%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD058-3 : 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 : n002.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 07:11:39 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 18 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 35 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 32 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| sum(additive_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_14,plain,
defined(additive_identity),
inference(clausify,[status(thm)],[well_definedness_of_additive_identity]) ).
fof(antisymmetry_of_order_relation,axiom,
! [VAR_0,VAR_1] :
( ~ less_or_equal(VAR_1,VAR_0)
| ~ less_or_equal(VAR_0,VAR_1)
| sum(additive_identity,VAR_0,VAR_1) ),
file('theBenchmark.p',antisymmetry_of_order_relation) ).
cnf(c_21,plain,
( ~ less_or_equal(B,A)
| ~ less_or_equal(A,B)
| sum(additive_identity,A,B) ),
inference(clausify,[status(thm)],[antisymmetry_of_order_relation]) ).
fof(transitivity_of_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_2,VAR_1)
| ~ less_or_equal(VAR_0,VAR_2)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_order_relation) ).
cnf(c_22,plain,
( ~ less_or_equal(C,B)
| ~ less_or_equal(A,C)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_order_relation]) ).
fof(totality_of_order_relation,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| less_or_equal(VAR_1,VAR_0)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',totality_of_order_relation) ).
cnf(c_23,plain,
( ~ defined(B)
| ~ defined(A)
| less_or_equal(B,A)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[totality_of_order_relation]) ).
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(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(additive_identity,a),
file('theBenchmark.p',less_or_equal_3) ).
cnf(c_29,plain,
less_or_equal(additive_identity,a),
inference(clausify,[status(thm)],[less_or_equal_3]) ).
fof(less_or_equal_4,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_4) ).
cnf(c_30,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_4]) ).
fof(not_sum_5,axiom,
~ sum(additive_identity,a,additive_identity),
file('theBenchmark.p',not_sum_5) ).
cnf(c_31,plain,
~ sum(additive_identity,a,additive_identity),
inference(clausify,[status(thm)],[not_sum_5]) ).
fof(sum_6,axiom,
sum(additive_identity,b,additive_identity),
file('theBenchmark.p',sum_6) ).
cnf(c_32,plain,
sum(additive_identity,b,additive_identity),
inference(clausify,[status(thm)],[sum_6]) ).
cnf(c_84,plain,
( ~ defined(A)
| less_or_equal(A,additive_identity)
| less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_203,plain,
( ~ defined(additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(factor,[status(thm)],[c_84]) ).
cnf(c_86,plain,
less_or_equal(additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_203]) ).
cnf(c_115,plain,
sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_204,plain,
( ~ less_or_equal(a,additive_identity)
| sum(additive_identity,a,additive_identity) ),
inference(resolve,[status(thm)],[c_29,c_21]) ).
cnf(c_119,plain,
~ less_or_equal(a,additive_identity),
inference(resolve,[status(thm)],[c_31,c_204]) ).
cnf(c_205,plain,
( ~ less_or_equal(A,additive_identity)
| ~ less_or_equal(a,A) ),
inference(resolve,[status(thm)],[c_22,c_119]) ).
cnf(c_158,plain,
~ less_or_equal(b,additive_identity),
inference(resolve,[status(thm)],[c_205,c_30]) ).
cnf(c_206,plain,
( ~ sum(B,C,additive_identity)
| ~ sum(A,C,b)
| ~ less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_24,c_158]) ).
cnf(c_207,plain,
( ~ sum(additive_identity,A,additive_identity)
| ~ sum(additive_identity,A,b) ),
inference(resolve,[status(thm)],[c_206,c_86]) ).
cnf(c_208,plain,
~ sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_207,c_32]) ).
cnf(c_202,plain,
$false,
inference(resolve,[status(thm)],[c_115,c_208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD058-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 02:34:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3150051 was started by sandbox2 on n002,
% 0.10/0.37 % Sun Sep 27 02:34:54 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.10/0.39 % Length of proof is 17.
% 0.10/0.39 % Level of proof is 3.
% 0.10/0.39 % Maximum clause weight is 14.000.
% 0.10/0.39 % Given clauses 64.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------