%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET167-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 02:42:40 PM UTC 2026
% Result : Unsatisfiable 8.15s 1.46s
% Output : Proof 8.15s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t109,axiom,
sF0 = member(x,y),
introduced(definition) ).
cnf(f112,negated_conjecture,
member(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_union2_1) ).
fof(f112_nnf,plain,
member(x,y),
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
member(x,y),
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(t6,plain,
member(x,y) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t124,plain,
member(x,y) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t1321,plain,
sF0 = true,
inference(step,[status(thm)],[t109,t124]) ).
cnf(t130,plain,
true = sF0,
inference(orient,[status(thm)],[t1321]) ).
cnf(t114,axiom,
sF5 = member(x,complement(intersection(complement(y),complement(z)))),
introduced(definition) ).
cnf(t110,axiom,
sF1 = complement(y),
introduced(definition) ).
cnf(t120,plain,
complement(y) = sF1,
inference(orient,[status(thm)],[t110]) ).
cnf(t1378,plain,
sF5 = member(x,complement(intersection(sF1,complement(z)))),
inference(step,[status(thm)],[t114,t120]) ).
cnf(t111,axiom,
sF2 = complement(z),
introduced(definition) ).
cnf(t121,plain,
complement(z) = sF2,
inference(orient,[status(thm)],[t111]) ).
cnf(t1379,plain,
sF5 = member(x,complement(intersection(sF1,sF2))),
inference(step,[status(thm)],[t1378,t121]) ).
cnf(t112,axiom,
sF3 = intersection(complement(y),complement(z)),
introduced(definition) ).
cnf(t1343,plain,
sF3 = intersection(sF1,complement(z)),
inference(step,[status(thm)],[t112,t120]) ).
cnf(t1344,plain,
sF3 = intersection(sF1,sF2),
inference(step,[status(thm)],[t1343,t121]) ).
cnf(t156,plain,
intersection(sF1,sF2) = sF3,
inference(orient,[status(thm)],[t1344]) ).
cnf(t1380,plain,
sF5 = member(x,complement(sF3)),
inference(step,[status(thm)],[t1379,t156]) ).
cnf(t113,axiom,
sF4 = complement(intersection(complement(y),complement(z))),
introduced(definition) ).
cnf(t1347,plain,
sF4 = complement(intersection(sF1,complement(z))),
inference(step,[status(thm)],[t113,t120]) ).
cnf(t1348,plain,
sF4 = complement(intersection(sF1,sF2)),
inference(step,[status(thm)],[t1347,t121]) ).
cnf(t1349,plain,
sF4 = complement(sF3),
inference(step,[status(thm)],[t1348,t156]) ).
cnf(t161,plain,
complement(sF3) = sF4,
inference(orient,[status(thm)],[t1349]) ).
cnf(t1381,plain,
sF5 = member(x,sF4),
inference(step,[status(thm)],[t1380,t161]) ).
cnf(f113,negated_conjecture,
~ member(x,union(y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_union2_2) ).
fof(f113_nnf,plain,
~ member(x,union(y,z)),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
~ member(x,union(y,z)),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
~ member(x,union(y,z)),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(u36,axiom,
member(x,union(y,z)) = false,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(f25,axiom,
complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f25_nnf,plain,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(d2,axiom,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t31,plain,
member(x,complement(intersection(complement(y),complement(z)))) = false,
inference(definition_unfolding,[status(thm)],[u36,d2]) ).
cnf(t1371,plain,
member(x,complement(intersection(sF1,complement(z)))) = false,
inference(step,[status(thm)],[t31,t120]) ).
cnf(t1372,plain,
member(x,complement(intersection(sF1,sF2))) = false,
inference(step,[status(thm)],[t1371,t121]) ).
cnf(t1373,plain,
member(x,complement(sF3)) = false,
inference(step,[status(thm)],[t1372,t156]) ).
cnf(t1374,plain,
member(x,sF4) = false,
inference(step,[status(thm)],[t1373,t161]) ).
cnf(t208,plain,
member(x,sF4) = false,
inference(orient,[status(thm)],[t1374]) ).
cnf(t1382,plain,
sF5 = false,
inference(step,[status(thm)],[t1381,t208]) ).
cnf(t216,plain,
false = sF5,
inference(orient,[status(thm)],[t1382]) ).
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(t46,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t1428,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),true) = true,
inference(step,[status(thm)],[t46,t130]) ).
cnf(t1429,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),sF0) = true,
inference(step,[status(thm)],[t1428,t130]) ).
cnf(t1430,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),sF0) = sF0,
inference(step,[status(thm)],[t1429,t130]) ).
cnf(t301,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),sF0) = sF0,
inference(orient,[status(thm)],[t1430]) ).
cnf(t305,plain,
sF0 = ifeq(member(X1,sF3),sF0,member(X1,sF1),sF0),
inference(cp,[status(thm)],[t301,t156]) ).
cnf(t317,plain,
ifeq(member(X1,sF3),sF0,member(X1,sF1),sF0) = sF0,
inference(orient,[status(thm)],[t305]) ).
cnf(f24,axiom,
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f24_nnf,plain,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t58,plain,
ifeq(member(X1,universal_class),true,or(member(X1,complement(X2)),member(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t1519,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),true) = true,
inference(step,[status(thm)],[t58,t130]) ).
cnf(t1520,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),sF0) = true,
inference(step,[status(thm)],[t1519,t130]) ).
cnf(t1521,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),sF0) = sF0,
inference(step,[status(thm)],[t1520,t130]) ).
cnf(t541,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),sF0) = sF0,
inference(orient,[status(thm)],[t1521]) ).
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(t66,plain,
ifeq(subclass(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t1630,plain,
ifeq(subclass(X1,X2),sF0,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t66,t130]) ).
cnf(t1631,plain,
ifeq(subclass(X1,X2),sF0,ifeq(member(X3,X1),sF0,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t1630,t130]) ).
cnf(t1632,plain,
ifeq(subclass(X1,X2),sF0,ifeq(member(X3,X1),sF0,member(X3,X2),sF0),true) = true,
inference(step,[status(thm)],[t1631,t130]) ).
cnf(t1633,plain,
ifeq(subclass(X1,X2),sF0,ifeq(member(X3,X1),sF0,member(X3,X2),sF0),sF0) = true,
inference(step,[status(thm)],[t1632,t130]) ).
cnf(t1634,plain,
ifeq(subclass(X1,X2),sF0,ifeq(member(X3,X1),sF0,member(X3,X2),sF0),sF0) = sF0,
inference(step,[status(thm)],[t1633,t130]) ).
cnf(t773,plain,
ifeq(subclass(X1,X2),sF0,ifeq(member(X3,X1),sF0,member(X3,X2),sF0),sF0) = sF0,
inference(orient,[status(thm)],[t1634]) ).
cnf(t1333,plain,
member(x,y) = sF0,
inference(step,[status(thm)],[t124,t130]) ).
cnf(t142,plain,
member(x,y) = sF0,
inference(orient,[status(thm)],[t1333]) ).
cnf(t776,plain,
sF0 = ifeq(subclass(y,X1),sF0,ifeq(sF0,sF0,member(x,X1),sF0),sF0),
inference(cp,[status(thm)],[t773,t142]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t151,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t1653,plain,
sF0 = ifeq(subclass(y,X1),sF0,member(x,X1),sF0),
inference(step,[status(thm)],[t776,t151]) ).
cnf(t930,plain,
ifeq(subclass(y,X1),sF0,member(x,X1),sF0) = sF0,
inference(orient,[status(thm)],[t1653]) ).
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(t11,plain,
subclass(X1,universal_class) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t129,plain,
subclass(X1,universal_class) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t1335,plain,
subclass(X1,universal_class) = sF0,
inference(step,[status(thm)],[t129,t130]) ).
cnf(t146,plain,
subclass(X1,universal_class) = sF0,
inference(orient,[status(thm)],[t1335]) ).
cnf(t931,plain,
sF0 = ifeq(sF0,sF0,member(x,universal_class),sF0),
inference(cp,[status(thm)],[t930,t146]) ).
cnf(t1655,plain,
sF0 = member(x,universal_class),
inference(step,[status(thm)],[t931,t151]) ).
cnf(t935,plain,
member(x,universal_class) = sF0,
inference(orient,[status(thm)],[t1655]) ).
cnf(t946,plain,
sF0 = ifeq(sF0,sF0,or(member(x,complement(X1)),member(x,X1)),sF0),
inference(cp,[status(thm)],[t541,t935]) ).
cnf(t1719,plain,
sF0 = or(member(x,complement(X1)),member(x,X1)),
inference(step,[status(thm)],[t946,t151]) ).
cnf(t1225,plain,
or(member(x,complement(X1)),member(x,X1)) = sF0,
inference(orient,[status(thm)],[t1719]) ).
cnf(t1227,plain,
sF0 = or(member(x,sF4),member(x,sF3)),
inference(cp,[status(thm)],[t1225,t161]) ).
cnf(t1388,plain,
member(x,sF4) = sF5,
inference(step,[status(thm)],[t208,t216]) ).
cnf(t224,plain,
member(x,sF4) = sF5,
inference(orient,[status(thm)],[t1388]) ).
cnf(t1720,plain,
sF0 = or(sF5,member(x,sF3)),
inference(step,[status(thm)],[t1227,t224]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t127,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t1385,plain,
or(sF5,X1) = X1,
inference(step,[status(thm)],[t127,t216]) ).
cnf(t219,plain,
or(sF5,X1) = X1,
inference(rw,[status(thm)],[t1385]) ).
cnf(t228,plain,
or(sF5,X1) = X1,
inference(orient,[status(thm)],[t219]) ).
cnf(t1721,plain,
sF0 = member(x,sF3),
inference(step,[status(thm)],[t1720,t228]) ).
cnf(t1228,plain,
member(x,sF3) = sF0,
inference(orient,[status(thm)],[t1721]) ).
cnf(t1230,plain,
sF0 = ifeq(sF0,sF0,member(x,sF1),sF0),
inference(cp,[status(thm)],[t317,t1228]) ).
cnf(t1722,plain,
sF0 = member(x,sF1),
inference(step,[status(thm)],[t1230,t151]) ).
cnf(t17,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t1345,plain,
ifeq(not(X1),sF0,X1,false) = false,
inference(step,[status(thm)],[t17,t130]) ).
cnf(t157,plain,
ifeq(not(X1),sF0,X1,false) = false,
inference(orient,[status(thm)],[t1345]) ).
cnf(t222,plain,
ifeq(not(X1),sF0,X1,sF5) = false,
inference(rw,[status(thm)],[t157]) ).
cnf(t1391,plain,
ifeq(not(X1),sF0,X1,sF5) = sF5,
inference(step,[status(thm)],[t222,t216]) ).
cnf(t230,plain,
ifeq(not(X1),sF0,X1,sF5) = sF5,
inference(orient,[status(thm)],[t1391]) ).
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(t44,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t1411,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF0,
inference(step,[status(thm)],[t44,t130]) ).
cnf(t271,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF0,
inference(orient,[status(thm)],[t1411]) ).
cnf(t275,plain,
sF0 = or(not(member(x,complement(y))),not(sF0)),
inference(cp,[status(thm)],[t271,t142]) ).
cnf(t1412,plain,
sF0 = or(not(member(x,sF1)),not(sF0)),
inference(step,[status(thm)],[t275,t120]) ).
cnf(t3,plain,
not(true) = false,
introduced(definition) ).
cnf(t119,plain,
not(true) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t1328,plain,
not(sF0) = false,
inference(step,[status(thm)],[t119,t130]) ).
cnf(t137,plain,
not(sF0) = false,
inference(rw,[status(thm)],[t1328]) ).
cnf(t148,plain,
not(sF0) = false,
inference(orient,[status(thm)],[t137]) ).
cnf(t1386,plain,
not(sF0) = sF5,
inference(step,[status(thm)],[t148,t216]) ).
cnf(t220,plain,
not(sF0) = sF5,
inference(orient,[status(thm)],[t1386]) ).
cnf(t1413,plain,
sF0 = or(not(member(x,sF1)),sF5),
inference(step,[status(thm)],[t1412,t220]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t125,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t1384,plain,
or(X1,sF5) = X1,
inference(step,[status(thm)],[t125,t216]) ).
cnf(t218,plain,
or(X1,sF5) = X1,
inference(rw,[status(thm)],[t1384]) ).
cnf(t227,plain,
or(X1,sF5) = X1,
inference(orient,[status(thm)],[t218]) ).
cnf(t1414,plain,
sF0 = not(member(x,sF1)),
inference(step,[status(thm)],[t1413,t227]) ).
cnf(t279,plain,
not(member(x,sF1)) = sF0,
inference(orient,[status(thm)],[t1414]) ).
cnf(t280,plain,
sF5 = ifeq(sF0,sF0,member(x,sF1),sF5),
inference(cp,[status(thm)],[t230,t279]) ).
cnf(t1415,plain,
sF5 = member(x,sF1),
inference(step,[status(thm)],[t280,t151]) ).
cnf(t281,plain,
member(x,sF1) = sF5,
inference(orient,[status(thm)],[t1415]) ).
cnf(t1723,plain,
sF0 = sF5,
inference(step,[status(thm)],[t1722,t281]) ).
cnf(t1236,plain,
sF5 = sF0,
inference(orient,[status(thm)],[t1723]) ).
cnf(t1728,plain,
false = sF0,
inference(step,[status(thm)],[t216,t1236]) ).
cnf(t1241,plain,
false = sF0,
inference(orient,[status(thm)],[t1728]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c113]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t130]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t1241]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET167-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 10:06:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.15/1.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.15/1.46 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------