%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG005-1 : 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 : n009.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 08:26:17 AM UTC 2026
% Result : Unsatisfiable 0.95s 0.49s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 84 ( 44 ~; 40 |; 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity1,axiom,
! [VAR_0] : sum(additive_identity,VAR_0,VAR_0),
file('theBenchmark.p',additive_identity1) ).
cnf(c_1,plain,
sum(additive_identity,A,A),
inference(clausify,[status(thm)],[additive_identity1]) ).
fof(additive_identity2,axiom,
! [VAR_0] : sum(VAR_0,additive_identity,VAR_0),
file('theBenchmark.p',additive_identity2) ).
cnf(c_2,plain,
sum(A,additive_identity,A),
inference(clausify,[status(thm)],[additive_identity2]) ).
fof(closure_of_addition,axiom,
! [VAR_0,VAR_1] : sum(VAR_0,VAR_1,add(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_addition) ).
cnf(c_4,plain,
sum(A,B,add(A,B)),
inference(clausify,[status(thm)],[closure_of_addition]) ).
fof(left_inverse,axiom,
! [VAR_0] : sum(additive_inverse(VAR_0),VAR_0,additive_identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_5,plain,
sum(additive_inverse(A),A,additive_identity),
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity_of_addition2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition2) ).
cnf(c_8,plain,
( sum(C,D,F)
| ~ sum(A,E,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition2]) ).
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_14,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(distributivity4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_2,VAR_4,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',distributivity4) ).
cnf(c_15,plain,
( product(F,B,V6)
| ~ sum(C,E,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity4]) ).
fof(a_times_b,axiom,
product(a,b,d),
file('theBenchmark.p',a_times_b) ).
cnf(c_18,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_19,plain,
product(additive_inverse(a),b,c),
inference(clausify,[status(thm)],[a_inverse_times_b]) ).
fof(prove_sum_is_additive_id,axiom,
~ sum(c,d,additive_identity),
file('theBenchmark.p',prove_sum_is_additive_id) ).
cnf(c_20,plain,
~ sum(c,d,additive_identity),
inference(clausify,[status(thm)],[prove_sum_is_additive_id]) ).
cnf(c_676,plain,
( product(C,b,D)
| ~ sum(c,B,D)
| ~ sum(additive_inverse(a),A,C)
| ~ product(A,b,B) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_677,plain,
( product(A,b,B)
| ~ sum(c,d,B)
| ~ sum(additive_inverse(a),a,A) ),
inference(resolve,[status(thm)],[c_676,c_18]) ).
cnf(c_678,plain,
( product(additive_identity,b,A)
| ~ sum(c,d,A) ),
inference(resolve,[status(thm)],[c_677,c_5]) ).
cnf(c_247,plain,
product(additive_identity,b,add(c,d)),
inference(resolve,[status(thm)],[c_678,c_4]) ).
cnf(c_679,plain,
( sum(A,B,D)
| ~ sum(additive_identity,C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_680,plain,
( sum(A,B,C)
| ~ sum(additive_identity,add(A,B),C) ),
inference(resolve,[status(thm)],[c_679,c_4]) ).
cnf(c_284,plain,
~ sum(additive_identity,add(c,d),additive_identity),
inference(resolve,[status(thm)],[c_680,c_20]) ).
cnf(c_681,plain,
( sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_682,plain,
( sum(additive_identity,B,additive_identity)
| ~ sum(A,B,A) ),
inference(resolve,[status(thm)],[c_681,c_5]) ).
cnf(c_454,plain,
~ sum(A,add(c,d),A),
inference(resolve,[status(thm)],[c_682,c_284]) ).
cnf(c_683,plain,
( sum(add(c,d),B,D)
| ~ product(C,b,D)
| ~ sum(additive_identity,A,C)
| ~ product(A,b,B) ),
inference(resolve,[status(thm)],[c_14,c_247]) ).
cnf(c_684,plain,
( sum(add(c,d),add(c,d),B)
| ~ product(A,b,B)
| ~ sum(additive_identity,additive_identity,A) ),
inference(resolve,[status(thm)],[c_683,c_247]) ).
cnf(c_685,plain,
( sum(add(c,d),add(c,d),A)
| ~ product(additive_identity,b,A) ),
inference(resolve,[status(thm)],[c_684,c_2]) ).
cnf(c_686,plain,
sum(add(c,d),add(c,d),add(c,d)),
inference(resolve,[status(thm)],[c_685,c_247]) ).
cnf(c_675,plain,
$false,
inference(resolve,[status(thm)],[c_454,c_686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.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
% 0.02/0.35 % CPULimit : 300
% 0.02/0.35 % WCLimit : 300
% 0.02/0.35 % DateTime : Sat Sep 26 05:43:44 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 3493886 was started by sandbox on n009,
% 0.02/0.36 % Sat Sep 26 05:43:44 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.36
% 0.02/0.36 % From the command line: assign(max_seconds, 300).
% 0.95/0.49
% 0.95/0.49 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (11).
% 0.95/0.49
% 0.95/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.95/0.49
% 0.95/0.49 % Proof 1 at 0.08 (+ 0.04) seconds.
% 0.95/0.49 % Length of proof is 14.
% 0.95/0.49 % Level of proof is 3.
% 0.95/0.49 % Maximum clause weight is 25.000.
% 0.95/0.49 % Given clauses 52.
% 0.95/0.49
% 0.95/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------