%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET062-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 02:41:51 PM UTC 2026
% Result : Unsatisfiable 2.71s 0.72s
% Output : Proof 2.71s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t105,axiom,
sF1 = ifeq(subclass(null_class,x),true,false,true),
introduced(definition) ).
cnf(f103,negated_conjecture,
~ subclass(null_class,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_class_is_subclass_1) ).
fof(f103_nnf,plain,
~ subclass(null_class,x),
inference(nnf_transformation,[status(thm)],[f103]) ).
fof(f103_sk,plain,
~ subclass(null_class,x),
inference(skolemisation,[status(esa)],[f103_nnf]) ).
cnf(c103,plain,
~ subclass(null_class,x),
inference(cnf_transformation,[status(esa)],[f103_sk]) ).
cnf(t13,plain,
subclass(null_class,x) = false,
inference(equality_encoding,[status(esa)],[c103]) ).
cnf(t119,plain,
subclass(null_class,x) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t104,axiom,
sF0 = subclass(null_class,x),
introduced(definition) ).
cnf(t328,plain,
sF0 = false,
inference(step,[status(thm)],[t104,t119]) ).
cnf(t120,plain,
false = sF0,
inference(orient,[status(thm)],[t328]) ).
cnf(t336,plain,
subclass(null_class,x) = sF0,
inference(step,[status(thm)],[t119,t120]) ).
cnf(t128,plain,
subclass(null_class,x) = sF0,
inference(orient,[status(thm)],[t336]) ).
cnf(t343,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t105,t128]) ).
cnf(t344,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t343,t120]) ).
cnf(f102,axiom,
~ member(Z,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f102_nnf,plain,
! [Z] : ~ member(Z,null_class),
inference(nnf_transformation,[status(thm)],[f102]) ).
fof(f102_sk,plain,
! [Z] : ~ member(Z,null_class),
inference(skolemisation,[status(esa)],[f102_nnf]) ).
cnf(c102,plain,
~ member(X0,null_class),
inference(cnf_transformation,[status(esa)],[f102_sk]) ).
cnf(t23,plain,
ifeq(member(X1,null_class),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t5,plain,
member(X1,null_class) = false,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t111,plain,
member(X1,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t332,plain,
member(X1,null_class) = sF0,
inference(step,[status(thm)],[t111,t120]) ).
cnf(t124,plain,
member(X1,null_class) = sF0,
inference(orient,[status(thm)],[t332]) ).
cnf(t341,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t23,t124]) ).
cnf(t342,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t341,t120]) ).
cnf(t156,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t342]) ).
cnf(t345,plain,
sF1 = true,
inference(step,[status(thm)],[t344,t156]) ).
cnf(t167,plain,
true = sF1,
inference(orient,[status(thm)],[t345]) ).
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(t38,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t407,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = sF1,
inference(step,[status(thm)],[t38,t167]) ).
cnf(t261,plain,
or(member(not_subclass_element(X1,X2),X1),subclass(X1,X2)) = sF1,
inference(orient,[status(thm)],[t407]) ).
cnf(t263,plain,
sF1 = or(member(not_subclass_element(null_class,x),null_class),sF0),
inference(cp,[status(thm)],[t261,t128]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t113,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t334,plain,
or(X1,sF0) = X1,
inference(step,[status(thm)],[t113,t120]) ).
cnf(t126,plain,
or(X1,sF0) = X1,
inference(rw,[status(thm)],[t334]) ).
cnf(t131,plain,
or(X1,sF0) = X1,
inference(orient,[status(thm)],[t126]) ).
cnf(t408,plain,
sF1 = member(not_subclass_element(null_class,x),null_class),
inference(step,[status(thm)],[t263,t131]) ).
cnf(t409,plain,
sF1 = sF0,
inference(step,[status(thm)],[t408,t124]) ).
cnf(t264,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t409]) ).
cnf(t432,plain,
true = sF0,
inference(step,[status(thm)],[t167,t264]) ).
cnf(t287,plain,
true = sF0,
inference(orient,[status(thm)],[t432]) ).
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(f101,axiom,
~ member(Y,intersection(complement(X),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f101_nnf,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c101,plain,
~ member(X0,intersection(complement(X1),X1)),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102,c103]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t287]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t120]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET062-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Thu Sep 24 09:31:13 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.71/0.72 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.71/0.72 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------