%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET132-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:42:32 PM UTC 2026
% Result : Unsatisfiable 10.52s 2.01s
% Output : Proof 10.52s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t91,axiom,
sF0 = member(u,universal_class),
introduced(definition) ).
cnf(f92,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_member_of_triple3_1) ).
fof(f92_nnf,plain,
member(u,universal_class),
inference(nnf_transformation,[status(thm)],[f92]) ).
cnf(c92,plain,
member(u,universal_class),
inference(cnf_transformation,[status(esa)],[f92_nnf]) ).
cnf(t6,plain,
member(u,universal_class) = true,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t116,plain,
member(u,universal_class) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t3024,plain,
sF0 = true,
inference(step,[status(thm)],[t91,t116]) ).
cnf(t122,plain,
true = sF0,
inference(orient,[status(thm)],[t3024]) ).
cnf(f20,axiom,
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/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(t38,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t3113,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),true) = true,
inference(step,[status(thm)],[t38,t122]) ).
cnf(t3114,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),sF0) = true,
inference(step,[status(thm)],[t3113,t122]) ).
cnf(t3115,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),sF0) = sF0,
inference(step,[status(thm)],[t3114,t122]) ).
cnf(t260,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),sF0) = sF0,
inference(orient,[status(thm)],[t3115]) ).
cnf(t99,axiom,
sF8 = intersection(complement(unordered_pair(u,u)),complement(null_class)),
introduced(definition) ).
cnf(t96,axiom,
sF5 = unordered_pair(u,u),
introduced(definition) ).
cnf(t143,plain,
unordered_pair(u,u) = sF5,
inference(orient,[status(thm)],[t96]) ).
cnf(t3061,plain,
sF8 = intersection(complement(sF5),complement(null_class)),
inference(step,[status(thm)],[t99,t143]) ).
cnf(t97,axiom,
sF6 = complement(unordered_pair(u,u)),
introduced(definition) ).
cnf(t3044,plain,
sF6 = complement(sF5),
inference(step,[status(thm)],[t97,t143]) ).
cnf(t149,plain,
complement(sF5) = sF6,
inference(orient,[status(thm)],[t3044]) ).
cnf(t3062,plain,
sF8 = intersection(sF6,complement(null_class)),
inference(step,[status(thm)],[t3061,t149]) ).
cnf(t98,axiom,
sF7 = complement(null_class),
introduced(definition) ).
cnf(t113,plain,
complement(null_class) = sF7,
inference(orient,[status(thm)],[t98]) ).
cnf(t3063,plain,
sF8 = intersection(sF6,sF7),
inference(step,[status(thm)],[t3062,t113]) ).
cnf(t185,plain,
intersection(sF6,sF7) = sF8,
inference(orient,[status(thm)],[t3063]) ).
cnf(t268,plain,
sF0 = ifeq(member(X1,sF8),sF0,member(X1,sF6),sF0),
inference(cp,[status(thm)],[t260,t185]) ).
cnf(t460,plain,
ifeq(member(X1,sF8),sF0,member(X1,sF6),sF0) = sF0,
inference(orient,[status(thm)],[t268]) ).
cnf(f24,axiom,
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox2/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(t49,plain,
ifeq(member(X1,universal_class),true,or(member(X1,complement(X2)),member(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t3214,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),true) = true,
inference(step,[status(thm)],[t49,t122]) ).
cnf(t3215,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),sF0) = true,
inference(step,[status(thm)],[t3214,t122]) ).
cnf(t3216,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),sF0) = sF0,
inference(step,[status(thm)],[t3215,t122]) ).
cnf(t613,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),sF0) = sF0,
inference(orient,[status(thm)],[t3216]) ).
cnf(t3036,plain,
member(u,universal_class) = sF0,
inference(step,[status(thm)],[t116,t122]) ).
cnf(t134,plain,
member(u,universal_class) = sF0,
inference(orient,[status(thm)],[t3036]) ).
cnf(t616,plain,
sF0 = ifeq(sF0,sF0,or(member(u,complement(X1)),member(u,X1)),sF0),
inference(cp,[status(thm)],[t613,t134]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t147,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t3320,plain,
sF0 = or(member(u,complement(X1)),member(u,X1)),
inference(step,[status(thm)],[t616,t147]) ).
cnf(t853,plain,
or(member(u,complement(X1)),member(u,X1)) = sF0,
inference(orient,[status(thm)],[t3320]) ).
cnf(t100,axiom,
sF9 = complement(intersection(complement(unordered_pair(u,u)),complement(null_class))),
introduced(definition) ).
cnf(t3074,plain,
sF9 = complement(intersection(complement(sF5),complement(null_class))),
inference(step,[status(thm)],[t100,t143]) ).
cnf(t3075,plain,
sF9 = complement(intersection(sF6,complement(null_class))),
inference(step,[status(thm)],[t3074,t149]) ).
cnf(t3076,plain,
sF9 = complement(intersection(sF6,sF7)),
inference(step,[status(thm)],[t3075,t113]) ).
cnf(t3077,plain,
sF9 = complement(sF8),
inference(step,[status(thm)],[t3076,t185]) ).
cnf(t203,plain,
complement(sF8) = sF9,
inference(orient,[status(thm)],[t3077]) ).
cnf(t857,plain,
sF0 = or(member(u,sF9),member(u,sF8)),
inference(cp,[status(thm)],[t853,t203]) ).
cnf(t862,plain,
or(member(u,sF9),member(u,sF8)) = sF0,
inference(orient,[status(thm)],[t857]) ).
cnf(t2656,plain,
or(false,member(u,sF8)) = sF0,
inference(rw,[status(thm)],[t862]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t119,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t3658,plain,
member(u,sF8) = sF0,
inference(step,[status(thm)],[t2656,t119]) ).
cnf(t2856,plain,
member(u,sF8) = sF0,
inference(orient,[status(thm)],[t3658]) ).
cnf(t2858,plain,
sF0 = ifeq(sF0,sF0,member(u,sF6),sF0),
inference(cp,[status(thm)],[t460,t2856]) ).
cnf(t3659,plain,
sF0 = member(u,sF6),
inference(step,[status(thm)],[t2858,t147]) ).
cnf(t16,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t3048,plain,
ifeq(not(X1),sF0,X1,false) = false,
inference(step,[status(thm)],[t16,t122]) ).
cnf(t159,plain,
ifeq(not(X1),sF0,X1,false) = false,
inference(orient,[status(thm)],[t3048]) ).
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(t36,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t3098,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF0,
inference(step,[status(thm)],[t36,t122]) ).
cnf(t231,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF0,
inference(orient,[status(thm)],[t3098]) ).
cnf(f8,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/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(t40,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t3129,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),true) = true,
inference(step,[status(thm)],[t40,t122]) ).
cnf(t3130,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = true,
inference(step,[status(thm)],[t3129,t122]) ).
cnf(t3131,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = sF0,
inference(step,[status(thm)],[t3130,t122]) ).
cnf(t319,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = sF0,
inference(orient,[status(thm)],[t3131]) ).
cnf(t324,plain,
sF0 = ifeq(member(u,universal_class),sF0,member(u,sF5),sF0),
inference(cp,[status(thm)],[t319,t143]) ).
cnf(t3132,plain,
sF0 = ifeq(sF0,sF0,member(u,sF5),sF0),
inference(step,[status(thm)],[t324,t134]) ).
cnf(t3133,plain,
sF0 = member(u,sF5),
inference(step,[status(thm)],[t3132,t147]) ).
cnf(t329,plain,
member(u,sF5) = sF0,
inference(orient,[status(thm)],[t3133]) ).
cnf(t330,plain,
sF0 = or(not(member(u,complement(sF5))),not(sF0)),
inference(cp,[status(thm)],[t231,t329]) ).
cnf(t3134,plain,
sF0 = or(not(member(u,sF6)),not(sF0)),
inference(step,[status(thm)],[t330,t149]) ).
cnf(t3,plain,
not(true) = false,
introduced(definition) ).
cnf(t112,plain,
not(true) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t3031,plain,
not(sF0) = false,
inference(step,[status(thm)],[t112,t122]) ).
cnf(t129,plain,
not(sF0) = false,
inference(rw,[status(thm)],[t3031]) ).
cnf(t140,plain,
not(sF0) = false,
inference(orient,[status(thm)],[t129]) ).
cnf(t3135,plain,
sF0 = or(not(member(u,sF6)),false),
inference(step,[status(thm)],[t3134,t140]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t117,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t3136,plain,
sF0 = not(member(u,sF6)),
inference(step,[status(thm)],[t3135,t117]) ).
cnf(t333,plain,
not(member(u,sF6)) = sF0,
inference(orient,[status(thm)],[t3136]) ).
cnf(t334,plain,
false = ifeq(sF0,sF0,member(u,sF6),false),
inference(cp,[status(thm)],[t159,t333]) ).
cnf(t3137,plain,
false = member(u,sF6),
inference(step,[status(thm)],[t334,t147]) ).
cnf(t335,plain,
member(u,sF6) = false,
inference(orient,[status(thm)],[t3137]) ).
cnf(t3660,plain,
sF0 = false,
inference(step,[status(thm)],[t3659,t335]) ).
cnf(t2867,plain,
false = sF0,
inference(orient,[status(thm)],[t3660]) ).
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(f93,negated_conjecture,
~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_member_of_triple3_2) ).
fof(f93_nnf,plain,
~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))),
inference(nnf_transformation,[status(thm)],[f93]) ).
fof(f93_sk,plain,
~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))),
inference(skolemisation,[status(esa)],[f93_nnf]) ).
cnf(c93,plain,
~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))),
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c93]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t122]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t2867]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET132-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 10:01:57 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.52/2.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.52/2.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------