%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET090-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 02:42:10 PM UTC 2026
% Result : Unsatisfiable 10.51s 1.82s
% Output : Proof 10.51s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t139,axiom,
sF0 = member(u,universal_class),
introduced(definition) ).
cnf(f133,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_singleton_is_unique_1) ).
fof(f133_nnf,plain,
member(u,universal_class),
inference(nnf_transformation,[status(thm)],[f133]) ).
cnf(c133,plain,
member(u,universal_class),
inference(cnf_transformation,[status(esa)],[f133_nnf]) ).
cnf(t8,plain,
member(u,universal_class) = true,
inference(equality_encoding,[status(esa)],[c133]) ).
cnf(t152,plain,
member(u,universal_class) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t3375,plain,
sF0 = true,
inference(step,[status(thm)],[t139,t152]) ).
cnf(t160,plain,
true = sF0,
inference(orient,[status(thm)],[t3375]) ).
cnf(t142,axiom,
sF3 = eq(member_of(unordered_pair(u,u)),u),
introduced(definition) ).
cnf(t140,axiom,
sF1 = unordered_pair(u,u),
introduced(definition) ).
cnf(t185,plain,
unordered_pair(u,u) = sF1,
inference(orient,[status(thm)],[t140]) ).
cnf(t3409,plain,
sF3 = eq(member_of(sF1),u),
inference(step,[status(thm)],[t142,t185]) ).
cnf(t141,axiom,
sF2 = member_of(unordered_pair(u,u)),
introduced(definition) ).
cnf(t3399,plain,
sF2 = member_of(sF1),
inference(step,[status(thm)],[t141,t185]) ).
cnf(t189,plain,
member_of(sF1) = sF2,
inference(orient,[status(thm)],[t3399]) ).
cnf(t3410,plain,
sF3 = eq(sF2,u),
inference(step,[status(thm)],[t3409,t189]) ).
cnf(f134,negated_conjecture,
member_of(singleton(u)) != u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_singleton_is_unique_2) ).
fof(f134_nnf,plain,
member_of(singleton(u)) != u,
inference(nnf_transformation,[status(thm)],[f134]) ).
fof(f134_sk,plain,
member_of(singleton(u)) != u,
inference(skolemisation,[status(esa)],[f134_nnf]) ).
cnf(c134,plain,
member_of(singleton(u)) != u,
inference(cnf_transformation,[status(esa)],[f134_sk]) ).
cnf(u29,axiom,
eq(member_of(singleton(u)),u) = false,
inference(equality_encoding,[status(esa)],[c134]) ).
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(t23,plain,
eq(member_of(unordered_pair(u,u)),u) = false,
inference(definition_unfolding,[status(thm)],[u29,d0]) ).
cnf(t3406,plain,
eq(member_of(sF1),u) = false,
inference(step,[status(thm)],[t23,t185]) ).
cnf(t3407,plain,
eq(sF2,u) = false,
inference(step,[status(thm)],[t3406,t189]) ).
cnf(t199,plain,
eq(sF2,u) = false,
inference(orient,[status(thm)],[t3407]) ).
cnf(t3411,plain,
sF3 = false,
inference(step,[status(thm)],[t3410,t199]) ).
cnf(t204,plain,
false = sF3,
inference(orient,[status(thm)],[t3411]) ).
cnf(t3419,plain,
eq(sF2,u) = sF3,
inference(step,[status(thm)],[t199,t204]) ).
cnf(t212,plain,
eq(sF2,u) = sF3,
inference(orient,[status(thm)],[t3419]) ).
cnf(t3137,plain,
eq(sF2,sF2) = sF3,
inference(rw,[status(thm)],[t212]) ).
cnf(t4,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t148,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t3383,plain,
eq(X1,X1) = sF0,
inference(step,[status(thm)],[t148,t160]) ).
cnf(t168,plain,
eq(X1,X1) = sF0,
inference(orient,[status(thm)],[t3383]) ).
cnf(t4136,plain,
sF0 = sF3,
inference(step,[status(thm)],[t3137,t168]) ).
cnf(t3207,plain,
sF3 = sF0,
inference(orient,[status(thm)],[t4136]) ).
cnf(t4141,plain,
false = sF0,
inference(step,[status(thm)],[t204,t3207]) ).
cnf(t3212,plain,
false = sF0,
inference(orient,[status(thm)],[t4141]) ).
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(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(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,c134]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t160]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t3212]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET090-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 09:41:38 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.51/1.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.51/1.82 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------