%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET056+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Sun Sep 27 08:35:31 AM UTC 2026
% Result : Theorem 22.95s 3.39s
% Output : CNFRefutation 22.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 78 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 81 ( 31 ~; 32 |; 15 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 26 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(extensionality,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('theBenchmark.p',extensionality) ).
fof(equality1,conjecture,
! [X,Y] :
( ? [W] :
( ~ member(W,X)
& member(W,Y) )
| ? [U] :
( ~ member(U,Y)
& member(U,X) )
| X = Y ),
file('theBenchmark.p',equality1) ).
fof(equality1_neg,negated_conjecture,
~ ! [X,Y] :
( ? [W] :
( ~ member(W,X)
& member(W,Y) )
| ? [U] :
( ~ member(U,Y)
& member(U,X) )
| X = Y ),
inference(assume_negation,[status(cth)],[equality1]) ).
fof(nnf_42,plain,
? [X,Y] :
( ! [W] :
( member(W,X)
| ~ member(W,Y) )
& ! [U] :
( member(U,Y)
| ~ member(U,X) )
& Y != X ),
inference(fof_nnf,[status(thm)],[equality1_neg]) ).
fof(sk_equality1_neg,plain,
( ! [W] :
( member(W,sK1)
| ~ member(W,sK0) )
& ! [U] :
( member(U,sK0)
| ~ member(U,sK1) )
& sK0 != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK1),skolemize(Y,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
( member(A,sK1)
| ~ member(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_equality1_neg]) ).
cnf(c_65,negated_conjecture,
( member(A,sK0)
| ~ member(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_equality1_neg]) ).
cnf(c_66,negated_conjecture,
sK0 != sK1,
inference(split_conjunct,[status(thm)],[sk_equality1_neg]) ).
cnf(c_135,plain,
( ~ subclass(A,B)
| ~ subclass(B,A)
| A = B ),
inference(clausify,[status(thm)],[extensionality]) ).
fof(nnf_1,plain,
! [X,Y] :
( ( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(fof_nnf,[status(thm)],[subclass_defn]) ).
fof(sk_subclass_defn_sk,plain,
! [X,Y] :
( ( ( ~ member(sK2(X,Y),Y)
& member(sK2(X,Y),X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U,sK2(X,Y))],[nnf_1]) ).
fof(sk_subclass_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK2(VAR_0,VAR_1),VAR_1)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK2(VAR_0,VAR_1),VAR_0)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subclass_defn_sk]) ).
cnf(c_139,plain,
( ~ member(sK2(A,B),B)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_140,plain,
( member(sK2(A,B),A)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_353,plain,
( ~ subclass(B,A)
| B = A
| member(sK2(A,B),A) ),
inference(resolve,[status(thm)],[c_140,c_135]) ).
cnf(c_399,plain,
( member(sK2(sK1,A),sK0)
| subclass(sK1,A) ),
inference(resolve,[status(thm)],[c_140,c_65]) ).
cnf(c_18824,plain,
( subclass(sK1,sK0)
| subclass(sK1,sK0) ),
inference(resolve,[status(thm)],[c_399,c_139]) ).
cnf(c_18560,plain,
subclass(sK1,sK0),
inference(copy,[status(thm)],[c_18824]) ).
cnf(c_18825,plain,
( sK1 = sK0
| member(sK2(sK0,sK1),sK0) ),
inference(resolve,[status(thm)],[c_18560,c_353]) ).
cnf(c_18826,plain,
( sK0 = sK1
| member(sK2(sK0,sK1),sK0) ),
inference(copy,[status(thm)],[c_18825]) ).
cnf(c_18696,negated_conjecture,
member(sK2(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_66,c_18826]) ).
cnf(c_18827,plain,
( ~ subclass(sK0,sK1)
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_18560,c_135]) ).
cnf(c_18828,plain,
( ~ subclass(sK0,sK1)
| sK0 = sK1 ),
inference(copy,[status(thm)],[c_18827]) ).
cnf(c_18697,negated_conjecture,
~ subclass(sK0,sK1),
inference(resolve,[status(thm)],[c_66,c_18828]) ).
cnf(c_18716,plain,
member(sK2(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_18696,c_64]) ).
cnf(c_18829,plain,
~ member(sK2(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_139,c_18697]) ).
cnf(c_18823,plain,
$false,
inference(resolve,[status(thm)],[c_18716,c_18829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET056+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 07:00:29 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 4031038 was started by sandbox2 on n011,
% 0.10/0.35 % Sat Sep 26 07:00:29 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 22.95/3.39
% 22.95/3.39 % given #500 (T,wt=16): 4007 member(f5(identity_relation),union(identity_relation,A)). [resolve(3851,a,97,b)].
% 22.95/3.39
% 22.95/3.39 % SZS status Theorem for theBenchmark
% 22.95/3.39
% 22.95/3.39 % Proof 1 at 2.15 (+ 0.80) seconds.
% 22.95/3.39 % Length of proof is 16.
% 22.95/3.39 % Level of proof is 6.
% 22.95/3.39 % Maximum clause weight is 21.000.
% 22.95/3.39 % Given clauses 984.
% 22.95/3.39
% 22.95/3.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------