%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO015-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 06:55:06 AM UTC 2026
% Result : Unsatisfiable 0.95s 0.66s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 14
% Syntax : Number of formulae : 149 ( 149 unt; 0 def)
% Number of atoms : 149 ( 148 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 278 ( 32 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(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_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(a_times_b_is_c,axiom,
multiply(a,b) = c,
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c_17,plain,
multiply(a,b) = c,
inference(clausify,[status(thm)],[a_times_b_is_c]) ).
cnf(c_18,plain,
c = multiply(a,b),
inference(copy,[status(thm)],[c_17]) ).
fof(a_inverse_plus_b_inverse_is_d,axiom,
add(inverse(a),inverse(b)) = d,
file('theBenchmark.p',a_inverse_plus_b_inverse_is_d) ).
cnf(c_19,plain,
add(inverse(a),inverse(b)) = d,
inference(clausify,[status(thm)],[a_inverse_plus_b_inverse_is_d]) ).
cnf(c_20,plain,
d = add(inverse(a),inverse(b)),
inference(copy,[status(thm)],[c_19]) ).
fof(prove_c_inverse_is_d,axiom,
inverse(c) != d,
file('theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c_21,plain,
inverse(c) != d,
inference(clausify,[status(thm)],[prove_c_inverse_is_d]) ).
cnf(c_383,plain,
inverse(multiply(a,b)) != d,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_22,plain,
inverse(multiply(a,b)) != add(inverse(a),inverse(b)),
inference(paramod,[status(thm)],[c_20,c_383]) ).
cnf(c_384,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_385,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_384]) ).
cnf(c_386,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_385]) ).
cnf(c_24,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_386]) ).
cnf(c_387,plain,
multiply(multiplicative_identity,A) = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_388,plain,
A = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_14,c_387]) ).
cnf(c_25,plain,
add(multiply(A,B),multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_388]) ).
cnf(c_389,plain,
multiply(A,multiplicative_identity) = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_390,plain,
A = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_13,c_389]) ).
cnf(c_26,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(copy,[status(thm)],[c_390]) ).
cnf(c_391,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_27,plain,
add(multiply(A,inverse(add(A,B))),multiply(B,inverse(add(A,B)))) = additive_identity,
inference(copy,[status(thm)],[c_391]) ).
cnf(c_33,plain,
inverse(additive_identity) = multiplicative_identity,
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_47,plain,
add(multiply(A,B),multiply(inverse(B),A)) = A,
inference(paramod,[status(thm)],[c_2,c_25]) ).
cnf(c_392,plain,
multiply(A,B) = add(multiply(multiply(C,A),B),multiply(multiply(inverse(C),A),B)),
inference(paramod,[status(thm)],[c_25,c_7]) ).
cnf(c_49,plain,
add(multiply(multiply(A,B),C),multiply(multiply(inverse(A),B),C)) = multiply(B,C),
inference(copy,[status(thm)],[c_392]) ).
cnf(c_393,plain,
add(additive_identity,multiply(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_11,c_25]) ).
cnf(c_52,plain,
multiply(inverse(A),inverse(A)) = inverse(A),
inference(paramod,[status(thm)],[c_16,c_393]) ).
cnf(c_394,plain,
add(multiply(A,inverse(inverse(A))),additive_identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_11,c_25]) ).
cnf(c_395,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1,c_394]) ).
cnf(c_53,plain,
multiply(A,inverse(inverse(A))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_16,c_395]) ).
cnf(c_396,plain,
add(A,add(multiply(inverse(B),B),multiply(inverse(B),inverse(B)))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_25,c_24]) ).
cnf(c_397,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_396]) ).
cnf(c_398,plain,
add(A,add(additive_identity,multiply(inverse(B),inverse(B)))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_11,c_397]) ).
cnf(c_399,plain,
add(A,add(additive_identity,inverse(B))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_52,c_398]) ).
cnf(c_400,plain,
add(A,inverse(B)) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_16,c_399]) ).
cnf(c_55,plain,
add(multiply(A,B),inverse(A)) = add(B,inverse(A)),
inference(copy,[status(thm)],[c_400]) ).
cnf(c_401,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = A,
inference(paramod,[status(thm)],[c_11,c_26]) ).
cnf(c_402,plain,
add(additive_identity,inverse(inverse(A))) = A,
inference(paramod,[status(thm)],[c_53,c_401]) ).
cnf(c_59,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_16,c_402]) ).
cnf(c_403,plain,
add(multiply(A,inverse(A)),multiply(additive_identity,inverse(add(A,additive_identity)))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_27]) ).
cnf(c_404,plain,
add(additive_identity,multiply(additive_identity,inverse(add(A,additive_identity)))) = additive_identity,
inference(paramod,[status(thm)],[c_11,c_403]) ).
cnf(c_405,plain,
add(additive_identity,multiply(additive_identity,inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_404]) ).
cnf(c_78,plain,
multiply(additive_identity,inverse(A)) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_405]) ).
cnf(c_406,plain,
add(additive_identity,multiply(additive_identity,inverse(inverse(A)))) = additive_identity,
inference(paramod,[status(thm)],[c_78,c_26]) ).
cnf(c_407,plain,
add(additive_identity,multiply(additive_identity,A)) = additive_identity,
inference(paramod,[status(thm)],[c_59,c_406]) ).
cnf(c_83,plain,
multiply(additive_identity,A) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_407]) ).
cnf(c_408,plain,
add(A,inverse(B)) = add(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_55,c_1]) ).
cnf(c_85,plain,
add(inverse(A),multiply(A,B)) = add(B,inverse(A)),
inference(copy,[status(thm)],[c_408]) ).
cnf(c_409,plain,
multiply(add(A,inverse(B)),C) = add(multiply(multiply(B,A),C),multiply(inverse(B),C)),
inference(paramod,[status(thm)],[c_55,c_7]) ).
cnf(c_410,plain,
add(multiply(A,C),multiply(inverse(B),C)) = add(multiply(multiply(B,A),C),multiply(inverse(B),C)),
inference(paramod,[status(thm)],[c_7,c_409]) ).
cnf(c_87,plain,
add(multiply(multiply(A,B),C),multiply(inverse(A),C)) = add(multiply(B,C),multiply(inverse(A),C)),
inference(copy,[status(thm)],[c_410]) ).
cnf(c_411,plain,
multiply(A,add(B,inverse(C))) = add(multiply(A,multiply(C,B)),multiply(A,inverse(C))),
inference(paramod,[status(thm)],[c_55,c_8]) ).
cnf(c_412,plain,
add(multiply(A,B),multiply(A,inverse(C))) = add(multiply(A,multiply(C,B)),multiply(A,inverse(C))),
inference(paramod,[status(thm)],[c_8,c_411]) ).
cnf(c_89,plain,
add(multiply(A,multiply(B,C)),multiply(A,inverse(B))) = add(multiply(A,C),multiply(A,inverse(B))),
inference(copy,[status(thm)],[c_412]) ).
cnf(c_413,plain,
add(multiply(additive_identity,A),multiplicative_identity) = add(A,inverse(additive_identity)),
inference(paramod,[status(thm)],[c_33,c_55]) ).
cnf(c_414,plain,
add(additive_identity,multiplicative_identity) = add(A,inverse(additive_identity)),
inference(paramod,[status(thm)],[c_83,c_413]) ).
cnf(c_415,plain,
multiplicative_identity = add(A,inverse(additive_identity)),
inference(paramod,[status(thm)],[c_16,c_414]) ).
cnf(c_416,plain,
multiplicative_identity = add(A,multiplicative_identity),
inference(paramod,[status(thm)],[c_33,c_415]) ).
cnf(c_93,plain,
add(A,multiplicative_identity) = multiplicative_identity,
inference(copy,[status(thm)],[c_416]) ).
cnf(c_417,plain,
multiply(multiplicative_identity,A) = add(multiply(B,A),multiply(multiplicative_identity,A)),
inference(paramod,[status(thm)],[c_93,c_7]) ).
cnf(c_418,plain,
A = add(multiply(B,A),multiply(multiplicative_identity,A)),
inference(paramod,[status(thm)],[c_14,c_417]) ).
cnf(c_419,plain,
A = add(multiply(B,A),A),
inference(paramod,[status(thm)],[c_14,c_418]) ).
cnf(c_420,plain,
A = add(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_419]) ).
cnf(c_96,plain,
add(A,multiply(B,A)) = A,
inference(copy,[status(thm)],[c_420]) ).
cnf(c_421,plain,
multiply(A,multiplicative_identity) = add(multiply(A,B),multiply(A,multiplicative_identity)),
inference(paramod,[status(thm)],[c_93,c_8]) ).
cnf(c_422,plain,
A = add(multiply(A,B),multiply(A,multiplicative_identity)),
inference(paramod,[status(thm)],[c_13,c_421]) ).
cnf(c_423,plain,
A = add(multiply(A,B),A),
inference(paramod,[status(thm)],[c_13,c_422]) ).
cnf(c_424,plain,
A = add(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_1,c_423]) ).
cnf(c_97,plain,
add(A,multiply(A,B)) = A,
inference(copy,[status(thm)],[c_424]) ).
cnf(c_425,plain,
multiply(A,B) = add(multiply(A,multiply(B,C)),multiply(A,multiply(inverse(C),B))),
inference(paramod,[status(thm)],[c_47,c_8]) ).
cnf(c_103,plain,
add(multiply(A,multiply(B,C)),multiply(A,multiply(inverse(C),B))) = multiply(A,B),
inference(copy,[status(thm)],[c_425]) ).
cnf(c_426,plain,
add(multiply(A,inverse(A)),multiply(multiply(B,A),inverse(add(A,multiply(B,A))))) = additive_identity,
inference(paramod,[status(thm)],[c_96,c_27]) ).
cnf(c_427,plain,
add(additive_identity,multiply(multiply(B,A),inverse(add(A,multiply(B,A))))) = additive_identity,
inference(paramod,[status(thm)],[c_11,c_426]) ).
cnf(c_428,plain,
add(additive_identity,multiply(multiply(B,A),inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_96,c_427]) ).
cnf(c_114,plain,
multiply(multiply(A,B),inverse(B)) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_428]) ).
cnf(c_429,plain,
add(multiply(A,inverse(A)),multiply(multiply(A,B),inverse(add(A,multiply(A,B))))) = additive_identity,
inference(paramod,[status(thm)],[c_97,c_27]) ).
cnf(c_430,plain,
add(additive_identity,multiply(multiply(A,B),inverse(add(A,multiply(A,B))))) = additive_identity,
inference(paramod,[status(thm)],[c_11,c_429]) ).
cnf(c_431,plain,
add(additive_identity,multiply(multiply(A,B),inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_97,c_430]) ).
cnf(c_119,plain,
multiply(multiply(A,B),inverse(A)) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_431]) ).
cnf(c_432,plain,
add(additive_identity,multiply(inverse(multiply(A,B)),inverse(B))) = inverse(B),
inference(paramod,[status(thm)],[c_114,c_25]) ).
cnf(c_433,plain,
add(additive_identity,multiply(inverse(B),inverse(multiply(A,B)))) = inverse(B),
inference(paramod,[status(thm)],[c_2,c_432]) ).
cnf(c_121,plain,
multiply(inverse(A),inverse(multiply(B,A))) = inverse(A),
inference(paramod,[status(thm)],[c_16,c_433]) ).
cnf(c_434,plain,
add(additive_identity,inverse(multiply(A,B))) = add(inverse(B),inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_114,c_55]) ).
cnf(c_435,plain,
inverse(multiply(A,B)) = add(inverse(B),inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_16,c_434]) ).
cnf(c_124,plain,
add(inverse(A),inverse(multiply(B,A))) = inverse(multiply(B,A)),
inference(copy,[status(thm)],[c_435]) ).
cnf(c_436,plain,
add(additive_identity,multiply(multiply(inverse(A),B),inverse(multiply(A,B)))) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_11,c_49]) ).
cnf(c_127,plain,
multiply(multiply(inverse(A),B),inverse(multiply(A,B))) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_16,c_436]) ).
cnf(c_437,plain,
additive_identity = multiply(inverse(A),multiply(A,B)),
inference(paramod,[status(thm)],[c_119,c_2]) ).
cnf(c_136,plain,
multiply(inverse(A),multiply(A,B)) = additive_identity,
inference(copy,[status(thm)],[c_437]) ).
cnf(c_438,plain,
add(additive_identity,multiply(inverse(multiply(A,B)),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_119,c_25]) ).
cnf(c_439,plain,
add(additive_identity,multiply(inverse(A),inverse(multiply(A,B)))) = inverse(A),
inference(paramod,[status(thm)],[c_2,c_438]) ).
cnf(c_137,plain,
multiply(inverse(A),inverse(multiply(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_16,c_439]) ).
cnf(c_143,plain,
add(inverse(A),multiply(A,B)) = add(inverse(A),B),
inference(paramod,[status(thm)],[c_85,c_1]) ).
cnf(c_440,plain,
add(multiply(multiply(A,B),multiply(A,C)),additive_identity) = add(multiply(B,multiply(A,C)),multiply(inverse(A),multiply(A,C))),
inference(paramod,[status(thm)],[c_136,c_87]) ).
cnf(c_441,plain,
add(additive_identity,multiply(multiply(A,B),multiply(A,C))) = add(multiply(B,multiply(A,C)),multiply(inverse(A),multiply(A,C))),
inference(paramod,[status(thm)],[c_1,c_440]) ).
cnf(c_442,plain,
multiply(multiply(A,B),multiply(A,C)) = add(multiply(B,multiply(A,C)),multiply(inverse(A),multiply(A,C))),
inference(paramod,[status(thm)],[c_16,c_441]) ).
cnf(c_443,plain,
multiply(multiply(A,B),multiply(A,C)) = add(multiply(B,multiply(A,C)),additive_identity),
inference(paramod,[status(thm)],[c_136,c_442]) ).
cnf(c_444,plain,
multiply(multiply(A,B),multiply(A,C)) = add(additive_identity,multiply(B,multiply(A,C))),
inference(paramod,[status(thm)],[c_1,c_443]) ).
cnf(c_228,plain,
multiply(multiply(A,B),multiply(A,C)) = multiply(B,multiply(A,C)),
inference(paramod,[status(thm)],[c_16,c_444]) ).
cnf(c_445,plain,
add(multiply(multiply(A,B),multiply(A,C)),additive_identity) = add(multiply(multiply(A,B),C),multiply(multiply(A,B),inverse(A))),
inference(paramod,[status(thm)],[c_119,c_89]) ).
cnf(c_446,plain,
add(multiply(B,multiply(A,C)),additive_identity) = add(multiply(multiply(A,B),C),multiply(multiply(A,B),inverse(A))),
inference(paramod,[status(thm)],[c_228,c_445]) ).
cnf(c_447,plain,
add(additive_identity,multiply(B,multiply(A,C))) = add(multiply(multiply(A,B),C),multiply(multiply(A,B),inverse(A))),
inference(paramod,[status(thm)],[c_1,c_446]) ).
cnf(c_448,plain,
multiply(B,multiply(A,C)) = add(multiply(multiply(A,B),C),multiply(multiply(A,B),inverse(A))),
inference(paramod,[status(thm)],[c_16,c_447]) ).
cnf(c_449,plain,
multiply(B,multiply(A,C)) = add(multiply(multiply(A,B),C),additive_identity),
inference(paramod,[status(thm)],[c_119,c_448]) ).
cnf(c_450,plain,
multiply(B,multiply(A,C)) = add(additive_identity,multiply(multiply(A,B),C)),
inference(paramod,[status(thm)],[c_1,c_449]) ).
cnf(c_451,plain,
multiply(B,multiply(A,C)) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_16,c_450]) ).
cnf(c_256,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(A,C)),
inference(copy,[status(thm)],[c_451]) ).
cnf(c_452,plain,
multiply(B,multiply(inverse(A),inverse(multiply(A,B)))) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_256,c_127]) ).
cnf(c_453,plain,
multiply(B,inverse(A)) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_137,c_452]) ).
cnf(c_276,plain,
multiply(A,inverse(multiply(B,A))) = multiply(A,inverse(B)),
inference(copy,[status(thm)],[c_453]) ).
cnf(c_454,plain,
add(multiply(A,multiply(inverse(multiply(B,C)),C)),multiply(A,inverse(C))) = multiply(A,inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_121,c_103]) ).
cnf(c_455,plain,
add(multiply(A,multiply(C,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(A,inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_2,c_454]) ).
cnf(c_456,plain,
add(multiply(A,multiply(C,inverse(B))),multiply(A,inverse(C))) = multiply(A,inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_276,c_455]) ).
cnf(c_457,plain,
add(multiply(A,inverse(B)),multiply(A,inverse(C))) = multiply(A,inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_89,c_456]) ).
cnf(c_325,plain,
multiply(A,inverse(multiply(B,C))) = add(multiply(A,inverse(B)),multiply(A,inverse(C))),
inference(copy,[status(thm)],[c_457]) ).
cnf(c_458,plain,
add(inverse(A),multiply(A,inverse(multiply(B,A)))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_124,c_143]) ).
cnf(c_459,plain,
add(inverse(A),add(multiply(A,inverse(B)),multiply(A,inverse(A)))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_325,c_458]) ).
cnf(c_460,plain,
add(inverse(A),add(multiply(A,inverse(B)),additive_identity)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_11,c_459]) ).
cnf(c_461,plain,
add(inverse(A),add(additive_identity,multiply(A,inverse(B)))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_460]) ).
cnf(c_462,plain,
add(inverse(A),multiply(A,inverse(B))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_16,c_461]) ).
cnf(c_463,plain,
add(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_143,c_462]) ).
cnf(c_365,plain,
inverse(multiply(A,B)) = add(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_463]) ).
cnf(c_464,plain,
add(inverse(b),inverse(a)) != add(inverse(a),inverse(b)),
inference(paramod,[status(thm)],[c_365,c_22]) ).
cnf(c_465,plain,
add(inverse(a),inverse(b)) != add(inverse(a),inverse(b)),
inference(paramod,[status(thm)],[c_1,c_464]) ).
cnf(c_382,plain,
$false,
inference(copy,[status(thm)],[c_465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO015-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.50 % Computer : n018.cluster.edu
% 0.09/0.50 % Model : x86_64 x86_64
% 0.09/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.50 % Memory : 8046.5625MB
% 0.09/0.50 % OS : Linux 6.8.0-71-generic
% 0.09/0.50 % CPULimit : 300
% 0.09/0.50 % WCLimit : 300
% 0.09/0.50 % DateTime : Sat Sep 26 22:37:54 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.51 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.51 % Process 1586058 was started by sandbox on n018,
% 0.09/0.51 % Sat Sep 26 22:37:54 2026
% 0.09/0.51 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.51
% 0.09/0.51 % From the command line: assign(max_seconds, 300).
% 0.95/0.66
% 0.95/0.66 % SZS status Unsatisfiable for theBenchmark
% 0.95/0.66
% 0.95/0.66 % Proof 1 at 0.10 (+ 0.04) seconds.
% 0.95/0.66 % Length of proof is 52.
% 0.95/0.66 % Level of proof is 14.
% 0.95/0.66 % Maximum clause weight is 33.000.
% 0.95/0.66 % Given clauses 83.
% 0.95/0.66
% 0.95/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------