%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET118-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 02:42:24 PM UTC 2026
% Result : Unsatisfiable 7.17s 6.50s
% Output : Proof 7.17s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t93,axiom,
sF2 = member(x,cross_product(universal_class,universal_class)),
introduced(definition) ).
cnf(t92,axiom,
sF1 = cross_product(universal_class,universal_class),
introduced(definition) ).
cnf(t116,plain,
cross_product(universal_class,universal_class) = sF1,
inference(orient,[status(thm)],[t92]) ).
cnf(t1041,plain,
sF2 = member(x,sF1),
inference(step,[status(thm)],[t93,t116]) ).
cnf(f91,negated_conjecture,
member(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_ordered_pairs_are_sets_1) ).
fof(f91_nnf,plain,
member(x,cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
member(x,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(t14,plain,
member(x,cross_product(universal_class,universal_class)) = true,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(t1038,plain,
member(x,sF1) = true,
inference(step,[status(thm)],[t14,t116]) ).
cnf(t121,plain,
member(x,sF1) = true,
inference(orient,[status(thm)],[t1038]) ).
cnf(t1042,plain,
sF2 = true,
inference(step,[status(thm)],[t1041,t121]) ).
cnf(t124,plain,
true = sF2,
inference(orient,[status(thm)],[t1042]) ).
cnf(f0,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f0_nnf,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t58,plain,
ifeq(subclass(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t1318,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t58,t124]) ).
cnf(t1319,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t1318,t124]) ).
cnf(t1320,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),sF2),true) = true,
inference(step,[status(thm)],[t1319,t124]) ).
cnf(t1321,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),sF2),sF2) = true,
inference(step,[status(thm)],[t1320,t124]) ).
cnf(t1322,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),sF2),sF2) = sF2,
inference(step,[status(thm)],[t1321,t124]) ).
cnf(t689,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),sF2),sF2) = sF2,
inference(orient,[status(thm)],[t1322]) ).
cnf(f92,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_ordered_pairs_are_sets_2) ).
fof(f92_nnf,plain,
~ member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f92]) ).
fof(f92_sk,plain,
~ member(x,universal_class),
inference(skolemisation,[status(esa)],[f92_nnf]) ).
cnf(c92,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f92_sk]) ).
cnf(t6,plain,
member(x,universal_class) = false,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t101,plain,
member(x,universal_class) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t91,axiom,
sF0 = member(x,universal_class),
introduced(definition) ).
cnf(t1030,plain,
sF0 = false,
inference(step,[status(thm)],[t91,t101]) ).
cnf(t107,plain,
false = sF0,
inference(orient,[status(thm)],[t1030]) ).
cnf(t1034,plain,
member(x,universal_class) = sF0,
inference(step,[status(thm)],[t101,t107]) ).
cnf(t111,plain,
member(x,universal_class) = sF0,
inference(orient,[status(thm)],[t1034]) ).
cnf(t693,plain,
sF2 = ifeq(subclass(X1,universal_class),sF2,ifeq(member(x,X1),sF2,sF0,sF2),sF2),
inference(cp,[status(thm)],[t689,t111]) ).
cnf(f3,axiom,
subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f3_nnf,plain,
! [X] : subclass(X,universal_class),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : subclass(X,universal_class),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t11,plain,
subclass(X1,universal_class) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t106,plain,
subclass(X1,universal_class) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t1052,plain,
subclass(X1,universal_class) = sF2,
inference(step,[status(thm)],[t106,t124]) ).
cnf(t136,plain,
subclass(X1,universal_class) = sF2,
inference(orient,[status(thm)],[t1052]) ).
cnf(t1340,plain,
sF2 = ifeq(sF2,sF2,ifeq(member(x,X1),sF2,sF0,sF2),sF2),
inference(step,[status(thm)],[t693,t136]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t119,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t1341,plain,
sF2 = ifeq(member(x,X1),sF2,sF0,sF2),
inference(step,[status(thm)],[t1340,t119]) ).
cnf(t808,plain,
ifeq(member(x,X1),sF2,sF0,sF2) = sF2,
inference(orient,[status(thm)],[t1341]) ).
cnf(t1058,plain,
member(x,sF1) = sF2,
inference(step,[status(thm)],[t121,t124]) ).
cnf(t142,plain,
member(x,sF1) = sF2,
inference(orient,[status(thm)],[t1058]) ).
cnf(t813,plain,
sF2 = ifeq(sF2,sF2,sF0,sF2),
inference(cp,[status(thm)],[t808,t142]) ).
cnf(t1346,plain,
sF2 = sF0,
inference(step,[status(thm)],[t813,t119]) ).
cnf(t815,plain,
sF2 = sF0,
inference(orient,[status(thm)],[t1346]) ).
cnf(t1367,plain,
true = sF0,
inference(step,[status(thm)],[t124,t815]) ).
cnf(t836,plain,
true = sF0,
inference(orient,[status(thm)],[t1367]) ).
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,c92]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t836]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t107]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET118-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/5.38 % Computer : n019.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 09:55:13 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.17/6.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.17/6.50 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------