%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD013-3 : 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 : n020.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 07:11:27 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 21 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 32 ~; 21 |; 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; 0-2 aty)
% Number of variables : 32 ( 0 sgn 12 !; 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(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(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(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(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(additive_identity,a,b),
file('theBenchmark.p',sum_5) ).
cnf(c_31,plain,
sum(additive_identity,a,b),
inference(clausify,[status(thm)],[sum_5]) ).
fof(sum_6,axiom,
sum(additive_identity,c,d),
file('theBenchmark.p',sum_6) ).
cnf(c_32,plain,
sum(additive_identity,c,d),
inference(clausify,[status(thm)],[sum_6]) ).
fof(not_sum_7,axiom,
~ sum(a,c,add(d,b)),
file('theBenchmark.p',not_sum_7) ).
cnf(c_33,plain,
~ sum(a,c,add(d,b)),
inference(clausify,[status(thm)],[not_sum_7]) ).
cnf(c_118,plain,
sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_134,plain,
sum(additive_identity,c,c),
inference(resolve,[status(thm)],[c_29,c_3]) ).
cnf(c_154,plain,
sum(a,additive_identity,b),
inference(resolve,[status(thm)],[c_31,c_5]) ).
cnf(c_163,plain,
sum(c,additive_identity,d),
inference(resolve,[status(thm)],[c_32,c_5]) ).
cnf(c_844,plain,
( ~ sum(B,C,add(d,b))
| ~ sum(A,C,c)
| ~ sum(a,A,B) ),
inference(resolve,[status(thm)],[c_1,c_33]) ).
cnf(c_845,plain,
( ~ sum(b,A,add(d,b))
| ~ sum(additive_identity,A,c) ),
inference(resolve,[status(thm)],[c_844,c_154]) ).
cnf(c_643,plain,
~ sum(b,c,add(d,b)),
inference(resolve,[status(thm)],[c_845,c_134]) ).
cnf(c_718,plain,
~ sum(c,b,add(d,b)),
inference(resolve,[status(thm)],[c_5,c_643]) ).
cnf(c_846,plain,
( ~ sum(B,C,add(d,b))
| ~ sum(A,C,b)
| ~ sum(c,A,B) ),
inference(resolve,[status(thm)],[c_1,c_718]) ).
cnf(c_847,plain,
( ~ sum(d,A,add(d,b))
| ~ sum(additive_identity,A,b) ),
inference(resolve,[status(thm)],[c_846,c_163]) ).
cnf(c_720,plain,
~ sum(d,b,add(d,b)),
inference(resolve,[status(thm)],[c_847,c_118]) ).
cnf(c_848,plain,
( ~ defined(b)
| ~ defined(d) ),
inference(resolve,[status(thm)],[c_19,c_720]) ).
cnf(c_849,plain,
~ defined(d),
inference(resolve,[status(thm)],[c_848,c_28]) ).
cnf(c_843,plain,
$false,
inference(resolve,[status(thm)],[c_30,c_849]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD013-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 02:23:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3015741 was started by sandbox2 on n020,
% 0.10/0.37 % Sun Sep 27 02:23:51 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.46
% 0.10/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.46
% 0.10/0.46 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.10/0.46 % Length of proof is 18.
% 0.10/0.46 % Level of proof is 5.
% 0.10/0.46 % Maximum clause weight is 16.000.
% 0.10/0.46 % Given clauses 115.
% 0.10/0.46
% 0.10/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------