%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET061-7 : 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 02:41:49 PM UTC 2026
% Result : Unsatisfiable 7.96s 1.57s
% Output : Proof 7.96s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t101,axiom,
sF0 = member(z,null_class),
introduced(definition) ).
cnf(f102,negated_conjecture,
member(z,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_null_class_1) ).
fof(f102_nnf,plain,
member(z,null_class),
inference(nnf_transformation,[status(thm)],[f102]) ).
cnf(c102,plain,
member(z,null_class),
inference(cnf_transformation,[status(esa)],[f102_nnf]) ).
cnf(t6,plain,
member(z,null_class) = true,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t108,plain,
member(z,null_class) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t198,plain,
sF0 = true,
inference(step,[status(thm)],[t101,t108]) ).
cnf(t115,plain,
true = sF0,
inference(orient,[status(thm)],[t198]) ).
cnf(t210,plain,
member(z,null_class) = sF0,
inference(step,[status(thm)],[t108,t115]) ).
cnf(t127,plain,
member(z,null_class) = sF0,
inference(orient,[status(thm)],[t210]) ).
cnf(f101,axiom,
~ member(Y,intersection(complement(X),X)),
file('/export/starexec/sandbox2/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(t18,plain,
member(X1,intersection(complement(X2),X2)) = false,
inference(equality_encoding,[status(esa)],[c101]) ).
cnf(t145,plain,
member(X1,intersection(complement(X2),X2)) = false,
inference(orient,[status(thm)],[t18]) ).
cnf(t21,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t226,plain,
ifeq(eq(X1,X2),sF0,X1,X2) = X2,
inference(step,[status(thm)],[t21,t115]) ).
cnf(t156,plain,
ifeq(eq(X1,X2),sF0,X1,X2) = X2,
inference(orient,[status(thm)],[t226]) ).
cnf(f65,axiom,
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f65_nnf,plain,
! [X] :
( member(regular(X),X)
| X = null_class ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [X] :
( member(regular(X),X)
| X = null_class ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(t28,plain,
or(eq(X1,null_class),member(regular(X1),X1)) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t241,plain,
or(eq(X1,null_class),member(regular(X1),X1)) = sF0,
inference(step,[status(thm)],[t28,t115]) ).
cnf(t178,plain,
or(eq(X1,null_class),member(regular(X1),X1)) = sF0,
inference(orient,[status(thm)],[t241]) ).
cnf(t179,plain,
sF0 = or(eq(intersection(complement(X1),X1),null_class),false),
inference(cp,[status(thm)],[t178,t145]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t109,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t242,plain,
sF0 = eq(intersection(complement(X1),X1),null_class),
inference(step,[status(thm)],[t179,t109]) ).
cnf(t180,plain,
eq(intersection(complement(X1),X1),null_class) = sF0,
inference(orient,[status(thm)],[t242]) ).
cnf(t181,plain,
null_class = ifeq(sF0,sF0,intersection(complement(X1),X1),null_class),
inference(cp,[status(thm)],[t156,t180]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t138,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t243,plain,
null_class = intersection(complement(X1),X1),
inference(step,[status(thm)],[t181,t138]) ).
cnf(t182,plain,
intersection(complement(X1),X1) = null_class,
inference(orient,[status(thm)],[t243]) ).
cnf(t244,plain,
member(X1,null_class) = false,
inference(step,[status(thm)],[t145,t182]) ).
cnf(t183,plain,
member(X1,null_class) = false,
inference(rw,[status(thm)],[t244]) ).
cnf(t185,plain,
member(X1,null_class) = false,
inference(orient,[status(thm)],[t183]) ).
cnf(t245,plain,
false = sF0,
inference(step,[status(thm)],[t127,t185]) ).
cnf(t186,plain,
false = sF0,
inference(rw,[status(thm)],[t245]) ).
cnf(t188,plain,
false = sF0,
inference(orient,[status(thm)],[t186]) ).
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(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,c101]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t115]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t188]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET061-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 09:34:29 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.96/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.96/1.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------