%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 2.68s 0.76s
% Output : CNFRefutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 39 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 47 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_3,VAR_5,VAR_2)
| ~ sum(VAR_4,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_2) ).
cnf(c_2,plain,
( ~ sum(D,F,C)
| ~ sum(E,B,F)
| ~ sum(D,E,A)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_2]) ).
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(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(additive_identity,add(b,additive_inverse(a))),
file('theBenchmark.p',less_or_equal_3) ).
cnf(c_29,plain,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(clausify,[status(thm)],[less_or_equal_3]) ).
fof(not_less_or_equal_4,axiom,
~ less_or_equal(a,b),
file('theBenchmark.p',not_less_or_equal_4) ).
cnf(c_30,plain,
~ less_or_equal(a,b),
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_99,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_105,plain,
( ~ defined(A)
| sum(b,A,add(b,A)) ),
inference(resolve,[status(thm)],[c_28,c_19]) ).
cnf(c_115,plain,
sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_2883,plain,
( ~ sum(B,C,b)
| ~ sum(A,C,a)
| ~ less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_24,c_30]) ).
cnf(c_2884,plain,
( ~ sum(add(b,additive_inverse(a)),A,b)
| ~ sum(additive_identity,A,a) ),
inference(resolve,[status(thm)],[c_2883,c_29]) ).
cnf(c_285,plain,
~ sum(add(b,additive_inverse(a)),a,b),
inference(resolve,[status(thm)],[c_2884,c_99]) ).
cnf(c_318,plain,
sum(b,additive_identity,b),
inference(resolve,[status(thm)],[c_115,c_5]) ).
cnf(c_2885,plain,
( ~ sum(A,C,b)
| ~ sum(B,a,C)
| ~ sum(A,B,add(b,additive_inverse(a))) ),
inference(resolve,[status(thm)],[c_2,c_285]) ).
cnf(c_2886,plain,
( ~ sum(A,additive_identity,b)
| ~ sum(A,additive_inverse(a),add(b,additive_inverse(a))) ),
inference(resolve,[status(thm)],[c_2885,c_98]) ).
cnf(c_2128,plain,
~ sum(b,additive_inverse(a),add(b,additive_inverse(a))),
inference(resolve,[status(thm)],[c_2886,c_318]) ).
cnf(c_2887,plain,
sum(b,additive_inverse(a),add(b,additive_inverse(a))),
inference(resolve,[status(thm)],[c_105,c_93]) ).
cnf(c_2882,plain,
$false,
inference(resolve,[status(thm)],[c_2128,c_2887]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 02:34:33 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2726144 was started by sandbox on n019,
% 0.08/0.35 % Sun Sep 27 02:34:33 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 2.68/0.76
% 2.68/0.76 % SZS status Unsatisfiable for theBenchmark
% 2.68/0.76
% 2.68/0.76 % Proof 1 at 0.26 (+ 0.09) seconds.
% 2.68/0.76 % Length of proof is 20.
% 2.68/0.76 % Level of proof is 4.
% 2.68/0.76 % Maximum clause weight is 23.000.
% 2.68/0.76 % Given clauses 371.
% 2.68/0.76
% 2.68/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------