%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM019-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 08:16:03 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.47s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [VAR_0] : equalish(VAR_0,VAR_0),
file('theBenchmark.p',reflexivity) ).
cnf(c_7,plain,
equalish(A,A),
inference(clausify,[status(thm)],[reflexivity]) ).
fof(transitivity,axiom,
! [VAR_0,VAR_1,VAR_2] :
( equalish(VAR_1,VAR_2)
| ~ equalish(VAR_0,VAR_2)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity) ).
cnf(c_8,plain,
( equalish(B,C)
| ~ equalish(A,C)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity]) ).
fof(a_equals_aa,axiom,
equalish(a,aa),
file('theBenchmark.p',a_equals_aa) ).
cnf(c_10,plain,
equalish(a,aa),
inference(clausify,[status(thm)],[a_equals_aa]) ).
fof(prove_b_equals_a,axiom,
~ equalish(aa,a),
file('theBenchmark.p',prove_b_equals_a) ).
cnf(c_11,plain,
~ equalish(aa,a),
inference(clausify,[status(thm)],[prove_b_equals_a]) ).
cnf(c_29,plain,
( equalish(aa,A)
| ~ equalish(a,A) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_27,plain,
equalish(aa,a),
inference(resolve,[status(thm)],[c_29,c_7]) ).
cnf(c_28,plain,
$false,
inference(resolve,[status(thm)],[c_27,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM019-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43 % Computer : n017.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8046.5625MB
% 0.11/0.43 % OS : Linux 6.8.0-71-generic
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Sat Sep 26 01:49:02 UTC 2026
% 0.11/0.43 % CPUTime :
% 0.11/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.44 % Process 3698791 was started by sandbox on n017,
% 0.11/0.44 % Sat Sep 26 01:49:02 2026
% 0.11/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.44
% 0.11/0.44 % From the command line: assign(max_seconds, 300).
% 0.11/0.47
% 0.11/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.47
% 0.11/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.47 % Length of proof is 6.
% 0.11/0.47 % Level of proof is 2.
% 0.11/0.47 % Maximum clause weight is 9.000.
% 0.11/0.47 % Given clauses 10.
% 0.11/0.47
% 0.11/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------