%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 08:26:18 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 25 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_inverse,axiom,
! [VAR_0] : sum(additive_inverse(VAR_0),VAR_0,additive_identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_14,plain,
sum(additive_inverse(A),A,additive_identity),
inference(clausify,[status(thm)],[left_inverse]) ).
fof(distributivity3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_0,VAR_3,VAR_5)
| ~ product(VAR_3,VAR_1,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity3) ).
cnf(c_23,plain,
( sum(C,E,V6)
| ~ product(F,B,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity3]) ).
fof(multiplicative_identity1,axiom,
! [VAR_0] : product(additive_identity,VAR_0,additive_identity),
file('theBenchmark.p',multiplicative_identity1) ).
cnf(c_27,plain,
product(additive_identity,A,additive_identity),
inference(clausify,[status(thm)],[multiplicative_identity1]) ).
fof(a_times_b,axiom,
product(a,b,d),
file('theBenchmark.p',a_times_b) ).
cnf(c_29,plain,
product(a,b,d),
inference(clausify,[status(thm)],[a_times_b]) ).
fof(a_inverse_times_b,axiom,
product(additive_inverse(a),b,c),
file('theBenchmark.p',a_inverse_times_b) ).
cnf(c_30,plain,
product(additive_inverse(a),b,c),
inference(clausify,[status(thm)],[a_inverse_times_b]) ).
fof(prove_sum_is_additive_identity,axiom,
~ sum(c,d,additive_identity),
file('theBenchmark.p',prove_sum_is_additive_identity) ).
cnf(c_31,plain,
~ sum(c,d,additive_identity),
inference(clausify,[status(thm)],[prove_sum_is_additive_identity]) ).
cnf(c_359,plain,
( sum(c,B,D)
| ~ product(C,b,D)
| ~ sum(additive_inverse(a),A,C)
| ~ product(A,b,B) ),
inference(resolve,[status(thm)],[c_23,c_30]) ).
cnf(c_360,plain,
( sum(c,d,B)
| ~ product(A,b,B)
| ~ sum(additive_inverse(a),a,A) ),
inference(resolve,[status(thm)],[c_359,c_29]) ).
cnf(c_361,plain,
( sum(c,d,A)
| ~ product(additive_identity,b,A) ),
inference(resolve,[status(thm)],[c_360,c_14]) ).
cnf(c_357,plain,
sum(c,d,additive_identity),
inference(resolve,[status(thm)],[c_361,c_27]) ).
cnf(c_358,plain,
$false,
inference(resolve,[status(thm)],[c_357,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 05:43:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 498868 was started by sandbox on n006,
% 0.10/0.37 % Sat Sep 26 05:43:26 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.41 % Length of proof is 8.
% 0.14/0.41 % Level of proof is 2.
% 0.14/0.41 % Maximum clause weight is 25.000.
% 0.14/0.41 % Given clauses 30.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------