%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD023-1 : 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 : n016.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 07:11:30 AM UTC 2026
% Result : Unsatisfiable 8.13s 1.55s
% Output : CNFRefutation 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 23 ~; 16 |; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(compatibility_of_equality_and_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_0,VAR_2)
| ~ defined(VAR_1)
| equalish(add(VAR_0,VAR_1),add(VAR_2,VAR_1)) ),
file('theBenchmark.p',compatibility_of_equality_and_addition) ).
cnf(c_24,plain,
( ~ equalish(A,C)
| ~ defined(B)
| equalish(add(A,B),add(C,B)) ),
inference(clausify,[status(thm)],[compatibility_of_equality_and_addition]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_28,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(a_equals_b_3,axiom,
equalish(a,b),
file('theBenchmark.p',a_equals_b_3) ).
cnf(c_30,plain,
equalish(a,b),
inference(clausify,[status(thm)],[a_equals_b_3]) ).
fof(additive_identity_not_equal_to_add_4,axiom,
~ equalish(additive_identity,add(b,additive_inverse(a))),
file('theBenchmark.p',additive_identity_not_equal_to_add_4) ).
cnf(c_31,plain,
~ equalish(additive_identity,add(b,additive_inverse(a))),
inference(clausify,[status(thm)],[additive_identity_not_equal_to_add_4]) ).
cnf(c_129,plain,
defined(additive_inverse(a)),
inference(resolve,[status(thm)],[c_28,c_12]) ).
cnf(c_144,plain,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_198,plain,
equalish(b,a),
inference(resolve,[status(thm)],[c_30,c_22]) ).
cnf(c_199,plain,
~ equalish(add(b,additive_inverse(a)),additive_identity),
inference(resolve,[status(thm)],[c_22,c_31]) ).
cnf(c_6710,plain,
( ~ equalish(A,additive_identity)
| ~ equalish(add(b,additive_inverse(a)),A) ),
inference(resolve,[status(thm)],[c_23,c_199]) ).
cnf(c_6234,plain,
~ equalish(add(b,additive_inverse(a)),add(a,additive_inverse(a))),
inference(resolve,[status(thm)],[c_6710,c_144]) ).
cnf(c_6711,plain,
( ~ equalish(b,a)
| ~ defined(additive_inverse(a)) ),
inference(resolve,[status(thm)],[c_24,c_6234]) ).
cnf(c_6712,plain,
~ defined(additive_inverse(a)),
inference(resolve,[status(thm)],[c_6711,c_198]) ).
cnf(c_6709,plain,
$false,
inference(resolve,[status(thm)],[c_129,c_6712]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD023-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47 % Computer : n016.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sun Sep 27 02:28:46 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/0.48 % Process 2219353 was started by sandbox2 on n016,
% 0.21/0.48 % Sun Sep 27 02:28:46 2026
% 0.21/0.48 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.49
% 0.21/0.49 % From the command line: assign(max_seconds, 300).
% 8.13/1.55
% 8.13/1.55 % SZS status Unsatisfiable for theBenchmark
% 8.13/1.55
% 8.13/1.55 % Proof 1 at 0.77 (+ 0.26) seconds.
% 8.13/1.55 % Length of proof is 14.
% 8.13/1.55 % Level of proof is 3.
% 8.13/1.55 % Maximum clause weight is 24.000.
% 8.13/1.55 % Given clauses 343.
% 8.13/1.55
% 8.13/1.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------