%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO021-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 06:55:07 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.80s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 2 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiply_add,axiom,
! [VAR_0,VAR_1] : multiply(add(VAR_0,VAR_1),VAR_1) = VAR_1,
file('theBenchmark.p',multiply_add) ).
cnf(c_1,plain,
multiply(add(A,B),B) = B,
inference(clausify,[status(thm)],[multiply_add]) ).
fof(multiply_add_property,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,VAR_2)) = add(multiply(VAR_1,VAR_0),multiply(VAR_2,VAR_0)),
file('theBenchmark.p',multiply_add_property) ).
cnf(c_2,plain,
multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)),
inference(clausify,[status(thm)],[multiply_add_property]) ).
fof(add_multiply,axiom,
! [VAR_0,VAR_1] : add(multiply(VAR_0,VAR_1),VAR_1) = VAR_1,
file('theBenchmark.p',add_multiply) ).
cnf(c_4,plain,
add(multiply(A,B),B) = B,
inference(clausify,[status(thm)],[add_multiply]) ).
fof(prove_commutativity_of_multiply,axiom,
multiply(b,a) != multiply(a,b),
file('theBenchmark.p',prove_commutativity_of_multiply) ).
cnf(c_8,plain,
multiply(b,a) != multiply(a,b),
inference(clausify,[status(thm)],[prove_commutativity_of_multiply]) ).
cnf(c_20,plain,
add(A,A) = A,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_65,plain,
multiply(A,B) = add(multiply(B,A),multiply(B,A)),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_63,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_20,c_65]) ).
cnf(c_64,plain,
$false,
inference(resolve,[status(thm)],[c_63,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO021-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.78 % Computer : n004.cluster.edu
% 0.09/0.78 % Model : x86_64 x86_64
% 0.09/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.78 % Memory : 8046.5625MB
% 0.09/0.78 % OS : Linux 6.8.0-71-generic
% 0.09/0.78 % CPULimit : 300
% 0.09/0.78 % WCLimit : 300
% 0.09/0.78 % DateTime : Sat Sep 26 22:36:38 UTC 2026
% 0.09/0.78 % CPUTime :
% 0.09/0.78 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.78 % Process 2797966 was started by sandbox on n004,
% 0.09/0.78 % Sat Sep 26 22:36:38 2026
% 0.09/0.78 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.79
% 0.09/0.79 % From the command line: assign(max_seconds, 300).
% 0.15/0.80
% 0.15/0.80 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.80
% 0.15/0.80 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.80 % Length of proof is 7.
% 0.15/0.80 % Level of proof is 3.
% 0.15/0.80 % Maximum clause weight is 13.000.
% 0.15/0.80 % Given clauses 10.
% 0.15/0.80
% 0.15/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------