%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET118-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 02:42:25 PM UTC 2026
% Result : Unsatisfiable 3.67s 1.50s
% Output : Proof 3.67s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t171,axiom,
sF2 = member(x,cross_product(universal_class,universal_class)),
introduced(definition) ).
cnf(t170,axiom,
sF1 = cross_product(universal_class,universal_class),
introduced(definition) ).
cnf(t200,plain,
cross_product(universal_class,universal_class) = sF1,
inference(orient,[status(thm)],[t170]) ).
cnf(t2073,plain,
sF2 = member(x,sF1),
inference(step,[status(thm)],[t171,t200]) ).
cnf(f163,negated_conjecture,
member(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_ordered_pairs_are_sets_1) ).
fof(f163_nnf,plain,
member(x,cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f163]) ).
cnf(c163,plain,
member(x,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f163_nnf]) ).
cnf(t20,plain,
member(x,cross_product(universal_class,universal_class)) = true,
inference(equality_encoding,[status(esa)],[c163]) ).
cnf(t2070,plain,
member(x,sF1) = true,
inference(step,[status(thm)],[t20,t200]) ).
cnf(t208,plain,
member(x,sF1) = true,
inference(orient,[status(thm)],[t2070]) ).
cnf(t2074,plain,
sF2 = true,
inference(step,[status(thm)],[t2073,t208]) ).
cnf(t211,plain,
true = sF2,
inference(orient,[status(thm)],[t2074]) ).
cnf(f0,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/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(t96,plain,
ifeq(subclass(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t2469,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t96,t211]) ).
cnf(t2470,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t2469,t211]) ).
cnf(t2471,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),sF2),true) = true,
inference(step,[status(thm)],[t2470,t211]) ).
cnf(t2472,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),sF2),sF2) = true,
inference(step,[status(thm)],[t2471,t211]) ).
cnf(t2473,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),sF2),sF2) = sF2,
inference(step,[status(thm)],[t2472,t211]) ).
cnf(t1515,plain,
ifeq(subclass(X1,X2),sF2,ifeq(member(X3,X1),sF2,member(X3,X2),sF2),sF2) = sF2,
inference(orient,[status(thm)],[t2473]) ).
cnf(f164,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_ordered_pairs_are_sets_2) ).
fof(f164_nnf,plain,
~ member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f164]) ).
fof(f164_sk,plain,
~ member(x,universal_class),
inference(skolemisation,[status(esa)],[f164_nnf]) ).
cnf(c164,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f164_sk]) ).
cnf(t8,plain,
member(x,universal_class) = false,
inference(equality_encoding,[status(esa)],[c164]) ).
cnf(t181,plain,
member(x,universal_class) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t169,axiom,
sF0 = member(x,universal_class),
introduced(definition) ).
cnf(t2059,plain,
sF0 = false,
inference(step,[status(thm)],[t169,t181]) ).
cnf(t189,plain,
false = sF0,
inference(orient,[status(thm)],[t2059]) ).
cnf(t2065,plain,
member(x,universal_class) = sF0,
inference(step,[status(thm)],[t181,t189]) ).
cnf(t195,plain,
member(x,universal_class) = sF0,
inference(orient,[status(thm)],[t2065]) ).
cnf(t1522,plain,
sF2 = ifeq(subclass(X1,universal_class),sF2,ifeq(member(x,X1),sF2,sF0,sF2),sF2),
inference(cp,[status(thm)],[t1515,t195]) ).
cnf(f3,axiom,
subclass(X,universal_class),
file('/export/starexec/sandbox2/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(t14,plain,
subclass(X1,universal_class) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t187,plain,
subclass(X1,universal_class) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t2088,plain,
subclass(X1,universal_class) = sF2,
inference(step,[status(thm)],[t187,t211]) ).
cnf(t227,plain,
subclass(X1,universal_class) = sF2,
inference(orient,[status(thm)],[t2088]) ).
cnf(t2485,plain,
sF2 = ifeq(sF2,sF2,ifeq(member(x,X1),sF2,sF0,sF2),sF2),
inference(step,[status(thm)],[t1522,t227]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t203,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t2486,plain,
sF2 = ifeq(member(x,X1),sF2,sF0,sF2),
inference(step,[status(thm)],[t2485,t203]) ).
cnf(t1662,plain,
ifeq(member(x,X1),sF2,sF0,sF2) = sF2,
inference(orient,[status(thm)],[t2486]) ).
cnf(t2098,plain,
member(x,sF1) = sF2,
inference(step,[status(thm)],[t208,t211]) ).
cnf(t237,plain,
member(x,sF1) = sF2,
inference(orient,[status(thm)],[t2098]) ).
cnf(t1667,plain,
sF2 = ifeq(sF2,sF2,sF0,sF2),
inference(cp,[status(thm)],[t1662,t237]) ).
cnf(t2496,plain,
sF2 = sF0,
inference(step,[status(thm)],[t1667,t203]) ).
cnf(t1734,plain,
sF2 = sF0,
inference(orient,[status(thm)],[t2496]) ).
cnf(t2523,plain,
true = sF0,
inference(step,[status(thm)],[t211,t1734]) ).
cnf(t1761,plain,
true = sF0,
inference(orient,[status(thm)],[t2523]) ).
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(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(f115,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,c164]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t1761]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t189]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET118-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 09:50:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.67/1.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.67/1.50 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------