%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO023-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 3.98s 0.96s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 8
% Syntax : Number of formulae : 235 ( 235 unt; 0 def)
% Number of atoms : 235 ( 234 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 417 ( 99 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_2045,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_2045]) ).
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_property,axiom,
add(a,multiply(b,c)) != multiply(add(a,b),add(a,c)),
file('theBenchmark.p',prove_add_multiply_property) ).
cnf(c_13,plain,
add(a,multiply(b,c)) != multiply(add(a,b),add(a,c)),
inference(clausify,[status(thm)],[prove_add_multiply_property]) ).
cnf(c_14,plain,
multiply(add(a,b),add(a,c)) != add(a,multiply(b,c)),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_15,plain,
multiply(multiply(A,add(B,C)),multiply(C,A)) = multiply(C,A),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_2046,plain,
add(A,multiply(B,A)) = multiply(A,add(add(C,A),B)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_16,plain,
multiply(A,add(add(B,A),C)) = add(A,multiply(C,A)),
inference(copy,[status(thm)],[c_2046]) ).
cnf(c_2047,plain,
add(multiply(A,B),B) = multiply(B,add(A,add(C,B))),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_17,plain,
multiply(A,add(B,add(C,A))) = add(multiply(B,A),A),
inference(copy,[status(thm)],[c_2047]) ).
cnf(c_19,plain,
multiply(n1,inverse(A)) = inverse(A),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_20,plain,
multiply(A,multiply(A,n1)) = multiply(A,n1),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_22,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_2048,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_15]) ).
cnf(c_2049,plain,
multiply(add(A,B),add(multiply(C,B),B)) = multiply(B,add(C,add(A,B))),
inference(paramod,[status(thm)],[c_17,c_2048]) ).
cnf(c_26,plain,
multiply(add(A,B),add(multiply(C,B),B)) = add(multiply(C,B),B),
inference(paramod,[status(thm)],[c_17,c_2049]) ).
cnf(c_32,plain,
multiply(multiply(A,B),multiply(multiply(C,add(B,inverse(C))),A)) = multiply(multiply(C,add(B,inverse(C))),A),
inference(paramod,[status(thm)],[c_10,c_15]) ).
cnf(c_2050,plain,
add(inverse(A),multiply(B,inverse(A))) = multiply(inverse(A),add(n1,B)),
inference(paramod,[status(thm)],[c_19,c_3]) ).
cnf(c_34,plain,
multiply(inverse(A),add(n1,B)) = add(inverse(A),multiply(B,inverse(A))),
inference(copy,[status(thm)],[c_2050]) ).
cnf(c_36,plain,
add(inverse(n1),multiply(A,n1)) = A,
inference(paramod,[status(thm)],[c_19,c_8]) ).
cnf(c_37,plain,
add(inverse(A),multiply(A,add(n1,inverse(A)))) = n1,
inference(paramod,[status(thm)],[c_19,c_10]) ).
cnf(c_38,plain,
add(inverse(A),multiply(n1,add(n1,inverse(A)))) = n1,
inference(paramod,[status(thm)],[c_19,c_12]) ).
cnf(c_40,plain,
add(inverse(n1),n1) = add(A,n1),
inference(paramod,[status(thm)],[c_1,c_36]) ).
cnf(c_42,plain,
add(A,n1) = add(B,n1),
inference(paramod,[status(thm)],[c_40,c_40]) ).
cnf(c_2051,plain,
add(multiply(A,B),multiply(n1,B)) = multiply(B,add(C,n1)),
inference(paramod,[status(thm)],[c_42,c_3]) ).
cnf(c_43,plain,
multiply(A,add(B,n1)) = multiply(A,add(C,n1)),
inference(paramod,[status(thm)],[c_3,c_2051]) ).
cnf(c_45,plain,
add(multiply(A,add(B,n1)),multiply(C,add(D,n1))) = multiply(add(D,n1),add(A,C)),
inference(paramod,[status(thm)],[c_43,c_3]) ).
cnf(c_2052,plain,
add(multiply(A,add(B,n1)),multiply(C,add(D,n1))) = multiply(add(B,n1),add(A,C)),
inference(paramod,[status(thm)],[c_43,c_3]) ).
cnf(c_46,plain,
multiply(add(A,n1),add(B,C)) = multiply(add(D,n1),add(B,C)),
inference(paramod,[status(thm)],[c_45,c_2052]) ).
cnf(c_58,plain,
multiply(A,add(B,n1)) = add(A,multiply(n1,A)),
inference(paramod,[status(thm)],[c_42,c_16]) ).
cnf(c_65,plain,
multiply(inverse(A),add(B,n1)) = add(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_19,c_58]) ).
cnf(c_2053,plain,
multiply(multiply(n1,n1),add(A,n1)) = add(multiply(n1,n1),multiply(n1,n1)),
inference(paramod,[status(thm)],[c_20,c_58]) ).
cnf(c_67,plain,
multiply(multiply(n1,n1),add(A,n1)) = multiply(n1,add(n1,n1)),
inference(paramod,[status(thm)],[c_3,c_2053]) ).
cnf(c_69,plain,
multiply(A,multiply(add(B,A),add(C,n1))) = add(A,multiply(multiply(n1,add(B,A)),A)),
inference(paramod,[status(thm)],[c_58,c_16]) ).
cnf(c_72,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_65,c_3]) ).
cnf(c_73,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_65,c_3]) ).
cnf(c_2054,plain,
add(multiply(A,inverse(B)),multiply(n1,inverse(B))) = add(inverse(B),inverse(B)),
inference(paramod,[status(thm)],[c_65,c_3]) ).
cnf(c_74,plain,
add(multiply(A,inverse(B)),inverse(B)) = add(inverse(B),inverse(B)),
inference(paramod,[status(thm)],[c_19,c_2054]) ).
cnf(c_78,plain,
add(multiply(inverse(A),inverse(A)),multiply(inverse(A),multiply(inverse(A),add(B,n1)))) = inverse(A),
inference(paramod,[status(thm)],[c_65,c_12]) ).
cnf(c_2055,plain,
multiply(add(A,n1),add(add(B,add(A,n1)),inverse(C))) = add(add(A,n1),add(inverse(C),inverse(C))),
inference(paramod,[status(thm)],[c_65,c_16]) ).
cnf(c_81,plain,
add(add(A,n1),multiply(inverse(B),add(A,n1))) = add(add(A,n1),add(inverse(B),inverse(B))),
inference(paramod,[status(thm)],[c_16,c_2055]) ).
cnf(c_2056,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_46]) ).
cnf(c_87,plain,
multiply(add(A,n1),B) = multiply(add(C,n1),B),
inference(paramod,[status(thm)],[c_8,c_2056]) ).
cnf(c_2057,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_67,c_3]) ).
cnf(c_2058,plain,
multiply(add(n1,n1),add(A,n1)) = multiply(add(B,n1),add(A,multiply(n1,n1))),
inference(paramod,[status(thm)],[c_45,c_2057]) ).
cnf(c_109,plain,
multiply(add(A,n1),add(B,multiply(n1,n1))) = multiply(add(n1,n1),add(B,n1)),
inference(copy,[status(thm)],[c_2058]) ).
cnf(c_134,plain,
multiply(inverse(A),add(n1,add(B,n1))) = add(inverse(A),multiply(add(C,n1),inverse(A))),
inference(paramod,[status(thm)],[c_87,c_34]) ).
cnf(c_2059,plain,
multiply(add(A,B),add(B,B)) = add(multiply(add(C,B),B),B),
inference(paramod,[status(thm)],[c_1,c_26]) ).
cnf(c_139,plain,
multiply(add(A,B),add(B,B)) = add(B,B),
inference(paramod,[status(thm)],[c_1,c_2059]) ).
cnf(c_2060,plain,
multiply(A,add(multiply(A,n1),multiply(A,n1))) = add(multiply(A,n1),multiply(A,n1)),
inference(paramod,[status(thm)],[c_8,c_139]) ).
cnf(c_2061,plain,
multiply(A,multiply(n1,add(A,A))) = add(multiply(A,n1),multiply(A,n1)),
inference(paramod,[status(thm)],[c_3,c_2060]) ).
cnf(c_164,plain,
multiply(A,multiply(n1,add(A,A))) = multiply(n1,add(A,A)),
inference(paramod,[status(thm)],[c_3,c_2061]) ).
cnf(c_169,plain,
multiply(add(A,n1),add(B,n1)) = add(n1,n1),
inference(paramod,[status(thm)],[c_42,c_139]) ).
cnf(c_173,plain,
multiply(add(A,n1),add(B,multiply(n1,n1))) = add(n1,n1),
inference(paramod,[status(thm)],[c_169,c_109]) ).
cnf(c_2062,plain,
add(add(n1,n1),multiply(A,add(B,multiply(n1,n1)))) = multiply(add(B,multiply(n1,n1)),add(add(C,n1),A)),
inference(paramod,[status(thm)],[c_173,c_3]) ).
cnf(c_195,plain,
multiply(add(A,multiply(n1,n1)),add(add(B,n1),C)) = add(add(n1,n1),multiply(C,add(A,multiply(n1,n1)))),
inference(copy,[status(thm)],[c_2062]) ).
cnf(c_2063,plain,
multiply(add(A,n1),n1) = add(n1,n1),
inference(paramod,[status(thm)],[c_8,c_173]) ).
cnf(c_2064,plain,
n1 = add(n1,n1),
inference(paramod,[status(thm)],[c_1,c_2063]) ).
cnf(c_198,plain,
add(n1,n1) = n1,
inference(copy,[status(thm)],[c_2064]) ).
cnf(c_2065,plain,
multiply(add(A,n1),add(B,multiply(n1,n1))) = add(C,n1),
inference(paramod,[status(thm)],[c_42,c_173]) ).
cnf(c_2066,plain,
add(n1,n1) = add(C,n1),
inference(paramod,[status(thm)],[c_173,c_2065]) ).
cnf(c_2067,plain,
n1 = add(C,n1),
inference(paramod,[status(thm)],[c_198,c_2066]) ).
cnf(c_200,plain,
add(A,n1) = n1,
inference(copy,[status(thm)],[c_2067]) ).
cnf(c_2068,plain,
multiply(add(A,n1),multiply(n1,add(B,n1))) = add(n1,n1),
inference(paramod,[status(thm)],[c_58,c_173]) ).
cnf(c_2069,plain,
multiply(n1,multiply(n1,add(B,n1))) = add(n1,n1),
inference(paramod,[status(thm)],[c_200,c_2068]) ).
cnf(c_2070,plain,
multiply(n1,multiply(n1,n1)) = add(n1,n1),
inference(paramod,[status(thm)],[c_200,c_2069]) ).
cnf(c_2071,plain,
multiply(n1,n1) = add(n1,n1),
inference(paramod,[status(thm)],[c_20,c_2070]) ).
cnf(c_203,plain,
multiply(n1,n1) = n1,
inference(paramod,[status(thm)],[c_200,c_2071]) ).
cnf(c_2072,plain,
multiply(add(A,n1),add(add(B,n1),C)) = add(add(n1,n1),multiply(C,add(A,multiply(n1,n1)))),
inference(paramod,[status(thm)],[c_203,c_195]) ).
cnf(c_2073,plain,
multiply(n1,add(add(B,n1),C)) = add(add(n1,n1),multiply(C,add(A,multiply(n1,n1)))),
inference(paramod,[status(thm)],[c_200,c_2072]) ).
cnf(c_2074,plain,
multiply(n1,add(n1,C)) = add(add(n1,n1),multiply(C,add(A,multiply(n1,n1)))),
inference(paramod,[status(thm)],[c_200,c_2073]) ).
cnf(c_2075,plain,
multiply(n1,add(n1,C)) = add(n1,multiply(C,add(A,multiply(n1,n1)))),
inference(paramod,[status(thm)],[c_200,c_2074]) ).
cnf(c_2076,plain,
multiply(n1,add(n1,C)) = add(n1,multiply(C,add(A,n1))),
inference(paramod,[status(thm)],[c_203,c_2075]) ).
cnf(c_2077,plain,
multiply(n1,add(n1,C)) = add(n1,multiply(C,n1)),
inference(paramod,[status(thm)],[c_200,c_2076]) ).
cnf(c_204,plain,
add(n1,multiply(A,n1)) = multiply(n1,add(n1,A)),
inference(copy,[status(thm)],[c_2077]) ).
cnf(c_2078,plain,
multiply(inverse(A),add(n1,n1)) = add(inverse(A),multiply(add(C,n1),inverse(A))),
inference(paramod,[status(thm)],[c_200,c_134]) ).
cnf(c_2079,plain,
multiply(inverse(A),n1) = add(inverse(A),multiply(add(C,n1),inverse(A))),
inference(paramod,[status(thm)],[c_200,c_2078]) ).
cnf(c_2080,plain,
multiply(inverse(A),n1) = add(inverse(A),multiply(n1,inverse(A))),
inference(paramod,[status(thm)],[c_200,c_2079]) ).
cnf(c_213,plain,
multiply(inverse(A),n1) = add(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_19,c_2080]) ).
cnf(c_2081,plain,
add(n1,multiply(inverse(B),add(A,n1))) = add(add(A,n1),add(inverse(B),inverse(B))),
inference(paramod,[status(thm)],[c_200,c_81]) ).
cnf(c_2082,plain,
add(n1,multiply(inverse(B),n1)) = add(add(A,n1),add(inverse(B),inverse(B))),
inference(paramod,[status(thm)],[c_200,c_2081]) ).
cnf(c_2083,plain,
multiply(n1,add(n1,inverse(B))) = add(add(A,n1),add(inverse(B),inverse(B))),
inference(paramod,[status(thm)],[c_204,c_2082]) ).
cnf(c_218,plain,
multiply(n1,add(n1,inverse(A))) = add(n1,add(inverse(A),inverse(A))),
inference(paramod,[status(thm)],[c_200,c_2083]) ).
cnf(c_2084,plain,
add(multiply(inverse(A),inverse(A)),multiply(inverse(A),multiply(inverse(A),n1))) = inverse(A),
inference(paramod,[status(thm)],[c_200,c_78]) ).
cnf(c_221,plain,
add(multiply(inverse(A),inverse(A)),multiply(inverse(A),n1)) = inverse(A),
inference(paramod,[status(thm)],[c_20,c_2084]) ).
cnf(c_2085,plain,
add(multiply(A,n1),add(inverse(C),inverse(C))) = multiply(add(B,n1),add(A,inverse(C))),
inference(paramod,[status(thm)],[c_200,c_73]) ).
cnf(c_225,plain,
add(multiply(A,n1),add(inverse(B),inverse(B))) = multiply(n1,add(A,inverse(B))),
inference(paramod,[status(thm)],[c_200,c_2085]) ).
cnf(c_2086,plain,
add(add(inverse(A),inverse(A)),multiply(B,n1)) = multiply(add(C,n1),add(inverse(A),B)),
inference(paramod,[status(thm)],[c_200,c_72]) ).
cnf(c_226,plain,
add(add(inverse(A),inverse(A)),multiply(B,n1)) = multiply(n1,add(inverse(A),B)),
inference(paramod,[status(thm)],[c_200,c_2086]) ).
cnf(c_2087,plain,
multiply(A,multiply(add(B,A),n1)) = add(A,multiply(multiply(n1,add(B,A)),A)),
inference(paramod,[status(thm)],[c_200,c_69]) ).
cnf(c_228,plain,
add(A,multiply(multiply(n1,add(B,A)),A)) = multiply(A,multiply(add(B,A),n1)),
inference(copy,[status(thm)],[c_2087]) ).
cnf(c_242,plain,
add(inverse(n1),add(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_213,c_36]) ).
cnf(c_243,plain,
multiply(inverse(A),add(inverse(A),inverse(A))) = multiply(inverse(A),n1),
inference(paramod,[status(thm)],[c_213,c_20]) ).
cnf(c_250,plain,
add(multiply(inverse(A),inverse(A)),add(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_213,c_221]) ).
cnf(c_251,plain,
add(multiply(inverse(A),n1),multiply(B,add(inverse(A),inverse(A)))) = multiply(add(inverse(A),inverse(A)),add(inverse(A),B)),
inference(paramod,[status(thm)],[c_243,c_3]) ).
cnf(c_2088,plain,
multiply(inverse(A),inverse(A)) = add(multiply(inverse(n1),inverse(A)),inverse(A)),
inference(paramod,[status(thm)],[c_242,c_17]) ).
cnf(c_2089,plain,
multiply(inverse(A),inverse(A)) = add(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_74,c_2088]) ).
cnf(c_270,plain,
add(inverse(A),inverse(A)) = multiply(inverse(A),inverse(A)),
inference(copy,[status(thm)],[c_2089]) ).
cnf(c_2090,plain,
add(multiply(inverse(A),n1),multiply(B,multiply(inverse(A),inverse(A)))) = multiply(add(inverse(A),inverse(A)),add(inverse(A),B)),
inference(paramod,[status(thm)],[c_270,c_251]) ).
cnf(c_281,plain,
add(multiply(inverse(A),n1),multiply(B,multiply(inverse(A),inverse(A)))) = multiply(multiply(inverse(A),inverse(A)),add(inverse(A),B)),
inference(paramod,[status(thm)],[c_270,c_2090]) ).
cnf(c_2091,plain,
add(multiply(inverse(A),inverse(A)),multiply(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_270,c_250]) ).
cnf(c_2092,plain,
multiply(inverse(A),add(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_3,c_2091]) ).
cnf(c_282,plain,
multiply(inverse(A),multiply(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_270,c_2092]) ).
cnf(c_2093,plain,
multiply(inverse(A),multiply(inverse(A),inverse(A))) = multiply(inverse(A),n1),
inference(paramod,[status(thm)],[c_270,c_243]) ).
cnf(c_2094,plain,
inverse(A) = multiply(inverse(A),n1),
inference(paramod,[status(thm)],[c_282,c_2093]) ).
cnf(c_285,plain,
multiply(inverse(A),n1) = inverse(A),
inference(copy,[status(thm)],[c_2094]) ).
cnf(c_286,plain,
add(inverse(n1),multiply(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_270,c_242]) ).
cnf(c_288,plain,
add(multiply(inverse(A),inverse(A)),multiply(B,n1)) = multiply(n1,add(inverse(A),B)),
inference(paramod,[status(thm)],[c_270,c_226]) ).
cnf(c_289,plain,
add(multiply(A,n1),multiply(inverse(B),inverse(B))) = multiply(n1,add(A,inverse(B))),
inference(paramod,[status(thm)],[c_270,c_225]) ).
cnf(c_292,plain,
multiply(n1,add(n1,inverse(A))) = add(n1,multiply(inverse(A),inverse(A))),
inference(paramod,[status(thm)],[c_270,c_218]) ).
cnf(c_2095,plain,
inverse(A) = add(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_285,c_213]) ).
cnf(c_2096,plain,
inverse(A) = multiply(inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_270,c_2095]) ).
cnf(c_294,plain,
multiply(inverse(A),inverse(A)) = inverse(A),
inference(copy,[status(thm)],[c_2096]) ).
cnf(c_2097,plain,
add(inverse(A),multiply(B,multiply(inverse(A),inverse(A)))) = multiply(multiply(inverse(A),inverse(A)),add(inverse(A),B)),
inference(paramod,[status(thm)],[c_285,c_281]) ).
cnf(c_2098,plain,
add(inverse(A),multiply(B,inverse(A))) = multiply(multiply(inverse(A),inverse(A)),add(inverse(A),B)),
inference(paramod,[status(thm)],[c_294,c_2097]) ).
cnf(c_301,plain,
add(inverse(A),multiply(B,inverse(A))) = multiply(inverse(A),add(inverse(A),B)),
inference(paramod,[status(thm)],[c_294,c_2098]) ).
cnf(c_311,plain,
multiply(n1,add(n1,inverse(A))) = add(n1,inverse(A)),
inference(paramod,[status(thm)],[c_294,c_292]) ).
cnf(c_312,plain,
add(multiply(A,n1),inverse(B)) = multiply(n1,add(A,inverse(B))),
inference(paramod,[status(thm)],[c_294,c_289]) ).
cnf(c_313,plain,
add(inverse(A),multiply(B,n1)) = multiply(n1,add(inverse(A),B)),
inference(paramod,[status(thm)],[c_294,c_288]) ).
cnf(c_315,plain,
add(inverse(n1),inverse(A)) = inverse(A),
inference(paramod,[status(thm)],[c_294,c_286]) ).
cnf(c_317,plain,
add(inverse(A),inverse(A)) = inverse(A),
inference(paramod,[status(thm)],[c_294,c_270]) ).
cnf(c_330,plain,
add(inverse(A),add(n1,inverse(A))) = n1,
inference(paramod,[status(thm)],[c_311,c_38]) ).
cnf(c_331,plain,
multiply(n1,add(inverse(n1),A)) = A,
inference(paramod,[status(thm)],[c_313,c_36]) ).
cnf(c_332,plain,
inverse(inverse(n1)) = n1,
inference(paramod,[status(thm)],[c_315,c_4]) ).
cnf(c_2099,plain,
add(multiply(inverse(n1),inverse(A)),multiply(inverse(n1),inverse(A))) = inverse(n1),
inference(paramod,[status(thm)],[c_315,c_12]) ).
cnf(c_2100,plain,
multiply(inverse(A),add(inverse(n1),inverse(n1))) = inverse(n1),
inference(paramod,[status(thm)],[c_3,c_2099]) ).
cnf(c_334,plain,
multiply(inverse(A),inverse(n1)) = inverse(n1),
inference(paramod,[status(thm)],[c_317,c_2100]) ).
cnf(c_2101,plain,
multiply(inverse(n1),multiply(A,inverse(A))) = multiply(A,add(inverse(n1),inverse(A))),
inference(paramod,[status(thm)],[c_315,c_22]) ).
cnf(c_335,plain,
multiply(inverse(n1),multiply(A,inverse(A))) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_315,c_2101]) ).
cnf(c_2102,plain,
add(inverse(n1),multiply(A,inverse(n1))) = multiply(inverse(n1),add(inverse(B),A)),
inference(paramod,[status(thm)],[c_334,c_3]) ).
cnf(c_337,plain,
multiply(inverse(n1),add(inverse(n1),A)) = multiply(inverse(n1),add(inverse(B),A)),
inference(paramod,[status(thm)],[c_301,c_2102]) ).
cnf(c_2103,plain,
add(multiply(A,n1),multiply(inverse(n1),add(A,inverse(inverse(n1))))) = A,
inference(paramod,[status(thm)],[c_332,c_10]) ).
cnf(c_2104,plain,
add(multiply(A,n1),multiply(inverse(n1),add(A,n1))) = A,
inference(paramod,[status(thm)],[c_332,c_2103]) ).
cnf(c_2105,plain,
add(multiply(A,n1),multiply(inverse(n1),n1)) = A,
inference(paramod,[status(thm)],[c_200,c_2104]) ).
cnf(c_2106,plain,
add(multiply(A,n1),inverse(n1)) = A,
inference(paramod,[status(thm)],[c_285,c_2105]) ).
cnf(c_340,plain,
multiply(n1,add(A,inverse(n1))) = A,
inference(paramod,[status(thm)],[c_312,c_2106]) ).
cnf(c_2107,plain,
add(multiply(A,n1),multiply(A,add(A,inverse(inverse(n1))))) = A,
inference(paramod,[status(thm)],[c_332,c_12]) ).
cnf(c_2108,plain,
add(multiply(A,n1),multiply(A,add(A,n1))) = A,
inference(paramod,[status(thm)],[c_332,c_2107]) ).
cnf(c_2109,plain,
add(multiply(A,n1),multiply(A,n1)) = A,
inference(paramod,[status(thm)],[c_200,c_2108]) ).
cnf(c_341,plain,
multiply(n1,add(A,A)) = A,
inference(paramod,[status(thm)],[c_3,c_2109]) ).
cnf(c_2110,plain,
multiply(A,multiply(inverse(n1),add(A,n1))) = multiply(inverse(n1),add(A,inverse(inverse(n1)))),
inference(paramod,[status(thm)],[c_332,c_22]) ).
cnf(c_2111,plain,
multiply(A,multiply(inverse(n1),n1)) = multiply(inverse(n1),add(A,inverse(inverse(n1)))),
inference(paramod,[status(thm)],[c_200,c_2110]) ).
cnf(c_2112,plain,
multiply(A,inverse(n1)) = multiply(inverse(n1),add(A,inverse(inverse(n1)))),
inference(paramod,[status(thm)],[c_285,c_2111]) ).
cnf(c_2113,plain,
multiply(A,inverse(n1)) = multiply(inverse(n1),add(A,n1)),
inference(paramod,[status(thm)],[c_332,c_2112]) ).
cnf(c_2114,plain,
multiply(A,inverse(n1)) = multiply(inverse(n1),n1),
inference(paramod,[status(thm)],[c_200,c_2113]) ).
cnf(c_342,plain,
multiply(A,inverse(n1)) = inverse(n1),
inference(paramod,[status(thm)],[c_285,c_2114]) ).
cnf(c_2115,plain,
multiply(A,A) = multiply(n1,add(A,A)),
inference(paramod,[status(thm)],[c_341,c_164]) ).
cnf(c_343,plain,
multiply(A,A) = A,
inference(paramod,[status(thm)],[c_341,c_2115]) ).
cnf(c_344,plain,
add(A,multiply(B,A)) = multiply(A,add(A,B)),
inference(paramod,[status(thm)],[c_343,c_3]) ).
cnf(c_345,plain,
add(multiply(A,B),B) = multiply(B,add(A,B)),
inference(paramod,[status(thm)],[c_343,c_3]) ).
cnf(c_351,plain,
multiply(A,add(A,multiply(n1,add(B,A)))) = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_344,c_228]) ).
cnf(c_382,plain,
multiply(A,add(B,add(C,A))) = multiply(A,add(B,A)),
inference(paramod,[status(thm)],[c_345,c_17]) ).
cnf(c_412,plain,
multiply(n1,multiply(A,add(B,B))) = multiply(B,A),
inference(paramod,[status(thm)],[c_3,c_341]) ).
cnf(c_2116,plain,
add(inverse(n1),multiply(A,inverse(n1))) = multiply(inverse(n1),add(B,A)),
inference(paramod,[status(thm)],[c_342,c_3]) ).
cnf(c_2117,plain,
add(inverse(n1),inverse(n1)) = multiply(inverse(n1),add(B,A)),
inference(paramod,[status(thm)],[c_342,c_2116]) ).
cnf(c_2118,plain,
inverse(n1) = multiply(inverse(n1),add(B,A)),
inference(paramod,[status(thm)],[c_317,c_2117]) ).
cnf(c_415,plain,
multiply(inverse(n1),add(A,B)) = inverse(n1),
inference(copy,[status(thm)],[c_2118]) ).
cnf(c_2119,plain,
add(inverse(n1),multiply(n1,add(A,inverse(n1)))) = A,
inference(paramod,[status(thm)],[c_342,c_10]) ).
cnf(c_416,plain,
add(inverse(n1),A) = A,
inference(paramod,[status(thm)],[c_340,c_2119]) ).
cnf(c_2120,plain,
multiply(inverse(n1),A) = multiply(inverse(n1),add(inverse(B),A)),
inference(paramod,[status(thm)],[c_416,c_337]) ).
cnf(c_419,plain,
multiply(inverse(n1),A) = inverse(n1),
inference(paramod,[status(thm)],[c_415,c_2120]) ).
cnf(c_421,plain,
multiply(n1,A) = A,
inference(paramod,[status(thm)],[c_416,c_331]) ).
cnf(c_2121,plain,
inverse(n1) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_419,c_335]) ).
cnf(c_422,plain,
multiply(A,inverse(A)) = inverse(n1),
inference(copy,[status(thm)],[c_2121]) ).
cnf(c_423,plain,
multiply(A,add(B,B)) = multiply(B,A),
inference(paramod,[status(thm)],[c_421,c_412]) ).
cnf(c_2122,plain,
multiply(A,add(A,add(B,A))) = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_421,c_351]) ).
cnf(c_2123,plain,
multiply(A,add(A,A)) = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_382,c_2122]) ).
cnf(c_2124,plain,
multiply(A,A) = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_423,c_2123]) ).
cnf(c_2125,plain,
A = multiply(A,multiply(add(B,A),n1)),
inference(paramod,[status(thm)],[c_343,c_2124]) ).
cnf(c_427,plain,
multiply(A,multiply(add(B,A),n1)) = A,
inference(copy,[status(thm)],[c_2125]) ).
cnf(c_429,plain,
multiply(A,n1) = A,
inference(paramod,[status(thm)],[c_423,c_341]) ).
cnf(c_437,plain,
multiply(A,add(B,A)) = add(A,A),
inference(paramod,[status(thm)],[c_423,c_139]) ).
cnf(c_2126,plain,
multiply(A,add(B,A)) = A,
inference(paramod,[status(thm)],[c_429,c_427]) ).
cnf(c_438,plain,
add(A,A) = A,
inference(paramod,[status(thm)],[c_437,c_2126]) ).
cnf(c_2127,plain,
add(multiply(A,B),B) = add(B,B),
inference(paramod,[status(thm)],[c_437,c_345]) ).
cnf(c_455,plain,
add(multiply(A,B),B) = B,
inference(paramod,[status(thm)],[c_438,c_2127]) ).
cnf(c_456,plain,
multiply(A,add(B,A)) = A,
inference(paramod,[status(thm)],[c_438,c_437]) ).
cnf(c_459,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_438,c_423]) ).
cnf(c_2128,plain,
add(A,multiply(B,A)) = multiply(A,add(n1,B)),
inference(paramod,[status(thm)],[c_421,c_3]) ).
cnf(c_2129,plain,
multiply(A,add(A,B)) = multiply(A,add(n1,B)),
inference(paramod,[status(thm)],[c_344,c_2128]) ).
cnf(c_471,plain,
multiply(A,add(n1,B)) = multiply(A,add(A,B)),
inference(copy,[status(thm)],[c_2129]) ).
cnf(c_479,plain,
add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)),
inference(paramod,[status(thm)],[c_459,c_3]) ).
cnf(c_487,plain,
multiply(A,multiply(multiply(B,add(n1,inverse(B))),A)) = multiply(multiply(B,add(n1,inverse(B))),A),
inference(paramod,[status(thm)],[c_429,c_32]) ).
cnf(c_494,plain,
add(A,multiply(B,add(C,A))) = multiply(add(C,A),add(A,B)),
inference(paramod,[status(thm)],[c_456,c_3]) ).
cnf(c_498,plain,
add(A,add(B,A)) = add(B,A),
inference(paramod,[status(thm)],[c_456,c_455]) ).
cnf(c_501,plain,
multiply(add(n1,inverse(A)),add(inverse(A),A)) = n1,
inference(paramod,[status(thm)],[c_494,c_37]) ).
cnf(c_504,plain,
add(n1,inverse(A)) = n1,
inference(paramod,[status(thm)],[c_498,c_330]) ).
cnf(c_2130,plain,
multiply(n1,add(inverse(A),A)) = n1,
inference(paramod,[status(thm)],[c_504,c_501]) ).
cnf(c_505,plain,
add(inverse(A),A) = n1,
inference(paramod,[status(thm)],[c_421,c_2130]) ).
cnf(c_2131,plain,
multiply(A,multiply(multiply(B,n1),A)) = multiply(multiply(B,add(n1,inverse(B))),A),
inference(paramod,[status(thm)],[c_504,c_487]) ).
cnf(c_2132,plain,
multiply(A,multiply(B,A)) = multiply(multiply(B,add(n1,inverse(B))),A),
inference(paramod,[status(thm)],[c_429,c_2131]) ).
cnf(c_2133,plain,
multiply(A,multiply(B,A)) = multiply(multiply(B,n1),A),
inference(paramod,[status(thm)],[c_504,c_2132]) ).
cnf(c_507,plain,
multiply(A,multiply(B,A)) = multiply(B,A),
inference(paramod,[status(thm)],[c_429,c_2133]) ).
cnf(c_2134,plain,
add(multiply(inverse(inverse(A)),inverse(A)),multiply(A,n1)) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_505,c_10]) ).
cnf(c_2135,plain,
add(multiply(inverse(A),inverse(inverse(A))),multiply(A,n1)) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_459,c_2134]) ).
cnf(c_2136,plain,
add(inverse(n1),multiply(A,n1)) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_422,c_2135]) ).
cnf(c_2137,plain,
add(inverse(n1),A) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_429,c_2136]) ).
cnf(c_2138,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_416,c_2137]) ).
cnf(c_517,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_2138]) ).
cnf(c_523,plain,
add(n1,A) = n1,
inference(paramod,[status(thm)],[c_517,c_504]) ).
cnf(c_2139,plain,
multiply(A,n1) = multiply(A,add(A,B)),
inference(paramod,[status(thm)],[c_523,c_471]) ).
cnf(c_2140,plain,
A = multiply(A,add(A,B)),
inference(paramod,[status(thm)],[c_429,c_2139]) ).
cnf(c_533,plain,
multiply(A,add(A,B)) = A,
inference(copy,[status(thm)],[c_2140]) ).
cnf(c_541,plain,
add(A,multiply(B,add(A,C))) = multiply(add(A,C),add(A,B)),
inference(paramod,[status(thm)],[c_533,c_3]) ).
cnf(c_2141,plain,
add(multiply(A,multiply(B,C)),multiply(B,C)) = multiply(multiply(B,C),add(A,C)),
inference(paramod,[status(thm)],[c_507,c_3]) ).
cnf(c_2142,plain,
multiply(B,C) = multiply(multiply(B,C),add(A,C)),
inference(paramod,[status(thm)],[c_455,c_2141]) ).
cnf(c_641,plain,
multiply(multiply(A,B),add(C,B)) = multiply(A,B),
inference(copy,[status(thm)],[c_2142]) ).
cnf(c_2143,plain,
add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,multiply(C,B))),
inference(paramod,[status(thm)],[c_507,c_479]) ).
cnf(c_2144,plain,
multiply(B,add(A,C)) = multiply(B,add(A,multiply(C,B))),
inference(paramod,[status(thm)],[c_3,c_2143]) ).
cnf(c_643,plain,
multiply(A,add(B,multiply(C,A))) = multiply(A,add(B,C)),
inference(copy,[status(thm)],[c_2144]) ).
cnf(c_2145,plain,
add(A,multiply(B,C)) = multiply(add(A,C),add(A,multiply(B,C))),
inference(paramod,[status(thm)],[c_641,c_541]) ).
cnf(c_2038,plain,
multiply(add(A,B),add(A,multiply(C,B))) = add(A,multiply(C,B)),
inference(copy,[status(thm)],[c_2145]) ).
cnf(c_2146,plain,
add(A,multiply(B,add(A,C))) = multiply(add(A,multiply(C,B)),add(A,B)),
inference(paramod,[status(thm)],[c_643,c_541]) ).
cnf(c_2147,plain,
multiply(add(A,C),add(A,B)) = multiply(add(A,multiply(C,B)),add(A,B)),
inference(paramod,[status(thm)],[c_541,c_2146]) ).
cnf(c_2148,plain,
multiply(add(A,C),add(A,B)) = multiply(add(A,B),add(A,multiply(C,B))),
inference(paramod,[status(thm)],[c_459,c_2147]) ).
cnf(c_2043,plain,
multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_2038,c_2148]) ).
cnf(c_2044,plain,
$false,
inference(resolve,[status(thm)],[c_2043,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO023-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.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 22:37:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 77955 was started by sandbox on n014,
% 0.11/0.38 % Sat Sep 26 22:37:01 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 3.98/0.96
% 3.98/0.96 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 3.98/0.96
% 3.98/0.96 % SZS status Unsatisfiable for theBenchmark
% 3.98/0.96
% 3.98/0.96 % Proof 1 at 0.42 (+ 0.14) seconds.
% 3.98/0.96 % Length of proof is 123.
% 3.98/0.96 % Level of proof is 37.
% 3.98/0.96 % Maximum clause weight is 71.000.
% 3.98/0.96 % Given clauses 170.
% 3.98/0.96
% 3.98/0.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------