%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET064-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 02:41:54 PM UTC 2026
% Result : Unsatisfiable 4.55s 1.02s
% Output : Proof 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 43 unt; 0 def)
% Number of atoms : 59 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 43 ( 35 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 32 ( 4 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t109,axiom,
sF1 = ifeq(z,null_class,false,true),
introduced(definition) ).
cnf(t108,axiom,
sF0 = eq(z,null_class),
introduced(definition) ).
cnf(f105,negated_conjecture,
z != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_class_is_unique_1) ).
fof(f105_nnf,plain,
z != null_class,
inference(nnf_transformation,[status(thm)],[f105]) ).
fof(f105_sk,plain,
z != null_class,
inference(skolemisation,[status(esa)],[f105_nnf]) ).
cnf(c105,plain,
z != null_class,
inference(cnf_transformation,[status(esa)],[f105_sk]) ).
cnf(t5,plain,
eq(z,null_class) = false,
inference(equality_encoding,[status(esa)],[c105]) ).
cnf(t118,plain,
eq(z,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t326,plain,
sF0 = false,
inference(step,[status(thm)],[t108,t118]) ).
cnf(t128,plain,
false = sF0,
inference(orient,[status(thm)],[t326]) ).
cnf(t339,plain,
sF1 = ifeq(z,null_class,sF0,true),
inference(step,[status(thm)],[t109,t128]) ).
cnf(t16,plain,
ifeq(z,null_class,false,true) = true,
inference(equality_encoding,[status(esa)],[c105]) ).
cnf(t336,plain,
ifeq(z,null_class,sF0,true) = true,
inference(step,[status(thm)],[t16,t128]) ).
cnf(t143,plain,
ifeq(z,null_class,sF0,true) = true,
inference(orient,[status(thm)],[t336]) ).
cnf(t340,plain,
sF1 = true,
inference(step,[status(thm)],[t339,t143]) ).
cnf(t148,plain,
true = sF1,
inference(orient,[status(thm)],[t340]) ).
cnf(t330,plain,
eq(z,null_class) = sF0,
inference(step,[status(thm)],[t118,t128]) ).
cnf(t132,plain,
eq(z,null_class) = sF0,
inference(orient,[status(thm)],[t330]) ).
cnf(t251,plain,
eq(z,z) = sF0,
inference(rw,[status(thm)],[t132]) ).
cnf(t4,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t117,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t346,plain,
eq(X1,X1) = sF1,
inference(step,[status(thm)],[t117,t148]) ).
cnf(t154,plain,
eq(X1,X1) = sF1,
inference(orient,[status(thm)],[t346]) ).
cnf(t428,plain,
sF1 = sF0,
inference(step,[status(thm)],[t251,t154]) ).
cnf(t268,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t428]) ).
cnf(t449,plain,
true = sF0,
inference(step,[status(thm)],[t148,t268]) ).
cnf(t289,plain,
true = sF0,
inference(orient,[status(thm)],[t449]) ).
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(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(f102,axiom,
~ member(Z,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f102_nnf,plain,
! [Z] : ~ member(Z,null_class),
inference(nnf_transformation,[status(thm)],[f102]) ).
fof(f102_sk,plain,
! [Z] : ~ member(Z,null_class),
inference(skolemisation,[status(esa)],[f102_nnf]) ).
cnf(c102,plain,
~ member(X0,null_class),
inference(cnf_transformation,[status(esa)],[f102_sk]) ).
cnf(f106,negated_conjecture,
~ member(not_subclass_element(z,null_class),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_class_is_unique_2) ).
fof(f106_nnf,plain,
~ member(not_subclass_element(z,null_class),z),
inference(nnf_transformation,[status(thm)],[f106]) ).
fof(f106_sk,plain,
~ member(not_subclass_element(z,null_class),z),
inference(skolemisation,[status(esa)],[f106_nnf]) ).
cnf(c106,plain,
~ member(not_subclass_element(z,null_class),z),
inference(cnf_transformation,[status(esa)],[f106_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102,c105,c106]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t289]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t128]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET064-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Thu Sep 24 09:31:35 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.55/1.02 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.55/1.02 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------