%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO004-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 06:55:01 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_of_multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = multiply(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_multiply) ).
cnf(c_2,plain,
multiply(A,B) = multiply(B,A),
inference(clausify,[status(thm)],[commutativity_of_multiply]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,multiply(VAR_1,VAR_2)) = multiply(add(VAR_0,VAR_1),add(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity1) ).
cnf(c_3,plain,
add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_4,plain,
multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)),
inference(copy,[status(thm)],[c_3]) ).
fof(distributivity2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,VAR_2)) = add(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity2) ).
cnf(c_5,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
cnf(c_6,plain,
add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)),
inference(copy,[status(thm)],[c_5]) ).
fof(additive_id1,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',additive_id1) ).
cnf(c_7,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[additive_id1]) ).
fof(multiplicative_id1,axiom,
! [VAR_0] : multiply(VAR_0,multiplicative_identity) = VAR_0,
file('theBenchmark.p',multiplicative_id1) ).
cnf(c_8,plain,
multiply(A,multiplicative_identity) = A,
inference(clausify,[status(thm)],[multiplicative_id1]) ).
fof(prove_a_plus_a_is_a,axiom,
add(a,a) != a,
file('theBenchmark.p',prove_a_plus_a_is_a) ).
cnf(c_11,plain,
add(a,a) != a,
inference(clausify,[status(thm)],[prove_a_plus_a_is_a]) ).
cnf(c_21,plain,
multiply(A,add(A,B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_68,plain,
A = multiply(multiplicative_identity,A),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_23,plain,
multiply(multiplicative_identity,A) = A,
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,plain,
multiply(A,add(A,multiplicative_identity)) = add(A,additive_identity),
inference(paramod,[status(thm)],[c_8,c_21]) ).
cnf(c_49,plain,
multiply(A,add(A,multiplicative_identity)) = A,
inference(paramod,[status(thm)],[c_7,c_69]) ).
cnf(c_70,plain,
multiplicative_identity = add(multiplicative_identity,multiplicative_identity),
inference(paramod,[status(thm)],[c_49,c_23]) ).
cnf(c_58,plain,
add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(copy,[status(thm)],[c_70]) ).
cnf(c_71,plain,
add(multiply(A,multiplicative_identity),multiply(A,multiplicative_identity)) = multiply(A,multiplicative_identity),
inference(paramod,[status(thm)],[c_58,c_6]) ).
cnf(c_72,plain,
add(A,multiply(A,multiplicative_identity)) = multiply(A,multiplicative_identity),
inference(paramod,[status(thm)],[c_8,c_71]) ).
cnf(c_73,plain,
add(A,A) = multiply(A,multiplicative_identity),
inference(paramod,[status(thm)],[c_8,c_72]) ).
cnf(c_66,plain,
add(A,A) = A,
inference(paramod,[status(thm)],[c_8,c_73]) ).
cnf(c_67,plain,
$false,
inference(resolve,[status(thm)],[c_66,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO004-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 22:37:10 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2105578 was started by sandbox2 on n026,
% 0.08/0.36 % Sat Sep 26 22:37:10 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.08/0.38 % Length of proof is 14.
% 0.08/0.38 % Level of proof is 6.
% 0.08/0.38 % Maximum clause weight is 28.000.
% 0.08/0.38 % Given clauses 18.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------