%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET386-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 02:43:09 PM UTC 2026
% Result : Unsatisfiable 6.56s 1.38s
% Output : Proof 6.56s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t112,axiom,
sF3 = ifeq(subclass(x,cross_product(universal_class,universal_class)),true,false,true),
introduced(definition) ).
cnf(t110,axiom,
sF1 = intersection(x,cross_product(universal_class,universal_class)),
introduced(definition) ).
cnf(t109,axiom,
sF0 = cross_product(universal_class,universal_class),
introduced(definition) ).
cnf(t124,plain,
cross_product(universal_class,universal_class) = sF0,
inference(orient,[status(thm)],[t109]) ).
cnf(t639,plain,
sF1 = intersection(x,sF0),
inference(step,[status(thm)],[t110,t124]) ).
cnf(f112,negated_conjecture,
restrict(x,universal_class,universal_class) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relation_property4_1) ).
fof(f112_nnf,plain,
restrict(x,universal_class,universal_class) = x,
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
restrict(x,universal_class,universal_class) = x,
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(u38,axiom,
restrict(x,universal_class,universal_class) = x,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(f27,axiom,
intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f27_nnf,plain,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(d4,axiom,
intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t12,plain,
intersection(x,cross_product(universal_class,universal_class)) = x,
inference(definition_unfolding,[status(thm)],[u38,d4]) ).
cnf(t634,plain,
intersection(x,sF0) = x,
inference(step,[status(thm)],[t12,t124]) ).
cnf(t126,plain,
intersection(x,sF0) = x,
inference(orient,[status(thm)],[t634]) ).
cnf(t640,plain,
sF1 = x,
inference(step,[status(thm)],[t639,t126]) ).
cnf(t132,plain,
x = sF1,
inference(orient,[status(thm)],[t640]) ).
cnf(t666,plain,
sF3 = ifeq(subclass(sF1,cross_product(universal_class,universal_class)),true,false,true),
inference(step,[status(thm)],[t112,t132]) ).
cnf(t667,plain,
sF3 = ifeq(subclass(sF1,sF0),true,false,true),
inference(step,[status(thm)],[t666,t124]) ).
cnf(f113,negated_conjecture,
~ subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relation_property4_2) ).
fof(f113_nnf,plain,
~ subclass(x,cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
~ subclass(x,cross_product(universal_class,universal_class)),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
~ subclass(x,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(t17,plain,
subclass(x,cross_product(universal_class,universal_class)) = false,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t638,plain,
subclass(x,sF0) = false,
inference(step,[status(thm)],[t17,t124]) ).
cnf(t131,plain,
subclass(x,sF0) = false,
inference(orient,[status(thm)],[t638]) ).
cnf(t641,plain,
subclass(sF1,sF0) = false,
inference(step,[status(thm)],[t131,t132]) ).
cnf(t134,plain,
subclass(sF1,sF0) = false,
inference(rw,[status(thm)],[t641]) ).
cnf(t138,plain,
subclass(sF1,sF0) = false,
inference(orient,[status(thm)],[t134]) ).
cnf(t111,axiom,
sF2 = subclass(x,cross_product(universal_class,universal_class)),
introduced(definition) ).
cnf(t643,plain,
sF2 = subclass(sF1,cross_product(universal_class,universal_class)),
inference(step,[status(thm)],[t111,t132]) ).
cnf(t644,plain,
sF2 = subclass(sF1,sF0),
inference(step,[status(thm)],[t643,t124]) ).
cnf(t645,plain,
sF2 = false,
inference(step,[status(thm)],[t644,t138]) ).
cnf(t139,plain,
false = sF2,
inference(orient,[status(thm)],[t645]) ).
cnf(t651,plain,
subclass(sF1,sF0) = sF2,
inference(step,[status(thm)],[t138,t139]) ).
cnf(t146,plain,
subclass(sF1,sF0) = sF2,
inference(orient,[status(thm)],[t651]) ).
cnf(t668,plain,
sF3 = ifeq(sF2,true,false,true),
inference(step,[status(thm)],[t667,t146]) ).
cnf(t669,plain,
sF3 = ifeq(sF2,true,sF2,true),
inference(step,[status(thm)],[t668,t139]) ).
cnf(t40,plain,
ifeq(subclass(x,cross_product(universal_class,universal_class)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t661,plain,
ifeq(subclass(sF1,cross_product(universal_class,universal_class)),true,false,true) = true,
inference(step,[status(thm)],[t40,t132]) ).
cnf(t662,plain,
ifeq(subclass(sF1,sF0),true,false,true) = true,
inference(step,[status(thm)],[t661,t124]) ).
cnf(t663,plain,
ifeq(sF2,true,false,true) = true,
inference(step,[status(thm)],[t662,t146]) ).
cnf(t664,plain,
ifeq(sF2,true,sF2,true) = true,
inference(step,[status(thm)],[t663,t139]) ).
cnf(t233,plain,
ifeq(sF2,true,sF2,true) = true,
inference(orient,[status(thm)],[t664]) ).
cnf(t670,plain,
sF3 = true,
inference(step,[status(thm)],[t669,t233]) ).
cnf(t237,plain,
true = sF3,
inference(orient,[status(thm)],[t670]) ).
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(t51,plain,
ifeq(member(not_subclass_element(X1,X2),X2),true,subclass(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t807,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF3,subclass(X1,X2),true) = true,
inference(step,[status(thm)],[t51,t237]) ).
cnf(t808,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF3,subclass(X1,X2),sF3) = true,
inference(step,[status(thm)],[t807,t237]) ).
cnf(t809,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF3,subclass(X1,X2),sF3) = sF3,
inference(step,[status(thm)],[t808,t237]) ).
cnf(t498,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF3,subclass(X1,X2),sF3) = sF3,
inference(orient,[status(thm)],[t809]) ).
cnf(t503,plain,
sF3 = ifeq(member(not_subclass_element(sF1,sF0),sF0),sF3,sF2,sF3),
inference(cp,[status(thm)],[t498,t146]) ).
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(t47,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t765,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X2),true) = true,
inference(step,[status(thm)],[t47,t237]) ).
cnf(t766,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X2),sF3) = true,
inference(step,[status(thm)],[t765,t237]) ).
cnf(t767,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X2),sF3) = sF3,
inference(step,[status(thm)],[t766,t237]) ).
cnf(t408,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X2),sF3) = sF3,
inference(orient,[status(thm)],[t767]) ).
cnf(t133,plain,
intersection(sF1,sF0) = x,
inference(rw,[status(thm)],[t126]) ).
cnf(t642,plain,
intersection(sF1,sF0) = sF1,
inference(step,[status(thm)],[t133,t132]) ).
cnf(t135,plain,
intersection(sF1,sF0) = sF1,
inference(orient,[status(thm)],[t642]) ).
cnf(f28,axiom,
intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
fof(f28_nnf,plain,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(u35,axiom,
intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t41,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(definition_unfolding,[status(thm)],[u35,d4]) ).
cnf(t329,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(orient,[status(thm)],[t41]) ).
cnf(t330,plain,
intersection(X1,cross_product(universal_class,universal_class)) = intersection(sF0,X1),
inference(cp,[status(thm)],[t329,t124]) ).
cnf(t742,plain,
intersection(X1,sF0) = intersection(sF0,X1),
inference(step,[status(thm)],[t330,t124]) ).
cnf(t358,plain,
intersection(X1,sF0) = intersection(sF0,X1),
inference(orient,[status(thm)],[t742]) ).
cnf(t743,plain,
intersection(sF0,sF1) = sF1,
inference(step,[status(thm)],[t135,t358]) ).
cnf(t359,plain,
intersection(sF0,sF1) = sF1,
inference(rw,[status(thm)],[t743]) ).
cnf(t360,plain,
intersection(sF0,sF1) = sF1,
inference(orient,[status(thm)],[t359]) ).
cnf(t417,plain,
sF3 = ifeq(member(X1,sF1),sF3,member(X1,sF0),sF3),
inference(cp,[status(thm)],[t408,t360]) ).
cnf(t486,plain,
ifeq(member(X1,sF1),sF3,member(X1,sF0),sF3) = sF3,
inference(orient,[status(thm)],[t417]) ).
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(t42,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t234,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(orient,[status(thm)],[t42]) ).
cnf(t235,plain,
true = or(member(not_subclass_element(sF1,sF0),sF1),sF2),
inference(cp,[status(thm)],[t234,t146]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t119,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t649,plain,
or(X1,sF2) = X1,
inference(step,[status(thm)],[t119,t139]) ).
cnf(t143,plain,
or(X1,sF2) = X1,
inference(rw,[status(thm)],[t649]) ).
cnf(t149,plain,
or(X1,sF2) = X1,
inference(orient,[status(thm)],[t143]) ).
cnf(t665,plain,
true = member(not_subclass_element(sF1,sF0),sF1),
inference(step,[status(thm)],[t235,t149]) ).
cnf(t236,plain,
member(not_subclass_element(sF1,sF0),sF1) = true,
inference(orient,[status(thm)],[t665]) ).
cnf(t717,plain,
member(not_subclass_element(sF1,sF0),sF1) = sF3,
inference(step,[status(thm)],[t236,t237]) ).
cnf(t323,plain,
member(not_subclass_element(sF1,sF0),sF1) = sF3,
inference(orient,[status(thm)],[t717]) ).
cnf(t487,plain,
sF3 = ifeq(sF3,sF3,member(not_subclass_element(sF1,sF0),sF0),sF3),
inference(cp,[status(thm)],[t486,t323]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t125,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t803,plain,
sF3 = member(not_subclass_element(sF1,sF0),sF0),
inference(step,[status(thm)],[t487,t125]) ).
cnf(t488,plain,
member(not_subclass_element(sF1,sF0),sF0) = sF3,
inference(orient,[status(thm)],[t803]) ).
cnf(t810,plain,
sF3 = ifeq(sF3,sF3,sF2,sF3),
inference(step,[status(thm)],[t503,t488]) ).
cnf(t811,plain,
sF3 = sF2,
inference(step,[status(thm)],[t810,t125]) ).
cnf(t512,plain,
sF3 = sF2,
inference(orient,[status(thm)],[t811]) ).
cnf(t854,plain,
true = sF2,
inference(step,[status(thm)],[t237,t512]) ).
cnf(t555,plain,
true = sF2,
inference(orient,[status(thm)],[t854]) ).
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,
sF2 != false,
inference(rw,[status(thm)],[goal_0,t555]) ).
cnf(g0_1,plain,
sF2 != sF2,
inference(rw,[status(thm)],[g0_0,t139]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET386-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 10:50:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.56/1.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.56/1.38 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------