%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD016-3 : 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 : n008.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 07:11:28 AM UTC 2026
% Result : Unsatisfiable 1.02s 0.51s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 22 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 61 ( 36 ~; 25 |; 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 : 40 ( 0 sgn 14 !; 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(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(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(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_29,plain,
defined(u),
inference(clausify,[status(thm)],[u_is_defined]) ).
fof(v_is_defined,axiom,
defined(v),
file('theBenchmark.p',v_is_defined) ).
cnf(c_30,plain,
defined(v),
inference(clausify,[status(thm)],[v_is_defined]) ).
fof(sum_5,axiom,
sum(a,u,b),
file('theBenchmark.p',sum_5) ).
cnf(c_31,plain,
sum(a,u,b),
inference(clausify,[status(thm)],[sum_5]) ).
fof(sum_6,axiom,
sum(a,v,b),
file('theBenchmark.p',sum_6) ).
cnf(c_32,plain,
sum(a,v,b),
inference(clausify,[status(thm)],[sum_6]) ).
fof(not_sum_7,axiom,
~ sum(additive_identity,u,v),
file('theBenchmark.p',not_sum_7) ).
cnf(c_33,plain,
~ sum(additive_identity,u,v),
inference(clausify,[status(thm)],[not_sum_7]) ).
cnf(c_62,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_101,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_134,plain,
sum(additive_identity,u,u),
inference(resolve,[status(thm)],[c_29,c_3]) ).
cnf(c_150,plain,
sum(additive_identity,v,v),
inference(resolve,[status(thm)],[c_30,c_3]) ).
cnf(c_1209,plain,
( ~ sum(B,C,v)
| ~ sum(A,C,u)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_1,c_33]) ).
cnf(c_1210,plain,
( ~ sum(additive_identity,A,v)
| ~ sum(additive_identity,A,u) ),
inference(resolve,[status(thm)],[c_1209,c_62]) ).
cnf(c_483,plain,
~ sum(additive_identity,v,u),
inference(resolve,[status(thm)],[c_1210,c_150]) ).
cnf(c_1211,plain,
( ~ sum(A,C,u)
| ~ sum(B,v,C)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_2,c_483]) ).
cnf(c_1212,plain,
( ~ sum(additive_inverse(a),A,u)
| ~ sum(a,v,A) ),
inference(resolve,[status(thm)],[c_1211,c_101]) ).
cnf(c_1177,plain,
~ sum(additive_inverse(a),b,u),
inference(resolve,[status(thm)],[c_1212,c_32]) ).
cnf(c_1213,plain,
( ~ sum(B,C,u)
| ~ sum(A,C,b)
| ~ sum(additive_inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_1,c_1177]) ).
cnf(c_1214,plain,
( ~ sum(A,u,u)
| ~ sum(additive_inverse(a),a,A) ),
inference(resolve,[status(thm)],[c_1213,c_31]) ).
cnf(c_1215,plain,
~ sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_1214,c_134]) ).
cnf(c_1208,plain,
$false,
inference(resolve,[status(thm)],[c_101,c_1215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD016-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n008.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sun Sep 27 02:23:09 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 820722 was started by sandbox on n008,
% 0.07/0.34 % Sun Sep 27 02:23:09 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.34
% 0.07/0.34 % From the command line: assign(max_seconds, 300).
% 1.02/0.51
% 1.02/0.51 % SZS status Unsatisfiable for theBenchmark
% 1.02/0.51
% 1.02/0.51 % Proof 1 at 0.11 (+ 0.04) seconds.
% 1.02/0.51 % Length of proof is 18.
% 1.02/0.51 % Level of proof is 4.
% 1.02/0.51 % Maximum clause weight is 21.000.
% 1.02/0.51 % Given clauses 200.
% 1.02/0.51
% 1.02/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------