%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET027+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:35:24 AM UTC 2026
% Result : Theorem 1.83s 0.71s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 51 ( 19 ~; 16 |; 12 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(transitivity,conjecture,
! [X,Y,Z] :
( ( subclass(Y,Z)
& subclass(X,Y) )
=> subclass(X,Z) ),
file('theBenchmark.p',transitivity) ).
fof(transitivity_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( subclass(Y,Z)
& subclass(X,Y) )
=> subclass(X,Z) ),
inference(assume_negation,[status(cth)],[transitivity]) ).
fof(nnf_42,plain,
? [X,Y,Z] :
( ~ subclass(X,Z)
& subclass(Y,Z)
& subclass(X,Y) ),
inference(fof_nnf,[status(thm)],[transitivity_neg]) ).
fof(sk_transitivity_neg,plain,
( ~ subclass(sK0,sK1)
& subclass(sK2,sK1)
& subclass(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(X,sK0),skolemize(Y,sK2),skolemize(Z,sK1)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
~ subclass(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_transitivity_neg]) ).
cnf(c_65,negated_conjecture,
subclass(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_transitivity_neg]) ).
cnf(c_66,negated_conjecture,
subclass(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_transitivity_neg]) ).
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(sK3(X,Y),Y)
& member(sK3(X,Y),X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U,sK3(X,Y))],[nnf_1]) ).
fof(sk_subclass_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(VAR_0,VAR_1),VAR_1)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(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(sK3(A,B),B)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_140,plain,
( member(sK3(A,B),A)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_141,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_379,negated_conjecture,
~ member(sK3(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_139,c_64]) ).
cnf(c_383,plain,
member(sK3(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_140,c_64]) ).
cnf(c_392,plain,
( member(A,sK2)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_141,c_66]) ).
cnf(c_393,plain,
( member(A,sK1)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_141,c_65]) ).
cnf(c_1088,plain,
member(sK3(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_383,c_392]) ).
cnf(c_2596,plain,
member(sK3(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_1088,c_393]) ).
cnf(c_2595,plain,
$false,
inference(resolve,[status(thm)],[c_379,c_2596]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET027+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 06:57:58 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3375756 was started by sandbox on n015,
% 0.16/0.43 % Sat Sep 26 06:57:58 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 1.83/0.71
% 1.83/0.71 % SZS status Theorem for theBenchmark
% 1.83/0.71
% 1.83/0.71 % Proof 1 at 0.20 (+ 0.05) seconds.
% 1.83/0.71 % Length of proof is 14.
% 1.83/0.71 % Level of proof is 4.
% 1.83/0.71 % Maximum clause weight is 18.000.
% 1.83/0.71 % Given clauses 265.
% 1.83/0.71
% 1.83/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------