%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD006-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:11:25 AM UTC 2026
% Result : Unsatisfiable 0.66s 0.48s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(add(additive_identity,VAR_0),VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_2,plain,
( ~ defined(A)
| equalish(add(additive_identity,A),A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(add(VAR_0,additive_inverse(VAR_0)),additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| equalish(add(A,additive_inverse(A)),additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_11,plain,
defined(additive_identity),
inference(clausify,[status(thm)],[well_definedness_of_additive_identity]) ).
fof(well_definedness_of_additive_inverse,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| defined(additive_inverse(VAR_0)) ),
file('theBenchmark.p',well_definedness_of_additive_inverse) ).
cnf(c_12,plain,
( ~ defined(A)
| defined(additive_inverse(A)) ),
inference(clausify,[status(thm)],[well_definedness_of_additive_inverse]) ).
fof(symmetry_of_equality,axiom,
! [VAR_0,VAR_1] :
( ~ equalish(VAR_1,VAR_0)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry_of_equality) ).
cnf(c_22,plain,
( ~ equalish(B,A)
| equalish(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_equality]) ).
fof(transitivity_of_equality,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_2,VAR_1)
| ~ equalish(VAR_0,VAR_2)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_equality) ).
cnf(c_23,plain,
( ~ equalish(C,B)
| ~ equalish(A,C)
| equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_equality]) ).
fof(additive_inverse_not_equal_to_additive_identity_1,axiom,
~ equalish(additive_inverse(additive_identity),additive_identity),
file('theBenchmark.p',additive_inverse_not_equal_to_additive_identity_1) ).
cnf(c_28,plain,
~ equalish(additive_inverse(additive_identity),additive_identity),
inference(clausify,[status(thm)],[additive_inverse_not_equal_to_additive_identity_1]) ).
cnf(c_62,plain,
equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),
inference(resolve,[status(thm)],[c_11,c_3]) ).
cnf(c_76,plain,
defined(additive_inverse(additive_identity)),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_225,plain,
equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)),
inference(resolve,[status(thm)],[c_76,c_2]) ).
cnf(c_971,plain,
( ~ equalish(A,additive_identity)
| ~ equalish(additive_inverse(additive_identity),A) ),
inference(resolve,[status(thm)],[c_23,c_28]) ).
cnf(c_772,plain,
~ equalish(additive_inverse(additive_identity),add(additive_identity,additive_inverse(additive_identity))),
inference(resolve,[status(thm)],[c_971,c_62]) ).
cnf(c_972,plain,
~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)),
inference(resolve,[status(thm)],[c_22,c_772]) ).
cnf(c_970,plain,
$false,
inference(resolve,[status(thm)],[c_225,c_972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD006-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 02:23:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1234706 was started by sandbox2 on n015,
% 0.11/0.38 % Sun Sep 27 02:23:59 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.66/0.48
% 0.66/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.66/0.48
% 0.66/0.48 % Proof 1 at 0.06 (+ 0.03) seconds.
% 0.66/0.48 % Length of proof is 12.
% 0.66/0.48 % Level of proof is 3.
% 0.66/0.48 % Maximum clause weight is 14.000.
% 0.66/0.48 % Given clauses 130.
% 0.66/0.48
% 0.66/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------