%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET131-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 02:42:31 PM UTC 2026
% Result : Unsatisfiable 9.48s 1.76s
% Output : Proof 9.48s
% 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_triple2_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(t2763,plain,
sF0 = true,
inference(step,[status(thm)],[t91,t116]) ).
cnf(t122,plain,
true = sF0,
inference(orient,[status(thm)],[t2763]) ).
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(t2852,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),true) = true,
inference(step,[status(thm)],[t38,t122]) ).
cnf(t2853,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),sF0) = true,
inference(step,[status(thm)],[t2852,t122]) ).
cnf(t2854,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),sF0) = sF0,
inference(step,[status(thm)],[t2853,t122]) ).
cnf(t260,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X2),sF0) = sF0,
inference(orient,[status(thm)],[t2854]) ).
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(t2952,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),true) = true,
inference(step,[status(thm)],[t49,t122]) ).
cnf(t2953,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),sF0) = true,
inference(step,[status(thm)],[t2952,t122]) ).
cnf(t2954,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),sF0) = sF0,
inference(step,[status(thm)],[t2953,t122]) ).
cnf(t613,plain,
ifeq(member(X1,universal_class),sF0,or(member(X1,complement(X2)),member(X1,X2)),sF0) = sF0,
inference(orient,[status(thm)],[t2954]) ).
cnf(t16,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t2787,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)],[t2787]) ).
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(t2837,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)],[t2837]) ).
cnf(f21,axiom,
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/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(t39,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t2865,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X3),true) = true,
inference(step,[status(thm)],[t39,t122]) ).
cnf(t2866,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X3),sF0) = true,
inference(step,[status(thm)],[t2865,t122]) ).
cnf(t2867,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X3),sF0) = sF0,
inference(step,[status(thm)],[t2866,t122]) ).
cnf(t293,plain,
ifeq(member(X1,intersection(X2,X3)),sF0,member(X1,X3),sF0) = sF0,
inference(orient,[status(thm)],[t2867]) ).
cnf(f93,negated_conjecture,
~ member(u,set_builder(x,set_builder(u,set_builder(z,null_class)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_member_of_triple2_2) ).
fof(f93_nnf,plain,
~ member(u,set_builder(x,set_builder(u,set_builder(z,null_class)))),
inference(nnf_transformation,[status(thm)],[f93]) ).
fof(f93_sk,plain,
~ member(u,set_builder(x,set_builder(u,set_builder(z,null_class)))),
inference(skolemisation,[status(esa)],[f93_nnf]) ).
cnf(c93,plain,
~ member(u,set_builder(x,set_builder(u,set_builder(z,null_class)))),
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(u50,axiom,
member(u,set_builder(x,set_builder(u,set_builder(z,null_class)))) = false,
inference(equality_encoding,[status(esa)],[c93]) ).
cnf(f91,axiom,
union(singleton(X),Y) = set_builder(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f91_nnf,plain,
! [X,Y] : union(singleton(X),Y) = set_builder(X,Y),
inference(nnf_transformation,[status(thm)],[f91]) ).
fof(f91_sk,plain,
! [X,Y] : union(singleton(X),Y) = set_builder(X,Y),
inference(skolemisation,[status(esa)],[f91_nnf]) ).
cnf(c91,plain,
union(singleton(X0),X1) = set_builder(X0,X1),
inference(cnf_transformation,[status(esa)],[f91_sk]) ).
cnf(u8,axiom,
union(singleton(X0),X1) = set_builder(X0,X1),
inference(equality_encoding,[status(esa)],[c91]) ).
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(f25,axiom,
complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox2/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(d15,axiom,
complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))) = set_builder(X0,X1),
inference(definition_unfolding,[status(thm)],[u8,d0,d2]) ).
cnf(t75,plain,
member(u,complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))) = false,
inference(definition_unfolding,[status(thm)],[u50,d15]) ).
cnf(t92,axiom,
sF1 = unordered_pair(x,x),
introduced(definition) ).
cnf(t141,plain,
unordered_pair(x,x) = sF1,
inference(orient,[status(thm)],[t92]) ).
cnf(t3312,plain,
member(u,complement(intersection(complement(sF1),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))) = false,
inference(step,[status(thm)],[t75,t141]) ).
cnf(t93,axiom,
sF2 = complement(unordered_pair(x,x)),
introduced(definition) ).
cnf(t2781,plain,
sF2 = complement(sF1),
inference(step,[status(thm)],[t93,t141]) ).
cnf(t146,plain,
complement(sF1) = sF2,
inference(orient,[status(thm)],[t2781]) ).
cnf(t3313,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))) = false,
inference(step,[status(thm)],[t3312,t146]) ).
cnf(t94,axiom,
sF3 = unordered_pair(u,u),
introduced(definition) ).
cnf(t142,plain,
unordered_pair(u,u) = sF3,
inference(orient,[status(thm)],[t94]) ).
cnf(t3314,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(complement(sF3),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))) = false,
inference(step,[status(thm)],[t3313,t142]) ).
cnf(t95,axiom,
sF4 = complement(unordered_pair(u,u)),
introduced(definition) ).
cnf(t2782,plain,
sF4 = complement(sF3),
inference(step,[status(thm)],[t95,t142]) ).
cnf(t148,plain,
complement(sF3) = sF4,
inference(orient,[status(thm)],[t2782]) ).
cnf(t3315,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(sF4,complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))) = false,
inference(step,[status(thm)],[t3314,t148]) ).
cnf(t96,axiom,
sF5 = unordered_pair(z,z),
introduced(definition) ).
cnf(t143,plain,
unordered_pair(z,z) = sF5,
inference(orient,[status(thm)],[t96]) ).
cnf(t3316,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(sF4,complement(complement(intersection(complement(sF5),complement(null_class)))))))))) = false,
inference(step,[status(thm)],[t3315,t143]) ).
cnf(t97,axiom,
sF6 = complement(unordered_pair(z,z)),
introduced(definition) ).
cnf(t2783,plain,
sF6 = complement(sF5),
inference(step,[status(thm)],[t97,t143]) ).
cnf(t149,plain,
complement(sF5) = sF6,
inference(orient,[status(thm)],[t2783]) ).
cnf(t3317,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(sF4,complement(complement(intersection(sF6,complement(null_class)))))))))) = false,
inference(step,[status(thm)],[t3316,t149]) ).
cnf(t98,axiom,
sF7 = complement(null_class),
introduced(definition) ).
cnf(t113,plain,
complement(null_class) = sF7,
inference(orient,[status(thm)],[t98]) ).
cnf(t3318,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(sF4,complement(complement(intersection(sF6,sF7))))))))) = false,
inference(step,[status(thm)],[t3317,t113]) ).
cnf(t99,axiom,
sF8 = intersection(complement(unordered_pair(z,z)),complement(null_class)),
introduced(definition) ).
cnf(t2800,plain,
sF8 = intersection(complement(sF5),complement(null_class)),
inference(step,[status(thm)],[t99,t143]) ).
cnf(t2801,plain,
sF8 = intersection(sF6,complement(null_class)),
inference(step,[status(thm)],[t2800,t149]) ).
cnf(t2802,plain,
sF8 = intersection(sF6,sF7),
inference(step,[status(thm)],[t2801,t113]) ).
cnf(t185,plain,
intersection(sF6,sF7) = sF8,
inference(orient,[status(thm)],[t2802]) ).
cnf(t3319,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(sF4,complement(complement(sF8)))))))) = false,
inference(step,[status(thm)],[t3318,t185]) ).
cnf(t100,axiom,
sF9 = complement(intersection(complement(unordered_pair(z,z)),complement(null_class))),
introduced(definition) ).
cnf(t2813,plain,
sF9 = complement(intersection(complement(sF5),complement(null_class))),
inference(step,[status(thm)],[t100,t143]) ).
cnf(t2814,plain,
sF9 = complement(intersection(sF6,complement(null_class))),
inference(step,[status(thm)],[t2813,t149]) ).
cnf(t2815,plain,
sF9 = complement(intersection(sF6,sF7)),
inference(step,[status(thm)],[t2814,t113]) ).
cnf(t2816,plain,
sF9 = complement(sF8),
inference(step,[status(thm)],[t2815,t185]) ).
cnf(t203,plain,
complement(sF8) = sF9,
inference(orient,[status(thm)],[t2816]) ).
cnf(t3320,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(sF4,complement(sF9))))))) = false,
inference(step,[status(thm)],[t3319,t203]) ).
cnf(t101,axiom,
sF10 = complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))),
introduced(definition) ).
cnf(t2827,plain,
sF10 = complement(complement(intersection(complement(sF5),complement(null_class)))),
inference(step,[status(thm)],[t101,t143]) ).
cnf(t2828,plain,
sF10 = complement(complement(intersection(sF6,complement(null_class)))),
inference(step,[status(thm)],[t2827,t149]) ).
cnf(t2829,plain,
sF10 = complement(complement(intersection(sF6,sF7))),
inference(step,[status(thm)],[t2828,t113]) ).
cnf(t2830,plain,
sF10 = complement(complement(sF8)),
inference(step,[status(thm)],[t2829,t185]) ).
cnf(t2831,plain,
sF10 = complement(sF9),
inference(step,[status(thm)],[t2830,t203]) ).
cnf(t210,plain,
complement(sF9) = sF10,
inference(orient,[status(thm)],[t2831]) ).
cnf(t3321,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(sF4,sF10)))))) = false,
inference(step,[status(thm)],[t3320,t210]) ).
cnf(t2131,plain,
member(u,complement(intersection(sF2,complement(complement(intersection(sF4,sF10)))))) = false,
inference(orient,[status(thm)],[t3321]) ).
cnf(t2135,plain,
sF0 = ifeq(member(u,universal_class),sF0,or(false,member(u,intersection(sF2,complement(complement(intersection(sF4,sF10)))))),sF0),
inference(cp,[status(thm)],[t613,t2131]) ).
cnf(t2775,plain,
member(u,universal_class) = sF0,
inference(step,[status(thm)],[t116,t122]) ).
cnf(t134,plain,
member(u,universal_class) = sF0,
inference(orient,[status(thm)],[t2775]) ).
cnf(t3340,plain,
sF0 = ifeq(sF0,sF0,or(false,member(u,intersection(sF2,complement(complement(intersection(sF4,sF10)))))),sF0),
inference(step,[status(thm)],[t2135,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(t3341,plain,
sF0 = or(false,member(u,intersection(sF2,complement(complement(intersection(sF4,sF10)))))),
inference(step,[status(thm)],[t3340,t147]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t119,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t3342,plain,
sF0 = member(u,intersection(sF2,complement(complement(intersection(sF4,sF10))))),
inference(step,[status(thm)],[t3341,t119]) ).
cnf(t2479,plain,
member(u,intersection(sF2,complement(complement(intersection(sF4,sF10))))) = sF0,
inference(orient,[status(thm)],[t3342]) ).
cnf(t2481,plain,
sF0 = ifeq(sF0,sF0,member(u,complement(complement(intersection(sF4,sF10)))),sF0),
inference(cp,[status(thm)],[t293,t2479]) ).
cnf(t3359,plain,
sF0 = member(u,complement(complement(intersection(sF4,sF10)))),
inference(step,[status(thm)],[t2481,t147]) ).
cnf(t2550,plain,
member(u,complement(complement(intersection(sF4,sF10)))) = sF0,
inference(orient,[status(thm)],[t3359]) ).
cnf(t2551,plain,
sF0 = or(not(sF0),not(member(u,complement(intersection(sF4,sF10))))),
inference(cp,[status(thm)],[t231,t2550]) ).
cnf(t3,plain,
not(true) = false,
introduced(definition) ).
cnf(t112,plain,
not(true) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t2770,plain,
not(sF0) = false,
inference(step,[status(thm)],[t112,t122]) ).
cnf(t129,plain,
not(sF0) = false,
inference(rw,[status(thm)],[t2770]) ).
cnf(t140,plain,
not(sF0) = false,
inference(orient,[status(thm)],[t129]) ).
cnf(t3364,plain,
sF0 = or(false,not(member(u,complement(intersection(sF4,sF10))))),
inference(step,[status(thm)],[t2551,t140]) ).
cnf(t3365,plain,
sF0 = not(member(u,complement(intersection(sF4,sF10)))),
inference(step,[status(thm)],[t3364,t119]) ).
cnf(t2582,plain,
not(member(u,complement(intersection(sF4,sF10)))) = sF0,
inference(orient,[status(thm)],[t3365]) ).
cnf(t2583,plain,
false = ifeq(sF0,sF0,member(u,complement(intersection(sF4,sF10))),false),
inference(cp,[status(thm)],[t159,t2582]) ).
cnf(t3366,plain,
false = member(u,complement(intersection(sF4,sF10))),
inference(step,[status(thm)],[t2583,t147]) ).
cnf(t2584,plain,
member(u,complement(intersection(sF4,sF10))) = false,
inference(orient,[status(thm)],[t3366]) ).
cnf(t2588,plain,
sF0 = ifeq(member(u,universal_class),sF0,or(false,member(u,intersection(sF4,sF10))),sF0),
inference(cp,[status(thm)],[t613,t2584]) ).
cnf(t3373,plain,
sF0 = ifeq(sF0,sF0,or(false,member(u,intersection(sF4,sF10))),sF0),
inference(step,[status(thm)],[t2588,t134]) ).
cnf(t3374,plain,
sF0 = or(false,member(u,intersection(sF4,sF10))),
inference(step,[status(thm)],[t3373,t147]) ).
cnf(t3375,plain,
sF0 = member(u,intersection(sF4,sF10)),
inference(step,[status(thm)],[t3374,t119]) ).
cnf(t2603,plain,
member(u,intersection(sF4,sF10)) = sF0,
inference(orient,[status(thm)],[t3375]) ).
cnf(t2604,plain,
sF0 = ifeq(sF0,sF0,member(u,sF4),sF0),
inference(cp,[status(thm)],[t260,t2603]) ).
cnf(t3376,plain,
sF0 = member(u,sF4),
inference(step,[status(thm)],[t2604,t147]) ).
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(t2868,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),true) = true,
inference(step,[status(thm)],[t40,t122]) ).
cnf(t2869,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = true,
inference(step,[status(thm)],[t2868,t122]) ).
cnf(t2870,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = sF0,
inference(step,[status(thm)],[t2869,t122]) ).
cnf(t319,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = sF0,
inference(orient,[status(thm)],[t2870]) ).
cnf(t323,plain,
sF0 = ifeq(member(u,universal_class),sF0,member(u,sF3),sF0),
inference(cp,[status(thm)],[t319,t142]) ).
cnf(t2871,plain,
sF0 = ifeq(sF0,sF0,member(u,sF3),sF0),
inference(step,[status(thm)],[t323,t134]) ).
cnf(t2872,plain,
sF0 = member(u,sF3),
inference(step,[status(thm)],[t2871,t147]) ).
cnf(t329,plain,
member(u,sF3) = sF0,
inference(orient,[status(thm)],[t2872]) ).
cnf(t330,plain,
sF0 = or(not(member(u,complement(sF3))),not(sF0)),
inference(cp,[status(thm)],[t231,t329]) ).
cnf(t2873,plain,
sF0 = or(not(member(u,sF4)),not(sF0)),
inference(step,[status(thm)],[t330,t148]) ).
cnf(t2874,plain,
sF0 = or(not(member(u,sF4)),false),
inference(step,[status(thm)],[t2873,t140]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t117,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t2875,plain,
sF0 = not(member(u,sF4)),
inference(step,[status(thm)],[t2874,t117]) ).
cnf(t333,plain,
not(member(u,sF4)) = sF0,
inference(orient,[status(thm)],[t2875]) ).
cnf(t334,plain,
false = ifeq(sF0,sF0,member(u,sF4),false),
inference(cp,[status(thm)],[t159,t333]) ).
cnf(t2876,plain,
false = member(u,sF4),
inference(step,[status(thm)],[t334,t147]) ).
cnf(t335,plain,
member(u,sF4) = false,
inference(orient,[status(thm)],[t2876]) ).
cnf(t3377,plain,
sF0 = false,
inference(step,[status(thm)],[t3376,t335]) ).
cnf(t2612,plain,
false = sF0,
inference(orient,[status(thm)],[t3377]) ).
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(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,t2612]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET131-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % 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 10:03:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.48/1.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.48/1.76 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------