%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD016-5 : 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 : 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 1.08s 0.57s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 26 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 42 ~; 28 |; 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 : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 44 ( 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_28,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_29,plain,
defined(v),
inference(clausify,[status(thm)],[v_is_defined]) ).
fof(sum_6,axiom,
sum(a,u,q),
file('theBenchmark.p',sum_6) ).
cnf(c_32,plain,
sum(a,u,q),
inference(clausify,[status(thm)],[sum_6]) ).
fof(sum_7,axiom,
sum(a,v,r),
file('theBenchmark.p',sum_7) ).
cnf(c_33,plain,
sum(a,v,r),
inference(clausify,[status(thm)],[sum_7]) ).
fof(sum_8,axiom,
sum(additive_identity,q,r),
file('theBenchmark.p',sum_8) ).
cnf(c_34,plain,
sum(additive_identity,q,r),
inference(clausify,[status(thm)],[sum_8]) ).
fof(not_sum_9,axiom,
~ sum(additive_identity,u,v),
file('theBenchmark.p',not_sum_9) ).
cnf(c_35,plain,
~ sum(additive_identity,u,v),
inference(clausify,[status(thm)],[not_sum_9]) ).
cnf(c_64,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_103,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_104,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_120,plain,
sum(additive_identity,u,u),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_136,plain,
sum(additive_identity,v,v),
inference(resolve,[status(thm)],[c_29,c_3]) ).
cnf(c_1551,plain,
( ~ sum(B,C,v)
| ~ sum(A,C,u)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_1,c_35]) ).
cnf(c_1552,plain,
( ~ sum(additive_identity,A,v)
| ~ sum(additive_identity,A,u) ),
inference(resolve,[status(thm)],[c_1551,c_64]) ).
cnf(c_487,plain,
~ sum(additive_identity,v,u),
inference(resolve,[status(thm)],[c_1552,c_136]) ).
cnf(c_1553,plain,
( ~ sum(A,C,u)
| ~ sum(B,v,C)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_2,c_487]) ).
cnf(c_1554,plain,
( ~ sum(additive_inverse(a),A,u)
| ~ sum(a,v,A) ),
inference(resolve,[status(thm)],[c_1553,c_103]) ).
cnf(c_1443,plain,
~ sum(additive_inverse(a),r,u),
inference(resolve,[status(thm)],[c_1554,c_33]) ).
cnf(c_1555,plain,
( ~ sum(B,C,u)
| ~ sum(A,C,r)
| ~ sum(additive_inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_1,c_1443]) ).
cnf(c_1556,plain,
( ~ sum(additive_identity,A,u)
| ~ sum(a,A,r) ),
inference(resolve,[status(thm)],[c_1555,c_103]) ).
cnf(c_1547,plain,
~ sum(a,u,r),
inference(resolve,[status(thm)],[c_1556,c_120]) ).
cnf(c_1557,plain,
( ~ sum(A,C,r)
| ~ sum(B,u,C)
| ~ sum(A,B,a) ),
inference(resolve,[status(thm)],[c_2,c_1547]) ).
cnf(c_1558,plain,
( ~ sum(A,q,r)
| ~ sum(A,a,a) ),
inference(resolve,[status(thm)],[c_1557,c_32]) ).
cnf(c_1559,plain,
~ sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_1558,c_34]) ).
cnf(c_1550,plain,
$false,
inference(resolve,[status(thm)],[c_104,c_1559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD016-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 02:23:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 820732 was started by sandbox2 on n008,
% 0.09/0.36 % Sun Sep 27 02:23:09 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 1.08/0.57
% 1.08/0.57 % SZS status Unsatisfiable for theBenchmark
% 1.08/0.57
% 1.08/0.57 % Proof 1 at 0.14 (+ 0.05) seconds.
% 1.08/0.57 % Length of proof is 21.
% 1.08/0.57 % Level of proof is 5.
% 1.08/0.57 % Maximum clause weight is 21.000.
% 1.08/0.57 % Given clauses 214.
% 1.08/0.57
% 1.08/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------