%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD068-4 : 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 : n026.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 0.24s 0.53s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 32 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 40 ( 0 sgn 16 !; 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(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(sum_4,axiom,
sum(b,additive_inverse(a),u),
file('theBenchmark.p',sum_4) ).
cnf(c_30,plain,
sum(b,additive_inverse(a),u),
inference(clausify,[status(thm)],[sum_4]) ).
fof(less_or_equal_5,axiom,
less_or_equal(additive_identity,u),
file('theBenchmark.p',less_or_equal_5) ).
cnf(c_31,plain,
less_or_equal(additive_identity,u),
inference(clausify,[status(thm)],[less_or_equal_5]) ).
fof(not_less_or_equal_6,axiom,
~ less_or_equal(a,b),
file('theBenchmark.p',not_less_or_equal_6) ).
cnf(c_32,plain,
~ less_or_equal(a,b),
inference(clausify,[status(thm)],[not_less_or_equal_6]) ).
cnf(c_100,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_101,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_117,plain,
sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_575,plain,
( ~ sum(B,C,b)
| ~ sum(A,C,a)
| ~ less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_24,c_32]) ).
cnf(c_576,plain,
( ~ sum(u,A,b)
| ~ sum(additive_identity,A,a) ),
inference(resolve,[status(thm)],[c_575,c_31]) ).
cnf(c_328,plain,
~ sum(u,a,b),
inference(resolve,[status(thm)],[c_576,c_101]) ).
cnf(c_357,plain,
sum(b,additive_identity,b),
inference(resolve,[status(thm)],[c_117,c_5]) ).
cnf(c_577,plain,
( ~ sum(A,C,b)
| ~ sum(B,a,C)
| ~ sum(A,B,u) ),
inference(resolve,[status(thm)],[c_2,c_328]) ).
cnf(c_578,plain,
( ~ sum(b,A,b)
| ~ sum(additive_inverse(a),a,A) ),
inference(resolve,[status(thm)],[c_577,c_30]) ).
cnf(c_579,plain,
~ sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_578,c_357]) ).
cnf(c_574,plain,
$false,
inference(resolve,[status(thm)],[c_100,c_579]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD068-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n026.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 02:37:10 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2451108 was started by sandbox on n026,
% 0.19/0.45 % Sun Sep 27 02:37:10 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.24/0.53
% 0.24/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.24/0.53
% 0.24/0.53 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.24/0.53 % Length of proof is 16.
% 0.24/0.53 % Level of proof is 3.
% 0.24/0.53 % Maximum clause weight is 21.000.
% 0.24/0.53 % Given clauses 97.
% 0.24/0.53
% 0.24/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------