%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET082-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 02:42:03 PM UTC 2026
% Result : Unsatisfiable 7.77s 1.54s
% Output : Proof 7.77s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t135,axiom,
sF3 = ifeq(member(x,universal_class),true,false,true),
introduced(definition) ).
cnf(f125,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_is_null_class_1) ).
fof(f125_nnf,plain,
~ member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f125]) ).
fof(f125_sk,plain,
~ member(x,universal_class),
inference(skolemisation,[status(esa)],[f125_nnf]) ).
cnf(c125,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f125_sk]) ).
cnf(t8,plain,
member(x,universal_class) = false,
inference(equality_encoding,[status(esa)],[c125]) ).
cnf(t145,plain,
member(x,universal_class) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t132,axiom,
sF0 = member(x,universal_class),
introduced(definition) ).
cnf(t1176,plain,
sF0 = false,
inference(step,[status(thm)],[t132,t145]) ).
cnf(t153,plain,
false = sF0,
inference(orient,[status(thm)],[t1176]) ).
cnf(t1182,plain,
member(x,universal_class) = sF0,
inference(step,[status(thm)],[t145,t153]) ).
cnf(t159,plain,
member(x,universal_class) = sF0,
inference(orient,[status(thm)],[t1182]) ).
cnf(t1198,plain,
sF3 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t135,t159]) ).
cnf(t1199,plain,
sF3 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t1198,t153]) ).
cnf(f102,axiom,
~ member(Z,null_class),
file('/export/starexec/sandbox/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(t29,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(t142,plain,
member(X1,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t1180,plain,
member(X1,null_class) = sF0,
inference(step,[status(thm)],[t142,t153]) ).
cnf(t157,plain,
member(X1,null_class) = sF0,
inference(orient,[status(thm)],[t1180]) ).
cnf(t1194,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t29,t157]) ).
cnf(t1195,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t1194,t153]) ).
cnf(t200,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t1195]) ).
cnf(t1200,plain,
sF3 = true,
inference(step,[status(thm)],[t1199,t200]) ).
cnf(t227,plain,
true = sF3,
inference(orient,[status(thm)],[t1200]) ).
cnf(f112,axiom,
( member(Y,universal_class)
| member(X,universal_class)
| unordered_pair(X,Y) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(f112_nnf,plain,
! [X,Y] :
( member(Y,universal_class)
| member(X,universal_class)
| unordered_pair(X,Y) = null_class ),
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
! [X,Y] :
( member(Y,universal_class)
| member(X,universal_class)
| unordered_pair(X,Y) = null_class ),
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(t74,plain,
or(eq(unordered_pair(X1,X2),null_class),or(member(X1,universal_class),member(X2,universal_class))) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t1452,plain,
or(eq(unordered_pair(X1,X2),null_class),or(member(X1,universal_class),member(X2,universal_class))) = sF3,
inference(step,[status(thm)],[t74,t227]) ).
cnf(t947,plain,
or(eq(unordered_pair(X1,X2),null_class),or(member(X1,universal_class),member(X2,universal_class))) = sF3,
inference(orient,[status(thm)],[t1452]) ).
cnf(t133,axiom,
sF1 = unordered_pair(x,x),
introduced(definition) ).
cnf(t164,plain,
unordered_pair(x,x) = sF1,
inference(orient,[status(thm)],[t133]) ).
cnf(t950,plain,
sF3 = or(eq(sF1,null_class),or(member(x,universal_class),member(x,universal_class))),
inference(cp,[status(thm)],[t947,t164]) ).
cnf(f126,negated_conjecture,
singleton(x) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_is_null_class_2) ).
fof(f126_nnf,plain,
singleton(x) != null_class,
inference(nnf_transformation,[status(thm)],[f126]) ).
fof(f126_sk,plain,
singleton(x) != null_class,
inference(skolemisation,[status(esa)],[f126_nnf]) ).
cnf(c126,plain,
singleton(x) != null_class,
inference(cnf_transformation,[status(esa)],[f126_sk]) ).
cnf(u22,axiom,
eq(singleton(x),null_class) = false,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f11_nnf,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(d0,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t16,plain,
eq(unordered_pair(x,x),null_class) = false,
inference(definition_unfolding,[status(thm)],[u22,d0]) ).
cnf(t1186,plain,
eq(sF1,null_class) = false,
inference(step,[status(thm)],[t16,t164]) ).
cnf(t1187,plain,
eq(sF1,null_class) = sF0,
inference(step,[status(thm)],[t1186,t153]) ).
cnf(t167,plain,
eq(sF1,null_class) = sF0,
inference(orient,[status(thm)],[t1187]) ).
cnf(t1453,plain,
sF3 = or(sF0,or(member(x,universal_class),member(x,universal_class))),
inference(step,[status(thm)],[t950,t167]) ).
cnf(t11,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t148,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t1185,plain,
or(sF0,X1) = X1,
inference(step,[status(thm)],[t148,t153]) ).
cnf(t162,plain,
or(sF0,X1) = X1,
inference(rw,[status(thm)],[t1185]) ).
cnf(t166,plain,
or(sF0,X1) = X1,
inference(orient,[status(thm)],[t162]) ).
cnf(t1454,plain,
sF3 = or(member(x,universal_class),member(x,universal_class)),
inference(step,[status(thm)],[t1453,t166]) ).
cnf(t1455,plain,
sF3 = or(sF0,member(x,universal_class)),
inference(step,[status(thm)],[t1454,t159]) ).
cnf(t1456,plain,
sF3 = member(x,universal_class),
inference(step,[status(thm)],[t1455,t166]) ).
cnf(t1457,plain,
sF3 = sF0,
inference(step,[status(thm)],[t1456,t159]) ).
cnf(t955,plain,
sF3 = sF0,
inference(orient,[status(thm)],[t1457]) ).
cnf(t1494,plain,
true = sF0,
inference(step,[status(thm)],[t227,t955]) ).
cnf(t992,plain,
true = sF0,
inference(orient,[status(thm)],[t1494]) ).
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(f101,axiom,
~ member(Y,intersection(complement(X),X)),
file('/export/starexec/sandbox/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(f115,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f115_nnf,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f115]) ).
fof(f115_sk,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f115_nnf]) ).
cnf(c115,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f115_sk]) ).
cnf(f116,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f116_nnf,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
( unordered_pair(X1,X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f117,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
fof(f117_nnf,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(nnf_transformation,[status(thm)],[f117]) ).
fof(f117_sk,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(skolemisation,[status(esa)],[f117_nnf]) ).
cnf(c117,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f117_sk]) ).
cnf(f122,axiom,
( singleton(X) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(f122_nnf,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f122]) ).
fof(f122_sk,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f122_nnf]) ).
cnf(c122,plain,
( singleton(X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f122_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102,c115,c116,c117,c122,c125,c126]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t992]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t153]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET082-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 09:39:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.77/1.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.77/1.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------