%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET184-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 02:42:45 PM UTC 2026
% Result : Unsatisfiable 4.68s 6.16s
% Output : Proof 4.68s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t111,axiom,
sF2 = ifeq(subclass(x,y),true,false,true),
introduced(definition) ).
cnf(t109,axiom,
sF0 = intersection(x,y),
introduced(definition) ).
cnf(f112,negated_conjecture,
intersection(x,y) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property2_1) ).
fof(f112_nnf,plain,
intersection(x,y) = x,
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
intersection(x,y) = x,
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(t5,plain,
intersection(x,y) = x,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t117,plain,
intersection(x,y) = x,
inference(orient,[status(thm)],[t5]) ).
cnf(t579,plain,
sF0 = x,
inference(step,[status(thm)],[t109,t117]) ).
cnf(t125,plain,
x = sF0,
inference(orient,[status(thm)],[t579]) ).
cnf(t594,plain,
sF2 = ifeq(subclass(sF0,y),true,false,true),
inference(step,[status(thm)],[t111,t125]) ).
cnf(t110,axiom,
sF1 = subclass(x,y),
introduced(definition) ).
cnf(t581,plain,
sF1 = subclass(sF0,y),
inference(step,[status(thm)],[t110,t125]) ).
cnf(t128,plain,
subclass(sF0,y) = sF1,
inference(orient,[status(thm)],[t581]) ).
cnf(t595,plain,
sF2 = ifeq(sF1,true,false,true),
inference(step,[status(thm)],[t594,t128]) ).
cnf(f113,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property2_2) ).
fof(f113_nnf,plain,
~ subclass(x,y),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
~ subclass(x,y),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
~ subclass(x,y),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(t12,plain,
subclass(x,y) = false,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t124,plain,
subclass(x,y) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t580,plain,
subclass(sF0,y) = false,
inference(step,[status(thm)],[t124,t125]) ).
cnf(t127,plain,
subclass(sF0,y) = false,
inference(rw,[status(thm)],[t580]) ).
cnf(t583,plain,
sF1 = false,
inference(step,[status(thm)],[t127,t128]) ).
cnf(t130,plain,
false = sF1,
inference(orient,[status(thm)],[t583]) ).
cnf(t596,plain,
sF2 = ifeq(sF1,true,sF1,true),
inference(step,[status(thm)],[t595,t130]) ).
cnf(t25,plain,
ifeq(subclass(x,y),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t591,plain,
ifeq(subclass(sF0,y),true,false,true) = true,
inference(step,[status(thm)],[t25,t125]) ).
cnf(t592,plain,
ifeq(sF1,true,false,true) = true,
inference(step,[status(thm)],[t591,t128]) ).
cnf(t593,plain,
ifeq(sF1,true,sF1,true) = true,
inference(step,[status(thm)],[t592,t130]) ).
cnf(t175,plain,
ifeq(sF1,true,sF1,true) = true,
inference(orient,[status(thm)],[t593]) ).
cnf(t597,plain,
sF2 = true,
inference(step,[status(thm)],[t596,t175]) ).
cnf(t187,plain,
true = sF2,
inference(orient,[status(thm)],[t597]) ).
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(t51,plain,
ifeq(member(not_subclass_element(X1,X2),X2),true,subclass(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t717,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),true) = true,
inference(step,[status(thm)],[t51,t187]) ).
cnf(t718,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),sF2) = true,
inference(step,[status(thm)],[t717,t187]) ).
cnf(t719,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),sF2) = sF2,
inference(step,[status(thm)],[t718,t187]) ).
cnf(t433,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),sF2) = sF2,
inference(orient,[status(thm)],[t719]) ).
cnf(t435,plain,
sF2 = ifeq(member(not_subclass_element(sF0,y),y),sF2,sF1,sF2),
inference(cp,[status(thm)],[t433,t128]) ).
cnf(f21,axiom,
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/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(t48,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t695,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),true) = true,
inference(step,[status(thm)],[t48,t187]) ).
cnf(t696,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = true,
inference(step,[status(thm)],[t695,t187]) ).
cnf(t697,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = sF2,
inference(step,[status(thm)],[t696,t187]) ).
cnf(t373,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = sF2,
inference(orient,[status(thm)],[t697]) ).
cnf(t126,plain,
intersection(sF0,y) = x,
inference(rw,[status(thm)],[t117]) ).
cnf(t582,plain,
intersection(sF0,y) = sF0,
inference(step,[status(thm)],[t126,t125]) ).
cnf(t129,plain,
intersection(sF0,y) = sF0,
inference(orient,[status(thm)],[t582]) ).
cnf(t375,plain,
sF2 = ifeq(member(X1,sF0),sF2,member(X1,y),sF2),
inference(cp,[status(thm)],[t373,t129]) ).
cnf(t386,plain,
ifeq(member(X1,sF0),sF2,member(X1,y),sF2) = sF2,
inference(orient,[status(thm)],[t375]) ).
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(t42,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t669,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = sF2,
inference(step,[status(thm)],[t42,t187]) ).
cnf(t296,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = sF2,
inference(orient,[status(thm)],[t669]) ).
cnf(t297,plain,
sF2 = or(member(not_subclass_element(sF0,y),sF0),sF1),
inference(cp,[status(thm)],[t296,t128]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t119,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t587,plain,
or(X1,sF1) = X1,
inference(step,[status(thm)],[t119,t130]) ).
cnf(t134,plain,
or(X1,sF1) = X1,
inference(rw,[status(thm)],[t587]) ).
cnf(t137,plain,
or(X1,sF1) = X1,
inference(orient,[status(thm)],[t134]) ).
cnf(t670,plain,
sF2 = member(not_subclass_element(sF0,y),sF0),
inference(step,[status(thm)],[t297,t137]) ).
cnf(t299,plain,
member(not_subclass_element(sF0,y),sF0) = sF2,
inference(orient,[status(thm)],[t670]) ).
cnf(t387,plain,
sF2 = ifeq(sF2,sF2,member(not_subclass_element(sF0,y),y),sF2),
inference(cp,[status(thm)],[t386,t299]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t139,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t698,plain,
sF2 = member(not_subclass_element(sF0,y),y),
inference(step,[status(thm)],[t387,t139]) ).
cnf(t388,plain,
member(not_subclass_element(sF0,y),y) = sF2,
inference(orient,[status(thm)],[t698]) ).
cnf(t720,plain,
sF2 = ifeq(sF2,sF2,sF1,sF2),
inference(step,[status(thm)],[t435,t388]) ).
cnf(t721,plain,
sF2 = sF1,
inference(step,[status(thm)],[t720,t139]) ).
cnf(t447,plain,
sF2 = sF1,
inference(orient,[status(thm)],[t721]) ).
cnf(t752,plain,
true = sF1,
inference(step,[status(thm)],[t187,t447]) ).
cnf(t478,plain,
true = sF1,
inference(orient,[status(thm)],[t752]) ).
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,
sF1 != false,
inference(rw,[status(thm)],[goal_0,t478]) ).
cnf(g0_1,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_0,t130]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET184-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n008.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 10:11:33 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.68/6.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.68/6.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------