%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD008-4 : 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 : n015.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 07:11:26 AM UTC 2026
% Result : Unsatisfiable 0.96s 0.58s
% Output : CNFRefutation 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 26 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 67 ( 40 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 46 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_4,VAR_5,VAR_2)
| ~ sum(VAR_3,VAR_5,VAR_1)
| ~ sum(VAR_0,VAR_3,VAR_4)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_1) ).
cnf(c_1,plain,
( ~ sum(E,F,C)
| ~ sum(D,F,B)
| ~ sum(A,D,E)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_1]) ).
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(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(c_is_defined,axiom,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(c_29,plain,
defined(c),
inference(clausify,[status(thm)],[c_is_defined]) ).
fof(d_is_defined,axiom,
defined(d),
file('theBenchmark.p',d_is_defined) ).
cnf(c_30,plain,
defined(d),
inference(clausify,[status(thm)],[d_is_defined]) ).
fof(sum_5,axiom,
sum(a,b,c),
file('theBenchmark.p',sum_5) ).
cnf(c_31,plain,
sum(a,b,c),
inference(clausify,[status(thm)],[sum_5]) ).
fof(sum_6,axiom,
sum(additive_inverse(a),additive_inverse(b),d),
file('theBenchmark.p',sum_6) ).
cnf(c_32,plain,
sum(additive_inverse(a),additive_inverse(b),d),
inference(clausify,[status(thm)],[sum_6]) ).
fof(not_sum_7,axiom,
~ sum(additive_identity,additive_inverse(c),d),
file('theBenchmark.p',not_sum_7) ).
cnf(c_33,plain,
~ sum(additive_identity,additive_inverse(c),d),
inference(clausify,[status(thm)],[not_sum_7]) ).
cnf(c_101,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_102,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_117,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_133,plain,
sum(additive_inverse(c),c,additive_identity),
inference(resolve,[status(thm)],[c_29,c_4]) ).
cnf(c_150,plain,
sum(additive_identity,d,d),
inference(resolve,[status(thm)],[c_30,c_3]) ).
cnf(c_154,plain,
sum(b,a,c),
inference(resolve,[status(thm)],[c_31,c_5]) ).
cnf(c_170,plain,
~ sum(additive_inverse(c),additive_identity,d),
inference(resolve,[status(thm)],[c_5,c_33]) ).
cnf(c_1566,plain,
( ~ sum(B,C,d)
| ~ sum(A,C,additive_identity)
| ~ sum(additive_inverse(c),A,B) ),
inference(resolve,[status(thm)],[c_1,c_170]) ).
cnf(c_1567,plain,
( ~ sum(additive_identity,A,d)
| ~ sum(c,A,additive_identity) ),
inference(resolve,[status(thm)],[c_1566,c_133]) ).
cnf(c_1482,plain,
~ sum(c,d,additive_identity),
inference(resolve,[status(thm)],[c_1567,c_150]) ).
cnf(c_1498,plain,
~ sum(d,c,additive_identity),
inference(resolve,[status(thm)],[c_5,c_1482]) ).
cnf(c_1568,plain,
( ~ sum(A,C,additive_identity)
| ~ sum(B,c,C)
| ~ sum(A,B,d) ),
inference(resolve,[status(thm)],[c_2,c_1498]) ).
cnf(c_1569,plain,
( ~ sum(additive_inverse(a),A,additive_identity)
| ~ sum(additive_inverse(b),c,A) ),
inference(resolve,[status(thm)],[c_1568,c_32]) ).
cnf(c_1501,plain,
~ sum(additive_inverse(b),c,a),
inference(resolve,[status(thm)],[c_1569,c_101]) ).
cnf(c_1570,plain,
( ~ sum(B,C,a)
| ~ sum(A,C,c)
| ~ sum(additive_inverse(b),A,B) ),
inference(resolve,[status(thm)],[c_1,c_1501]) ).
cnf(c_1571,plain,
( ~ sum(A,a,a)
| ~ sum(additive_inverse(b),b,A) ),
inference(resolve,[status(thm)],[c_1570,c_154]) ).
cnf(c_1572,plain,
~ sum(additive_inverse(b),b,additive_identity),
inference(resolve,[status(thm)],[c_1571,c_102]) ).
cnf(c_1565,plain,
$false,
inference(resolve,[status(thm)],[c_117,c_1572]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD008-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 02:24:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1237488 was started by sandbox on n015,
% 0.08/0.36 % Sun Sep 27 02:24:45 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.96/0.58
% 0.96/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.96/0.58
% 0.96/0.58 % Proof 1 at 0.17 (+ 0.04) seconds.
% 0.96/0.58 % Length of proof is 23.
% 0.96/0.58 % Level of proof is 5.
% 0.96/0.58 % Maximum clause weight is 21.000.
% 0.96/0.58 % Given clauses 316.
% 0.96/0.58
% 0.96/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------