%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 06:55:03 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 72 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 107 ( 13 sgn 19 !; 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(distributivity2,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',distributivity2) ).
cnf(c_5,plain,
add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
cnf(c_6,plain,
multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)),
inference(copy,[status(thm)],[c_5]) ).
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_id1,axiom,
! [VAR_0] : multiply(VAR_0,multiplicative_identity) = VAR_0,
file('theBenchmark.p',multiplicative_id1) ).
cnf(c_13,plain,
multiply(A,multiplicative_identity) = A,
inference(clausify,[status(thm)],[multiplicative_id1]) ).
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_operation,axiom,
multiply(a,add(a,b)) != a,
file('theBenchmark.p',prove_operation) ).
cnf(c_17,plain,
multiply(a,add(a,b)) != a,
inference(clausify,[status(thm)],[prove_operation]) ).
cnf(c_18,plain,
add(multiply(a,a),multiply(a,b)) != a,
inference(paramod,[status(thm)],[c_8,c_17]) ).
cnf(c_207,plain,
add(multiply(add(A,B),A),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_208,plain,
add(multiply(A,add(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_2,c_207]) ).
cnf(c_209,plain,
add(add(multiply(A,A),multiply(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_8,c_208]) ).
cnf(c_19,plain,
add(add(multiply(A,A),multiply(A,B)),add(multiply(A,C),multiply(B,C))) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_7,c_209]) ).
cnf(c_210,plain,
multiply(multiplicative_identity,A) = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_211,plain,
A = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_14,c_210]) ).
cnf(c_22,plain,
add(multiply(A,B),multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_211]) ).
cnf(c_212,plain,
multiply(A,multiplicative_identity) = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_213,plain,
A = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_13,c_212]) ).
cnf(c_23,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(copy,[status(thm)],[c_213]) ).
cnf(c_214,plain,
additive_identity = add(multiply(A,inverse(add(A,B))),multiply(B,inverse(add(A,B)))),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_24,plain,
add(multiply(A,inverse(add(A,B))),multiply(B,inverse(add(A,B)))) = additive_identity,
inference(copy,[status(thm)],[c_214]) ).
cnf(c_25,plain,
inverse(multiplicative_identity) = additive_identity,
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_215,plain,
add(add(multiplicative_identity,multiply(multiplicative_identity,A)),add(multiply(multiplicative_identity,B),multiply(A,B))) = add(multiplicative_identity,multiply(A,B)),
inference(paramod,[status(thm)],[c_13,c_19]) ).
cnf(c_216,plain,
add(add(multiplicative_identity,A),add(multiply(multiplicative_identity,B),multiply(A,B))) = add(multiplicative_identity,multiply(A,B)),
inference(paramod,[status(thm)],[c_14,c_215]) ).
cnf(c_45,plain,
add(add(multiplicative_identity,A),add(B,multiply(A,B))) = add(multiplicative_identity,multiply(A,B)),
inference(paramod,[status(thm)],[c_14,c_216]) ).
cnf(c_217,plain,
add(multiply(A,inverse(inverse(A))),additive_identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_11,c_22]) ).
cnf(c_218,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1,c_217]) ).
cnf(c_102,plain,
multiply(A,inverse(inverse(A))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_16,c_218]) ).
cnf(c_219,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = A,
inference(paramod,[status(thm)],[c_11,c_23]) ).
cnf(c_220,plain,
add(additive_identity,inverse(inverse(A))) = A,
inference(paramod,[status(thm)],[c_102,c_219]) ).
cnf(c_118,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_16,c_220]) ).
cnf(c_221,plain,
add(multiply(A,A),additive_identity) = A,
inference(paramod,[status(thm)],[c_11,c_23]) ).
cnf(c_222,plain,
add(additive_identity,multiply(A,A)) = A,
inference(paramod,[status(thm)],[c_1,c_221]) ).
cnf(c_119,plain,
multiply(A,A) = A,
inference(paramod,[status(thm)],[c_16,c_222]) ).
cnf(c_152,plain,
add(a,multiply(a,b)) != a,
inference(paramod,[status(thm)],[c_119,c_18]) ).
cnf(c_223,plain,
add(multiply(A,inverse(A)),multiply(additive_identity,inverse(add(A,additive_identity)))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_24]) ).
cnf(c_224,plain,
add(additive_identity,multiply(additive_identity,inverse(add(A,additive_identity)))) = additive_identity,
inference(paramod,[status(thm)],[c_11,c_223]) ).
cnf(c_225,plain,
add(additive_identity,multiply(additive_identity,inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_224]) ).
cnf(c_170,plain,
multiply(additive_identity,inverse(A)) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_225]) ).
cnf(c_226,plain,
add(additive_identity,multiply(additive_identity,inverse(inverse(A)))) = additive_identity,
inference(paramod,[status(thm)],[c_170,c_23]) ).
cnf(c_227,plain,
add(additive_identity,multiply(additive_identity,A)) = additive_identity,
inference(paramod,[status(thm)],[c_118,c_226]) ).
cnf(c_183,plain,
multiply(additive_identity,A) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_227]) ).
cnf(c_228,plain,
add(multiplicative_identity,add(A,multiply(inverse(multiplicative_identity),A))) = add(multiplicative_identity,multiply(inverse(multiplicative_identity),A)),
inference(paramod,[status(thm)],[c_9,c_45]) ).
cnf(c_229,plain,
add(multiplicative_identity,add(A,multiply(additive_identity,A))) = add(multiplicative_identity,multiply(inverse(multiplicative_identity),A)),
inference(paramod,[status(thm)],[c_25,c_228]) ).
cnf(c_230,plain,
add(multiplicative_identity,add(A,additive_identity)) = add(multiplicative_identity,multiply(inverse(multiplicative_identity),A)),
inference(paramod,[status(thm)],[c_183,c_229]) ).
cnf(c_231,plain,
add(multiplicative_identity,A) = add(multiplicative_identity,multiply(inverse(multiplicative_identity),A)),
inference(paramod,[status(thm)],[c_15,c_230]) ).
cnf(c_232,plain,
add(multiplicative_identity,A) = add(multiplicative_identity,multiply(additive_identity,A)),
inference(paramod,[status(thm)],[c_25,c_231]) ).
cnf(c_233,plain,
add(multiplicative_identity,A) = add(multiplicative_identity,additive_identity),
inference(paramod,[status(thm)],[c_183,c_232]) ).
cnf(c_234,plain,
add(multiplicative_identity,A) = add(additive_identity,multiplicative_identity),
inference(paramod,[status(thm)],[c_1,c_233]) ).
cnf(c_201,plain,
add(multiplicative_identity,A) = multiplicative_identity,
inference(paramod,[status(thm)],[c_16,c_234]) ).
cnf(c_235,plain,
multiply(A,multiplicative_identity) = add(multiply(A,multiplicative_identity),multiply(A,B)),
inference(paramod,[status(thm)],[c_201,c_8]) ).
cnf(c_236,plain,
A = add(multiply(A,multiplicative_identity),multiply(A,B)),
inference(paramod,[status(thm)],[c_13,c_235]) ).
cnf(c_237,plain,
A = add(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_13,c_236]) ).
cnf(c_205,plain,
add(A,multiply(A,B)) = A,
inference(copy,[status(thm)],[c_237]) ).
cnf(c_206,plain,
$false,
inference(resolve,[status(thm)],[c_205,c_152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 22:39:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1887223 was started by sandbox on n016,
% 0.10/0.37 % Sat Sep 26 22:39:15 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 29.
% 0.10/0.40 % Level of proof is 7.
% 0.10/0.40 % Maximum clause weight is 21.000.
% 0.10/0.40 % Given clauses 31.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------