%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET080-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 02:42:01 PM UTC 2026
% Result : Unsatisfiable 5.57s 6.26s
% Output : Proof 5.57s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t92,axiom,
sF2 = ifeq(member(null_class,unordered_pair(null_class,null_class)),true,false,true),
introduced(definition) ).
cnf(t90,axiom,
sF0 = unordered_pair(null_class,null_class),
introduced(definition) ).
cnf(t104,plain,
unordered_pair(null_class,null_class) = sF0,
inference(orient,[status(thm)],[t90]) ).
cnf(t1187,plain,
sF2 = ifeq(member(null_class,sF0),true,false,true),
inference(step,[status(thm)],[t92,t104]) ).
cnf(f91,negated_conjecture,
~ member(null_class,singleton(null_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_class_in_its_singleton_1) ).
fof(f91_nnf,plain,
~ member(null_class,singleton(null_class)),
inference(nnf_transformation,[status(thm)],[f91]) ).
fof(f91_sk,plain,
~ member(null_class,singleton(null_class)),
inference(skolemisation,[status(esa)],[f91_nnf]) ).
cnf(c91,plain,
~ member(null_class,singleton(null_class)),
inference(cnf_transformation,[status(esa)],[f91_sk]) ).
cnf(u11,axiom,
member(null_class,singleton(null_class)) = false,
inference(equality_encoding,[status(esa)],[c91]) ).
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(t12,plain,
member(null_class,unordered_pair(null_class,null_class)) = false,
inference(definition_unfolding,[status(thm)],[u11,d0]) ).
cnf(t1171,plain,
member(null_class,sF0) = false,
inference(step,[status(thm)],[t12,t104]) ).
cnf(t106,plain,
member(null_class,sF0) = false,
inference(orient,[status(thm)],[t1171]) ).
cnf(t91,axiom,
sF1 = member(null_class,unordered_pair(null_class,null_class)),
introduced(definition) ).
cnf(t1172,plain,
sF1 = member(null_class,sF0),
inference(step,[status(thm)],[t91,t104]) ).
cnf(t1173,plain,
sF1 = false,
inference(step,[status(thm)],[t1172,t106]) ).
cnf(t112,plain,
false = sF1,
inference(orient,[status(thm)],[t1173]) ).
cnf(t1179,plain,
member(null_class,sF0) = sF1,
inference(step,[status(thm)],[t106,t112]) ).
cnf(t118,plain,
member(null_class,sF0) = sF1,
inference(orient,[status(thm)],[t1179]) ).
cnf(t1188,plain,
sF2 = ifeq(sF1,true,false,true),
inference(step,[status(thm)],[t1187,t118]) ).
cnf(t1189,plain,
sF2 = ifeq(sF1,true,sF1,true),
inference(step,[status(thm)],[t1188,t112]) ).
cnf(u9,axiom,
ifeq(member(null_class,singleton(null_class)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(t32,plain,
ifeq(member(null_class,unordered_pair(null_class,null_class)),true,false,true) = true,
inference(definition_unfolding,[status(thm)],[u9,d0]) ).
cnf(t1184,plain,
ifeq(member(null_class,sF0),true,false,true) = true,
inference(step,[status(thm)],[t32,t104]) ).
cnf(t1185,plain,
ifeq(sF1,true,false,true) = true,
inference(step,[status(thm)],[t1184,t118]) ).
cnf(t1186,plain,
ifeq(sF1,true,sF1,true) = true,
inference(step,[status(thm)],[t1185,t112]) ).
cnf(t173,plain,
ifeq(sF1,true,sF1,true) = true,
inference(orient,[status(thm)],[t1186]) ).
cnf(t1190,plain,
sF2 = true,
inference(step,[status(thm)],[t1189,t173]) ).
cnf(t176,plain,
true = sF2,
inference(orient,[status(thm)],[t1190]) ).
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(t41,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t1280,plain,
ifeq(member(X1,universal_class),sF2,member(X1,unordered_pair(X1,X2)),true) = true,
inference(step,[status(thm)],[t41,t176]) ).
cnf(t1281,plain,
ifeq(member(X1,universal_class),sF2,member(X1,unordered_pair(X1,X2)),sF2) = true,
inference(step,[status(thm)],[t1280,t176]) ).
cnf(t1282,plain,
ifeq(member(X1,universal_class),sF2,member(X1,unordered_pair(X1,X2)),sF2) = sF2,
inference(step,[status(thm)],[t1281,t176]) ).
cnf(t357,plain,
ifeq(member(X1,universal_class),sF2,member(X1,unordered_pair(X1,X2)),sF2) = sF2,
inference(orient,[status(thm)],[t1282]) ).
cnf(t359,plain,
sF2 = ifeq(member(null_class,universal_class),sF2,member(null_class,sF0),sF2),
inference(cp,[status(thm)],[t357,t104]) ).
cnf(t1285,plain,
sF2 = ifeq(member(null_class,universal_class),sF2,sF1,sF2),
inference(step,[status(thm)],[t359,t118]) ).
cnf(t370,plain,
ifeq(member(null_class,universal_class),sF2,sF1,sF2) = sF2,
inference(orient,[status(thm)],[t1285]) ).
cnf(t942,plain,
ifeq(sF2,sF2,sF1,sF2) = sF2,
inference(rw,[status(thm)],[t370]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t105,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t1498,plain,
sF1 = sF2,
inference(step,[status(thm)],[t942,t105]) ).
cnf(t955,plain,
sF2 = sF1,
inference(orient,[status(thm)],[t1498]) ).
cnf(t1533,plain,
true = sF1,
inference(step,[status(thm)],[t176,t955]) ).
cnf(t990,plain,
true = sF1,
inference(orient,[status(thm)],[t1533]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c91]) ).
cnf(g0_0,plain,
sF1 != false,
inference(rw,[status(thm)],[goal_0,t990]) ).
cnf(g0_1,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_0,t112]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET080-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n020.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 09:39:54 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.57/6.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.57/6.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------