1483,t177]) ).
cnf(t1485,plain,
sF6 = domain_of(sF5),
inference(step,[status(thm)],[t1484,t223]) ).
cnf(t277,plain,
domain_of(sF5) = sF6,
inference(orient,[status(thm)],[t1485]) ).
cnf(t1726,plain,
subclass(intersection(sF0,complement(sF6)),domain_of(x)) = false,
inference(step,[status(thm)],[t1725,t277]) ).
cnf(t115,axiom,
sF7 = complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation))),
introduced(definition) ).
cnf(t1516,plain,
sF7 = complement(domain_of(intersection(compose(domain_of(flip(sF1)),x),identity_relation))),
inference(step,[status(thm)],[t115,t131]) ).
cnf(t1517,plain,
sF7 = complement(domain_of(intersection(compose(domain_of(sF2),x),identity_relation))),
inference(step,[status(thm)],[t1516,t132]) ).
cnf(t1518,plain,
sF7 = complement(domain_of(intersection(compose(sF3,x),identity_relation))),
inference(step,[status(thm)],[t1517,t138]) ).
cnf(t1519,plain,
sF7 = complement(domain_of(intersection(sF4,identity_relation))),
inference(step,[status(thm)],[t1518,t177]) ).
cnf(t1520,plain,
sF7 = complement(domain_of(sF5)),
inference(step,[status(thm)],[t1519,t223]) ).
cnf(t1521,plain,
sF7 = complement(sF6),
inference(step,[status(thm)],[t1520,t277]) ).
cnf(t452,plain,
complement(sF6) = sF7,
inference(orient,[status(thm)],[t1521]) ).
cnf(t1727,plain,
subclass(intersection(sF0,sF7),domain_of(x)) = false,
inference(step,[status(thm)],[t1726,t452]) ).
cnf(t1728,plain,
subclass(intersection(sF0,sF7),sF0) = false,
inference(step,[status(thm)],[t1727,t123]) ).
cnf(t1293,plain,
subclass(intersection(sF0,sF7),sF0) = false,
inference(orient,[status(thm)],[t1728]) ).
cnf(t1296,plain,
true = or(member(not_subclass_element(intersection(sF0,sF7),sF0),intersection(sF0,sF7)),false),
inference(cp,[status(thm)],[t222,t1293]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t126,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t1741,plain,
true = member(not_subclass_element(intersection(sF0,sF7),sF0),intersection(sF0,sF7)),
inference(step,[status(thm)],[t1296,t126]) ).
cnf(t1350,plain,
member(not_subclass_element(intersection(sF0,sF7),sF0),intersection(sF0,sF7)) = true,
inference(orient,[status(thm)],[t1741]) ).
cnf(t1352,plain,
true = ifeq(true,true,member(not_subclass_element(intersection(sF0,sF7),sF0),sF0),true),
inference(cp,[status(thm)],[t284,t1350]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t133,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t1742,plain,
true = member(not_subclass_element(intersection(sF0,sF7),sF0),sF0),
inference(step,[status(thm)],[t1352,t133]) ).
cnf(t1364,plain,
member(not_subclass_element(intersection(sF0,sF7),sF0),sF0) = true,
inference(orient,[status(thm)],[t1742]) ).
cnf(t1368,plain,
true = ifeq(true,true,subclass(intersection(sF0,sF7),sF0),true),
inference(cp,[status(thm)],[t362,t1364]) ).
cnf(t1743,plain,
true = subclass(intersection(sF0,sF7),sF0),
inference(step,[status(thm)],[t1368,t133]) ).
cnf(t1744,plain,
true = false,
inference(step,[status(thm)],[t1743,t1293]) ).
cnf(t1374,plain,
false = true,
inference(orient,[status(thm)],[t1744]) ).
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,c112]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1374]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET553-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.42 % Computer : n001.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Thu Sep 24 11:22:07 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.94/2.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.94/2.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------