%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 02:42:14 PM UTC 2026
% Result : Unsatisfiable 17.48s 2.79s
% Output : Proof 17.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 29
% Syntax : Number of formulae : 228 ( 184 unt; 0 def)
% Number of atoms : 280 ( 203 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 135 ( 83 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 11 con; 0-4 aty)
% Number of variables : 208 ( 40 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t150,axiom,
sF1 = ifeq(x,null_class,false,true),
introduced(definition) ).
cnf(t149,axiom,
sF0 = eq(x,null_class),
introduced(definition) ).
cnf(f143,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_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(t163,plain,
eq(x,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t6827,plain,
sF0 = false,
inference(step,[status(thm)],[t149,t163]) ).
cnf(t174,plain,
false = sF0,
inference(orient,[status(thm)],[t6827]) ).
cnf(t6839,plain,
sF1 = ifeq(x,null_class,sF0,true),
inference(step,[status(thm)],[t150,t174]) ).
cnf(t17,plain,
ifeq(x,null_class,false,true) = true,
inference(equality_encoding,[status(esa)],[c143]) ).
cnf(t6837,plain,
ifeq(x,null_class,sF0,true) = true,
inference(step,[status(thm)],[t17,t174]) ).
cnf(t189,plain,
ifeq(x,null_class,sF0,true) = true,
inference(orient,[status(thm)],[t6837]) ).
cnf(t6840,plain,
sF1 = true,
inference(step,[status(thm)],[t6839,t189]) ).
cnf(t196,plain,
true = sF1,
inference(orient,[status(thm)],[t6840]) ).
cnf(f20,axiom,
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f20_nnf,plain,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t61,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t6985,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X2),true) = true,
inference(step,[status(thm)],[t61,t196]) ).
cnf(t6986,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X2),sF1) = true,
inference(step,[status(thm)],[t6985,t196]) ).
cnf(t6987,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X2),sF1) = sF1,
inference(step,[status(thm)],[t6986,t196]) ).
cnf(t472,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X2),sF1) = sF1,
inference(orient,[status(thm)],[t6987]) ).
cnf(t156,axiom,
sF7 = intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),
introduced(definition) ).
cnf(t151,axiom,
sF2 = not_subclass_element(x,null_class),
introduced(definition) ).
cnf(t185,plain,
not_subclass_element(x,null_class) = sF2,
inference(orient,[status(thm)],[t151]) ).
cnf(t7051,plain,
sF7 = intersection(complement(unordered_pair(sF2,not_subclass_element(x,null_class))),x),
inference(step,[status(thm)],[t156,t185]) ).
cnf(t7052,plain,
sF7 = intersection(complement(unordered_pair(sF2,sF2)),x),
inference(step,[status(thm)],[t7051,t185]) ).
cnf(t152,axiom,
sF3 = unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
introduced(definition) ).
cnf(t6895,plain,
sF3 = unordered_pair(sF2,not_subclass_element(x,null_class)),
inference(step,[status(thm)],[t152,t185]) ).
cnf(t6896,plain,
sF3 = unordered_pair(sF2,sF2),
inference(step,[status(thm)],[t6895,t185]) ).
cnf(t272,plain,
unordered_pair(sF2,sF2) = sF3,
inference(orient,[status(thm)],[t6896]) ).
cnf(t7053,plain,
sF7 = intersection(complement(sF3),x),
inference(step,[status(thm)],[t7052,t272]) ).
cnf(t155,axiom,
sF6 = complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),
introduced(definition) ).
cnf(t6910,plain,
sF6 = complement(unordered_pair(sF2,not_subclass_element(x,null_class))),
inference(step,[status(thm)],[t155,t185]) ).
cnf(t6911,plain,
sF6 = complement(unordered_pair(sF2,sF2)),
inference(step,[status(thm)],[t6910,t185]) ).
cnf(t6912,plain,
sF6 = complement(sF3),
inference(step,[status(thm)],[t6911,t272]) ).
cnf(t316,plain,
complement(sF3) = sF6,
inference(orient,[status(thm)],[t6912]) ).
cnf(t7054,plain,
sF7 = intersection(sF6,x),
inference(step,[status(thm)],[t7053,t316]) ).
cnf(t721,plain,
intersection(sF6,x) = sF7,
inference(orient,[status(thm)],[t7054]) ).
cnf(t722,plain,
sF1 = ifeq(member(X1,sF7),sF1,member(X1,sF6),sF1),
inference(cp,[status(thm)],[t472,t721]) ).
cnf(t726,plain,
ifeq(member(X1,sF7),sF1,member(X1,sF6),sF1) = sF1,
inference(orient,[status(thm)],[t722]) ).
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(t138,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(t7846,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)],[t138,t196]) ).
cnf(t6021,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)],[t7846]) ).
cnf(t6831,plain,
eq(x,null_class) = sF0,
inference(step,[status(thm)],[t163,t174]) ).
cnf(t178,plain,
eq(x,null_class) = sF0,
inference(orient,[status(thm)],[t6831]) ).
cnf(t6022,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)],[t6021,t178]) ).
cnf(t7847,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)],[t6022,t185]) ).
cnf(t7848,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)],[t7847,t185]) ).
cnf(t7849,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)],[t7848,t272]) ).
cnf(t7850,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)],[t7849,t316]) ).
cnf(t7851,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)],[t7850,t721]) ).
cnf(f141,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).
fof(f141_nnf,plain,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(nnf_transformation,[status(thm)],[f141]) ).
cnf(c141,plain,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(cnf_transformation,[status(esa)],[f141_nnf]) ).
cnf(u31,axiom,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(equality_encoding,[status(esa)],[c141]) ).
cnf(t91,plain,
not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(definition_unfolding,[status(thm)],[u31,d0]) ).
cnf(t7260,plain,
not_subclass_element(intersection(complement(unordered_pair(sF2,not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(step,[status(thm)],[t91,t185]) ).
cnf(t7261,plain,
not_subclass_element(intersection(complement(unordered_pair(sF2,sF2)),x),null_class) = not_subclass_element(x,null_class),
inference(step,[status(thm)],[t7260,t185]) ).
cnf(t7262,plain,
not_subclass_element(intersection(complement(sF3),x),null_class) = not_subclass_element(x,null_class),
inference(step,[status(thm)],[t7261,t272]) ).
cnf(t7263,plain,
not_subclass_element(intersection(sF6,x),null_class) = not_subclass_element(x,null_class),
inference(step,[status(thm)],[t7262,t316]) ).
cnf(t7264,plain,
not_subclass_element(sF7,null_class) = not_subclass_element(x,null_class),
inference(step,[status(thm)],[t7263,t721]) ).
cnf(t7265,plain,
not_subclass_element(sF7,null_class) = sF2,
inference(step,[status(thm)],[t7264,t185]) ).
cnf(t1501,plain,
not_subclass_element(sF7,null_class) = sF2,
inference(orient,[status(thm)],[t7265]) ).
cnf(t7852,plain,
sF1 = or(member(sF2,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)],[t7851,t1501]) ).
cnf(t7853,plain,
sF1 = or(member(sF2,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)],[t7852,t185]) ).
cnf(t7854,plain,
sF1 = or(member(sF2,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)],[t7853,t185]) ).
cnf(t7855,plain,
sF1 = or(member(sF2,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)],[t7854,t272]) ).
cnf(t7856,plain,
sF1 = or(member(sF2,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)],[t7855,t316]) ).
cnf(t7857,plain,
sF1 = or(member(sF2,sF7),or(eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),sF0)),
inference(step,[status(thm)],[t7856,t721]) ).
cnf(t9,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t167,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t6835,plain,
or(X1,sF0) = X1,
inference(step,[status(thm)],[t167,t174]) ).
cnf(t182,plain,
or(X1,sF0) = X1,
inference(rw,[status(thm)],[t6835]) ).
cnf(t186,plain,
or(X1,sF0) = X1,
inference(orient,[status(thm)],[t182]) ).
cnf(t7858,plain,
sF1 = or(member(sF2,sF7),eq(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x)),
inference(step,[status(thm)],[t7857,t186]) ).
cnf(t7859,plain,
sF1 = or(member(sF2,sF7),eq(unordered_pair(sF2,not_subclass_element(x,null_class)),x)),
inference(step,[status(thm)],[t7858,t185]) ).
cnf(t7860,plain,
sF1 = or(member(sF2,sF7),eq(unordered_pair(sF2,sF2),x)),
inference(step,[status(thm)],[t7859,t185]) ).
cnf(t7861,plain,
sF1 = or(member(sF2,sF7),eq(sF3,x)),
inference(step,[status(thm)],[t7860,t272]) ).
cnf(f142,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_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(u37,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)],[u37,d0]) ).
cnf(t6913,plain,
eq(unordered_pair(sF2,not_subclass_element(x,null_class)),x) = false,
inference(step,[status(thm)],[t42,t185]) ).
cnf(t6914,plain,
eq(unordered_pair(sF2,sF2),x) = false,
inference(step,[status(thm)],[t6913,t185]) ).
cnf(t6915,plain,
eq(sF3,x) = false,
inference(step,[status(thm)],[t6914,t272]) ).
cnf(t6916,plain,
eq(sF3,x) = sF0,
inference(step,[status(thm)],[t6915,t174]) ).
cnf(t320,plain,
eq(sF3,x) = sF0,
inference(orient,[status(thm)],[t6916]) ).
cnf(t7862,plain,
sF1 = or(member(sF2,sF7),sF0),
inference(step,[status(thm)],[t7861,t320]) ).
cnf(t7863,plain,
sF1 = member(sF2,sF7),
inference(step,[status(thm)],[t7862,t186]) ).
cnf(t6048,plain,
member(sF2,sF7) = sF1,
inference(orient,[status(thm)],[t7863]) ).
cnf(t6055,plain,
sF1 = ifeq(sF1,sF1,member(sF2,sF6),sF1),
inference(cp,[status(thm)],[t726,t6048]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t188,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t7864,plain,
sF1 = member(sF2,sF6),
inference(step,[status(thm)],[t6055,t188]) ).
cnf(t24,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t6871,plain,
ifeq(not(X1),sF1,X1,false) = false,
inference(step,[status(thm)],[t24,t196]) ).
cnf(t6872,plain,
ifeq(not(X1),sF1,X1,sF0) = false,
inference(step,[status(thm)],[t6871,t174]) ).
cnf(t6873,plain,
ifeq(not(X1),sF1,X1,sF0) = sF0,
inference(step,[status(thm)],[t6872,t174]) ).
cnf(t232,plain,
ifeq(not(X1),sF1,X1,sF0) = sF0,
inference(orient,[status(thm)],[t6873]) ).
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(t58,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t6952,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF1,
inference(step,[status(thm)],[t58,t196]) ).
cnf(t399,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF1,
inference(orient,[status(thm)],[t6952]) ).
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(t64,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t7009,plain,
ifeq(member(X1,universal_class),sF1,member(X1,unordered_pair(X1,X2)),true) = true,
inference(step,[status(thm)],[t64,t196]) ).
cnf(t7010,plain,
ifeq(member(X1,universal_class),sF1,member(X1,unordered_pair(X1,X2)),sF1) = true,
inference(step,[status(thm)],[t7009,t196]) ).
cnf(t7011,plain,
ifeq(member(X1,universal_class),sF1,member(X1,unordered_pair(X1,X2)),sF1) = sF1,
inference(step,[status(thm)],[t7010,t196]) ).
cnf(t576,plain,
ifeq(member(X1,universal_class),sF1,member(X1,unordered_pair(X1,X2)),sF1) = sF1,
inference(orient,[status(thm)],[t7011]) ).
cnf(f0,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/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(t95,plain,
ifeq(subclass(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t7308,plain,
ifeq(subclass(X1,X2),sF1,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t95,t196]) ).
cnf(t7309,plain,
ifeq(subclass(X1,X2),sF1,ifeq(member(X3,X1),sF1,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t7308,t196]) ).
cnf(t7310,plain,
ifeq(subclass(X1,X2),sF1,ifeq(member(X3,X1),sF1,member(X3,X2),sF1),true) = true,
inference(step,[status(thm)],[t7309,t196]) ).
cnf(t7311,plain,
ifeq(subclass(X1,X2),sF1,ifeq(member(X3,X1),sF1,member(X3,X2),sF1),sF1) = true,
inference(step,[status(thm)],[t7310,t196]) ).
cnf(t7312,plain,
ifeq(subclass(X1,X2),sF1,ifeq(member(X3,X1),sF1,member(X3,X2),sF1),sF1) = sF1,
inference(step,[status(thm)],[t7311,t196]) ).
cnf(t1695,plain,
ifeq(subclass(X1,X2),sF1,ifeq(member(X3,X1),sF1,member(X3,X2),sF1),sF1) = sF1,
inference(orient,[status(thm)],[t7312]) ).
cnf(f3,axiom,
subclass(X,universal_class),
file('/export/starexec/sandbox/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(t172,plain,
subclass(X1,universal_class) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t6854,plain,
subclass(X1,universal_class) = sF1,
inference(step,[status(thm)],[t172,t196]) ).
cnf(t212,plain,
subclass(X1,universal_class) = sF1,
inference(orient,[status(thm)],[t6854]) ).
cnf(t1702,plain,
sF1 = ifeq(sF1,sF1,ifeq(member(X1,X2),sF1,member(X1,universal_class),sF1),sF1),
inference(cp,[status(thm)],[t1695,t212]) ).
cnf(t7461,plain,
sF1 = ifeq(member(X1,X2),sF1,member(X1,universal_class),sF1),
inference(step,[status(thm)],[t1702,t188]) ).
cnf(t2963,plain,
ifeq(member(X1,X2),sF1,member(X1,universal_class),sF1) = sF1,
inference(orient,[status(thm)],[t7461]) ).
cnf(f105,axiom,
( member(not_subclass_element(Z,null_class),Z)
| Z = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_unique) ).
fof(f105_nnf,plain,
! [Z] :
( member(not_subclass_element(Z,null_class),Z)
| Z = null_class ),
inference(nnf_transformation,[status(thm)],[f105]) ).
fof(f105_sk,plain,
! [Z] :
( member(not_subclass_element(Z,null_class),Z)
| Z = null_class ),
inference(skolemisation,[status(esa)],[f105_nnf]) ).
cnf(c105,plain,
( member(not_subclass_element(X0,null_class),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(esa)],[f105_sk]) ).
cnf(t49,plain,
or(eq(X1,null_class),member(not_subclass_element(X1,null_class),X1)) = true,
inference(equality_encoding,[status(esa)],[c105]) ).
cnf(t6929,plain,
or(eq(X1,null_class),member(not_subclass_element(X1,null_class),X1)) = sF1,
inference(step,[status(thm)],[t49,t196]) ).
cnf(t337,plain,
or(eq(X1,null_class),member(not_subclass_element(X1,null_class),X1)) = sF1,
inference(orient,[status(thm)],[t6929]) ).
cnf(t338,plain,
sF1 = or(sF0,member(not_subclass_element(x,null_class),x)),
inference(cp,[status(thm)],[t337,t178]) ).
cnf(t11,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t169,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t6836,plain,
or(sF0,X1) = X1,
inference(step,[status(thm)],[t169,t174]) ).
cnf(t183,plain,
or(sF0,X1) = X1,
inference(rw,[status(thm)],[t6836]) ).
cnf(t187,plain,
or(sF0,X1) = X1,
inference(orient,[status(thm)],[t183]) ).
cnf(t6930,plain,
sF1 = member(not_subclass_element(x,null_class),x),
inference(step,[status(thm)],[t338,t187]) ).
cnf(t6931,plain,
sF1 = member(sF2,x),
inference(step,[status(thm)],[t6930,t185]) ).
cnf(t339,plain,
member(sF2,x) = sF1,
inference(orient,[status(thm)],[t6931]) ).
cnf(t2965,plain,
sF1 = ifeq(sF1,sF1,member(sF2,universal_class),sF1),
inference(cp,[status(thm)],[t2963,t339]) ).
cnf(t7462,plain,
sF1 = member(sF2,universal_class),
inference(step,[status(thm)],[t2965,t188]) ).
cnf(t2984,plain,
member(sF2,universal_class) = sF1,
inference(orient,[status(thm)],[t7462]) ).
cnf(t2992,plain,
sF1 = ifeq(sF1,sF1,member(sF2,unordered_pair(sF2,X1)),sF1),
inference(cp,[status(thm)],[t576,t2984]) ).
cnf(t7472,plain,
sF1 = member(sF2,unordered_pair(sF2,X1)),
inference(step,[status(thm)],[t2992,t188]) ).
cnf(t3052,plain,
member(sF2,unordered_pair(sF2,X1)) = sF1,
inference(orient,[status(thm)],[t7472]) ).
cnf(t3053,plain,
sF1 = member(sF2,sF3),
inference(cp,[status(thm)],[t3052,t272]) ).
cnf(t3062,plain,
member(sF2,sF3) = sF1,
inference(orient,[status(thm)],[t3053]) ).
cnf(t3063,plain,
sF1 = or(not(member(sF2,complement(sF3))),not(sF1)),
inference(cp,[status(thm)],[t399,t3062]) ).
cnf(t7473,plain,
sF1 = or(not(member(sF2,sF6)),not(sF1)),
inference(step,[status(thm)],[t3063,t316]) ).
cnf(t3,plain,
not(true) = false,
introduced(definition) ).
cnf(t161,plain,
not(true) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t6829,plain,
not(true) = sF0,
inference(step,[status(thm)],[t161,t174]) ).
cnf(t176,plain,
not(true) = sF0,
inference(orient,[status(thm)],[t6829]) ).
cnf(t6845,plain,
not(sF1) = sF0,
inference(step,[status(thm)],[t176,t196]) ).
cnf(t201,plain,
not(sF1) = sF0,
inference(rw,[status(thm)],[t6845]) ).
cnf(t227,plain,
not(sF1) = sF0,
inference(orient,[status(thm)],[t201]) ).
cnf(t7474,plain,
sF1 = or(not(member(sF2,sF6)),sF0),
inference(step,[status(thm)],[t7473,t227]) ).
cnf(t7475,plain,
sF1 = not(member(sF2,sF6)),
inference(step,[status(thm)],[t7474,t186]) ).
cnf(t3070,plain,
not(member(sF2,sF6)) = sF1,
inference(orient,[status(thm)],[t7475]) ).
cnf(t3071,plain,
sF0 = ifeq(sF1,sF1,member(sF2,sF6),sF0),
inference(cp,[status(thm)],[t232,t3070]) ).
cnf(t7476,plain,
sF0 = member(sF2,sF6),
inference(step,[status(thm)],[t3071,t188]) ).
cnf(t3072,plain,
member(sF2,sF6) = sF0,
inference(orient,[status(thm)],[t7476]) ).
cnf(t7865,plain,
sF1 = sF0,
inference(step,[status(thm)],[t7864,t3072]) ).
cnf(t6066,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t7865]) ).
cnf(t7890,plain,
true = sF0,
inference(step,[status(thm)],[t196,t6066]) ).
cnf(t6091,plain,
true = sF0,
inference(orient,[status(thm)],[t7890]) ).
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,c142,c143]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t6091]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t174]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 09:48:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.48/2.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.48/2.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------