%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG037-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 08:26:28 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 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 : 31 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_inverse2,axiom,
! [VAR_0] : sum(VAR_0,additive_inverse(VAR_0),additive_identity),
file('theBenchmark.p',additive_inverse2) ).
cnf(c_13,plain,
sum(A,additive_inverse(A),additive_identity),
inference(clausify,[status(thm)],[additive_inverse2]) ).
fof(commutativity_of_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_of_addition) ).
cnf(c_16,plain,
( sum(B,A,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_of_addition]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_1,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity1) ).
cnf(c_19,plain,
( sum(C,E,V6)
| ~ product(A,F,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity1]) ).
fof(multiplicative_identity2,axiom,
! [VAR_0] : product(VAR_0,additive_identity,additive_identity),
file('theBenchmark.p',multiplicative_identity2) ).
cnf(c_26,plain,
product(A,additive_identity,additive_identity),
inference(clausify,[status(thm)],[multiplicative_identity2]) ).
fof(a_times_b,axiom,
product(a,b,d),
file('theBenchmark.p',a_times_b) ).
cnf(c_27,plain,
product(a,b,d),
inference(clausify,[status(thm)],[a_times_b]) ).
fof(a_inverse_times_b,axiom,
product(a,additive_inverse(b),c),
file('theBenchmark.p',a_inverse_times_b) ).
cnf(c_28,plain,
product(a,additive_inverse(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_29,plain,
~ sum(c,d,additive_identity),
inference(clausify,[status(thm)],[prove_sum_is_additive_identity]) ).
cnf(c_280,plain,
( sum(d,B,D)
| ~ product(a,C,D)
| ~ sum(b,A,C)
| ~ product(a,A,B) ),
inference(resolve,[status(thm)],[c_19,c_27]) ).
cnf(c_281,plain,
( sum(d,c,B)
| ~ product(a,A,B)
| ~ sum(b,additive_inverse(b),A) ),
inference(resolve,[status(thm)],[c_280,c_28]) ).
cnf(c_282,plain,
( sum(d,c,A)
| ~ product(a,additive_identity,A) ),
inference(resolve,[status(thm)],[c_281,c_13]) ).
cnf(c_255,plain,
sum(d,c,additive_identity),
inference(resolve,[status(thm)],[c_282,c_26]) ).
cnf(c_278,plain,
~ sum(d,c,additive_identity),
inference(resolve,[status(thm)],[c_29,c_16]) ).
cnf(c_279,plain,
$false,
inference(resolve,[status(thm)],[c_278,c_255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 05:51:00 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.39 % Process 3931543 was started by sandbox2 on n011,
% 0.12/0.39 % Sat Sep 26 05:51:00 2026
% 0.12/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 0.12/0.44
% 0.12/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.44
% 0.12/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.12/0.44 % Length of proof is 10.
% 0.12/0.44 % Level of proof is 2.
% 0.12/0.44 % Maximum clause weight is 20.000.
% 0.12/0.44 % Given clauses 29.
% 0.12/0.44
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------