%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET098-7 : 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 02:42:13 PM UTC 2026
% Result : Unsatisfiable 22.55s 3.72s
% Output : Proof 22.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 22
% Syntax : Number of formulae : 150 ( 118 unt; 0 def)
% Number of atoms : 186 ( 133 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 111 ( 75 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-4 aty)
% Number of variables : 117 ( 21 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t151,axiom,
sF1 = ifeq(x,null_class,false,true),
introduced(definition) ).
cnf(t150,axiom,
sF0 = eq(x,null_class),
introduced(definition) ).
cnf(f143,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_3) ).
fof(f143_nnf,plain,
x != null_class,
inference(nnf_transformation,[status(thm)],[f143]) ).
fof(f143_sk,plain,
x != null_class,
inference(skolemisation,[status(esa)],[f143_nnf]) ).
cnf(c143,plain,
x != null_class,
inference(cnf_transformation,[status(esa)],[f143_sk]) ).
cnf(t5,plain,
eq(x,null_class) = false,
inference(equality_encoding,[status(esa)],[c143]) ).
cnf(t166,plain,
eq(x,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t6906,plain,
sF0 = false,
inference(step,[status(thm)],[t150,t166]) ).
cnf(t177,plain,
false = sF0,
inference(orient,[status(thm)],[t6906]) ).
cnf(t6918,plain,
sF1 = ifeq(x,null_class,sF0,true),
inference(step,[status(thm)],[t151,t177]) ).
cnf(t17,plain,
ifeq(x,null_class,false,true) = true,
inference(equality_encoding,[status(esa)],[c143]) ).
cnf(t6916,plain,
ifeq(x,null_class,sF0,true) = true,
inference(step,[status(thm)],[t17,t177]) ).
cnf(t192,plain,
ifeq(x,null_class,sF0,true) = true,
inference(orient,[status(thm)],[t6916]) ).
cnf(t6919,plain,
sF1 = true,
inference(step,[status(thm)],[t6918,t192]) ).
cnf(t199,plain,
true = sF1,
inference(orient,[status(thm)],[t6919]) ).
cnf(f21,axiom,
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f21_nnf,plain,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t62,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t7071,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X3),true) = true,
inference(step,[status(thm)],[t62,t199]) ).
cnf(t7072,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X3),sF1) = true,
inference(step,[status(thm)],[t7071,t199]) ).
cnf(t7073,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X3),sF1) = sF1,
inference(step,[status(thm)],[t7072,t199]) ).
cnf(t518,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X3),sF1) = sF1,
inference(orient,[status(thm)],[t7073]) ).
cnf(t157,axiom,
sF7 = intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),
introduced(definition) ).
cnf(t152,axiom,
sF2 = not_subclass_element(x,null_class),
introduced(definition) ).
cnf(t188,plain,
not_subclass_element(x,null_class) = sF2,
inference(orient,[status(thm)],[t152]) ).
cnf(t7130,plain,
sF7 = intersection(complement(unordered_pair(sF2,not_subclass_element(x,null_class))),x),
inference(step,[status(thm)],[t157,t188]) ).
cnf(t7131,plain,
sF7 = intersection(complement(unordered_pair(sF2,sF2)),x),
inference(step,[status(thm)],[t7130,t188]) ).
cnf(t153,axiom,
sF3 = unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
introduced(definition) ).
cnf(t6974,plain,
sF3 = unordered_pair(sF2,not_subclass_element(x,null_class)),
inference(step,[status(thm)],[t153,t188]) ).
cnf(t6975,plain,
sF3 = unordered_pair(sF2,sF2),
inference(step,[status(thm)],[t6974,t188]) ).
cnf(t275,plain,
unordered_pair(sF2,sF2) = sF3,
inference(orient,[status(thm)],[t6975]) ).
cnf(t7132,plain,
sF7 = intersection(complement(sF3),x),
inference(step,[status(thm)],[t7131,t275]) ).
cnf(t156,axiom,
sF6 = complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),
introduced(definition) ).
cnf(t6989,plain,
sF6 = complement(unordered_pair(sF2,not_subclass_element(x,null_class))),
inference(step,[status(thm)],[t156,t188]) ).
cnf(t6990,plain,
sF6 = complement(unordered_pair(sF2,sF2)),
inference(step,[status(thm)],[t6989,t188]) ).
cnf(t6991,plain,
sF6 = complement(sF3),
inference(step,[status(thm)],[t6990,t275]) ).
cnf(t319,plain,
complement(sF3) = sF6,
inference(orient,[status(thm)],[t6991]) ).
cnf(t7133,plain,
sF7 = intersection(sF6,x),
inference(step,[status(thm)],[t7132,t319]) ).
cnf(t724,plain,
intersection(sF6,x) = sF7,
inference(orient,[status(thm)],[t7133]) ).
cnf(t726,plain,
sF1 = ifeq(member(X1,sF7),sF1,member(X1,x),sF1),
inference(cp,[status(thm)],[t518,t724]) ).
cnf(t730,plain,
ifeq(member(X1,sF7),sF1,member(X1,x),sF1) = sF1,
inference(orient,[status(thm)],[t726]) ).
cnf(f140,axiom,
( X = null_class
| singleton(not_subclass_element(X,null_class)) = X
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',number_of_elements_in_class) ).
fof(f140_nnf,plain,
! [X] :
( X = null_class
| singleton(not_subclass_element(X,null_class)) = X
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ),
inference(nnf_transformation,[status(thm)],[f140]) ).
fof(f140_sk,plain,
! [X] :
( X = null_class
| singleton(not_subclass_element(X,null_class)) = X
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ),
inference(skolemisation,[status(esa)],[f140_nnf]) ).
cnf(c140,plain,
( X0 = null_class
| singleton(not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0)) ),
inference(cnf_transformation,[status(esa)],[f140_sk]) ).
cnf(u30,axiom,
or(member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0)),or(eq(singleton(not_subclass_element(X0,null_class)),X0),eq(X0,null_class))) = true,
inference(equality_encoding,[status(esa)],[c140]) ).
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(t139,plain,
or(member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1)),or(eq(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class)),X1),eq(X1,null_class))) = true,
inference(definition_unfolding,[status(thm)],[u30,d0]) ).
cnf(t7931,plain,
or(member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1)),or(eq(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class)),X1),eq(X1,null_class))) = sF1,
inference(step,[status(thm)],[t139,t199]) ).
cnf(t6101,plain,
or(member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1)),or(eq(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class)),X1),eq(X1,null_class))) = sF1,
inference(orient,[status(thm)],[t7931]) ).
cnf(t6910,plain,
eq(x,null_class) = sF0,
inference(step,[status(thm)],[t166,t177]) ).
cnf(t181,plain,
eq(x,null_class) = sF0,
inference(orient,[status(thm)],[t6910]) ).
cnf(t6102,plain,
sF1 = or(member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(cp,[status(thm)],[t6101,t181]) ).
cnf(t7932,plain,
sF1 = or(member(not_subclass_element(intersection(complement(unordered_pair(sF2,not_subclass_element(x,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t6102,t188]) ).
cnf(t7933,plain,
sF1 = or(member(not_subclass_element(intersection(complement(unordered_pair(sF2,sF2)),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7932,t188]) ).
cnf(t7934,plain,
sF1 = or(member(not_subclass_element(intersection(complement(sF3),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7933,t275]) ).
cnf(t7935,plain,
sF1 = or(member(not_subclass_element(intersection(sF6,x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7934,t319]) ).
cnf(t7936,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7935,t724]) ).
cnf(t7937,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),intersection(complement(unordered_pair(sF2,not_subclass_element(x,null_class))),x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7936,t188]) ).
cnf(t7938,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),intersection(complement(unordered_pair(sF2,sF2)),x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7937,t188]) ).
cnf(t7939,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),intersection(complement(sF3),x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7938,t275]) ).
cnf(t7940,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),intersection(sF6,x)),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7939,t319]) ).
cnf(t7941,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),sF7),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7940,t724]) ).
cnf(t9,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t170,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t6914,plain,
or(X1,sF0) = X1,
inference(step,[status(thm)],[t170,t177]) ).
cnf(t185,plain,
or(X1,sF0) = X1,
inference(rw,[status(thm)],[t6914]) ).
cnf(t189,plain,
or(X1,sF0) = X1,
inference(orient,[status(thm)],[t185]) ).
cnf(t7942,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),sF7),eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x)),
inference(step,[status(thm)],[t7941,t189]) ).
cnf(t7943,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),sF7),eq(unordered_pair(sF2,not_subclass_element(x,null_class)),x)),
inference(step,[status(thm)],[t7942,t188]) ).
cnf(t7944,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),sF7),eq(unordered_pair(sF2,sF2),x)),
inference(step,[status(thm)],[t7943,t188]) ).
cnf(t7945,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),sF7),eq(sF3,x)),
inference(step,[status(thm)],[t7944,t275]) ).
cnf(f142,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_2) ).
fof(f142_nnf,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(nnf_transformation,[status(thm)],[f142]) ).
fof(f142_sk,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(skolemisation,[status(esa)],[f142_nnf]) ).
cnf(c142,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[status(esa)],[f142_sk]) ).
cnf(u38,axiom,
eq(singleton(not_subclass_element(x,null_class)),x) = false,
inference(equality_encoding,[status(esa)],[c142]) ).
cnf(t42,plain,
eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x) = false,
inference(definition_unfolding,[status(thm)],[u38,d0]) ).
cnf(t6992,plain,
eq(unordered_pair(sF2,not_subclass_element(x,null_class)),x) = false,
inference(step,[status(thm)],[t42,t188]) ).
cnf(t6993,plain,
eq(unordered_pair(sF2,sF2),x) = false,
inference(step,[status(thm)],[t6992,t188]) ).
cnf(t6994,plain,
eq(sF3,x) = false,
inference(step,[status(thm)],[t6993,t275]) ).
cnf(t6995,plain,
eq(sF3,x) = sF0,
inference(step,[status(thm)],[t6994,t177]) ).
cnf(t323,plain,
eq(sF3,x) = sF0,
inference(orient,[status(thm)],[t6995]) ).
cnf(t7946,plain,
sF1 = or(member(not_subclass_element(sF7,null_class),sF7),sF0),
inference(step,[status(thm)],[t7945,t323]) ).
cnf(t7947,plain,
sF1 = member(not_subclass_element(sF7,null_class),sF7),
inference(step,[status(thm)],[t7946,t189]) ).
cnf(t6127,plain,
member(not_subclass_element(sF7,null_class),sF7) = sF1,
inference(orient,[status(thm)],[t7947]) ).
cnf(t6132,plain,
sF1 = ifeq(sF1,sF1,member(not_subclass_element(sF7,null_class),x),sF1),
inference(cp,[status(thm)],[t730,t6127]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t191,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t7948,plain,
sF1 = member(not_subclass_element(sF7,null_class),x),
inference(step,[status(thm)],[t6132,t191]) ).
cnf(f141,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_1) ).
fof(f141_nnf,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
inference(nnf_transformation,[status(thm)],[f141]) ).
fof(f141_sk,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
inference(skolemisation,[status(esa)],[f141_nnf]) ).
cnf(c141,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
inference(cnf_transformation,[status(esa)],[f141_sk]) ).
cnf(u37,axiom,
member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x) = false,
inference(equality_encoding,[status(esa)],[c141]) ).
cnf(t91,plain,
member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) = false,
inference(definition_unfolding,[status(thm)],[u37,d0]) ).
cnf(t7339,plain,
member(not_subclass_element(intersection(complement(unordered_pair(sF2,not_subclass_element(x,null_class))),x),null_class),x) = false,
inference(step,[status(thm)],[t91,t188]) ).
cnf(t7340,plain,
member(not_subclass_element(intersection(complement(unordered_pair(sF2,sF2)),x),null_class),x) = false,
inference(step,[status(thm)],[t7339,t188]) ).
cnf(t7341,plain,
member(not_subclass_element(intersection(complement(sF3),x),null_class),x) = false,
inference(step,[status(thm)],[t7340,t275]) ).
cnf(t7342,plain,
member(not_subclass_element(intersection(sF6,x),null_class),x) = false,
inference(step,[status(thm)],[t7341,t319]) ).
cnf(t7343,plain,
member(not_subclass_element(sF7,null_class),x) = false,
inference(step,[status(thm)],[t7342,t724]) ).
cnf(t7344,plain,
member(not_subclass_element(sF7,null_class),x) = sF0,
inference(step,[status(thm)],[t7343,t177]) ).
cnf(t1504,plain,
member(not_subclass_element(sF7,null_class),x) = sF0,
inference(orient,[status(thm)],[t7344]) ).
cnf(t7949,plain,
sF1 = sF0,
inference(step,[status(thm)],[t7948,t1504]) ).
cnf(t6144,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t7949]) ).
cnf(t7974,plain,
true = sF0,
inference(step,[status(thm)],[t199,t6144]) ).
cnf(t6169,plain,
true = sF0,
inference(orient,[status(thm)],[t7974]) ).
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,c141,c142,c143]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t6169]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t177]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET098-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 09:46:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.55/3.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.55/3.72 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------