%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET411-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 02:43:12 PM UTC 2026
% Result : Unsatisfiable 29.12s 9.32s
% Output : Proof 29.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 48 unt; 0 def)
% Number of atoms : 92 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 38 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-4 aty)
% Number of variables : 84 ( 13 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t102,plain,
ifeq(subclass(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t176,plain,
ifeq(subclass(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t102]) ).
cnf(f3,axiom,
subclass(X,universal_class),
file('/export/starexec/sandbox2/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(t276,plain,
subclass(X1,universal_class) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t282,plain,
true = ifeq(true,true,ifeq(member(X1,X2),true,member(X1,universal_class),true),true),
inference(cp,[status(thm)],[t176,t276]) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t127,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t8994,plain,
true = ifeq(member(X1,X2),true,member(X1,universal_class),true),
inference(step,[status(thm)],[t282,t127]) ).
cnf(t5610,plain,
ifeq(member(X1,X2),true,member(X1,universal_class),true) = true,
inference(orient,[status(thm)],[t8994]) ).
cnf(f18,axiom,
( member(X,Y)
| ~ member(ordered_pair(X,Y),element_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
fof(f18_nnf,plain,
! [X,Y] :
( member(X,Y)
| ~ member(ordered_pair(X,Y),element_relation) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y] :
( member(X,Y)
| ~ member(ordered_pair(X,Y),element_relation) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t77,plain,
ifeq(member(ordered_pair(X1,X2),element_relation),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t165,plain,
ifeq(member(ordered_pair(X1,X2),element_relation),true,member(X1,X2),true) = true,
inference(orient,[status(thm)],[t77]) ).
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(t73,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t154,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(orient,[status(thm)],[t73]) ).
cnf(f103,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_can_define_singleton) ).
fof(f103_nnf,plain,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(nnf_transformation,[status(thm)],[f103]) ).
cnf(c103,plain,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(cnf_transformation,[status(esa)],[f103_nnf]) ).
cnf(t34,plain,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(equality_encoding,[status(esa)],[c103]) ).
cnf(t557,plain,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(orient,[status(thm)],[t34]) ).
cnf(t560,plain,
true = ifeq(member(X1,singleton_relation),true,member(X1,element_relation),true),
inference(cp,[status(thm)],[t154,t557]) ).
cnf(t8404,plain,
ifeq(member(X1,singleton_relation),true,member(X1,element_relation),true) = true,
inference(orient,[status(thm)],[t560]) ).
cnf(f112,negated_conjecture,
member(ordered_pair(x,y),singleton_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compose_condition_for_singleton_membership1_1) ).
fof(f112_nnf,plain,
member(ordered_pair(x,y),singleton_relation),
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
member(ordered_pair(x,y),singleton_relation),
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(t16,plain,
member(ordered_pair(x,y),singleton_relation) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t213,plain,
member(ordered_pair(x,y),singleton_relation) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t8405,plain,
true = ifeq(true,true,member(ordered_pair(x,y),element_relation),true),
inference(cp,[status(thm)],[t8404,t213]) ).
cnf(t9230,plain,
true = member(ordered_pair(x,y),element_relation),
inference(step,[status(thm)],[t8405,t127]) ).
cnf(t8406,plain,
member(ordered_pair(x,y),element_relation) = true,
inference(orient,[status(thm)],[t9230]) ).
cnf(t8409,plain,
true = ifeq(true,true,member(x,y),true),
inference(cp,[status(thm)],[t165,t8406]) ).
cnf(t9231,plain,
true = member(x,y),
inference(step,[status(thm)],[t8409,t127]) ).
cnf(t8424,plain,
member(x,y) = true,
inference(orient,[status(thm)],[t9231]) ).
cnf(t8425,plain,
true = ifeq(true,true,member(x,universal_class),true),
inference(cp,[status(thm)],[t5610,t8424]) ).
cnf(t9232,plain,
true = member(x,universal_class),
inference(step,[status(thm)],[t8425,t127]) ).
cnf(f113,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compose_condition_for_singleton_membership1_2) ).
fof(f113_nnf,plain,
~ member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
~ member(x,universal_class),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(t6,plain,
member(x,universal_class) = false,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t398,plain,
member(x,universal_class) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t9233,plain,
true = false,
inference(step,[status(thm)],[t9232,t398]) ).
cnf(t8439,plain,
false = true,
inference(orient,[status(thm)],[t9233]) ).
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,c113]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t8439]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET411-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n005.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 10:51:39 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.12/9.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.12/9.32 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------