%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO013-4 : 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 : n020.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 06:55:05 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 81 ( 81 unt; 0 def)
% Number of atoms : 81 ( 80 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 91 ( 7 sgn 14 !; 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(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]) ).
fof(additive_id1,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',additive_id1) ).
cnf(c_6,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_7,plain,
multiply(A,multiplicative_identity) = A,
inference(clausify,[status(thm)],[multiplicative_id1]) ).
fof(additive_inverse1,axiom,
! [VAR_0] : add(VAR_0,inverse(VAR_0)) = multiplicative_identity,
file('theBenchmark.p',additive_inverse1) ).
cnf(c_8,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_9,plain,
multiply(A,inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[multiplicative_inverse1]) ).
fof(b_a_multiplicative_identity,axiom,
add(a,b) = multiplicative_identity,
file('theBenchmark.p',b_a_multiplicative_identity) ).
cnf(c_10,plain,
add(a,b) = multiplicative_identity,
inference(clausify,[status(thm)],[b_a_multiplicative_identity]) ).
fof(b_an_additive_identity,axiom,
multiply(a,b) = additive_identity,
file('theBenchmark.p',b_an_additive_identity) ).
cnf(c_11,plain,
multiply(a,b) = additive_identity,
inference(clausify,[status(thm)],[b_an_additive_identity]) ).
fof(prove_a_inverse_is_b,axiom,
b != inverse(a),
file('theBenchmark.p',prove_a_inverse_is_b) ).
cnf(c_12,plain,
b != inverse(a),
inference(clausify,[status(thm)],[prove_a_inverse_is_b]) ).
cnf(c_13,plain,
inverse(a) != b,
inference(copy,[status(thm)],[c_12]) ).
cnf(c_219,plain,
add(multiply(add(A,B),A),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_220,plain,
add(multiply(A,add(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_2,c_219]) ).
cnf(c_14,plain,
add(add(multiply(A,A),multiply(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_5,c_220]) ).
cnf(c_221,plain,
A = add(additive_identity,A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_16,plain,
add(additive_identity,A) = A,
inference(copy,[status(thm)],[c_221]) ).
cnf(c_222,plain,
multiply(A,B) = add(multiply(A,B),multiply(A,additive_identity)),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_17,plain,
add(multiply(A,B),multiply(A,additive_identity)) = multiply(A,B),
inference(copy,[status(thm)],[c_222]) ).
cnf(c_223,plain,
A = multiply(multiplicative_identity,A),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_18,plain,
multiply(multiplicative_identity,A) = A,
inference(copy,[status(thm)],[c_223]) ).
cnf(c_224,plain,
multiply(A,multiplicative_identity) = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_225,plain,
A = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_7,c_224]) ).
cnf(c_19,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(copy,[status(thm)],[c_225]) ).
cnf(c_226,plain,
multiply(A,multiplicative_identity) = add(multiply(A,a),multiply(A,b)),
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_227,plain,
A = add(multiply(A,a),multiply(A,b)),
inference(paramod,[status(thm)],[c_7,c_226]) ).
cnf(c_20,plain,
add(multiply(A,a),multiply(A,b)) = A,
inference(copy,[status(thm)],[c_227]) ).
cnf(c_228,plain,
add(add(multiply(a,a),multiply(a,b)),multiply(multiplicative_identity,A)) = add(a,multiply(b,A)),
inference(paramod,[status(thm)],[c_10,c_14]) ).
cnf(c_229,plain,
add(add(multiply(a,a),additive_identity),multiply(multiplicative_identity,A)) = add(a,multiply(b,A)),
inference(paramod,[status(thm)],[c_11,c_228]) ).
cnf(c_230,plain,
add(add(additive_identity,multiply(a,a)),multiply(multiplicative_identity,A)) = add(a,multiply(b,A)),
inference(paramod,[status(thm)],[c_1,c_229]) ).
cnf(c_231,plain,
add(multiply(a,a),multiply(multiplicative_identity,A)) = add(a,multiply(b,A)),
inference(paramod,[status(thm)],[c_16,c_230]) ).
cnf(c_232,plain,
add(multiply(a,a),A) = add(a,multiply(b,A)),
inference(paramod,[status(thm)],[c_18,c_231]) ).
cnf(c_35,plain,
add(a,multiply(b,A)) = add(multiply(a,a),A),
inference(copy,[status(thm)],[c_232]) ).
cnf(c_233,plain,
add(additive_identity,multiply(A,additive_identity)) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_9,c_17]) ).
cnf(c_234,plain,
multiply(A,additive_identity) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_16,c_233]) ).
cnf(c_67,plain,
multiply(A,additive_identity) = additive_identity,
inference(paramod,[status(thm)],[c_9,c_234]) ).
cnf(c_235,plain,
additive_identity = multiply(additive_identity,A),
inference(paramod,[status(thm)],[c_67,c_2]) ).
cnf(c_72,plain,
multiply(additive_identity,A) = additive_identity,
inference(copy,[status(thm)],[c_235]) ).
cnf(c_236,plain,
add(add(multiply(A,A),additive_identity),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_67,c_14]) ).
cnf(c_237,plain,
add(add(additive_identity,multiply(A,A)),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_1,c_236]) ).
cnf(c_238,plain,
add(multiply(A,A),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_16,c_237]) ).
cnf(c_239,plain,
add(multiply(A,A),multiply(A,B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_6,c_238]) ).
cnf(c_240,plain,
add(multiply(A,A),multiply(A,B)) = add(A,additive_identity),
inference(paramod,[status(thm)],[c_72,c_239]) ).
cnf(c_73,plain,
add(multiply(A,A),multiply(A,B)) = A,
inference(paramod,[status(thm)],[c_6,c_240]) ).
cnf(c_241,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = A,
inference(paramod,[status(thm)],[c_9,c_19]) ).
cnf(c_95,plain,
multiply(A,inverse(inverse(A))) = A,
inference(paramod,[status(thm)],[c_16,c_241]) ).
cnf(c_242,plain,
add(multiply(A,A),additive_identity) = A,
inference(paramod,[status(thm)],[c_9,c_19]) ).
cnf(c_243,plain,
add(additive_identity,multiply(A,A)) = A,
inference(paramod,[status(thm)],[c_1,c_242]) ).
cnf(c_96,plain,
multiply(A,A) = A,
inference(paramod,[status(thm)],[c_16,c_243]) ).
cnf(c_244,plain,
add(additive_identity,multiply(a,inverse(b))) = a,
inference(paramod,[status(thm)],[c_11,c_19]) ).
cnf(c_97,plain,
multiply(a,inverse(b)) = a,
inference(paramod,[status(thm)],[c_16,c_244]) ).
cnf(c_105,plain,
add(A,multiply(A,B)) = A,
inference(paramod,[status(thm)],[c_96,c_73]) ).
cnf(c_106,plain,
add(a,multiply(b,A)) = add(a,A),
inference(paramod,[status(thm)],[c_96,c_35]) ).
cnf(c_123,plain,
add(multiply(a,A),multiply(A,b)) = A,
inference(paramod,[status(thm)],[c_2,c_20]) ).
cnf(c_127,plain,
add(A,multiply(B,A)) = A,
inference(paramod,[status(thm)],[c_2,c_105]) ).
cnf(c_245,plain,
add(inverse(b),a) = inverse(b),
inference(paramod,[status(thm)],[c_97,c_127]) ).
cnf(c_157,plain,
add(a,inverse(b)) = inverse(b),
inference(paramod,[status(thm)],[c_1,c_245]) ).
cnf(c_246,plain,
add(a,additive_identity) = add(a,inverse(b)),
inference(paramod,[status(thm)],[c_9,c_106]) ).
cnf(c_247,plain,
add(additive_identity,a) = add(a,inverse(b)),
inference(paramod,[status(thm)],[c_1,c_246]) ).
cnf(c_248,plain,
a = add(a,inverse(b)),
inference(paramod,[status(thm)],[c_16,c_247]) ).
cnf(c_249,plain,
a = inverse(b),
inference(paramod,[status(thm)],[c_157,c_248]) ).
cnf(c_166,plain,
inverse(b) = a,
inference(copy,[status(thm)],[c_249]) ).
cnf(c_211,plain,
multiply(b,inverse(a)) = b,
inference(paramod,[status(thm)],[c_166,c_95]) ).
cnf(c_250,plain,
add(additive_identity,multiply(inverse(a),b)) = inverse(a),
inference(paramod,[status(thm)],[c_9,c_123]) ).
cnf(c_251,plain,
add(additive_identity,multiply(b,inverse(a))) = inverse(a),
inference(paramod,[status(thm)],[c_2,c_250]) ).
cnf(c_252,plain,
add(additive_identity,b) = inverse(a),
inference(paramod,[status(thm)],[c_211,c_251]) ).
cnf(c_253,plain,
b = inverse(a),
inference(paramod,[status(thm)],[c_16,c_252]) ).
cnf(c_217,plain,
inverse(a) = b,
inference(copy,[status(thm)],[c_253]) ).
cnf(c_218,plain,
$false,
inference(resolve,[status(thm)],[c_217,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 22:36:20 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2688359 was started by sandbox2 on n020,
% 0.17/0.43 % Sat Sep 26 22:36:20 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.51
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.51
% 0.17/0.51 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.17/0.51 % Length of proof is 35.
% 0.17/0.51 % Level of proof is 11.
% 0.17/0.51 % Maximum clause weight is 19.000.
% 0.17/0.51 % Given clauses 41.
% 0.17/0.51
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------