%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET253-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 02:42:58 PM UTC 2026
% Result : Unsatisfiable 5.58s 6.37s
% Output : Proof 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 87 ( 67 unt; 0 def)
% Number of atoms : 107 ( 66 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 51 ( 31 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-4 aty)
% Number of variables : 107 ( 6 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t49,plain,
ifeq(member(not_subclass_element(X1,X2),X2),true,subclass(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t383,plain,
ifeq(member(not_subclass_element(X1,X2),X2),true,subclass(X1,X2),true) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(f112,negated_conjecture,
~ subclass(restrict(x,y,z),cross_product(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_property4_1) ).
fof(f112_nnf,plain,
~ subclass(restrict(x,y,z),cross_product(y,z)),
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
~ subclass(restrict(x,y,z),cross_product(y,z)),
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
~ subclass(restrict(x,y,z),cross_product(y,z)),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(u39,axiom,
subclass(restrict(x,y,z),cross_product(y,z)) = false,
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(t40,plain,
subclass(intersection(x,cross_product(y,z)),cross_product(y,z)) = false,
inference(definition_unfolding,[status(thm)],[u39,d4]) ).
cnf(t108,axiom,
sF0 = cross_product(y,z),
introduced(definition) ).
cnf(t123,plain,
cross_product(y,z) = sF0,
inference(orient,[status(thm)],[t108]) ).
cnf(t532,plain,
subclass(intersection(x,sF0),cross_product(y,z)) = false,
inference(step,[status(thm)],[t40,t123]) ).
cnf(t109,axiom,
sF1 = intersection(x,cross_product(y,z)),
introduced(definition) ).
cnf(t530,plain,
sF1 = intersection(x,sF0),
inference(step,[status(thm)],[t109,t123]) ).
cnf(t129,plain,
intersection(x,sF0) = sF1,
inference(orient,[status(thm)],[t530]) ).
cnf(t533,plain,
subclass(sF1,cross_product(y,z)) = false,
inference(step,[status(thm)],[t532,t129]) ).
cnf(t534,plain,
subclass(sF1,sF0) = false,
inference(step,[status(thm)],[t533,t123]) ).
cnf(t199,plain,
subclass(sF1,sF0) = false,
inference(orient,[status(thm)],[t534]) ).
cnf(t110,axiom,
sF2 = subclass(intersection(x,cross_product(y,z)),cross_product(y,z)),
introduced(definition) ).
cnf(t536,plain,
sF2 = subclass(intersection(x,sF0),cross_product(y,z)),
inference(step,[status(thm)],[t110,t123]) ).
cnf(t537,plain,
sF2 = subclass(sF1,cross_product(y,z)),
inference(step,[status(thm)],[t536,t129]) ).
cnf(t538,plain,
sF2 = subclass(sF1,sF0),
inference(step,[status(thm)],[t537,t123]) ).
cnf(t539,plain,
sF2 = false,
inference(step,[status(thm)],[t538,t199]) ).
cnf(t206,plain,
false = sF2,
inference(orient,[status(thm)],[t539]) ).
cnf(t545,plain,
subclass(sF1,sF0) = sF2,
inference(step,[status(thm)],[t199,t206]) ).
cnf(t214,plain,
subclass(sF1,sF0) = sF2,
inference(orient,[status(thm)],[t545]) ).
cnf(t395,plain,
true = ifeq(member(not_subclass_element(sF1,sF0),sF0),true,sF2,true),
inference(cp,[status(thm)],[t383,t214]) ).
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(t45,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)],[t45]) ).
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(t38,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(definition_unfolding,[status(thm)],[u35,d4]) ).
cnf(t219,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(orient,[status(thm)],[t38]) ).
cnf(t220,plain,
intersection(X1,cross_product(y,z)) = intersection(sF0,X1),
inference(cp,[status(thm)],[t219,t123]) ).
cnf(t551,plain,
intersection(X1,sF0) = intersection(sF0,X1),
inference(step,[status(thm)],[t220,t123]) ).
cnf(t227,plain,
intersection(X1,sF0) = intersection(sF0,X1),
inference(orient,[status(thm)],[t551]) ).
cnf(t552,plain,
intersection(sF0,x) = sF1,
inference(step,[status(thm)],[t129,t227]) ).
cnf(t228,plain,
intersection(sF0,x) = sF1,
inference(rw,[status(thm)],[t552]) ).
cnf(t229,plain,
intersection(sF0,x) = sF1,
inference(orient,[status(thm)],[t228]) ).
cnf(t291,plain,
true = ifeq(member(X1,sF1),true,member(X1,sF0),true),
inference(cp,[status(thm)],[t284,t229]) ).
cnf(t300,plain,
ifeq(member(X1,sF1),true,member(X1,sF0),true) = true,
inference(orient,[status(thm)],[t291]) ).
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(t39,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t198,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(t202,plain,
true = or(member(not_subclass_element(sF1,sF0),sF1),false),
inference(cp,[status(thm)],[t198,t199]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t118,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t535,plain,
true = member(not_subclass_element(sF1,sF0),sF1),
inference(step,[status(thm)],[t202,t118]) ).
cnf(t205,plain,
member(not_subclass_element(sF1,sF0),sF1) = true,
inference(orient,[status(thm)],[t535]) ).
cnf(t301,plain,
true = ifeq(true,true,member(not_subclass_element(sF1,sF0),sF0),true),
inference(cp,[status(thm)],[t300,t205]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t124,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t566,plain,
true = member(not_subclass_element(sF1,sF0),sF0),
inference(step,[status(thm)],[t301,t124]) ).
cnf(t302,plain,
member(not_subclass_element(sF1,sF0),sF0) = true,
inference(orient,[status(thm)],[t566]) ).
cnf(t586,plain,
true = ifeq(true,true,sF2,true),
inference(step,[status(thm)],[t395,t302]) ).
cnf(t587,plain,
true = sF2,
inference(step,[status(thm)],[t586,t124]) ).
cnf(t397,plain,
true = sF2,
inference(orient,[status(thm)],[t587]) ).
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,
sF2 != false,
inference(rw,[status(thm)],[goal_0,t397]) ).
cnf(g0_1,plain,
sF2 != sF2,
inference(rw,[status(thm)],[g0_0,t206]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET253-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.59 % Computer : n009.cluster.edu
% 0.09/5.59 % Model : x86_64 x86_64
% 0.09/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.59 % Memory : 8046.5625MB
% 0.09/5.59 % OS : Linux 6.8.0-71-generic
% 0.09/5.59 % CPULimit : 300
% 0.09/5.59 % WCLimit : 300
% 0.09/5.59 % DateTime : Thu Sep 24 10:23:35 UTC 2026
% 0.09/5.59 % CPUTime :
% 0.09/5.59 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.58/6.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.58/6.37 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------