%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD067-3 : 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 : n012.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 07:11:42 AM UTC 2026
% Result : Unsatisfiable 2.58s 0.67s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 25 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_inverse(VAR_0),VAR_0,additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_4,plain,
( ~ defined(A)
| sum(additive_inverse(A),A,additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(commutativity_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ sum(VAR_1,VAR_0,VAR_2)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_5,plain,
( ~ sum(B,A,C)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_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_15,plain,
( ~ defined(A)
| defined(additive_inverse(A)) ),
inference(clausify,[status(thm)],[well_definedness_of_additive_inverse]) ).
fof(totality_of_addition,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| sum(VAR_0,VAR_1,add(VAR_0,VAR_1)) ),
file('theBenchmark.p',totality_of_addition) ).
cnf(c_19,plain,
( ~ defined(B)
| ~ defined(A)
| sum(A,B,add(A,B)) ),
inference(clausify,[status(thm)],[totality_of_addition]) ).
fof(compatibility_of_order_relation_and_addition,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ sum(VAR_3,VAR_4,VAR_1)
| ~ sum(VAR_2,VAR_4,VAR_0)
| ~ less_or_equal(VAR_2,VAR_3)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',compatibility_of_order_relation_and_addition) ).
cnf(c_24,plain,
( ~ sum(D,E,B)
| ~ sum(C,E,A)
| ~ less_or_equal(C,D)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_27,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_28,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(less_or_equal_3,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_3) ).
cnf(c_29,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_3]) ).
fof(not_less_or_equal_4,axiom,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('theBenchmark.p',not_less_or_equal_4) ).
cnf(c_30,plain,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(clausify,[status(thm)],[not_less_or_equal_4]) ).
cnf(c_93,plain,
defined(additive_inverse(a)),
inference(resolve,[status(thm)],[c_27,c_15]) ).
cnf(c_98,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_105,plain,
( ~ defined(A)
| sum(b,A,add(b,A)) ),
inference(resolve,[status(thm)],[c_28,c_19]) ).
cnf(c_1957,plain,
sum(a,additive_inverse(a),additive_identity),
inference(resolve,[status(thm)],[c_98,c_5]) ).
cnf(c_3048,plain,
( ~ sum(B,C,add(b,additive_inverse(a)))
| ~ sum(A,C,additive_identity)
| ~ less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_24,c_30]) ).
cnf(c_3049,plain,
( ~ sum(b,A,add(b,additive_inverse(a)))
| ~ sum(a,A,additive_identity) ),
inference(resolve,[status(thm)],[c_3048,c_29]) ).
cnf(c_2696,plain,
~ sum(b,additive_inverse(a),add(b,additive_inverse(a))),
inference(resolve,[status(thm)],[c_3049,c_1957]) ).
cnf(c_3050,plain,
sum(b,additive_inverse(a),add(b,additive_inverse(a))),
inference(resolve,[status(thm)],[c_105,c_93]) ).
cnf(c_3047,plain,
$false,
inference(resolve,[status(thm)],[c_2696,c_3050]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD067-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 27 02:33:34 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 1982461 was started by sandbox2 on n012,
% 0.02/0.30 % Sun Sep 27 02:33:34 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 2.58/0.67
% 2.58/0.67 % SZS status Unsatisfiable for theBenchmark
% 2.58/0.67
% 2.58/0.67 % Proof 1 at 0.21 (+ 0.08) seconds.
% 2.58/0.67 % Length of proof is 15.
% 2.58/0.67 % Level of proof is 4.
% 2.58/0.67 % Maximum clause weight is 16.000.
% 2.58/0.67 % Given clauses 249.
% 2.58/0.67
% 2.58/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------