%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO005-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 06:55:01 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 55 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 9 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_of_add,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c_1,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
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(multiply(VAR_0,VAR_1),VAR_2) = multiply(add(VAR_0,VAR_2),add(VAR_1,VAR_2)),
file('theBenchmark.p',distributivity1) ).
cnf(c_3,plain,
add(multiply(A,B),C) = multiply(add(A,C),add(B,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_4,plain,
multiply(add(A,B),add(C,B)) = add(multiply(A,C),B),
inference(copy,[status(thm)],[c_3]) ).
fof(distributivity3,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(add(VAR_0,VAR_1),VAR_2) = add(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',distributivity3) ).
cnf(c_7,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[distributivity3]) ).
fof(distributivity4,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',distributivity4) ).
cnf(c_8,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[distributivity4]) ).
fof(additive_inverse1,axiom,
! [VAR_0] : add(VAR_0,inverse(VAR_0)) = multiplicative_identity,
file('theBenchmark.p',additive_inverse1) ).
cnf(c_9,plain,
add(A,inverse(A)) = multiplicative_identity,
inference(clausify,[status(thm)],[additive_inverse1]) ).
fof(multiplicative_inverse1,axiom,
! [VAR_0] : multiply(VAR_0,inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',multiplicative_inverse1) ).
cnf(c_11,plain,
multiply(A,inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[multiplicative_inverse1]) ).
fof(multiplicative_id2,axiom,
! [VAR_0] : multiply(multiplicative_identity,VAR_0) = VAR_0,
file('theBenchmark.p',multiplicative_id2) ).
cnf(c_14,plain,
multiply(multiplicative_identity,A) = A,
inference(clausify,[status(thm)],[multiplicative_id2]) ).
fof(additive_id1,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',additive_id1) ).
cnf(c_15,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[additive_id1]) ).
fof(additive_id2,axiom,
! [VAR_0] : add(additive_identity,VAR_0) = VAR_0,
file('theBenchmark.p',additive_id2) ).
cnf(c_16,plain,
add(additive_identity,A) = A,
inference(clausify,[status(thm)],[additive_id2]) ).
fof(prove_a_plus_1_is_a,axiom,
add(a,multiplicative_identity) != multiplicative_identity,
file('theBenchmark.p',prove_a_plus_1_is_a) ).
cnf(c_17,plain,
add(a,multiplicative_identity) != multiplicative_identity,
inference(clausify,[status(thm)],[prove_a_plus_1_is_a]) ).
cnf(c_18,plain,
add(multiplicative_identity,a) != multiplicative_identity,
inference(paramod,[status(thm)],[c_1,c_17]) ).
cnf(c_194,plain,
add(multiply(add(A,B),C),multiply(add(A,B),B)) = add(multiply(A,C),B),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_195,plain,
add(add(multiply(A,C),multiply(B,C)),multiply(add(A,B),B)) = add(multiply(A,C),B),
inference(paramod,[status(thm)],[c_7,c_194]) ).
cnf(c_196,plain,
add(add(multiply(A,C),multiply(B,C)),multiply(B,add(A,B))) = add(multiply(A,C),B),
inference(paramod,[status(thm)],[c_2,c_195]) ).
cnf(c_20,plain,
add(add(multiply(A,B),multiply(C,B)),add(multiply(C,A),multiply(C,C))) = add(multiply(A,B),C),
inference(paramod,[status(thm)],[c_8,c_196]) ).
cnf(c_197,plain,
multiply(multiplicative_identity,A) = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_198,plain,
A = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_14,c_197]) ).
cnf(c_22,plain,
add(multiply(A,B),multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_198]) ).
cnf(c_199,plain,
multiply(A,B) = add(multiply(A,B),multiply(A,additive_identity)),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_27,plain,
add(multiply(A,B),multiply(A,additive_identity)) = multiply(A,B),
inference(copy,[status(thm)],[c_199]) ).
cnf(c_30,plain,
inverse(additive_identity) = multiplicative_identity,
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_200,plain,
add(additive_identity,multiply(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_11,c_22]) ).
cnf(c_95,plain,
multiply(inverse(A),inverse(A)) = inverse(A),
inference(paramod,[status(thm)],[c_16,c_200]) ).
cnf(c_201,plain,
add(A,add(multiply(inverse(B),B),multiply(inverse(B),inverse(B)))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_22,c_20]) ).
cnf(c_202,plain,
add(A,add(multiply(B,inverse(B)),multiply(inverse(B),inverse(B)))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_2,c_201]) ).
cnf(c_203,plain,
add(A,add(additive_identity,multiply(inverse(B),inverse(B)))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_11,c_202]) ).
cnf(c_204,plain,
add(A,add(additive_identity,inverse(B))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_95,c_203]) ).
cnf(c_205,plain,
add(A,inverse(B)) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_16,c_204]) ).
cnf(c_98,plain,
add(multiply(A,B),inverse(A)) = add(B,inverse(A)),
inference(copy,[status(thm)],[c_205]) ).
cnf(c_206,plain,
add(additive_identity,multiply(A,additive_identity)) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_11,c_27]) ).
cnf(c_207,plain,
multiply(A,additive_identity) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_16,c_206]) ).
cnf(c_178,plain,
multiply(A,additive_identity) = additive_identity,
inference(paramod,[status(thm)],[c_11,c_207]) ).
cnf(c_208,plain,
additive_identity = multiply(additive_identity,A),
inference(paramod,[status(thm)],[c_178,c_2]) ).
cnf(c_180,plain,
multiply(additive_identity,A) = additive_identity,
inference(copy,[status(thm)],[c_208]) ).
cnf(c_209,plain,
add(multiply(additive_identity,A),multiplicative_identity) = add(A,inverse(additive_identity)),
inference(paramod,[status(thm)],[c_30,c_98]) ).
cnf(c_210,plain,
add(additive_identity,multiplicative_identity) = add(A,inverse(additive_identity)),
inference(paramod,[status(thm)],[c_180,c_209]) ).
cnf(c_211,plain,
multiplicative_identity = add(A,inverse(additive_identity)),
inference(paramod,[status(thm)],[c_16,c_210]) ).
cnf(c_212,plain,
multiplicative_identity = add(A,multiplicative_identity),
inference(paramod,[status(thm)],[c_30,c_211]) ).
cnf(c_190,plain,
add(A,multiplicative_identity) = multiplicative_identity,
inference(copy,[status(thm)],[c_212]) ).
cnf(c_213,plain,
multiplicative_identity = add(multiplicative_identity,A),
inference(paramod,[status(thm)],[c_190,c_1]) ).
cnf(c_192,plain,
add(multiplicative_identity,A) = multiplicative_identity,
inference(copy,[status(thm)],[c_213]) ).
cnf(c_193,plain,
$false,
inference(resolve,[status(thm)],[c_192,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO005-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 22:34:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1712805 was started by sandbox2 on n011,
% 0.09/0.37 % Sat Sep 26 22:34:14 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.41
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.41
% 0.09/0.41 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.09/0.41 % Length of proof is 24.
% 0.09/0.41 % Level of proof is 6.
% 0.09/0.41 % Maximum clause weight is 51.000.
% 0.09/0.41 % Given clauses 29.
% 0.09/0.41
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------