%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET073-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 02:41:57 PM UTC 2026
% Result : Unsatisfiable 5.22s 7.03s
% Output : Proof 5.22s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t116,axiom,
sF0 = member(x,universal_class),
introduced(definition) ).
cnf(f115,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom1_1) ).
fof(f115_nnf,plain,
member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f115]) ).
cnf(c115,plain,
member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f115_nnf]) ).
cnf(t8,plain,
member(x,universal_class) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(t126,plain,
member(x,universal_class) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t408,plain,
sF0 = true,
inference(step,[status(thm)],[t116,t126]) ).
cnf(t135,plain,
true = sF0,
inference(orient,[status(thm)],[t408]) ).
cnf(f8,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f8_nnf,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t53,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t530,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),true) = true,
inference(step,[status(thm)],[t53,t135]) ).
cnf(t531,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = true,
inference(step,[status(thm)],[t530,t135]) ).
cnf(t532,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = sF0,
inference(step,[status(thm)],[t531,t135]) ).
cnf(t369,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = sF0,
inference(orient,[status(thm)],[t532]) ).
cnf(f104,axiom,
( X = null_class
| ~ subclass(X,null_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(f104_nnf,plain,
! [X] :
( X = null_class
| ~ subclass(X,null_class) ),
inference(nnf_transformation,[status(thm)],[f104]) ).
fof(f104_sk,plain,
! [X] :
( X = null_class
| ~ subclass(X,null_class) ),
inference(skolemisation,[status(esa)],[f104_nnf]) ).
cnf(c104,plain,
( X0 = null_class
| ~ subclass(X0,null_class) ),
inference(cnf_transformation,[status(esa)],[f104_sk]) ).
cnf(t30,plain,
ifeq(subclass(X1,null_class),true,X1,null_class) = null_class,
inference(equality_encoding,[status(esa)],[c104]) ).
cnf(t117,axiom,
sF1 = unordered_pair(x,y),
introduced(definition) ).
cnf(f116,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom1_2) ).
fof(f116_nnf,plain,
unordered_pair(x,y) = null_class,
inference(nnf_transformation,[status(thm)],[f116]) ).
cnf(c116,plain,
unordered_pair(x,y) = null_class,
inference(cnf_transformation,[status(esa)],[f116_nnf]) ).
cnf(t16,plain,
unordered_pair(x,y) = null_class,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(t134,plain,
unordered_pair(x,y) = null_class,
inference(orient,[status(thm)],[t16]) ).
cnf(t430,plain,
sF1 = null_class,
inference(step,[status(thm)],[t117,t134]) ).
cnf(t160,plain,
null_class = sF1,
inference(orient,[status(thm)],[t430]) ).
cnf(t459,plain,
ifeq(subclass(X1,sF1),true,X1,null_class) = null_class,
inference(step,[status(thm)],[t30,t160]) ).
cnf(t460,plain,
ifeq(subclass(X1,sF1),sF0,X1,null_class) = null_class,
inference(step,[status(thm)],[t459,t135]) ).
cnf(t461,plain,
ifeq(subclass(X1,sF1),sF0,X1,sF1) = null_class,
inference(step,[status(thm)],[t460,t160]) ).
cnf(t462,plain,
ifeq(subclass(X1,sF1),sF0,X1,sF1) = sF1,
inference(step,[status(thm)],[t461,t160]) ).
cnf(t205,plain,
ifeq(subclass(X1,sF1),sF0,X1,sF1) = sF1,
inference(orient,[status(thm)],[t462]) ).
cnf(f109,axiom,
subclass(singleton(Y),unordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
fof(f109_nnf,plain,
! [Y,X] : subclass(singleton(Y),unordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [Y,X] : subclass(singleton(Y),unordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
subclass(singleton(X0),unordered_pair(X1,X0)),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(u9,axiom,
subclass(singleton(X0),unordered_pair(X1,X0)) = true,
inference(equality_encoding,[status(esa)],[c109]) ).
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(t34,plain,
subclass(unordered_pair(X1,X1),unordered_pair(X2,X1)) = true,
inference(definition_unfolding,[status(thm)],[u9,d0]) ).
cnf(t466,plain,
subclass(unordered_pair(X1,X1),unordered_pair(X2,X1)) = sF0,
inference(step,[status(thm)],[t34,t135]) ).
cnf(t219,plain,
subclass(unordered_pair(X1,X1),unordered_pair(X2,X1)) = sF0,
inference(orient,[status(thm)],[t466]) ).
cnf(t434,plain,
unordered_pair(x,y) = sF1,
inference(step,[status(thm)],[t134,t160]) ).
cnf(t164,plain,
unordered_pair(x,y) = sF1,
inference(orient,[status(thm)],[t434]) ).
cnf(f107,axiom,
unordered_pair(X,Y) = unordered_pair(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f107_nnf,plain,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
inference(nnf_transformation,[status(thm)],[f107]) ).
fof(f107_sk,plain,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
inference(skolemisation,[status(esa)],[f107_nnf]) ).
cnf(c107,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f107_sk]) ).
cnf(t21,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(t175,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t21]) ).
cnf(t441,plain,
unordered_pair(y,x) = sF1,
inference(step,[status(thm)],[t164,t175]) ).
cnf(t176,plain,
unordered_pair(y,x) = sF1,
inference(rw,[status(thm)],[t441]) ).
cnf(t177,plain,
unordered_pair(y,x) = sF1,
inference(orient,[status(thm)],[t176]) ).
cnf(t220,plain,
sF0 = subclass(unordered_pair(x,x),sF1),
inference(cp,[status(thm)],[t219,t177]) ).
cnf(t223,plain,
subclass(unordered_pair(x,x),sF1) = sF0,
inference(orient,[status(thm)],[t220]) ).
cnf(t224,plain,
sF1 = ifeq(sF0,sF0,unordered_pair(x,x),sF1),
inference(cp,[status(thm)],[t205,t223]) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t167,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t17]) ).
cnf(t467,plain,
sF1 = unordered_pair(x,x),
inference(step,[status(thm)],[t224,t167]) ).
cnf(t225,plain,
unordered_pair(x,x) = sF1,
inference(orient,[status(thm)],[t467]) ).
cnf(t376,plain,
sF0 = ifeq(member(x,universal_class),sF0,member(x,sF1),sF0),
inference(cp,[status(thm)],[t369,t225]) ).
cnf(t422,plain,
member(x,universal_class) = sF0,
inference(step,[status(thm)],[t126,t135]) ).
cnf(t149,plain,
member(x,universal_class) = sF0,
inference(orient,[status(thm)],[t422]) ).
cnf(t533,plain,
sF0 = ifeq(sF0,sF0,member(x,sF1),sF0),
inference(step,[status(thm)],[t376,t149]) ).
cnf(t534,plain,
sF0 = member(x,sF1),
inference(step,[status(thm)],[t533,t167]) ).
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(t5,plain,
member(X1,null_class) = false,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t123,plain,
member(X1,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t431,plain,
member(X1,sF1) = false,
inference(step,[status(thm)],[t123,t160]) ).
cnf(t161,plain,
member(X1,sF1) = false,
inference(rw,[status(thm)],[t431]) ).
cnf(t169,plain,
member(X1,sF1) = false,
inference(orient,[status(thm)],[t161]) ).
cnf(t535,plain,
sF0 = false,
inference(step,[status(thm)],[t534,t169]) ).
cnf(t377,plain,
false = sF0,
inference(orient,[status(thm)],[t535]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t135]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t377]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET073-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/6.20 % Computer : n013.cluster.edu
% 0.09/6.20 % Model : x86_64 x86_64
% 0.09/6.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/6.20 % Memory : 8046.5625MB
% 0.09/6.20 % OS : Linux 6.8.0-71-generic
% 0.09/6.20 % CPULimit : 300
% 0.09/6.20 % WCLimit : 300
% 0.09/6.20 % DateTime : Thu Sep 24 09:35:57 UTC 2026
% 0.09/6.20 % CPUTime :
% 0.09/6.20 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.22/7.03 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.22/7.03 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------