%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP180-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 07:28:15 AM UTC 2026
% Result : Unsatisfiable 81.91s 11.82s
% Output : CNFRefutation 81.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 106
% Number of leaves : 16
% Syntax : Number of formulae : 353 ( 353 unt; 0 def)
% Number of atoms : 353 ( 352 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 60 ( 60 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 547 ( 10 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(symmetry_of_glb,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,VAR_1) = greatest_lower_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_glb) ).
cnf(c_4,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_glb]) ).
fof(symmetry_of_lub,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,VAR_1) = least_upper_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_lub) ).
cnf(c_5,plain,
least_upper_bound(A,B) = least_upper_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_lub]) ).
fof(associativity_of_glb,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(greatest_lower_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_glb) ).
cnf(c_6,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_glb]) ).
cnf(c_7,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(associativity_of_lub,axiom,
! [VAR_0,VAR_1,VAR_2] : least_upper_bound(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(least_upper_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_lub) ).
cnf(c_8,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_lub]) ).
cnf(c_9,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(idempotence_of_lub,axiom,
! [VAR_0] : least_upper_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_lub) ).
cnf(c_10,plain,
least_upper_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_lub]) ).
fof(idempotence_of_gld,axiom,
! [VAR_0] : greatest_lower_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_gld) ).
cnf(c_11,plain,
greatest_lower_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_gld]) ).
fof(lub_absorbtion,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,greatest_lower_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',lub_absorbtion) ).
cnf(c_12,plain,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
inference(clausify,[status(thm)],[lub_absorbtion]) ).
fof(glb_absorbtion,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',glb_absorbtion) ).
cnf(c_13,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
inference(clausify,[status(thm)],[glb_absorbtion]) ).
fof(monotony_lub1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_lub1) ).
cnf(c_14,plain,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_lub1]) ).
cnf(c_15,plain,
least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_14]) ).
fof(monotony_glb1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_glb1) ).
cnf(c_16,plain,
multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_glb1]) ).
cnf(c_17,plain,
greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_16]) ).
fof(monotony_lub2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(least_upper_bound(VAR_0,VAR_1),VAR_2) = least_upper_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_lub2) ).
cnf(c_18,plain,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_lub2]) ).
cnf(c_19,plain,
least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B),
inference(copy,[status(thm)],[c_18]) ).
fof(monotony_glb2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(greatest_lower_bound(VAR_0,VAR_1),VAR_2) = greatest_lower_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_glb2) ).
cnf(c_20,plain,
multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_glb2]) ).
cnf(c_21,plain,
greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B),
inference(copy,[status(thm)],[c_20]) ).
fof(prove_p11,axiom,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != least_upper_bound(a,b),
file('theBenchmark.p',prove_p11) ).
cnf(c_22,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != least_upper_bound(a,b),
inference(clausify,[status(thm)],[prove_p11]) ).
cnf(c_23,plain,
least_upper_bound(a,b) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_9389,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_9390,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_9389]) ).
cnf(c_24,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_9390]) ).
cnf(c_9391,plain,
least_upper_bound(A,B) = least_upper_bound(A,least_upper_bound(A,B)),
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_29,plain,
least_upper_bound(A,least_upper_bound(A,B)) = least_upper_bound(A,B),
inference(copy,[status(thm)],[c_9391]) ).
cnf(c_9392,plain,
least_upper_bound(least_upper_bound(A,B),B) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_31,plain,
least_upper_bound(A,least_upper_bound(B,A)) = least_upper_bound(B,A),
inference(paramod,[status(thm)],[c_5,c_9392]) ).
cnf(c_9393,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_32,plain,
greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B),
inference(copy,[status(thm)],[c_9393]) ).
cnf(c_35,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
cnf(c_9394,plain,
least_upper_bound(A,B) = least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,C),B)),
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_37,plain,
least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,B),C)) = least_upper_bound(A,C),
inference(copy,[status(thm)],[c_9394]) ).
cnf(c_39,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_9395,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(A,C),B)),
inference(paramod,[status(thm)],[c_13,c_7]) ).
cnf(c_40,plain,
greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(A,B),C)) = greatest_lower_bound(A,C),
inference(copy,[status(thm)],[c_9395]) ).
cnf(c_43,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_46,plain,
greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_49,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_9396,plain,
least_upper_bound(multiply(A,B),B) = multiply(least_upper_bound(A,identity),B),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_50,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A),
inference(paramod,[status(thm)],[c_5,c_9396]) ).
cnf(c_9397,plain,
least_upper_bound(multiply(A,B),identity) = multiply(least_upper_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_2,c_19]) ).
cnf(c_52,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_5,c_9397]) ).
cnf(c_56,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_9398,plain,
greatest_lower_bound(multiply(A,B),B) = multiply(greatest_lower_bound(A,identity),B),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_57,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(B,identity),A),
inference(paramod,[status(thm)],[c_4,c_9398]) ).
cnf(c_9399,plain,
greatest_lower_bound(multiply(A,B),identity) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_2,c_21]) ).
cnf(c_59,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_4,c_9399]) ).
cnf(c_70,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_24]) ).
cnf(c_71,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_24]) ).
cnf(c_80,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_24,c_24]) ).
cnf(c_81,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_80,c_70]) ).
cnf(c_82,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_81,c_2]) ).
cnf(c_83,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_81,c_15]) ).
cnf(c_9400,plain,
least_upper_bound(multiply(A,B),A) = multiply(A,least_upper_bound(B,identity)),
inference(paramod,[status(thm)],[c_81,c_15]) ).
cnf(c_84,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(B,identity)),
inference(paramod,[status(thm)],[c_5,c_9400]) ).
cnf(c_85,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_81,c_17]) ).
cnf(c_9401,plain,
greatest_lower_bound(multiply(A,B),A) = multiply(A,greatest_lower_bound(B,identity)),
inference(paramod,[status(thm)],[c_81,c_17]) ).
cnf(c_86,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(B,identity)),
inference(paramod,[status(thm)],[c_4,c_9401]) ).
cnf(c_112,plain,
multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(B,multiply(A,B))) = B,
inference(paramod,[status(thm)],[c_49,c_24]) ).
cnf(c_114,plain,
least_upper_bound(A,multiply(least_upper_bound(identity,B),A)) = least_upper_bound(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_49,c_29]) ).
cnf(c_145,plain,
greatest_lower_bound(A,multiply(greatest_lower_bound(identity,B),A)) = greatest_lower_bound(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_56,c_32]) ).
cnf(c_157,plain,
multiply(inverse(greatest_lower_bound(A,identity)),greatest_lower_bound(B,multiply(A,B))) = B,
inference(paramod,[status(thm)],[c_57,c_24]) ).
cnf(c_9402,plain,
least_upper_bound(inverse(A),identity) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_83]) ).
cnf(c_158,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_9402]) ).
cnf(c_175,plain,
least_upper_bound(inverse(A),B) = multiply(inverse(A),least_upper_bound(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_24,c_83]) ).
cnf(c_176,plain,
least_upper_bound(A,multiply(A,least_upper_bound(identity,B))) = least_upper_bound(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_83,c_29]) ).
cnf(c_9403,plain,
multiply(A,least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),A),
inference(paramod,[status(thm)],[c_83,c_49]) ).
cnf(c_178,plain,
multiply(least_upper_bound(identity,A),A) = multiply(A,least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_9403]) ).
cnf(c_9404,plain,
multiply(A,least_upper_bound(A,identity)) = multiply(least_upper_bound(A,identity),A),
inference(paramod,[status(thm)],[c_84,c_50]) ).
cnf(c_204,plain,
multiply(least_upper_bound(A,identity),A) = multiply(A,least_upper_bound(A,identity)),
inference(copy,[status(thm)],[c_9404]) ).
cnf(c_9405,plain,
greatest_lower_bound(inverse(A),identity) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_85]) ).
cnf(c_206,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_4,c_9405]) ).
cnf(c_9406,plain,
multiply(inverse(A),greatest_lower_bound(A,multiply(A,B))) = greatest_lower_bound(identity,B),
inference(paramod,[status(thm)],[c_85,c_24]) ).
cnf(c_219,plain,
greatest_lower_bound(identity,A) = multiply(inverse(B),greatest_lower_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_9406]) ).
cnf(c_220,plain,
greatest_lower_bound(inverse(A),B) = multiply(inverse(A),greatest_lower_bound(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_24,c_85]) ).
cnf(c_9407,plain,
multiply(A,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),A),
inference(paramod,[status(thm)],[c_85,c_56]) ).
cnf(c_226,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_9407]) ).
cnf(c_9408,plain,
greatest_lower_bound(inverse(greatest_lower_bound(A,identity)),multiply(inverse(greatest_lower_bound(A,identity)),A)) = identity,
inference(paramod,[status(thm)],[c_86,c_2]) ).
cnf(c_234,plain,
multiply(inverse(greatest_lower_bound(A,identity)),greatest_lower_bound(identity,A)) = identity,
inference(paramod,[status(thm)],[c_85,c_9408]) ).
cnf(c_258,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(A,least_upper_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_178,c_24]) ).
cnf(c_9409,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(A,least_upper_bound(identity,A))) = multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_178,c_85]) ).
cnf(c_9410,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_56,c_9409]) ).
cnf(c_259,plain,
multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_9410]) ).
cnf(c_9411,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(A,least_upper_bound(identity,A))) = multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_178,c_86]) ).
cnf(c_9412,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_56,c_9411]) ).
cnf(c_260,plain,
multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_9412]) ).
cnf(c_9413,plain,
greatest_lower_bound(least_upper_bound(A,identity),multiply(A,least_upper_bound(A,identity))) = multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_204,c_85]) ).
cnf(c_9414,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(A,identity)) = multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_56,c_9413]) ).
cnf(c_269,plain,
multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(A,identity)),
inference(copy,[status(thm)],[c_9414]) ).
cnf(c_9415,plain,
multiply(multiply(A,greatest_lower_bound(identity,A)),B) = multiply(greatest_lower_bound(identity,A),multiply(A,B)),
inference(paramod,[status(thm)],[c_226,c_3]) ).
cnf(c_9416,plain,
multiply(A,multiply(greatest_lower_bound(identity,A),B)) = multiply(greatest_lower_bound(identity,A),multiply(A,B)),
inference(paramod,[status(thm)],[c_3,c_9415]) ).
cnf(c_275,plain,
multiply(greatest_lower_bound(identity,A),multiply(A,B)) = multiply(A,multiply(greatest_lower_bound(identity,A),B)),
inference(copy,[status(thm)],[c_9416]) ).
cnf(c_9417,plain,
multiply(identity,A) = multiply(inverse(greatest_lower_bound(B,identity)),multiply(greatest_lower_bound(identity,B),A)),
inference(paramod,[status(thm)],[c_234,c_3]) ).
cnf(c_9418,plain,
A = multiply(inverse(greatest_lower_bound(B,identity)),multiply(greatest_lower_bound(identity,B),A)),
inference(paramod,[status(thm)],[c_1,c_9417]) ).
cnf(c_377,plain,
multiply(inverse(greatest_lower_bound(A,identity)),multiply(greatest_lower_bound(identity,A),B)) = B,
inference(copy,[status(thm)],[c_9418]) ).
cnf(c_455,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_80,c_2]) ).
cnf(c_460,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_80,c_24]) ).
cnf(c_9419,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_80,c_81]) ).
cnf(c_9420,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_81,c_9419]) ).
cnf(c_461,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_9420]) ).
cnf(c_9421,plain,
least_upper_bound(multiply(A,B),identity) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_455,c_15]) ).
cnf(c_463,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_5,c_9421]) ).
cnf(c_465,plain,
least_upper_bound(identity,multiply(A,inverse(B))) = multiply(least_upper_bound(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_455,c_19]) ).
cnf(c_9422,plain,
least_upper_bound(inverse(A),identity) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_455,c_49]) ).
cnf(c_9423,plain,
least_upper_bound(identity,inverse(A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_5,c_9422]) ).
cnf(c_9424,plain,
multiply(inverse(A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_158,c_9423]) ).
cnf(c_469,plain,
multiply(least_upper_bound(identity,A),inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_9424]) ).
cnf(c_9425,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_455,c_56]) ).
cnf(c_9426,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_9425]) ).
cnf(c_9427,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_206,c_9426]) ).
cnf(c_472,plain,
multiply(greatest_lower_bound(identity,A),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_9427]) ).
cnf(c_9428,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_455,c_57]) ).
cnf(c_9429,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_9428]) ).
cnf(c_9430,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_206,c_9429]) ).
cnf(c_473,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_9430]) ).
cnf(c_9431,plain,
multiply(multiply(inverse(A),least_upper_bound(identity,A)),B) = multiply(least_upper_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_469,c_3]) ).
cnf(c_9432,plain,
multiply(inverse(A),multiply(least_upper_bound(identity,A),B)) = multiply(least_upper_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_3,c_9431]) ).
cnf(c_475,plain,
multiply(least_upper_bound(identity,A),multiply(inverse(A),B)) = multiply(inverse(A),multiply(least_upper_bound(identity,A),B)),
inference(copy,[status(thm)],[c_9432]) ).
cnf(c_9433,plain,
multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),B) = multiply(greatest_lower_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_472,c_3]) ).
cnf(c_9434,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B)) = multiply(greatest_lower_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_3,c_9433]) ).
cnf(c_503,plain,
multiply(greatest_lower_bound(identity,A),multiply(inverse(A),B)) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B)),
inference(copy,[status(thm)],[c_9434]) ).
cnf(c_516,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_4,c_473]) ).
cnf(c_9435,plain,
multiply(multiply(inverse(A),greatest_lower_bound(A,identity)),B) = multiply(greatest_lower_bound(A,identity),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_516,c_3]) ).
cnf(c_9436,plain,
multiply(inverse(A),multiply(greatest_lower_bound(A,identity),B)) = multiply(greatest_lower_bound(A,identity),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_3,c_9435]) ).
cnf(c_542,plain,
multiply(greatest_lower_bound(A,identity),multiply(inverse(A),B)) = multiply(inverse(A),multiply(greatest_lower_bound(A,identity),B)),
inference(copy,[status(thm)],[c_9436]) ).
cnf(c_555,plain,
least_upper_bound(multiply(A,B),C) = multiply(A,least_upper_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_460,c_15]) ).
cnf(c_556,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_460,c_17]) ).
cnf(c_803,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(A,least_upper_bound(A,identity))) = A,
inference(paramod,[status(thm)],[c_84,c_112]) ).
cnf(c_852,plain,
multiply(inverse(greatest_lower_bound(A,identity)),multiply(A,greatest_lower_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_85,c_157]) ).
cnf(c_9437,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(least_upper_bound(identity,A)),greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_469,c_219]) ).
cnf(c_9438,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_206,c_9437]) ).
cnf(c_9439,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),multiply(greatest_lower_bound(identity,inverse(A)),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_56,c_9438]) ).
cnf(c_9440,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_206,c_9439]) ).
cnf(c_9441,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_3,c_9440]) ).
cnf(c_948,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_9441]) ).
cnf(c_9442,plain,
multiply(A,least_upper_bound(B,inverse(A))) = multiply(least_upper_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_463,c_52]) ).
cnf(c_1036,plain,
multiply(least_upper_bound(A,inverse(B)),B) = multiply(A,least_upper_bound(B,inverse(A))),
inference(copy,[status(thm)],[c_9442]) ).
cnf(c_9443,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(A,B),C),least_upper_bound(A,C)) = least_upper_bound(greatest_lower_bound(A,B),C),
inference(paramod,[status(thm)],[c_37,c_39]) ).
cnf(c_1117,plain,
greatest_lower_bound(least_upper_bound(A,B),least_upper_bound(greatest_lower_bound(A,C),B)) = least_upper_bound(greatest_lower_bound(A,C),B),
inference(paramod,[status(thm)],[c_4,c_9443]) ).
cnf(c_1687,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_43,c_13]) ).
cnf(c_1760,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_5,c_1687]) ).
cnf(c_9444,plain,
least_upper_bound(multiply(inverse(A),B),multiply(least_upper_bound(identity,A),multiply(inverse(A),B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_460,c_114]) ).
cnf(c_9445,plain,
least_upper_bound(multiply(inverse(A),B),multiply(inverse(A),multiply(least_upper_bound(identity,A),B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_475,c_9444]) ).
cnf(c_9446,plain,
multiply(inverse(A),least_upper_bound(B,multiply(inverse(inverse(A)),multiply(inverse(A),multiply(least_upper_bound(identity,A),B))))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_555,c_9445]) ).
cnf(c_9447,plain,
multiply(inverse(A),least_upper_bound(B,multiply(A,multiply(inverse(A),multiply(least_upper_bound(identity,A),B))))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_461,c_9446]) ).
cnf(c_9448,plain,
multiply(inverse(A),least_upper_bound(B,multiply(least_upper_bound(identity,A),B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_460,c_9447]) ).
cnf(c_9449,plain,
multiply(inverse(A),least_upper_bound(B,multiply(A,B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_114,c_9448]) ).
cnf(c_9450,plain,
multiply(inverse(A),least_upper_bound(B,multiply(A,B))) = least_upper_bound(B,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_5,c_9449]) ).
cnf(c_2072,plain,
least_upper_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_9450]) ).
cnf(c_9451,plain,
greatest_lower_bound(multiply(inverse(A),B),multiply(greatest_lower_bound(identity,A),multiply(inverse(A),B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_460,c_145]) ).
cnf(c_9452,plain,
greatest_lower_bound(multiply(inverse(A),B),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_503,c_9451]) ).
cnf(c_9453,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(inverse(inverse(A)),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B))))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_556,c_9452]) ).
cnf(c_9454,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(A,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B))))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_461,c_9453]) ).
cnf(c_9455,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(greatest_lower_bound(identity,A),B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_460,c_9454]) ).
cnf(c_9456,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(A,B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_145,c_9455]) ).
cnf(c_9457,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(A,B))) = greatest_lower_bound(B,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_4,c_9456]) ).
cnf(c_2105,plain,
greatest_lower_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),greatest_lower_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_9457]) ).
cnf(c_9458,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,inverse(A)))) = least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),greatest_lower_bound(A,identity))),
inference(paramod,[status(thm)],[c_516,c_176]) ).
cnf(c_9459,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(A,identity),multiply(inverse(A),least_upper_bound(identity,A)))) = least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),greatest_lower_bound(A,identity))),
inference(paramod,[status(thm)],[c_158,c_9458]) ).
cnf(c_9460,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),greatest_lower_bound(A,identity))),
inference(paramod,[status(thm)],[c_542,c_9459]) ).
cnf(c_9461,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_49,c_9460]) ).
cnf(c_9462,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = multiply(multiply(inverse(A),least_upper_bound(identity,A)),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_158,c_9461]) ).
cnf(c_9463,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = multiply(inverse(A),multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity))),
inference(paramod,[status(thm)],[c_3,c_9462]) ).
cnf(c_2261,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_260,c_9463]) ).
cnf(c_9464,plain,
least_upper_bound(identity,multiply(multiply(least_upper_bound(identity,A),B),inverse(B))) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_114,c_465]) ).
cnf(c_9465,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,A),multiply(B,inverse(B)))) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_3,c_9464]) ).
cnf(c_9466,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,A),identity)) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_455,c_9465]) ).
cnf(c_9467,plain,
least_upper_bound(identity,least_upper_bound(identity,A)) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_81,c_9466]) ).
cnf(c_2682,plain,
least_upper_bound(identity,A) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_29,c_9467]) ).
cnf(c_9468,plain,
least_upper_bound(identity,least_upper_bound(identity,A)) = multiply(least_upper_bound(greatest_lower_bound(identity,A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_259,c_2682]) ).
cnf(c_9469,plain,
least_upper_bound(identity,A) = multiply(least_upper_bound(greatest_lower_bound(identity,A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_29,c_9468]) ).
cnf(c_9470,plain,
least_upper_bound(identity,A) = multiply(multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,least_upper_bound(identity,A))),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_83,c_9469]) ).
cnf(c_9471,plain,
least_upper_bound(identity,A) = multiply(multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_29,c_9470]) ).
cnf(c_9472,plain,
least_upper_bound(identity,A) = multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(identity,A),inverse(greatest_lower_bound(identity,A)))),
inference(paramod,[status(thm)],[c_3,c_9471]) ).
cnf(c_2838,plain,
multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(identity,A),inverse(greatest_lower_bound(identity,A)))) = least_upper_bound(identity,A),
inference(copy,[status(thm)],[c_9472]) ).
cnf(c_9473,plain,
least_upper_bound(identity,least_upper_bound(A,identity)) = multiply(least_upper_bound(greatest_lower_bound(identity,A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,identity))),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_269,c_2682]) ).
cnf(c_9474,plain,
least_upper_bound(A,identity) = multiply(least_upper_bound(greatest_lower_bound(identity,A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,identity))),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_31,c_9473]) ).
cnf(c_9475,plain,
least_upper_bound(A,identity) = multiply(multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,least_upper_bound(A,identity))),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_83,c_9474]) ).
cnf(c_9476,plain,
least_upper_bound(A,identity) = multiply(multiply(greatest_lower_bound(identity,A),least_upper_bound(A,identity)),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_31,c_9475]) ).
cnf(c_9477,plain,
least_upper_bound(A,identity) = multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(A,identity),inverse(greatest_lower_bound(identity,A)))),
inference(paramod,[status(thm)],[c_3,c_9476]) ).
cnf(c_2841,plain,
multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(A,identity),inverse(greatest_lower_bound(identity,A)))) = least_upper_bound(A,identity),
inference(copy,[status(thm)],[c_9477]) ).
cnf(c_9478,plain,
multiply(A,multiply(least_upper_bound(inverse(A),inverse(B)),B)) = least_upper_bound(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_1036,c_460]) ).
cnf(c_9479,plain,
multiply(A,multiply(multiply(inverse(A),least_upper_bound(identity,multiply(A,inverse(B)))),B)) = least_upper_bound(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_175,c_9478]) ).
cnf(c_9480,plain,
multiply(A,multiply(inverse(A),multiply(least_upper_bound(identity,multiply(A,inverse(B))),B))) = least_upper_bound(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_3,c_9479]) ).
cnf(c_9481,plain,
multiply(least_upper_bound(identity,multiply(A,inverse(B))),B) = least_upper_bound(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_460,c_9480]) ).
cnf(c_9482,plain,
multiply(least_upper_bound(identity,multiply(A,inverse(B))),B) = least_upper_bound(B,A),
inference(paramod,[status(thm)],[c_461,c_9481]) ).
cnf(c_3310,plain,
least_upper_bound(A,B) = multiply(least_upper_bound(identity,multiply(B,inverse(A))),A),
inference(copy,[status(thm)],[c_9482]) ).
cnf(c_9483,plain,
multiply(A,B) = multiply(inverse(least_upper_bound(identity,A)),multiply(multiply(A,least_upper_bound(identity,A)),B)),
inference(paramod,[status(thm)],[c_258,c_3]) ).
cnf(c_9484,plain,
multiply(A,B) = multiply(inverse(least_upper_bound(identity,A)),multiply(A,multiply(least_upper_bound(identity,A),B))),
inference(paramod,[status(thm)],[c_3,c_9483]) ).
cnf(c_3521,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(A,multiply(least_upper_bound(identity,A),B))) = multiply(A,B),
inference(copy,[status(thm)],[c_9484]) ).
cnf(c_9485,plain,
multiply(inverse(greatest_lower_bound(inverse(A),identity)),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_59,c_377]) ).
cnf(c_9486,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(A))),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_4,c_9485]) ).
cnf(c_9487,plain,
multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_206,c_9486]) ).
cnf(c_3612,plain,
multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),greatest_lower_bound(identity,A)) = A,
inference(paramod,[status(thm)],[c_1,c_9487]) ).
cnf(c_9488,plain,
multiply(A,B) = multiply(inverse(least_upper_bound(identity,A)),multiply(multiply(A,least_upper_bound(A,identity)),B)),
inference(paramod,[status(thm)],[c_803,c_3]) ).
cnf(c_9489,plain,
multiply(A,B) = multiply(inverse(least_upper_bound(identity,A)),multiply(A,multiply(least_upper_bound(A,identity),B))),
inference(paramod,[status(thm)],[c_3,c_9488]) ).
cnf(c_3654,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(A,multiply(least_upper_bound(A,identity),B))) = multiply(A,B),
inference(copy,[status(thm)],[c_9489]) ).
cnf(c_9490,plain,
least_upper_bound(inverse(inverse(greatest_lower_bound(A,identity))),multiply(A,greatest_lower_bound(identity,A))) = multiply(inverse(inverse(greatest_lower_bound(A,identity))),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_852,c_175]) ).
cnf(c_9491,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(A,greatest_lower_bound(identity,A))) = multiply(inverse(inverse(greatest_lower_bound(A,identity))),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_461,c_9490]) ).
cnf(c_3704,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(A,greatest_lower_bound(identity,A))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_461,c_9491]) ).
cnf(c_9492,plain,
greatest_lower_bound(multiply(A,least_upper_bound(identity,B)),least_upper_bound(greatest_lower_bound(A,C),multiply(A,B))) = least_upper_bound(greatest_lower_bound(A,C),multiply(A,B)),
inference(paramod,[status(thm)],[c_83,c_1117]) ).
cnf(c_5268,plain,
multiply(A,greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),least_upper_bound(greatest_lower_bound(A,C),multiply(A,B))))) = least_upper_bound(greatest_lower_bound(A,C),multiply(A,B)),
inference(paramod,[status(thm)],[c_556,c_9492]) ).
cnf(c_9493,plain,
greatest_lower_bound(least_upper_bound(identity,A),least_upper_bound(multiply(greatest_lower_bound(B,inverse(C)),C),A)) = least_upper_bound(greatest_lower_bound(identity,multiply(B,C)),A),
inference(paramod,[status(thm)],[c_59,c_1117]) ).
cnf(c_9494,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(greatest_lower_bound(B,inverse(C)),least_upper_bound(C,multiply(inverse(greatest_lower_bound(B,inverse(C))),A)))) = least_upper_bound(greatest_lower_bound(identity,multiply(B,C)),A),
inference(paramod,[status(thm)],[c_555,c_9493]) ).
cnf(c_5287,plain,
least_upper_bound(greatest_lower_bound(identity,multiply(A,B)),C) = greatest_lower_bound(least_upper_bound(identity,C),multiply(greatest_lower_bound(A,inverse(B)),least_upper_bound(B,multiply(inverse(greatest_lower_bound(A,inverse(B))),C)))),
inference(copy,[status(thm)],[c_9494]) ).
cnf(c_9495,plain,
greatest_lower_bound(least_upper_bound(identity,A),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(B),C)),A)) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_46,c_1117]) ).
cnf(c_9496,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(greatest_lower_bound(inverse(B),inverse(C)),least_upper_bound(C,multiply(inverse(greatest_lower_bound(inverse(B),inverse(C))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_5287,c_9495]) ).
cnf(c_9497,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C)))),least_upper_bound(C,multiply(inverse(greatest_lower_bound(inverse(B),inverse(C))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_220,c_9496]) ).
cnf(c_9498,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C)))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_220,c_9497]) ).
cnf(c_9499,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A)))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_3,c_9498]) ).
cnf(c_9500,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_32,c_9499]) ).
cnf(c_9501,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A))))) = multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,C),multiply(inverse(inverse(B)),A))),
inference(paramod,[status(thm)],[c_555,c_9500]) ).
cnf(c_9502,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A))))) = multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,C),multiply(B,A))),
inference(paramod,[status(thm)],[c_461,c_9501]) ).
cnf(c_5323,plain,
multiply(inverse(A),least_upper_bound(greatest_lower_bound(A,B),multiply(A,C))) = greatest_lower_bound(least_upper_bound(identity,C),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(B))),least_upper_bound(B,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(B))))),C))))),
inference(copy,[status(thm)],[c_9502]) ).
cnf(c_9503,plain,
multiply(A,greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(C))))),B))))))) = least_upper_bound(greatest_lower_bound(A,C),multiply(A,B)),
inference(paramod,[status(thm)],[c_5323,c_5268]) ).
cnf(c_9504,plain,
multiply(A,greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(C))))),B)))))) = least_upper_bound(greatest_lower_bound(A,C),multiply(A,B)),
inference(paramod,[status(thm)],[c_32,c_9503]) ).
cnf(c_5434,plain,
least_upper_bound(greatest_lower_bound(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(least_upper_bound(identity,C),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(B))),least_upper_bound(B,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(B))))),C)))))),
inference(copy,[status(thm)],[c_9504]) ).
cnf(c_9505,plain,
multiply(A,greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,A)),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(identity))),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(identity))))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5434,c_3704]) ).
cnf(c_9506,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(identity))),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(identity))))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_12,c_9505]) ).
cnf(c_9507,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,identity)),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(identity))))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_82,c_9506]) ).
cnf(c_9508,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(identity))))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_9507]) ).
cnf(c_9509,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,identity)))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_82,c_9508]) ).
cnf(c_9510,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_9509]) ).
cnf(c_5474,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_3612,c_9510]) ).
cnf(c_9511,plain,
greatest_lower_bound(A,multiply(inverse(B),greatest_lower_bound(least_upper_bound(A,C),multiply(B,least_upper_bound(A,C))))) = greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(A,C))),
inference(paramod,[status(thm)],[c_2105,c_40]) ).
cnf(c_6405,plain,
greatest_lower_bound(A,multiply(inverse(B),multiply(greatest_lower_bound(identity,B),least_upper_bound(A,C)))) = greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(A,C))),
inference(paramod,[status(thm)],[c_56,c_9511]) ).
cnf(c_9512,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(identity,A)))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_6405,c_5474]) ).
cnf(c_9513,plain,
multiply(A,identity) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_1760,c_9512]) ).
cnf(c_9514,plain,
A = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_9513]) ).
cnf(c_6459,plain,
multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)) = A,
inference(copy,[status(thm)],[c_9514]) ).
cnf(c_9515,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),A)) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_6459,c_2261]) ).
cnf(c_9516,plain,
least_upper_bound(greatest_lower_bound(A,identity),identity) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_2,c_9515]) ).
cnf(c_9517,plain,
least_upper_bound(identity,greatest_lower_bound(A,identity)) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_5,c_9516]) ).
cnf(c_9518,plain,
identity = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_35,c_9517]) ).
cnf(c_6462,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))) = identity,
inference(copy,[status(thm)],[c_9518]) ).
cnf(c_9519,plain,
multiply(inverse(least_upper_bound(identity,A)),identity) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_6462,c_948]) ).
cnf(c_6463,plain,
inverse(least_upper_bound(identity,A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_9519]) ).
cnf(c_9520,plain,
multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),multiply(A,multiply(least_upper_bound(A,identity),B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_6463,c_3654]) ).
cnf(c_9521,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),multiply(A,multiply(least_upper_bound(A,identity),B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_3,c_9520]) ).
cnf(c_9522,plain,
multiply(inverse(A),multiply(A,multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(A,identity),B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_275,c_9521]) ).
cnf(c_6613,plain,
multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(A,identity),B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_24,c_9522]) ).
cnf(c_9523,plain,
multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),multiply(A,multiply(least_upper_bound(identity,A),B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_6463,c_3521]) ).
cnf(c_9524,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),multiply(A,multiply(least_upper_bound(identity,A),B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_3,c_9523]) ).
cnf(c_9525,plain,
multiply(inverse(A),multiply(A,multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(identity,A),B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_275,c_9524]) ).
cnf(c_6638,plain,
multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(identity,A),B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_24,c_9525]) ).
cnf(c_9526,plain,
multiply(A,inverse(greatest_lower_bound(identity,A))) = least_upper_bound(A,identity),
inference(paramod,[status(thm)],[c_6613,c_2841]) ).
cnf(c_6876,plain,
least_upper_bound(A,identity) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(copy,[status(thm)],[c_9526]) ).
cnf(c_9527,plain,
multiply(A,inverse(greatest_lower_bound(identity,A))) = least_upper_bound(identity,A),
inference(paramod,[status(thm)],[c_6638,c_2838]) ).
cnf(c_6877,plain,
least_upper_bound(identity,A) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(copy,[status(thm)],[c_9527]) ).
cnf(c_9528,plain,
least_upper_bound(A,B) = multiply(multiply(multiply(B,inverse(A)),inverse(greatest_lower_bound(identity,multiply(B,inverse(A))))),A),
inference(paramod,[status(thm)],[c_6877,c_3310]) ).
cnf(c_9529,plain,
least_upper_bound(A,B) = multiply(multiply(B,multiply(inverse(A),inverse(greatest_lower_bound(identity,multiply(B,inverse(A)))))),A),
inference(paramod,[status(thm)],[c_3,c_9528]) ).
cnf(c_9530,plain,
least_upper_bound(A,B) = multiply(B,multiply(multiply(inverse(A),inverse(greatest_lower_bound(identity,multiply(B,inverse(A))))),A)),
inference(paramod,[status(thm)],[c_3,c_9529]) ).
cnf(c_7916,plain,
least_upper_bound(A,B) = multiply(B,multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(A)))),A))),
inference(paramod,[status(thm)],[c_3,c_9530]) ).
cnf(c_9531,plain,
multiply(multiply(inverse(B),A),multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,multiply(multiply(inverse(B),A),inverse(A)))),A))) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_7916,c_2072]) ).
cnf(c_9532,plain,
multiply(multiply(inverse(B),A),multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(B),multiply(A,inverse(A))))),A))) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_3,c_9531]) ).
cnf(c_9533,plain,
multiply(multiply(inverse(B),A),multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(B),identity))),A))) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_455,c_9532]) ).
cnf(c_9534,plain,
multiply(multiply(inverse(B),A),multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,inverse(B))),A))) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_81,c_9533]) ).
cnf(c_9535,plain,
multiply(multiply(inverse(B),A),multiply(inverse(A),multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,B))),A))) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_206,c_9534]) ).
cnf(c_9536,plain,
multiply(inverse(B),multiply(A,multiply(inverse(A),multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,B))),A)))) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_3,c_9535]) ).
cnf(c_9537,plain,
multiply(inverse(B),multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,B))),A)) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_460,c_9536]) ).
cnf(c_9538,plain,
multiply(inverse(B),multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,B))),A)) = multiply(inverse(B),multiply(multiply(B,A),multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,multiply(multiply(B,A),inverse(A)))),A)))),
inference(paramod,[status(thm)],[c_7916,c_9537]) ).
cnf(c_9539,plain,
multiply(inverse(B),multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,B))),A)) = multiply(inverse(B),multiply(multiply(B,A),multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,multiply(B,multiply(A,inverse(A))))),A)))),
inference(paramod,[status(thm)],[c_3,c_9538]) ).
cnf(c_9540,plain,
multiply(inverse(B),multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,B))),A)) = multiply(inverse(B),multiply(multiply(B,A),multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,multiply(B,identity))),A)))),
inference(paramod,[status(thm)],[c_455,c_9539]) ).
cnf(c_9541,plain,
multiply(inverse(B),multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,B))),A)) = multiply(inverse(B),multiply(multiply(B,A),multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,B)),A)))),
inference(paramod,[status(thm)],[c_81,c_9540]) ).
cnf(c_9542,plain,
multiply(inverse(B),multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,B))),A)) = multiply(inverse(B),multiply(B,multiply(A,multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,B)),A))))),
inference(paramod,[status(thm)],[c_3,c_9541]) ).
cnf(c_9543,plain,
multiply(inverse(B),multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,B))),A)) = multiply(inverse(B),multiply(B,multiply(inverse(greatest_lower_bound(identity,B)),A))),
inference(paramod,[status(thm)],[c_460,c_9542]) ).
cnf(c_8169,plain,
multiply(inverse(A),multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),B)) = multiply(inverse(greatest_lower_bound(identity,A)),B),
inference(paramod,[status(thm)],[c_24,c_9543]) ).
cnf(c_9544,plain,
multiply(identity,multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,multiply(identity,inverse(A)))),A))) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_7916,c_6876]) ).
cnf(c_9545,plain,
multiply(identity,multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,inverse(A))),A))) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_1,c_9544]) ).
cnf(c_9546,plain,
multiply(identity,multiply(inverse(A),multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),A))) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_206,c_9545]) ).
cnf(c_9547,plain,
multiply(identity,multiply(inverse(greatest_lower_bound(identity,A)),A)) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_8169,c_9546]) ).
cnf(c_8246,plain,
multiply(inverse(greatest_lower_bound(identity,A)),A) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_1,c_9547]) ).
cnf(c_9548,plain,
multiply(b,multiply(inverse(a),multiply(inverse(greatest_lower_bound(identity,multiply(b,inverse(a)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_7916,c_23]) ).
cnf(c_8477,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(b,multiply(inverse(a),multiply(inverse(greatest_lower_bound(identity,multiply(b,inverse(a)))),a))),
inference(copy,[status(thm)],[c_9548]) ).
cnf(c_9549,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(b,multiply(inverse(a),multiply(inverse(multiply(inverse(A),greatest_lower_bound(A,multiply(A,multiply(b,inverse(a)))))),a))),
inference(paramod,[status(thm)],[c_219,c_8477]) ).
cnf(c_8536,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(inverse(A),greatest_lower_bound(A,multiply(A,multiply(b,inverse(a)))))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(copy,[status(thm)],[c_9549]) ).
cnf(c_9550,plain,
multiply(inverse(multiply(A,B)),multiply(A,identity)) = inverse(B),
inference(paramod,[status(thm)],[c_455,c_71]) ).
cnf(c_8676,plain,
multiply(inverse(multiply(A,B)),A) = inverse(B),
inference(paramod,[status(thm)],[c_81,c_9550]) ).
cnf(c_9551,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_24,c_8676]) ).
cnf(c_8719,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_9551]) ).
cnf(c_9552,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(inverse(inverse(multiply(multiply(b,inverse(a)),A))),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8676,c_8536]) ).
cnf(c_9553,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(inverse(inverse(multiply(b,multiply(inverse(a),A)))),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9552]) ).
cnf(c_9554,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(a),A)),inverse(b))),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9553]) ).
cnf(c_9555,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(inverse(multiply(multiply(inverse(A),inverse(inverse(a))),inverse(b))),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9554]) ).
cnf(c_9556,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(inverse(multiply(multiply(inverse(A),a),inverse(b))),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_461,c_9555]) ).
cnf(c_9557,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(inverse(multiply(inverse(A),multiply(a,inverse(b)))),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9556]) ).
cnf(c_9558,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(inverse(multiply(a,inverse(b))),inverse(inverse(A))),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9557]) ).
cnf(c_9559,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(multiply(inverse(inverse(b)),inverse(a)),inverse(inverse(A))),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9558]) ).
cnf(c_9560,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(multiply(b,inverse(a)),inverse(inverse(A))),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_461,c_9559]) ).
cnf(c_9561,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(multiply(b,inverse(a)),A),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_461,c_9560]) ).
cnf(c_9562,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(b,multiply(inverse(a),A)),greatest_lower_bound(inverse(multiply(multiply(b,inverse(a)),A)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9561]) ).
cnf(c_9563,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(b,multiply(inverse(a),A)),greatest_lower_bound(inverse(multiply(b,multiply(inverse(a),A))),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9562]) ).
cnf(c_9564,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(b,multiply(inverse(a),A)),greatest_lower_bound(multiply(inverse(multiply(inverse(a),A)),inverse(b)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9563]) ).
cnf(c_9565,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(b,multiply(inverse(a),A)),greatest_lower_bound(multiply(multiply(inverse(A),inverse(inverse(a))),inverse(b)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9564]) ).
cnf(c_9566,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(b,multiply(inverse(a),A)),greatest_lower_bound(multiply(multiply(inverse(A),a),inverse(b)),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_461,c_9565]) ).
cnf(c_9567,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(b,multiply(inverse(a),A)),greatest_lower_bound(multiply(inverse(A),multiply(a,inverse(b))),inverse(A)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9566]) ).
cnf(c_9568,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(b,multiply(inverse(a),A)),greatest_lower_bound(inverse(A),multiply(inverse(A),multiply(a,inverse(b)))))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_4,c_9567]) ).
cnf(c_9569,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(multiply(b,multiply(inverse(a),A)),multiply(inverse(A),greatest_lower_bound(identity,multiply(a,inverse(b)))))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_85,c_9568]) ).
cnf(c_9570,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(b,multiply(multiply(inverse(a),A),multiply(inverse(A),greatest_lower_bound(identity,multiply(a,inverse(b))))))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9569]) ).
cnf(c_9571,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(b,multiply(inverse(a),multiply(A,multiply(inverse(A),greatest_lower_bound(identity,multiply(a,inverse(b)))))))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9570]) ).
cnf(c_9572,plain,
multiply(b,multiply(inverse(a),multiply(inverse(multiply(b,multiply(inverse(a),greatest_lower_bound(identity,multiply(a,inverse(b)))))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_460,c_9571]) ).
cnf(c_9573,plain,
multiply(b,multiply(inverse(a),multiply(multiply(inverse(multiply(inverse(a),greatest_lower_bound(identity,multiply(a,inverse(b))))),inverse(b)),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9572]) ).
cnf(c_9574,plain,
multiply(b,multiply(inverse(a),multiply(multiply(multiply(inverse(greatest_lower_bound(identity,multiply(a,inverse(b)))),inverse(inverse(a))),inverse(b)),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9573]) ).
cnf(c_9575,plain,
multiply(b,multiply(inverse(a),multiply(multiply(multiply(inverse(greatest_lower_bound(identity,multiply(a,inverse(b)))),a),inverse(b)),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_461,c_9574]) ).
cnf(c_9576,plain,
multiply(b,multiply(inverse(a),multiply(multiply(inverse(greatest_lower_bound(identity,multiply(a,inverse(b)))),multiply(a,inverse(b))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9575]) ).
cnf(c_9577,plain,
multiply(b,multiply(inverse(a),multiply(multiply(multiply(a,inverse(b)),inverse(greatest_lower_bound(identity,multiply(a,inverse(b))))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8246,c_9576]) ).
cnf(c_9578,plain,
multiply(b,multiply(inverse(a),multiply(multiply(a,multiply(inverse(b),inverse(greatest_lower_bound(identity,multiply(a,inverse(b)))))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9577]) ).
cnf(c_9579,plain,
multiply(b,multiply(inverse(a),multiply(a,multiply(multiply(inverse(b),inverse(greatest_lower_bound(identity,multiply(a,inverse(b))))),a)))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9578]) ).
cnf(c_9580,plain,
multiply(b,multiply(inverse(a),multiply(a,multiply(inverse(b),multiply(inverse(greatest_lower_bound(identity,multiply(a,inverse(b)))),a))))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9579]) ).
cnf(c_9581,plain,
multiply(b,multiply(inverse(b),multiply(inverse(greatest_lower_bound(identity,multiply(a,inverse(b)))),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_24,c_9580]) ).
cnf(c_9582,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(a,inverse(b)))),a) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_460,c_9581]) ).
cnf(c_8733,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(inverse(greatest_lower_bound(identity,multiply(a,inverse(b)))),a),
inference(copy,[status(thm)],[c_9582]) ).
cnf(c_9583,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(inverse(multiply(inverse(A),greatest_lower_bound(A,multiply(A,multiply(a,inverse(b)))))),a),
inference(paramod,[status(thm)],[c_219,c_8733]) ).
cnf(c_9584,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(multiply(inverse(greatest_lower_bound(A,multiply(A,multiply(a,inverse(b))))),inverse(inverse(A))),a),
inference(paramod,[status(thm)],[c_8719,c_9583]) ).
cnf(c_9585,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(multiply(inverse(greatest_lower_bound(A,multiply(A,multiply(a,inverse(b))))),A),a),
inference(paramod,[status(thm)],[c_461,c_9584]) ).
cnf(c_9586,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(inverse(greatest_lower_bound(A,multiply(A,multiply(a,inverse(b))))),multiply(A,a)),
inference(paramod,[status(thm)],[c_3,c_9585]) ).
cnf(c_9088,plain,
multiply(inverse(greatest_lower_bound(A,multiply(A,multiply(a,inverse(b))))),multiply(A,a)) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(copy,[status(thm)],[c_9586]) ).
cnf(c_9587,plain,
multiply(inverse(greatest_lower_bound(inverse(multiply(a,inverse(b))),identity)),multiply(inverse(multiply(a,inverse(b))),a)) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_2,c_9088]) ).
cnf(c_9588,plain,
multiply(inverse(greatest_lower_bound(multiply(inverse(inverse(b)),inverse(a)),identity)),multiply(inverse(multiply(a,inverse(b))),a)) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9587]) ).
cnf(c_9589,plain,
multiply(inverse(greatest_lower_bound(multiply(b,inverse(a)),identity)),multiply(inverse(multiply(a,inverse(b))),a)) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_461,c_9588]) ).
cnf(c_9590,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(b,inverse(a)))),multiply(inverse(multiply(a,inverse(b))),a)) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_4,c_9589]) ).
cnf(c_9591,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(b,inverse(a)))),multiply(multiply(inverse(inverse(b)),inverse(a)),a)) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_8719,c_9590]) ).
cnf(c_9592,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(b,inverse(a)))),multiply(multiply(b,inverse(a)),a)) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_461,c_9591]) ).
cnf(c_9593,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(b,inverse(a)))),multiply(b,multiply(inverse(a),a))) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9592]) ).
cnf(c_9594,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(b,inverse(a)))),multiply(b,identity)) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_2,c_9593]) ).
cnf(c_9595,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(b,inverse(a)))),b) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_81,c_9594]) ).
cnf(c_9384,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(inverse(greatest_lower_bound(identity,multiply(b,inverse(a)))),b),
inference(copy,[status(thm)],[c_9595]) ).
cnf(c_9596,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(inverse(multiply(greatest_lower_bound(b,inverse(inverse(a))),inverse(a))),b),
inference(paramod,[status(thm)],[c_59,c_9384]) ).
cnf(c_9597,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(inverse(multiply(greatest_lower_bound(b,a),inverse(a))),b),
inference(paramod,[status(thm)],[c_461,c_9596]) ).
cnf(c_9598,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(inverse(multiply(greatest_lower_bound(a,b),inverse(a))),b),
inference(paramod,[status(thm)],[c_4,c_9597]) ).
cnf(c_9599,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(multiply(inverse(inverse(a)),inverse(greatest_lower_bound(a,b))),b),
inference(paramod,[status(thm)],[c_8719,c_9598]) ).
cnf(c_9600,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(multiply(a,inverse(greatest_lower_bound(a,b))),b),
inference(paramod,[status(thm)],[c_461,c_9599]) ).
cnf(c_9601,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),
inference(paramod,[status(thm)],[c_3,c_9600]) ).
cnf(c_9388,plain,
$false,
inference(copy,[status(thm)],[c_9601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP180-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.40 % Computer : n010.cluster.edu
% 0.17/0.40 % Model : x86_64 x86_64
% 0.17/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.40 % Memory : 8046.5625MB
% 0.17/0.40 % OS : Linux 6.8.0-71-generic
% 0.17/0.40 % CPULimit : 300
% 0.17/0.40 % WCLimit : 300
% 0.17/0.40 % DateTime : Fri Sep 25 14:34:45 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.41 % Process 974067 was started by sandbox2 on n010,
% 0.17/0.41 % Fri Sep 25 14:34:45 2026
% 0.17/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.41
% 0.17/0.41 % From the command line: assign(max_seconds, 300).
% 81.91/11.82
% 81.91/11.82 % SZS status Unsatisfiable for theBenchmark
% 81.91/11.82
% 81.91/11.82 % Proof 1 at 2.68 (+ 0.65) seconds.
% 81.91/11.82 % Length of proof is 124.
% 81.91/11.82 % Level of proof is 21.
% 81.91/11.82 % Maximum clause weight is 100.000.
% 81.91/11.82 % Given clauses 264.
% 81.91/11.82
% 81.91/11.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------