%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 06:55:08 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 8
% Syntax : Number of formulae : 147 ( 147 unt; 0 def)
% Number of atoms : 147 ( 146 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 251 ( 62 sgn 15 !; 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]) ).
cnf(c_3,plain,
add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(additive_inverse,axiom,
! [VAR_0] : add(VAR_0,inverse(VAR_0)) = n1,
file('theBenchmark.p',additive_inverse) ).
cnf(c_4,plain,
add(A,inverse(A)) = n1,
inference(clausify,[status(thm)],[additive_inverse]) ).
fof(pixley_defn,axiom,
! [VAR_0,VAR_1,VAR_2] : pixley(VAR_0,VAR_1,VAR_2) = add(multiply(VAR_0,inverse(VAR_1)),add(multiply(VAR_0,VAR_2),multiply(inverse(VAR_1),VAR_2))),
file('theBenchmark.p',pixley_defn) ).
cnf(c_5,plain,
pixley(A,B,C) = add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C))),
inference(clausify,[status(thm)],[pixley_defn]) ).
cnf(c_6,plain,
pixley(A,B,C) = add(multiply(A,inverse(B)),multiply(C,add(A,inverse(B)))),
inference(paramod,[status(thm)],[c_3,c_5]) ).
fof(pixley1,axiom,
! [VAR_0,VAR_1] : pixley(VAR_0,VAR_0,VAR_1) = VAR_1,
file('theBenchmark.p',pixley1) ).
cnf(c_7,plain,
pixley(A,A,B) = B,
inference(clausify,[status(thm)],[pixley1]) ).
cnf(c_401,plain,
add(multiply(A,inverse(A)),multiply(B,add(A,inverse(A)))) = B,
inference(paramod,[status(thm)],[c_6,c_7]) ).
cnf(c_8,plain,
add(multiply(A,inverse(A)),multiply(B,n1)) = B,
inference(paramod,[status(thm)],[c_4,c_401]) ).
fof(pixley2,axiom,
! [VAR_0,VAR_1] : pixley(VAR_0,VAR_1,VAR_1) = VAR_0,
file('theBenchmark.p',pixley2) ).
cnf(c_9,plain,
pixley(A,B,B) = A,
inference(clausify,[status(thm)],[pixley2]) ).
cnf(c_10,plain,
add(multiply(A,inverse(B)),multiply(B,add(A,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_6,c_9]) ).
fof(pixley3,axiom,
! [VAR_0,VAR_1] : pixley(VAR_0,VAR_1,VAR_0) = VAR_0,
file('theBenchmark.p',pixley3) ).
cnf(c_11,plain,
pixley(A,B,A) = A,
inference(clausify,[status(thm)],[pixley3]) ).
cnf(c_12,plain,
add(multiply(A,inverse(B)),multiply(A,add(A,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_6,c_11]) ).
fof(prove_add_multiply,axiom,
add(multiply(a,b),b) != b,
file('theBenchmark.p',prove_add_multiply) ).
cnf(c_13,plain,
add(multiply(a,b),b) != b,
inference(clausify,[status(thm)],[prove_add_multiply]) ).
cnf(c_14,plain,
multiply(multiply(A,add(B,C)),multiply(C,A)) = multiply(C,A),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_402,plain,
add(A,multiply(B,A)) = multiply(A,add(add(C,A),B)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_15,plain,
multiply(A,add(add(B,A),C)) = add(A,multiply(C,A)),
inference(copy,[status(thm)],[c_402]) ).
cnf(c_403,plain,
add(multiply(A,B),B) = multiply(B,add(A,add(C,B))),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_16,plain,
multiply(A,add(B,add(C,A))) = add(multiply(B,A),A),
inference(copy,[status(thm)],[c_403]) ).
cnf(c_18,plain,
multiply(n1,inverse(A)) = inverse(A),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_19,plain,
multiply(A,multiply(A,n1)) = multiply(A,n1),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_21,plain,
multiply(A,multiply(B,add(A,inverse(B)))) = multiply(B,add(A,inverse(B))),
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_404,plain,
multiply(add(A,B),multiply(B,add(C,add(A,B)))) = multiply(B,add(C,add(A,B))),
inference(paramod,[status(thm)],[c_1,c_14]) ).
cnf(c_405,plain,
multiply(add(A,B),add(multiply(C,B),B)) = multiply(B,add(C,add(A,B))),
inference(paramod,[status(thm)],[c_16,c_404]) ).
cnf(c_25,plain,
multiply(add(A,B),add(multiply(C,B),B)) = add(multiply(C,B),B),
inference(paramod,[status(thm)],[c_16,c_405]) ).
cnf(c_406,plain,
add(inverse(A),multiply(B,inverse(A))) = multiply(inverse(A),add(n1,B)),
inference(paramod,[status(thm)],[c_18,c_3]) ).
cnf(c_33,plain,
multiply(inverse(A),add(n1,B)) = add(inverse(A),multiply(B,inverse(A))),
inference(copy,[status(thm)],[c_406]) ).
cnf(c_35,plain,
add(inverse(n1),multiply(A,n1)) = A,
inference(paramod,[status(thm)],[c_18,c_8]) ).
cnf(c_39,plain,
add(inverse(n1),n1) = add(A,n1),
inference(paramod,[status(thm)],[c_1,c_35]) ).
cnf(c_41,plain,
add(A,n1) = add(B,n1),
inference(paramod,[status(thm)],[c_39,c_39]) ).
cnf(c_407,plain,
add(multiply(A,B),multiply(n1,B)) = multiply(B,add(C,n1)),
inference(paramod,[status(thm)],[c_41,c_3]) ).
cnf(c_42,plain,
multiply(A,add(B,n1)) = multiply(A,add(C,n1)),
inference(paramod,[status(thm)],[c_3,c_407]) ).
cnf(c_47,plain,
add(multiply(A,add(B,n1)),multiply(C,add(D,n1))) = multiply(add(D,n1),add(A,C)),
inference(paramod,[status(thm)],[c_42,c_3]) ).
cnf(c_408,plain,
add(multiply(A,add(B,n1)),multiply(C,add(D,n1))) = multiply(add(B,n1),add(A,C)),
inference(paramod,[status(thm)],[c_42,c_3]) ).
cnf(c_48,plain,
multiply(add(A,n1),add(B,C)) = multiply(add(D,n1),add(B,C)),
inference(paramod,[status(thm)],[c_47,c_408]) ).
cnf(c_57,plain,
multiply(A,add(B,n1)) = add(A,multiply(n1,A)),
inference(paramod,[status(thm)],[c_41,c_15]) ).
cnf(c_64,plain,
multiply(inverse(A),add(B,n1)) = add(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_18,c_57]) ).
cnf(c_409,plain,
multiply(multiply(n1,n1),add(A,n1)) = add(multiply(n1,n1),multiply(n1,n1)),
inference(paramod,[status(thm)],[c_19,c_57]) ).
cnf(c_65,plain,
multiply(multiply(n1,n1),add(A,n1)) = multiply(n1,add(n1,n1)),
inference(paramod,[status(thm)],[c_3,c_409]) ).
cnf(c_68,plain,
multiply(A,multiply(add(B,A),add(C,n1))) = add(A,multiply(multiply(n1,add(B,A)),A)),
inference(paramod,[status(thm)],[c_57,c_15]) ).
cnf(c_71,plain,
add(add(inverse(A),inverse(A)),multiply(B,add(C,n1))) = multiply(add(C,n1),add(inverse(A),B)),
inference(paramod,[status(thm)],[c_64,c_3]) ).
cnf(c_72,plain,
add(multiply(A,add(B,n1)),add(inverse(C),inverse(C))) = multiply(add(B,n1),add(A,inverse(C))),
inference(paramod,[status(thm)],[c_64,c_3]) ).
cnf(c_410,plain,
add(multiply(A,inverse(B)),multiply(n1,inverse(B))) = add(inverse(B),inverse(B)),
inference(paramod,[status(thm)],[c_64,c_3]) ).
cnf(c_73,plain,
add(multiply(A,inverse(B)),inverse(B)) = add(inverse(B),inverse(B)),
inference(paramod,[status(thm)],[c_18,c_410]) ).
cnf(c_77,plain,
add(multiply(inverse(A),inverse(A)),multiply(inverse(A),multiply(inverse(A),add(B,n1)))) = inverse(A),
inference(paramod,[status(thm)],[c_64,c_12]) ).
cnf(c_411,plain,
multiply(add(A,n1),B) = multiply(add(C,n1),add(multiply(D,inverse(D)),multiply(B,n1))),
inference(paramod,[status(thm)],[c_8,c_48]) ).
cnf(c_86,plain,
multiply(add(A,n1),B) = multiply(add(C,n1),B),
inference(paramod,[status(thm)],[c_8,c_411]) ).
cnf(c_412,plain,
add(multiply(A,add(B,n1)),multiply(n1,add(n1,n1))) = multiply(add(B,n1),add(A,multiply(n1,n1))),
inference(paramod,[status(thm)],[c_65,c_3]) ).
cnf(c_413,plain,
multiply(add(n1,n1),add(A,n1)) = multiply(add(B,n1),add(A,multiply(n1,n1))),
inference(paramod,[status(thm)],[c_47,c_412]) ).
cnf(c_105,plain,
multiply(add(A,n1),add(B,multiply(n1,n1))) = multiply(add(n1,n1),add(B,n1)),
inference(copy,[status(thm)],[c_413]) ).
cnf(c_133,plain,
multiply(inverse(A),add(n1,add(B,n1))) = add(inverse(A),multiply(add(C,n1),inverse(A))),
inference(paramod,[status(thm)],[c_86,c_33]) ).
cnf(c_414,plain,
multiply(add(A,B),add(B,B)) = add(multiply(add(C,B),B),B),
inference(paramod,[status(thm)],[c_1,c_25]) ).
cnf(c_140,plain,
multiply(add(A,B),add(B,B)) = add(B,B),
inference(paramod,[status(thm)],[c_1,c_414]) ).
cnf(c_415,plain,
multiply(A,add(multiply(A,n1),multiply(A,n1))) = add(multiply(A,n1),multiply(A,n1)),
inference(paramod,[status(thm)],[c_8,c_140]) ).
cnf(c_416,plain,
multiply(A,multiply(n1,add(A,A))) = add(multiply(A,n1),multiply(A,n1)),
inference(paramod,[status(thm)],[c_3,c_415]) ).
cnf(c_173,plain,
multiply(A,multiply(n1,add(A,A))) = multiply(n1,add(A,A)),
inference(paramod,[status(thm)],[c_3,c_416]) ).
cnf(c_178,plain,
multiply(add(A,n1),add(B,n1)) = add(n1,n1),
inference(paramod,[status(thm)],[c_41,c_140]) ).
cnf(c_183,plain,
multiply(add(A,n1),add(B,multiply(n1,n1))) = add(n1,n1),
inference(paramod,[status(thm)],[c_178,c_105]) ).
cnf(c_417,plain,
multiply(add(A,n1),n1) = add(n1,n1),
inference(paramod,[status(thm)],[c_8,c_183]) ).
cnf(c_418,plain,
n1 = add(n1,n1),
inference(paramod,[status(thm)],[c_1,c_417]) ).
cnf(c_199,plain,
add(n1,n1) = n1,
inference(copy,[status(thm)],[c_418]) ).
cnf(c_419,plain,
multiply(add(A,n1),add(B,multiply(n1,n1))) = add(C,n1),
inference(paramod,[status(thm)],[c_41,c_183]) ).
cnf(c_420,plain,
add(n1,n1) = add(C,n1),
inference(paramod,[status(thm)],[c_183,c_419]) ).
cnf(c_421,plain,
n1 = add(C,n1),
inference(paramod,[status(thm)],[c_199,c_420]) ).
cnf(c_201,plain,
add(A,n1) = n1,
inference(copy,[status(thm)],[c_421]) ).
cnf(c_422,plain,
multiply(inverse(A),add(n1,n1)) = add(inverse(A),multiply(add(C,n1),inverse(A))),
inference(paramod,[status(thm)],[c_201,c_133]) ).
cnf(c_423,plain,
multiply(inverse(A),n1) = add(inverse(A),multiply(add(C,n1),inverse(A))),
inference(paramod,[status(thm)],[c_201,c_422]) ).
cnf(c_424,plain,
multiply(inverse(A),n1) = add(inverse(A),multiply(n1,inverse(A))),
inference(paramod,[status(thm)],[c_201,c_423]) ).
cnf(c_216,plain,
multiply(inverse(A),n1) = add(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_18,c_424]) ).
cnf(c_425,plain,
add(multiply(inverse(A),inverse(A)),multiply(inverse(A),multiply(inverse(A),n1))) = inverse(A),
inference(paramod,[status(thm)],[c_201,c_77]) ).
cnf(c_224,plain,
add(multiply(inverse(A),inverse(A)),multiply(inverse(A),n1)) = inverse(A),
inference(paramod,[status(thm)],[c_19,c_425]) ).
cnf(c_426,plain,
add(multiply(A,n1),add(inverse(C),inverse(C))) = multiply(add(B,n1),add(A,inverse(C))),
inference(paramod,[status(thm)],[c_201,c_72]) ).
cnf(c_228,plain,
add(multiply(A,n1),add(inverse(B),inverse(B))) = multiply(n1,add(A,inverse(B))),
inference(paramod,[status(thm)],[c_201,c_426]) ).
cnf(c_427,plain,
add(add(inverse(A),inverse(A)),multiply(B,n1)) = multiply(add(C,n1),add(inverse(A),B)),
inference(paramod,[status(thm)],[c_201,c_71]) ).
cnf(c_229,plain,
add(add(inverse(A),inverse(A)),multiply(B,n1)) = multiply(n1,add(inverse(A),B)),
inference(paramod,[status(thm)],[c_201,c_427]) ).
cnf(c_428,plain,
multiply(A,multiply(add(B,A),n1)) = add(A,multiply(multiply(n1,add(B,A)),A)),
inference(paramod,[status(thm)],[c_201,c_68]) ).
cnf(c_231,plain,
add(A,multiply(multiply(n1,add(B,A)),A)) = multiply(A,multiply(add(B,A),n1)),
inference(copy,[status(thm)],[c_428]) ).
cnf(c_245,plain,
add(inverse(n1),add(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_216,c_35]) ).
cnf(c_246,plain,
multiply(inverse(A),add(inverse(A),inverse(A))) = multiply(inverse(A),n1),
inference(paramod,[status(thm)],[c_216,c_19]) ).
cnf(c_262,plain,
add(multiply(inverse(A),inverse(A)),add(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_216,c_224]) ).
cnf(c_429,plain,
multiply(inverse(A),inverse(A)) = add(multiply(inverse(n1),inverse(A)),inverse(A)),
inference(paramod,[status(thm)],[c_245,c_16]) ).
cnf(c_430,plain,
multiply(inverse(A),inverse(A)) = add(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_73,c_429]) ).
cnf(c_266,plain,
add(inverse(A),inverse(A)) = multiply(inverse(A),inverse(A)),
inference(copy,[status(thm)],[c_430]) ).
cnf(c_431,plain,
add(multiply(inverse(A),inverse(A)),multiply(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_266,c_262]) ).
cnf(c_432,plain,
multiply(inverse(A),add(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_3,c_431]) ).
cnf(c_272,plain,
multiply(inverse(A),multiply(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_266,c_432]) ).
cnf(c_433,plain,
multiply(inverse(A),multiply(inverse(A),inverse(A))) = multiply(inverse(A),n1),
inference(paramod,[status(thm)],[c_266,c_246]) ).
cnf(c_434,plain,
inverse(A) = multiply(inverse(A),n1),
inference(paramod,[status(thm)],[c_272,c_433]) ).
cnf(c_277,plain,
multiply(inverse(A),n1) = inverse(A),
inference(copy,[status(thm)],[c_434]) ).
cnf(c_278,plain,
add(inverse(n1),multiply(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_266,c_245]) ).
cnf(c_280,plain,
add(multiply(inverse(A),inverse(A)),multiply(B,n1)) = multiply(n1,add(inverse(A),B)),
inference(paramod,[status(thm)],[c_266,c_229]) ).
cnf(c_281,plain,
add(multiply(A,n1),multiply(inverse(B),inverse(B))) = multiply(n1,add(A,inverse(B))),
inference(paramod,[status(thm)],[c_266,c_228]) ).
cnf(c_435,plain,
inverse(A) = add(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_277,c_216]) ).
cnf(c_436,plain,
inverse(A) = multiply(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_266,c_435]) ).
cnf(c_286,plain,
multiply(inverse(A),inverse(A)) = inverse(A),
inference(copy,[status(thm)],[c_436]) ).
cnf(c_304,plain,
add(multiply(A,n1),inverse(B)) = multiply(n1,add(A,inverse(B))),
inference(paramod,[status(thm)],[c_286,c_281]) ).
cnf(c_305,plain,
add(inverse(A),multiply(B,n1)) = multiply(n1,add(inverse(A),B)),
inference(paramod,[status(thm)],[c_286,c_280]) ).
cnf(c_307,plain,
add(inverse(n1),inverse(A)) = inverse(A),
inference(paramod,[status(thm)],[c_286,c_278]) ).
cnf(c_323,plain,
multiply(n1,add(inverse(n1),A)) = A,
inference(paramod,[status(thm)],[c_305,c_35]) ).
cnf(c_324,plain,
inverse(inverse(n1)) = n1,
inference(paramod,[status(thm)],[c_307,c_4]) ).
cnf(c_437,plain,
add(multiply(A,n1),multiply(inverse(n1),add(A,inverse(inverse(n1))))) = A,
inference(paramod,[status(thm)],[c_324,c_10]) ).
cnf(c_438,plain,
add(multiply(A,n1),multiply(inverse(n1),add(A,n1))) = A,
inference(paramod,[status(thm)],[c_324,c_437]) ).
cnf(c_439,plain,
add(multiply(A,n1),multiply(inverse(n1),n1)) = A,
inference(paramod,[status(thm)],[c_201,c_438]) ).
cnf(c_440,plain,
add(multiply(A,n1),inverse(n1)) = A,
inference(paramod,[status(thm)],[c_277,c_439]) ).
cnf(c_329,plain,
multiply(n1,add(A,inverse(n1))) = A,
inference(paramod,[status(thm)],[c_304,c_440]) ).
cnf(c_441,plain,
add(multiply(A,n1),multiply(A,add(A,inverse(inverse(n1))))) = A,
inference(paramod,[status(thm)],[c_324,c_12]) ).
cnf(c_442,plain,
add(multiply(A,n1),multiply(A,add(A,n1))) = A,
inference(paramod,[status(thm)],[c_324,c_441]) ).
cnf(c_443,plain,
add(multiply(A,n1),multiply(A,n1)) = A,
inference(paramod,[status(thm)],[c_201,c_442]) ).
cnf(c_330,plain,
multiply(n1,add(A,A)) = A,
inference(paramod,[status(thm)],[c_3,c_443]) ).
cnf(c_444,plain,
multiply(A,multiply(inverse(n1),add(A,n1))) = multiply(inverse(n1),add(A,inverse(inverse(n1)))),
inference(paramod,[status(thm)],[c_324,c_21]) ).
cnf(c_445,plain,
multiply(A,multiply(inverse(n1),n1)) = multiply(inverse(n1),add(A,inverse(inverse(n1)))),
inference(paramod,[status(thm)],[c_201,c_444]) ).
cnf(c_446,plain,
multiply(A,inverse(n1)) = multiply(inverse(n1),add(A,inverse(inverse(n1)))),
inference(paramod,[status(thm)],[c_277,c_445]) ).
cnf(c_447,plain,
multiply(A,inverse(n1)) = multiply(inverse(n1),add(A,n1)),
inference(paramod,[status(thm)],[c_324,c_446]) ).
cnf(c_448,plain,
multiply(A,inverse(n1)) = multiply(inverse(n1),n1),
inference(paramod,[status(thm)],[c_201,c_447]) ).
cnf(c_331,plain,
multiply(A,inverse(n1)) = inverse(n1),
inference(paramod,[status(thm)],[c_277,c_448]) ).
cnf(c_449,plain,
multiply(A,A) = multiply(n1,add(A,A)),
inference(paramod,[status(thm)],[c_330,c_173]) ).
cnf(c_332,plain,
multiply(A,A) = A,
inference(paramod,[status(thm)],[c_330,c_449]) ).
cnf(c_333,plain,
add(A,multiply(B,A)) = multiply(A,add(A,B)),
inference(paramod,[status(thm)],[c_332,c_3]) ).
cnf(c_334,plain,
add(multiply(A,B),B) = multiply(B,add(A,B)),
inference(paramod,[status(thm)],[c_332,c_3]) ).
cnf(c_340,plain,
multiply(A,add(A,multiply(n1,add(B,A)))) = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_333,c_231]) ).
cnf(c_371,plain,
multiply(A,add(B,add(C,A))) = multiply(A,add(B,A)),
inference(paramod,[status(thm)],[c_334,c_16]) ).
cnf(c_372,plain,
multiply(b,add(a,b)) != b,
inference(paramod,[status(thm)],[c_334,c_13]) ).
cnf(c_375,plain,
multiply(n1,multiply(A,add(B,B))) = multiply(B,A),
inference(paramod,[status(thm)],[c_3,c_330]) ).
cnf(c_450,plain,
add(inverse(n1),multiply(n1,add(A,inverse(n1)))) = A,
inference(paramod,[status(thm)],[c_331,c_10]) ).
cnf(c_378,plain,
add(inverse(n1),A) = A,
inference(paramod,[status(thm)],[c_329,c_450]) ).
cnf(c_381,plain,
multiply(n1,A) = A,
inference(paramod,[status(thm)],[c_378,c_323]) ).
cnf(c_382,plain,
multiply(A,add(B,B)) = multiply(B,A),
inference(paramod,[status(thm)],[c_381,c_375]) ).
cnf(c_451,plain,
multiply(A,add(A,add(B,A))) = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_381,c_340]) ).
cnf(c_452,plain,
multiply(A,add(A,A)) = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_371,c_451]) ).
cnf(c_453,plain,
multiply(A,A) = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_382,c_452]) ).
cnf(c_454,plain,
A = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_332,c_453]) ).
cnf(c_384,plain,
multiply(A,multiply(add(B,A),n1)) = A,
inference(copy,[status(thm)],[c_454]) ).
cnf(c_386,plain,
multiply(A,n1) = A,
inference(paramod,[status(thm)],[c_382,c_330]) ).
cnf(c_394,plain,
multiply(A,add(B,A)) = add(A,A),
inference(paramod,[status(thm)],[c_382,c_140]) ).
cnf(c_455,plain,
multiply(A,add(B,A)) = A,
inference(paramod,[status(thm)],[c_386,c_384]) ).
cnf(c_395,plain,
add(A,A) = A,
inference(paramod,[status(thm)],[c_394,c_455]) ).
cnf(c_456,plain,
add(b,b) != b,
inference(paramod,[status(thm)],[c_394,c_372]) ).
cnf(c_457,plain,
b != b,
inference(paramod,[status(thm)],[c_395,c_456]) ).
cnf(c_400,plain,
$false,
inference(copy,[status(thm)],[c_457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 22:39:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1588355 was started by sandbox2 on n018,
% 0.11/0.37 % Sat Sep 26 22:39:37 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.44
% 0.11/0.44 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.11/0.44
% 0.11/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.44
% 0.11/0.44 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.11/0.44 % Length of proof is 82.
% 0.11/0.44 % Level of proof is 27.
% 0.11/0.44 % Maximum clause weight is 48.000.
% 0.11/0.44 % Given clauses 55.
% 0.11/0.44
% 0.11/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------