%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD067-1 : 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 : n003.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 07:11:41 AM UTC 2026
% Result : Unsatisfiable 4.36s 1.02s
% Output : CNFRefutation 4.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 20 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 8 !; 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(compatibility_of_order_relation_and_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_0,VAR_2)
| ~ defined(VAR_1)
| less_or_equal(add(VAR_0,VAR_1),add(VAR_2,VAR_1)) ),
file('theBenchmark.p',compatibility_of_order_relation_and_addition) ).
cnf(c_19,plain,
( ~ less_or_equal(A,C)
| ~ defined(B)
| less_or_equal(add(A,B),add(C,B)) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
fof(compatibility_of_equality_and_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_2,VAR_0)
| ~ less_or_equal(VAR_2,VAR_1)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',compatibility_of_equality_and_order_relation) ).
cnf(c_26,plain,
( ~ equalish(C,A)
| ~ less_or_equal(C,B)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[compatibility_of_equality_and_order_relation]) ).
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(less_or_equal_3,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_3) ).
cnf(c_30,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_31,plain,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(clausify,[status(thm)],[not_less_or_equal_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_7353,plain,
( ~ equalish(A,additive_identity)
| ~ less_or_equal(A,add(b,additive_inverse(a))) ),
inference(resolve,[status(thm)],[c_26,c_31]) ).
cnf(c_6356,plain,
~ less_or_equal(add(a,additive_inverse(a)),add(b,additive_inverse(a))),
inference(resolve,[status(thm)],[c_7353,c_144]) ).
cnf(c_7354,plain,
( ~ less_or_equal(a,b)
| ~ defined(additive_inverse(a)) ),
inference(resolve,[status(thm)],[c_19,c_6356]) ).
cnf(c_7355,plain,
~ defined(additive_inverse(a)),
inference(resolve,[status(thm)],[c_7354,c_30]) ).
cnf(c_7352,plain,
$false,
inference(resolve,[status(thm)],[c_129,c_7355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD067-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n003.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 27 02:35:39 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 103858 was started by sandbox2 on n003,
% 0.16/0.44 % Sun Sep 27 02:35:39 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 4.36/1.02
% 4.36/1.02 % SZS status Unsatisfiable for theBenchmark
% 4.36/1.02
% 4.36/1.02 % Proof 1 at 0.43 (+ 0.12) seconds.
% 4.36/1.02 % Length of proof is 11.
% 4.36/1.02 % Level of proof is 3.
% 4.36/1.02 % Maximum clause weight is 24.000.
% 4.36/1.02 % Given clauses 394.
% 4.36/1.02
% 4.36/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------