%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET055-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Unsatisfiable 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_69,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_70,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
fof(subclass_implies_equal,axiom,
! [VAR_0,VAR_1] :
( equalish(VAR_0,VAR_1)
| ~ subclass(VAR_1,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_implies_equal) ).
cnf(c_74,plain,
( equalish(A,B)
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
fof(prove_reflexivity,axiom,
~ equalish(x,x),
file('theBenchmark.p',prove_reflexivity) ).
cnf(c_159,plain,
~ equalish(x,x),
inference(clausify,[status(thm)],[prove_reflexivity]) ).
cnf(c_160,plain,
( equalish(A,A)
| ~ subclass(A,A) ),
inference(factor,[status(thm)],[c_74]) ).
cnf(c_176,plain,
( subclass(A,A)
| subclass(A,A) ),
inference(resolve,[status(thm)],[c_70,c_69]) ).
cnf(c_173,plain,
subclass(A,A),
inference(copy,[status(thm)],[c_176]) ).
cnf(c_174,plain,
equalish(A,A),
inference(resolve,[status(thm)],[c_173,c_160]) ).
cnf(c_175,plain,
$false,
inference(resolve,[status(thm)],[c_174,c_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET055-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n017.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 06:55:49 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 86998 was started by sandbox on n017,
% 0.17/0.42 % Sat Sep 26 06:55:49 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.47
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47
% 0.17/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.47 % Length of proof is 8.
% 0.17/0.47 % Level of proof is 3.
% 0.17/0.47 % Maximum clause weight is 18.000.
% 0.17/0.47 % Given clauses 70.
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------