%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET104-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:42:16 PM UTC 2026
% Result : Unsatisfiable 20.72s 3.16s
% Output : Proof 20.72s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t155,axiom,
sF1 = ifeq(member(x,universal_class),true,false,true),
introduced(definition) ).
cnf(f148,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_2_of_ordered_pair_3) ).
fof(f148_nnf,plain,
~ member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f148]) ).
fof(f148_sk,plain,
~ member(x,universal_class),
inference(skolemisation,[status(esa)],[f148_nnf]) ).
cnf(c148,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f148_sk]) ).
cnf(t8,plain,
member(x,universal_class) = false,
inference(equality_encoding,[status(esa)],[c148]) ).
cnf(t172,plain,
member(x,universal_class) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t154,axiom,
sF0 = member(x,universal_class),
introduced(definition) ).
cnf(t3942,plain,
sF0 = false,
inference(step,[status(thm)],[t154,t172]) ).
cnf(t180,plain,
false = sF0,
inference(orient,[status(thm)],[t3942]) ).
cnf(t3948,plain,
member(x,universal_class) = sF0,
inference(step,[status(thm)],[t172,t180]) ).
cnf(t186,plain,
member(x,universal_class) = sF0,
inference(orient,[status(thm)],[t3948]) ).
cnf(t3961,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t155,t186]) ).
cnf(t3962,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t3961,t180]) ).
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(t28,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(t169,plain,
member(X1,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t3946,plain,
member(X1,null_class) = sF0,
inference(step,[status(thm)],[t169,t180]) ).
cnf(t184,plain,
member(X1,null_class) = sF0,
inference(orient,[status(thm)],[t3946]) ).
cnf(t3958,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t28,t184]) ).
cnf(t3959,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t3958,t180]) ).
cnf(t233,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t3959]) ).
cnf(t3963,plain,
sF1 = true,
inference(step,[status(thm)],[t3962,t233]) ).
cnf(t286,plain,
true = sF1,
inference(orient,[status(thm)],[t3963]) ).
cnf(f147,negated_conjecture,
unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_2_of_ordered_pair_2) ).
fof(f147_nnf,plain,
unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y),
inference(nnf_transformation,[status(thm)],[f147]) ).
fof(f147_sk,plain,
unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y),
inference(skolemisation,[status(esa)],[f147_nnf]) ).
cnf(c147,plain,
unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y),
inference(cnf_transformation,[status(esa)],[f147_sk]) ).
cnf(u41,axiom,
eq(unordered_pair(null_class,singleton(singleton(y))),ordered_pair(x,y)) = false,
inference(equality_encoding,[status(esa)],[c147]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/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(f12,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f12_nnf,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(u0,axiom,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(d1,axiom,
unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = ordered_pair(X0,X1),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(t116,plain,
eq(unordered_pair(null_class,unordered_pair(unordered_pair(y,y),unordered_pair(y,y))),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(definition_unfolding,[status(thm)],[u41,d0,d1]) ).
cnf(t27,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t230,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t27]) ).
cnf(t4000,plain,
ifeq(eq(X1,X2),sF1,X1,X2) = X2,
inference(step,[status(thm)],[t230,t286]) ).
cnf(t328,plain,
ifeq(eq(X1,X2),sF1,X1,X2) = X2,
inference(rw,[status(thm)],[t4000]) ).
cnf(t423,plain,
ifeq(eq(X1,X2),sF1,X1,X2) = X2,
inference(orient,[status(thm)],[t328]) ).
cnf(f125,axiom,
( singleton(X) = null_class
| member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f125_nnf,plain,
! [X] :
( singleton(X) = null_class
| member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f125]) ).
fof(f125_sk,plain,
! [X] :
( singleton(X) = null_class
| member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f125_nnf]) ).
cnf(c125,plain,
( singleton(X0) = null_class
| member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f125_sk]) ).
cnf(u17,axiom,
or(member(X0,universal_class),eq(singleton(X0),null_class)) = true,
inference(equality_encoding,[status(esa)],[c125]) ).
cnf(t49,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X1),null_class)) = true,
inference(definition_unfolding,[status(thm)],[u17,d0]) ).
cnf(t4066,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X1),null_class)) = sF1,
inference(step,[status(thm)],[t49,t286]) ).
cnf(t485,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X1),null_class)) = sF1,
inference(orient,[status(thm)],[t4066]) ).
cnf(t486,plain,
sF1 = or(sF0,eq(unordered_pair(x,x),null_class)),
inference(cp,[status(thm)],[t485,t186]) ).
cnf(t11,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t175,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t3951,plain,
or(sF0,X1) = X1,
inference(step,[status(thm)],[t175,t180]) ).
cnf(t189,plain,
or(sF0,X1) = X1,
inference(rw,[status(thm)],[t3951]) ).
cnf(t195,plain,
or(sF0,X1) = X1,
inference(orient,[status(thm)],[t189]) ).
cnf(t4067,plain,
sF1 = eq(unordered_pair(x,x),null_class),
inference(step,[status(thm)],[t486,t195]) ).
cnf(t159,axiom,
sF5 = unordered_pair(x,x),
introduced(definition) ).
cnf(t192,plain,
unordered_pair(x,x) = sF5,
inference(orient,[status(thm)],[t159]) ).
cnf(t4068,plain,
sF1 = eq(sF5,null_class),
inference(step,[status(thm)],[t4067,t192]) ).
cnf(t488,plain,
eq(sF5,null_class) = sF1,
inference(orient,[status(thm)],[t4068]) ).
cnf(t489,plain,
null_class = ifeq(sF1,sF1,sF5,null_class),
inference(cp,[status(thm)],[t423,t488]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t194,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t4069,plain,
null_class = sF5,
inference(step,[status(thm)],[t489,t194]) ).
cnf(t490,plain,
null_class = sF5,
inference(orient,[status(thm)],[t4069]) ).
cnf(t4696,plain,
eq(unordered_pair(sF5,unordered_pair(unordered_pair(y,y),unordered_pair(y,y))),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t116,t490]) ).
cnf(f111,axiom,
( unordered_pair(X,Y) = singleton(Y)
| member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f111_nnf,plain,
! [X,Y] :
( unordered_pair(X,Y) = singleton(Y)
| member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f111]) ).
fof(f111_sk,plain,
! [X,Y] :
( unordered_pair(X,Y) = singleton(Y)
| member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f111_nnf]) ).
cnf(c111,plain,
( unordered_pair(X0,X1) = singleton(X1)
| member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f111_sk]) ).
cnf(u11,axiom,
or(member(X0,universal_class),eq(unordered_pair(X0,X1),singleton(X1))) = true,
inference(equality_encoding,[status(esa)],[c111]) ).
cnf(t69,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X2),unordered_pair(X2,X2))) = true,
inference(definition_unfolding,[status(thm)],[u11,d0]) ).
cnf(t4244,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X2),unordered_pair(X2,X2))) = sF1,
inference(step,[status(thm)],[t69,t286]) ).
cnf(t1051,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X2),unordered_pair(X2,X2))) = sF1,
inference(orient,[status(thm)],[t4244]) ).
cnf(t1052,plain,
sF1 = or(sF0,eq(unordered_pair(x,X1),unordered_pair(X1,X1))),
inference(cp,[status(thm)],[t1051,t186]) ).
cnf(t4245,plain,
sF1 = eq(unordered_pair(x,X1),unordered_pair(X1,X1)),
inference(step,[status(thm)],[t1052,t195]) ).
cnf(t1057,plain,
eq(unordered_pair(x,X1),unordered_pair(X1,X1)) = sF1,
inference(orient,[status(thm)],[t4245]) ).
cnf(t1061,plain,
unordered_pair(X1,X1) = ifeq(sF1,sF1,unordered_pair(x,X1),unordered_pair(X1,X1)),
inference(cp,[status(thm)],[t423,t1057]) ).
cnf(t4286,plain,
unordered_pair(X1,X1) = unordered_pair(x,X1),
inference(step,[status(thm)],[t1061,t194]) ).
cnf(t1175,plain,
unordered_pair(X1,X1) = unordered_pair(x,X1),
inference(orient,[status(thm)],[t4286]) ).
cnf(t4697,plain,
eq(unordered_pair(sF5,unordered_pair(x,unordered_pair(y,y))),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t4696,t1175]) ).
cnf(t156,axiom,
sF2 = unordered_pair(y,y),
introduced(definition) ).
cnf(t191,plain,
unordered_pair(y,y) = sF2,
inference(orient,[status(thm)],[t156]) ).
cnf(t4698,plain,
eq(unordered_pair(sF5,unordered_pair(x,sF2)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t4697,t191]) ).
cnf(f107,axiom,
unordered_pair(X,Y) = unordered_pair(Y,X),
file('/export/starexec/sandbox2/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(t22,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(t208,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t22]) ).
cnf(t4699,plain,
eq(unordered_pair(sF5,unordered_pair(sF2,x)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t4698,t208]) ).
cnf(t1180,plain,
unordered_pair(x,X1) = unordered_pair(X1,X1),
inference(cp,[status(thm)],[t1175,t208]) ).
cnf(t1359,plain,
unordered_pair(x,X1) = unordered_pair(X1,X1),
inference(orient,[status(thm)],[t1180]) ).
cnf(t1360,plain,
unordered_pair(X1,X1) = unordered_pair(X1,x),
inference(cp,[status(thm)],[t1359,t208]) ).
cnf(t1382,plain,
unordered_pair(X1,X1) = unordered_pair(X1,x),
inference(orient,[status(thm)],[t1360]) ).
cnf(t4700,plain,
eq(unordered_pair(sF5,unordered_pair(sF2,sF2)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t4699,t1382]) ).
cnf(t157,axiom,
sF3 = unordered_pair(unordered_pair(y,y),unordered_pair(y,y)),
introduced(definition) ).
cnf(t4040,plain,
sF3 = unordered_pair(sF2,unordered_pair(y,y)),
inference(step,[status(thm)],[t157,t191]) ).
cnf(t4041,plain,
sF3 = unordered_pair(sF2,sF2),
inference(step,[status(thm)],[t4040,t191]) ).
cnf(t383,plain,
unordered_pair(sF2,sF2) = sF3,
inference(orient,[status(thm)],[t4041]) ).
cnf(t4701,plain,
eq(unordered_pair(sF5,sF3),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t4700,t383]) ).
cnf(t4702,plain,
eq(unordered_pair(sF3,sF5),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t4701,t208]) ).
cnf(t158,axiom,
sF4 = unordered_pair(null_class,unordered_pair(unordered_pair(y,y),unordered_pair(y,y))),
introduced(definition) ).
cnf(t4100,plain,
sF4 = unordered_pair(sF5,unordered_pair(unordered_pair(y,y),unordered_pair(y,y))),
inference(step,[status(thm)],[t158,t490]) ).
cnf(t4101,plain,
sF4 = unordered_pair(sF5,unordered_pair(sF2,unordered_pair(y,y))),
inference(step,[status(thm)],[t4100,t191]) ).
cnf(t4102,plain,
sF4 = unordered_pair(sF5,unordered_pair(sF2,sF2)),
inference(step,[status(thm)],[t4101,t191]) ).
cnf(t4103,plain,
sF4 = unordered_pair(sF5,sF3),
inference(step,[status(thm)],[t4102,t383]) ).
cnf(t4104,plain,
sF4 = unordered_pair(sF3,sF5),
inference(step,[status(thm)],[t4103,t208]) ).
cnf(t537,plain,
unordered_pair(sF3,sF5) = sF4,
inference(orient,[status(thm)],[t4104]) ).
cnf(t4703,plain,
eq(sF4,unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t4702,t537]) ).
cnf(t4704,plain,
eq(sF4,unordered_pair(sF5,unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t4703,t192]) ).
cnf(t4705,plain,
eq(sF4,unordered_pair(sF5,unordered_pair(x,sF2))) = false,
inference(step,[status(thm)],[t4704,t191]) ).
cnf(t4706,plain,
eq(sF4,unordered_pair(sF5,unordered_pair(sF2,x))) = false,
inference(step,[status(thm)],[t4705,t208]) ).
cnf(t4707,plain,
eq(sF4,unordered_pair(sF5,unordered_pair(sF2,sF2))) = false,
inference(step,[status(thm)],[t4706,t1382]) ).
cnf(t4708,plain,
eq(sF4,unordered_pair(sF5,sF3)) = false,
inference(step,[status(thm)],[t4707,t383]) ).
cnf(t4709,plain,
eq(sF4,unordered_pair(sF3,sF5)) = false,
inference(step,[status(thm)],[t4708,t208]) ).
cnf(t4710,plain,
eq(sF4,sF4) = false,
inference(step,[status(thm)],[t4709,t537]) ).
cnf(t4,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t168,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t3969,plain,
eq(X1,X1) = sF1,
inference(step,[status(thm)],[t168,t286]) ).
cnf(t292,plain,
eq(X1,X1) = sF1,
inference(orient,[status(thm)],[t3969]) ).
cnf(t4711,plain,
sF1 = false,
inference(step,[status(thm)],[t4710,t292]) ).
cnf(t4712,plain,
sF1 = sF0,
inference(step,[status(thm)],[t4711,t180]) ).
cnf(t3526,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t4712]) ).
cnf(t4747,plain,
true = sF0,
inference(step,[status(thm)],[t286,t3526]) ).
cnf(t3561,plain,
true = sF0,
inference(orient,[status(thm)],[t4747]) ).
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(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,c147,c148]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t3561]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t180]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET104-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.44 % Computer : n020.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Thu Sep 24 09:51:35 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.72/3.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.72/3.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------