%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET197-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 02:42:50 PM UTC 2026
% Result : Unsatisfiable 5.43s 1.15s
% Output : Proof 5.43s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t110,axiom,
sF2 = ifeq(subclass(intersection(x,y),y),true,false,true),
introduced(definition) ).
cnf(t108,axiom,
sF0 = intersection(x,y),
introduced(definition) ).
cnf(t122,plain,
intersection(x,y) = sF0,
inference(orient,[status(thm)],[t108]) ).
cnf(t624,plain,
sF2 = ifeq(subclass(sF0,y),true,false,true),
inference(step,[status(thm)],[t110,t122]) ).
cnf(f112,negated_conjecture,
~ subclass(intersection(x,y),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lattice_lower_bound2_1) ).
fof(f112_nnf,plain,
~ subclass(intersection(x,y),y),
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
~ subclass(intersection(x,y),y),
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
~ subclass(intersection(x,y),y),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(t15,plain,
subclass(intersection(x,y),y) = false,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t607,plain,
subclass(sF0,y) = false,
inference(step,[status(thm)],[t15,t122]) ).
cnf(t127,plain,
subclass(sF0,y) = false,
inference(orient,[status(thm)],[t607]) ).
cnf(t109,axiom,
sF1 = subclass(intersection(x,y),y),
introduced(definition) ).
cnf(t608,plain,
sF1 = subclass(sF0,y),
inference(step,[status(thm)],[t109,t122]) ).
cnf(t609,plain,
sF1 = false,
inference(step,[status(thm)],[t608,t127]) ).
cnf(t129,plain,
false = sF1,
inference(orient,[status(thm)],[t609]) ).
cnf(t615,plain,
subclass(sF0,y) = sF1,
inference(step,[status(thm)],[t127,t129]) ).
cnf(t135,plain,
subclass(sF0,y) = sF1,
inference(orient,[status(thm)],[t615]) ).
cnf(t625,plain,
sF2 = ifeq(sF1,true,false,true),
inference(step,[status(thm)],[t624,t135]) ).
cnf(t626,plain,
sF2 = ifeq(sF1,true,sF1,true),
inference(step,[status(thm)],[t625,t129]) ).
cnf(t39,plain,
ifeq(subclass(intersection(x,y),y),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t620,plain,
ifeq(subclass(sF0,y),true,false,true) = true,
inference(step,[status(thm)],[t39,t122]) ).
cnf(t621,plain,
ifeq(sF1,true,false,true) = true,
inference(step,[status(thm)],[t620,t135]) ).
cnf(t622,plain,
ifeq(sF1,true,sF1,true) = true,
inference(step,[status(thm)],[t621,t129]) ).
cnf(t212,plain,
ifeq(sF1,true,sF1,true) = true,
inference(orient,[status(thm)],[t622]) ).
cnf(t627,plain,
sF2 = true,
inference(step,[status(thm)],[t626,t212]) ).
cnf(t217,plain,
true = sF2,
inference(orient,[status(thm)],[t627]) ).
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(t50,plain,
ifeq(member(not_subclass_element(X1,X2),X2),true,subclass(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t751,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),true) = true,
inference(step,[status(thm)],[t50,t217]) ).
cnf(t752,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),sF2) = true,
inference(step,[status(thm)],[t751,t217]) ).
cnf(t753,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),sF2) = sF2,
inference(step,[status(thm)],[t752,t217]) ).
cnf(t465,plain,
ifeq(member(not_subclass_element(X1,X2),X2),sF2,subclass(X1,X2),sF2) = sF2,
inference(orient,[status(thm)],[t753]) ).
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(t47,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t726,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),true) = true,
inference(step,[status(thm)],[t47,t217]) ).
cnf(t727,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = true,
inference(step,[status(thm)],[t726,t217]) ).
cnf(t728,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = sF2,
inference(step,[status(thm)],[t727,t217]) ).
cnf(t400,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = sF2,
inference(orient,[status(thm)],[t728]) ).
cnf(t402,plain,
sF2 = ifeq(member(X1,sF0),sF2,member(X1,y),sF2),
inference(cp,[status(thm)],[t400,t122]) ).
cnf(t479,plain,
ifeq(member(X1,sF0),sF2,member(X1,y),sF2) = sF2,
inference(orient,[status(thm)],[t402]) ).
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(t41,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t214,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t215,plain,
true = or(member(not_subclass_element(sF0,y),sF0),sF1),
inference(cp,[status(thm)],[t214,t135]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t117,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t613,plain,
or(X1,sF1) = X1,
inference(step,[status(thm)],[t117,t129]) ).
cnf(t133,plain,
or(X1,sF1) = X1,
inference(rw,[status(thm)],[t613]) ).
cnf(t138,plain,
or(X1,sF1) = X1,
inference(orient,[status(thm)],[t133]) ).
cnf(t623,plain,
true = member(not_subclass_element(sF0,y),sF0),
inference(step,[status(thm)],[t215,t138]) ).
cnf(t216,plain,
member(not_subclass_element(sF0,y),sF0) = true,
inference(orient,[status(thm)],[t623]) ).
cnf(t674,plain,
member(not_subclass_element(sF0,y),sF0) = sF2,
inference(step,[status(thm)],[t216,t217]) ).
cnf(t293,plain,
member(not_subclass_element(sF0,y),sF0) = sF2,
inference(orient,[status(thm)],[t674]) ).
cnf(t480,plain,
sF2 = ifeq(sF2,sF2,member(not_subclass_element(sF0,y),y),sF2),
inference(cp,[status(thm)],[t479,t293]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t123,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t754,plain,
sF2 = member(not_subclass_element(sF0,y),y),
inference(step,[status(thm)],[t480,t123]) ).
cnf(t481,plain,
member(not_subclass_element(sF0,y),y) = sF2,
inference(orient,[status(thm)],[t754]) ).
cnf(t485,plain,
sF2 = ifeq(sF2,sF2,subclass(sF0,y),sF2),
inference(cp,[status(thm)],[t465,t481]) ).
cnf(t755,plain,
sF2 = subclass(sF0,y),
inference(step,[status(thm)],[t485,t123]) ).
cnf(t756,plain,
sF2 = sF1,
inference(step,[status(thm)],[t755,t135]) ).
cnf(t486,plain,
sF2 = sF1,
inference(orient,[status(thm)],[t756]) ).
cnf(t799,plain,
true = sF1,
inference(step,[status(thm)],[t217,t486]) ).
cnf(t529,plain,
true = sF1,
inference(orient,[status(thm)],[t799]) ).
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,
sF1 != false,
inference(rw,[status(thm)],[goal_0,t529]) ).
cnf(g0_1,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_0,t129]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET197-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 10:16:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.43/1.15 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.43/1.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------