%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG041-1 : 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 : n015.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 0.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 43 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 36 ( 4 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_multiplication2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_2,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_4,VAR_5)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_multiplication2) ).
cnf(c_11,plain,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_multiplication2]) ).
fof(multiplication_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',multiplication_is_well_defined) ).
cnf(c_17,plain,
( C = D
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[multiplication_is_well_defined]) ).
fof(multiplicative_identity1,axiom,
! [VAR_0] : product(additive_identity,VAR_0,additive_identity),
file('theBenchmark.p',multiplicative_identity1) ).
cnf(c_18,plain,
product(additive_identity,A,additive_identity),
inference(clausify,[status(thm)],[multiplicative_identity1]) ).
fof(right_multiplicative_identity,axiom,
! [VAR_0] : product(VAR_0,multiplicative_identity,VAR_0),
file('theBenchmark.p',right_multiplicative_identity) ).
cnf(c_20,plain,
product(A,multiplicative_identity,A),
inference(clausify,[status(thm)],[right_multiplicative_identity]) ).
fof(clause41,axiom,
! [VAR_0] :
( VAR_0 = additive_identity
| product(VAR_0,h(VAR_0),multiplicative_identity) ),
file('theBenchmark.p',clause41) ).
cnf(c_22,plain,
( A = additive_identity
| product(A,h(A),multiplicative_identity) ),
inference(clausify,[status(thm)],[clause41]) ).
cnf(c_23,plain,
( additive_identity = A
| product(A,h(A),multiplicative_identity) ),
inference(copy,[status(thm)],[c_22]) ).
fof(a_times_b,axiom,
product(a,b,additive_identity),
file('theBenchmark.p',a_times_b) ).
cnf(c_26,plain,
product(a,b,additive_identity),
inference(clausify,[status(thm)],[a_times_b]) ).
fof(a_not_additive_identity,axiom,
a != additive_identity,
file('theBenchmark.p',a_not_additive_identity) ).
cnf(c_27,plain,
a != additive_identity,
inference(clausify,[status(thm)],[a_not_additive_identity]) ).
fof(prove_b_is_additive_identity,axiom,
b != additive_identity,
file('theBenchmark.p',prove_b_is_additive_identity) ).
cnf(c_28,plain,
b != additive_identity,
inference(clausify,[status(thm)],[prove_b_is_additive_identity]) ).
cnf(c_389,plain,
( B = additive_identity
| ~ product(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_226,plain,
~ product(additive_identity,A,a),
inference(resolve,[status(thm)],[c_389,c_27]) ).
cnf(c_390,plain,
( A = additive_identity
| product(A,h(A),multiplicative_identity) ),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_235,plain,
product(b,h(b),multiplicative_identity),
inference(resolve,[status(thm)],[c_28,c_390]) ).
cnf(c_391,plain,
( product(additive_identity,A,C)
| ~ product(a,B,C)
| ~ product(b,A,B) ),
inference(resolve,[status(thm)],[c_11,c_26]) ).
cnf(c_392,plain,
( product(additive_identity,A,a)
| ~ product(b,A,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_391,c_20]) ).
cnf(c_387,plain,
~ product(b,A,multiplicative_identity),
inference(resolve,[status(thm)],[c_392,c_226]) ).
cnf(c_388,plain,
$false,
inference(resolve,[status(thm)],[c_387,c_235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 05:54:43 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 3283564 was started by sandbox2 on n015,
% 0.12/0.38 % Sat Sep 26 05:54:43 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 0.12/0.48
% 0.12/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.48
% 0.12/0.48 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.12/0.48 % Length of proof is 13.
% 0.12/0.48 % Level of proof is 3.
% 0.12/0.48 % Maximum clause weight is 21.000.
% 0.12/0.48 % Given clauses 56.
% 0.12/0.48
% 0.12/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------