%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 02:41:55 PM UTC 2026
% Result : Theorem 0.16s 11.00s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 30 unt; 0 def)
% Number of atoms : 129 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 55 ~; 39 |; 30 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 70 ( 5 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43,conjecture,
member(null_class,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f43_neg,negated_conjecture,
~ member(null_class,universal_class),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
~ member(null_class,universal_class),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
~ member(null_class,universal_class),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c89,plain,
~ member(null_class,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t72,plain,
ifeq(member(null_class,universal_class),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c89]) ).
fof(f28,axiom,
! [X] :
( inductive(X)
<=> ( subclass(image(successor_relation,X),X)
& member(null_class,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_defn) ).
fof(f28_nnf,plain,
! [X] :
( ( ~ subclass(image(successor_relation,X),X)
| ~ member(null_class,X)
| inductive(X) )
& ( ( subclass(image(successor_relation,X),X)
& member(null_class,X) )
| ~ inductive(X) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X] :
( ( ~ subclass(image(successor_relation,X),X)
| ~ member(null_class,X)
| inductive(X) )
& ( ( subclass(image(successor_relation,X),X)
& member(null_class,X) )
| ~ inductive(X) ) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c55,plain,
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi49,axiom,
ifeq(inductive(X0),true,member(null_class,X0),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
fof(f29,axiom,
? [X] :
( ! [Y] :
( inductive(Y)
=> subclass(X,Y) )
& inductive(X)
& member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity) ).
fof(f29_nnf,plain,
? [X] :
( ! [Y] :
( subclass(X,Y)
| ~ inductive(Y) )
& inductive(X)
& member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [Y] :
( ( subclass(sk1,Y)
| ~ inductive(Y) )
& inductive(sk1)
& member(sk1,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f29_nnf]) ).
cnf(c59,plain,
inductive(sk1),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(hi56,axiom,
inductive(sk1) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
cnf(h2,plain,
member(null_class,sk1) = true,
inference(hyper_resolution,[status(thm)],[hi49,hi56]) ).
fof(f0,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,U] :
( ( ( ~ member(sk0(X,Y),Y)
& member(sk0(X,Y),X) )
| subclass(X,Y) )
& ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(subclass(X0,X1),true,ifeq(member(X2,X0),true,member(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f1,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f1_nnf,plain,
! [X] : subclass(X,universal_class),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : subclass(X,universal_class),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi3,axiom,
subclass(X0,universal_class) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t9,plain,
member(null_class,universal_class) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h2]) ).
cnf(t199,plain,
member(null_class,universal_class) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t877,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t72,t199]) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t169,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t32]) ).
cnf(t878,plain,
false = true,
inference(step,[status(thm)],[t877,t169]) ).
cnf(t868,plain,
false = true,
inference(orient,[status(thm)],[t878]) ).
fof(f13,axiom,
! [X,Z] :
( member(Z,complement(X))
<=> ( ~ member(Z,X)
& member(Z,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
fof(f13_nnf,plain,
! [X,Z] :
( ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
& ( ( ~ member(Z,X)
& member(Z,universal_class) )
| ~ member(Z,complement(X)) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Z,X] :
( ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
& ( ( ~ member(Z,X)
& member(Z,universal_class) )
| ~ member(Z,complement(X)) ) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c28,plain,
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f15,axiom,
! [X] : ~ member(X,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
fof(f15_nnf,plain,
! [X] : ~ member(X,null_class),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X] : ~ member(X,null_class),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c31,plain,
~ member(X0,null_class),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f16,axiom,
! [X,Z] :
( member(Z,domain_of(X))
<=> ( restrict(X,singleton(Z),universal_class) != null_class
& member(Z,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of) ).
fof(f16_nnf,plain,
! [X,Z] :
( ( restrict(X,singleton(Z),universal_class) = null_class
| ~ member(Z,universal_class)
| member(Z,domain_of(X)) )
& ( ( restrict(X,singleton(Z),universal_class) != null_class
& member(Z,universal_class) )
| ~ member(Z,domain_of(X)) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Z,X] :
( ( restrict(X,singleton(Z),universal_class) = null_class
| ~ member(Z,universal_class)
| member(Z,domain_of(X)) )
& ( ( restrict(X,singleton(Z),universal_class) != null_class
& member(Z,universal_class) )
| ~ member(Z,domain_of(X)) ) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c33,plain,
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f39,axiom,
! [X,Y] :
( disjoint(X,Y)
<=> ! [U] :
~ ( member(U,Y)
& member(U,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f39_nnf,plain,
! [X,Y] :
( ( ? [U] :
( member(U,Y)
& member(U,X) )
| disjoint(X,Y) )
& ( ! [U] :
( ~ member(U,Y)
| ~ member(U,X) )
| ~ disjoint(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [X,Y,U] :
( ( ( member(sk4(X,Y),Y)
& member(sk4(X,Y),X) )
| disjoint(X,Y) )
& ( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f39_nnf]) ).
cnf(c80,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c28,c31,c33,c80,c89]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t868]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/10.39 % Computer : n002.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Thu Sep 24 09:35:05 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/11.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/11.00 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------