%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP183-2 : 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 : n003.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 07:28:16 AM UTC 2026
% Result : Unsatisfiable 97.23s 14.16s
% Output : CNFRefutation 97.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 19
% Syntax : Number of formulae : 302 ( 302 unt; 0 def)
% Number of atoms : 302 ( 301 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 31 ( 31 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 568 ( 30 sgn 36 !; 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(p20_1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p20_1) ).
cnf(c_22,plain,
inverse(identity) = identity,
inference(clausify,[status(thm)],[p20_1]) ).
fof(p20_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',p20_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[p20_2]) ).
fof(p20_3,axiom,
! [VAR_0,VAR_1] : inverse(multiply(VAR_0,VAR_1)) = multiply(inverse(VAR_1),inverse(VAR_0)),
file('theBenchmark.p',p20_3) ).
cnf(c_24,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(clausify,[status(thm)],[p20_3]) ).
fof(prove_p20,axiom,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity,
file('theBenchmark.p',prove_p20) ).
cnf(c_25,plain,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity,
inference(clausify,[status(thm)],[prove_p20]) ).
cnf(c_9365,plain,
greatest_lower_bound(least_upper_bound(identity,a),inverse(greatest_lower_bound(a,identity))) != identity,
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_9366,plain,
greatest_lower_bound(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_4,c_9365]) ).
cnf(c_26,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != identity,
inference(paramod,[status(thm)],[c_4,c_9366]) ).
cnf(c_9367,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_9368,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_9367]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_9368]) ).
cnf(c_9369,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(B,greatest_lower_bound(A,C)),
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_29,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(B,greatest_lower_bound(A,C)),
inference(paramod,[status(thm)],[c_7,c_9369]) ).
cnf(c_9370,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_34,plain,
least_upper_bound(A,least_upper_bound(B,A)) = least_upper_bound(B,A),
inference(paramod,[status(thm)],[c_5,c_9370]) ).
cnf(c_9371,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_35,plain,
greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B),
inference(copy,[status(thm)],[c_9371]) ).
cnf(c_9372,plain,
greatest_lower_bound(greatest_lower_bound(A,B),B) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_37,plain,
greatest_lower_bound(A,greatest_lower_bound(B,A)) = greatest_lower_bound(B,A),
inference(paramod,[status(thm)],[c_4,c_9372]) ).
cnf(c_39,plain,
least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(A,greatest_lower_bound(B,C))) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_7,c_12]) ).
cnf(c_9373,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_40,plain,
least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,B),C)) = least_upper_bound(A,C),
inference(copy,[status(thm)],[c_9373]) ).
cnf(c_42,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_9374,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_43,plain,
greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(A,B),C)) = greatest_lower_bound(A,C),
inference(copy,[status(thm)],[c_9374]) ).
cnf(c_45,plain,
greatest_lower_bound(least_upper_bound(A,B),least_upper_bound(A,least_upper_bound(B,C))) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_46,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_9375,plain,
least_upper_bound(multiply(inverse(A),B),identity) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_47,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_5,c_9375]) ).
cnf(c_49,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_9376,plain,
greatest_lower_bound(multiply(inverse(A),B),identity) = multiply(inverse(A),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_50,plain,
greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_4,c_9376]) ).
cnf(c_52,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_59,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_9377,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_62,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_4,c_9377]) ).
cnf(c_66,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_9378,plain,
inverse(A) = multiply(inverse(A),inverse(identity)),
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_9379,plain,
inverse(A) = multiply(inverse(A),identity),
inference(paramod,[status(thm)],[c_22,c_9378]) ).
cnf(c_67,plain,
multiply(inverse(A),identity) = inverse(A),
inference(copy,[status(thm)],[c_9379]) ).
cnf(c_9380,plain,
multiply(identity,A) = multiply(B,multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_66,c_3]) ).
cnf(c_9381,plain,
A = multiply(B,multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_9380]) ).
cnf(c_68,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_9381]) ).
cnf(c_75,plain,
greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_66,c_21]) ).
cnf(c_9382,plain,
greatest_lower_bound(multiply(A,inverse(B)),identity) = multiply(greatest_lower_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_66,c_21]) ).
cnf(c_76,plain,
greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_4,c_9382]) ).
cnf(c_9383,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(C,A),B)),
inference(paramod,[status(thm)],[c_42,c_7]) ).
cnf(c_80,plain,
greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(B,A),C)) = greatest_lower_bound(A,C),
inference(copy,[status(thm)],[c_9383]) ).
cnf(c_9384,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_23,c_67]) ).
cnf(c_89,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_23,c_9384]) ).
cnf(c_90,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_89,c_15]) ).
cnf(c_92,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_89,c_17]) ).
cnf(c_9385,plain,
greatest_lower_bound(A,greatest_lower_bound(B,greatest_lower_bound(C,A))) = greatest_lower_bound(greatest_lower_bound(B,C),A),
inference(paramod,[status(thm)],[c_7,c_37]) ).
cnf(c_109,plain,
greatest_lower_bound(A,greatest_lower_bound(B,greatest_lower_bound(C,A))) = greatest_lower_bound(B,greatest_lower_bound(C,A)),
inference(paramod,[status(thm)],[c_7,c_9385]) ).
cnf(c_9386,plain,
least_upper_bound(inverse(A),identity) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_66,c_52]) ).
cnf(c_127,plain,
least_upper_bound(identity,inverse(A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_5,c_9386]) ).
cnf(c_9387,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_66,c_59]) ).
cnf(c_162,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_9387]) ).
cnf(c_164,plain,
greatest_lower_bound(A,multiply(greatest_lower_bound(identity,B),A)) = greatest_lower_bound(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_59,c_35]) ).
cnf(c_9388,plain,
least_upper_bound(inverse(A),identity) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_90]) ).
cnf(c_9389,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_9388]) ).
cnf(c_179,plain,
multiply(least_upper_bound(identity,A),inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_127,c_9389]) ).
cnf(c_185,plain,
greatest_lower_bound(A,multiply(A,least_upper_bound(identity,B))) = A,
inference(paramod,[status(thm)],[c_90,c_13]) ).
cnf(c_9390,plain,
multiply(A,least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),A),
inference(paramod,[status(thm)],[c_90,c_52]) ).
cnf(c_200,plain,
multiply(least_upper_bound(identity,A),A) = multiply(A,least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_9390]) ).
cnf(c_208,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_179,c_127]) ).
cnf(c_9391,plain,
greatest_lower_bound(inverse(A),identity) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_92]) ).
cnf(c_9392,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_4,c_9391]) ).
cnf(c_229,plain,
multiply(greatest_lower_bound(identity,A),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_162,c_9392]) ).
cnf(c_9393,plain,
multiply(inverse(A),greatest_lower_bound(A,multiply(A,B))) = greatest_lower_bound(identity,B),
inference(paramod,[status(thm)],[c_92,c_27]) ).
cnf(c_243,plain,
greatest_lower_bound(identity,A) = multiply(inverse(B),greatest_lower_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_9393]) ).
cnf(c_244,plain,
greatest_lower_bound(inverse(A),B) = multiply(inverse(A),greatest_lower_bound(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_27,c_92]) ).
cnf(c_9394,plain,
multiply(A,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),A),
inference(paramod,[status(thm)],[c_92,c_59]) ).
cnf(c_250,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_9394]) ).
cnf(c_255,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_229,c_162]) ).
cnf(c_258,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)))) != identity,
inference(paramod,[status(thm)],[c_244,c_26]) ).
cnf(c_9395,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_200,c_92]) ).
cnf(c_9396,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_59,c_9395]) ).
cnf(c_283,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_9396]) ).
cnf(c_9397,plain,
inverse(multiply(A,greatest_lower_bound(identity,A))) = multiply(inverse(A),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_250,c_24]) ).
cnf(c_305,plain,
multiply(inverse(greatest_lower_bound(identity,A)),inverse(A)) = multiply(inverse(A),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_24,c_9397]) ).
cnf(c_321,plain,
multiply(least_upper_bound(A,identity),inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_179]) ).
cnf(c_9398,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_229,c_3]) ).
cnf(c_9399,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_9398]) ).
cnf(c_333,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_9399]) ).
cnf(c_334,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_4,c_229]) ).
cnf(c_9400,plain,
inverse(multiply(inverse(A),greatest_lower_bound(identity,A))) = multiply(inverse(inverse(A)),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_229,c_24]) ).
cnf(c_9401,plain,
multiply(inverse(greatest_lower_bound(identity,A)),inverse(inverse(A))) = multiply(inverse(inverse(A)),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_24,c_9400]) ).
cnf(c_9402,plain,
multiply(inverse(greatest_lower_bound(identity,A)),A) = multiply(inverse(inverse(A)),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_23,c_9401]) ).
cnf(c_343,plain,
multiply(inverse(greatest_lower_bound(identity,A)),A) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_23,c_9402]) ).
cnf(c_348,plain,
multiply(least_upper_bound(A,identity),inverse(A)) = multiply(inverse(A),least_upper_bound(A,identity)),
inference(paramod,[status(thm)],[c_5,c_321]) ).
cnf(c_9403,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(least_upper_bound(A,identity),inverse(A))) = multiply(greatest_lower_bound(identity,inverse(A)),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_321,c_59]) ).
cnf(c_9404,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))) = multiply(greatest_lower_bound(identity,inverse(A)),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_348,c_9403]) ).
cnf(c_9405,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))) = multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_255,c_9404]) ).
cnf(c_360,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_3,c_9405]) ).
cnf(c_365,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_4,c_334]) ).
cnf(c_9406,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(greatest_lower_bound(A,identity),inverse(A))) = multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_334,c_52]) ).
cnf(c_9407,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(inverse(A),greatest_lower_bound(A,identity))) = multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_365,c_9406]) ).
cnf(c_9408,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(inverse(A),greatest_lower_bound(A,identity))) = multiply(multiply(inverse(A),least_upper_bound(identity,A)),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_208,c_9407]) ).
cnf(c_9409,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(inverse(A),greatest_lower_bound(A,identity))) = multiply(inverse(A),multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_3,c_9408]) ).
cnf(c_376,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(inverse(A),greatest_lower_bound(A,identity))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_283,c_9409]) ).
cnf(c_9410,plain,
inverse(multiply(inverse(A),least_upper_bound(A,identity))) = multiply(inverse(inverse(A)),inverse(least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_348,c_24]) ).
cnf(c_9411,plain,
multiply(inverse(least_upper_bound(A,identity)),inverse(inverse(A))) = multiply(inverse(inverse(A)),inverse(least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_24,c_9410]) ).
cnf(c_9412,plain,
multiply(inverse(least_upper_bound(A,identity)),A) = multiply(inverse(inverse(A)),inverse(least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_23,c_9411]) ).
cnf(c_387,plain,
multiply(inverse(least_upper_bound(A,identity)),A) = multiply(A,inverse(least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_23,c_9412]) ).
cnf(c_9413,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(multiply(A,least_upper_bound(identity,C)),B)),
inference(paramod,[status(thm)],[c_185,c_7]) ).
cnf(c_431,plain,
greatest_lower_bound(A,greatest_lower_bound(multiply(A,least_upper_bound(identity,B)),C)) = greatest_lower_bound(A,C),
inference(copy,[status(thm)],[c_9413]) ).
cnf(c_484,plain,
least_upper_bound(multiply(A,B),C) = multiply(A,least_upper_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_68,c_15]) ).
cnf(c_485,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_68,c_17]) ).
cnf(c_539,plain,
greatest_lower_bound(A,multiply(A,greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),C)))) = greatest_lower_bound(A,C),
inference(paramod,[status(thm)],[c_485,c_431]) ).
cnf(c_9414,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(greatest_lower_bound(identity,a),inverse(least_upper_bound(identity,a))),least_upper_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_62,c_258]) ).
cnf(c_774,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(least_upper_bound(identity,a)))),least_upper_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_7,c_9414]) ).
cnf(c_9415,plain,
greatest_lower_bound(greatest_lower_bound(A,inverse(least_upper_bound(identity,B))),greatest_lower_bound(identity,multiply(A,least_upper_bound(identity,B)))) = greatest_lower_bound(A,inverse(least_upper_bound(identity,B))),
inference(paramod,[status(thm)],[c_62,c_185]) ).
cnf(c_9416,plain,
greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(A,inverse(least_upper_bound(identity,B))),multiply(A,least_upper_bound(identity,B)))) = greatest_lower_bound(A,inverse(least_upper_bound(identity,B))),
inference(paramod,[status(thm)],[c_29,c_9415]) ).
cnf(c_9417,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(A,least_upper_bound(identity,B)),greatest_lower_bound(A,inverse(least_upper_bound(identity,B))))) = greatest_lower_bound(A,inverse(least_upper_bound(identity,B))),
inference(paramod,[status(thm)],[c_4,c_9416]) ).
cnf(c_9418,plain,
greatest_lower_bound(identity,greatest_lower_bound(A,greatest_lower_bound(multiply(A,least_upper_bound(identity,B)),inverse(least_upper_bound(identity,B))))) = greatest_lower_bound(A,inverse(least_upper_bound(identity,B))),
inference(paramod,[status(thm)],[c_29,c_9417]) ).
cnf(c_9419,plain,
greatest_lower_bound(identity,greatest_lower_bound(A,multiply(A,greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),inverse(least_upper_bound(identity,B))))))) = greatest_lower_bound(A,inverse(least_upper_bound(identity,B))),
inference(paramod,[status(thm)],[c_485,c_9418]) ).
cnf(c_786,plain,
greatest_lower_bound(identity,greatest_lower_bound(A,inverse(least_upper_bound(identity,B)))) = greatest_lower_bound(A,inverse(least_upper_bound(identity,B))),
inference(paramod,[status(thm)],[c_539,c_9419]) ).
cnf(c_803,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(a,inverse(least_upper_bound(identity,a))),least_upper_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_786,c_774]) ).
cnf(c_929,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a)))) != identity,
inference(paramod,[status(thm)],[c_62,c_803]) ).
cnf(c_9420,plain,
multiply(inverse(multiply(inverse(A),greatest_lower_bound(A,multiply(A,a)))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a)))) != identity,
inference(paramod,[status(thm)],[c_243,c_929]) ).
cnf(c_9421,plain,
multiply(multiply(inverse(greatest_lower_bound(A,multiply(A,a))),inverse(inverse(A))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a)))) != identity,
inference(paramod,[status(thm)],[c_24,c_9420]) ).
cnf(c_9422,plain,
multiply(multiply(inverse(greatest_lower_bound(A,multiply(A,a))),A),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a)))) != identity,
inference(paramod,[status(thm)],[c_23,c_9421]) ).
cnf(c_1094,plain,
multiply(inverse(greatest_lower_bound(A,multiply(A,a))),multiply(A,greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_3,c_9422]) ).
cnf(c_1105,plain,
multiply(inverse(greatest_lower_bound(A,greatest_lower_bound(B,multiply(greatest_lower_bound(A,B),a)))),multiply(greatest_lower_bound(A,B),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_7,c_1094]) ).
cnf(c_9423,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_40,c_42]) ).
cnf(c_1164,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_9423]) ).
cnf(c_9424,plain,
greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(A,B),greatest_lower_bound(C,A))) = greatest_lower_bound(C,A),
inference(paramod,[status(thm)],[c_37,c_43]) ).
cnf(c_1458,plain,
greatest_lower_bound(least_upper_bound(A,B),greatest_lower_bound(C,A)) = greatest_lower_bound(C,A),
inference(paramod,[status(thm)],[c_109,c_9424]) ).
cnf(c_1460,plain,
greatest_lower_bound(A,multiply(greatest_lower_bound(identity,B),least_upper_bound(A,C))) = greatest_lower_bound(A,multiply(B,least_upper_bound(A,C))),
inference(paramod,[status(thm)],[c_59,c_43]) ).
cnf(c_9425,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = multiply(inverse(A),A),
inference(paramod,[status(thm)],[c_12,c_46]) ).
cnf(c_1826,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_2,c_9425]) ).
cnf(c_1827,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_46,c_13]) ).
cnf(c_9426,plain,
greatest_lower_bound(A,identity) = greatest_lower_bound(identity,greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(B,C)))),
inference(paramod,[status(thm)],[c_1827,c_29]) ).
cnf(c_1931,plain,
greatest_lower_bound(identity,greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(B,C)))) = greatest_lower_bound(A,identity),
inference(copy,[status(thm)],[c_9426]) ).
cnf(c_9427,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(A,B),greatest_lower_bound(greatest_lower_bound(C,A),multiply(greatest_lower_bound(C,A),a)))),multiply(greatest_lower_bound(least_upper_bound(A,B),greatest_lower_bound(C,A)),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_1458,c_1105]) ).
cnf(c_9428,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(A,B),multiply(greatest_lower_bound(C,A),greatest_lower_bound(identity,a)))),multiply(greatest_lower_bound(least_upper_bound(A,B),greatest_lower_bound(C,A)),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_92,c_9427]) ).
cnf(c_2412,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(A,B),multiply(greatest_lower_bound(C,A),greatest_lower_bound(identity,a)))),multiply(greatest_lower_bound(C,A),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_1458,c_9428]) ).
cnf(c_9429,plain,
greatest_lower_bound(identity,multiply(multiply(A,B),inverse(A))) = multiply(multiply(A,greatest_lower_bound(identity,B)),inverse(A)),
inference(paramod,[status(thm)],[c_92,c_75]) ).
cnf(c_9430,plain,
greatest_lower_bound(identity,multiply(A,multiply(B,inverse(A)))) = multiply(multiply(A,greatest_lower_bound(identity,B)),inverse(A)),
inference(paramod,[status(thm)],[c_3,c_9429]) ).
cnf(c_2509,plain,
greatest_lower_bound(identity,multiply(A,multiply(B,inverse(A)))) = multiply(A,multiply(greatest_lower_bound(identity,B),inverse(A))),
inference(paramod,[status(thm)],[c_3,c_9430]) ).
cnf(c_9431,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_68,c_164]) ).
cnf(c_9432,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_333,c_9431]) ).
cnf(c_9433,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_485,c_9432]) ).
cnf(c_9434,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_23,c_9433]) ).
cnf(c_9435,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_68,c_9434]) ).
cnf(c_9436,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(A,B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_164,c_9435]) ).
cnf(c_9437,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_9436]) ).
cnf(c_3039,plain,
greatest_lower_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),greatest_lower_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_9437]) ).
cnf(c_5473,plain,
least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(B,A)) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_37,c_39]) ).
cnf(c_9438,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A))) = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_5473,c_46]) ).
cnf(c_5596,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_2,c_9438]) ).
cnf(c_9439,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A))) = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_5473,c_47]) ).
cnf(c_9440,plain,
identity = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_5596,c_9439]) ).
cnf(c_5598,plain,
multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)) = identity,
inference(copy,[status(thm)],[c_9440]) ).
cnf(c_5656,plain,
greatest_lower_bound(least_upper_bound(A,B),least_upper_bound(B,A)) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_34,c_45]) ).
cnf(c_9441,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A))) = multiply(inverse(least_upper_bound(A,B)),least_upper_bound(A,B)),
inference(paramod,[status(thm)],[c_5656,c_49]) ).
cnf(c_5730,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_2,c_9441]) ).
cnf(c_9442,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A))) = multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_5656,c_50]) ).
cnf(c_9443,plain,
identity = multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_5730,c_9442]) ).
cnf(c_5731,plain,
multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A)) = identity,
inference(copy,[status(thm)],[c_9443]) ).
cnf(c_9444,plain,
multiply(multiply(inverse(A),inverse(greatest_lower_bound(identity,A))),B) = multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_305,c_3]) ).
cnf(c_9445,plain,
multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,A)),B)) = multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_3,c_9444]) ).
cnf(c_5867,plain,
multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),B)) = multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,A)),B)),
inference(copy,[status(thm)],[c_9445]) ).
cnf(c_9446,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_62,c_1164]) ).
cnf(c_9447,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_484,c_9446]) ).
cnf(c_7485,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_9447]) ).
cnf(c_9448,plain,
greatest_lower_bound(least_upper_bound(identity,A),least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,multiply(B,C))),A)) = least_upper_bound(greatest_lower_bound(identity,C),A),
inference(paramod,[status(thm)],[c_243,c_1164]) ).
cnf(c_9449,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,multiply(B,C)),multiply(inverse(inverse(B)),A)))) = least_upper_bound(greatest_lower_bound(identity,C),A),
inference(paramod,[status(thm)],[c_484,c_9448]) ).
cnf(c_9450,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,multiply(B,C)),multiply(B,A)))) = least_upper_bound(greatest_lower_bound(identity,C),A),
inference(paramod,[status(thm)],[c_23,c_9449]) ).
cnf(c_7494,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),least_upper_bound(greatest_lower_bound(C,multiply(C,A)),multiply(C,B)))),
inference(copy,[status(thm)],[c_9450]) ).
cnf(c_9451,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_49,c_1164]) ).
cnf(c_9452,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_7485,c_9451]) ).
cnf(c_9453,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_244,c_9452]) ).
cnf(c_9454,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_244,c_9453]) ).
cnf(c_9455,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(multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(C)))),inverse(inverse(B))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_24,c_9454]) ).
cnf(c_9456,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(multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(C)))),B),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_23,c_9455]) ).
cnf(c_9457,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(identity,multiply(B,inverse(C)))),multiply(B,A)))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_3,c_9456]) ).
cnf(c_9458,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(greatest_lower_bound(identity,multiply(B,inverse(C)))),multiply(B,A))))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_3,c_9457]) ).
cnf(c_9459,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(greatest_lower_bound(identity,multiply(B,inverse(C)))),multiply(B,A)))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_35,c_9458]) ).
cnf(c_9460,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(greatest_lower_bound(identity,multiply(B,inverse(C)))),multiply(B,A)))))) = multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,C),multiply(inverse(inverse(B)),A))),
inference(paramod,[status(thm)],[c_484,c_9459]) ).
cnf(c_9461,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(greatest_lower_bound(identity,multiply(B,inverse(C)))),multiply(B,A)))))) = multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,C),multiply(B,A))),
inference(paramod,[status(thm)],[c_23,c_9460]) ).
cnf(c_7521,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(greatest_lower_bound(identity,multiply(A,inverse(B)))),multiply(A,C)))))),
inference(copy,[status(thm)],[c_9461]) ).
cnf(c_9462,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A)))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_7521,c_7494]) ).
cnf(c_9463,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(greatest_lower_bound(identity,multiply(C,multiply(inverse(A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_9462]) ).
cnf(c_9464,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(greatest_lower_bound(identity,inverse(A)),inverse(C))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_2509,c_9463]) ).
cnf(c_9465,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),inverse(C))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_255,c_9464]) ).
cnf(c_9466,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_9465]) ).
cnf(c_9467,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,multiply(inverse(A),inverse(C))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_9466]) ).
cnf(c_9468,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(multiply(C,multiply(greatest_lower_bound(identity,inverse(A)),inverse(C)))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_2509,c_9467]) ).
cnf(c_9469,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(multiply(C,multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),inverse(C)))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_255,c_9468]) ).
cnf(c_9470,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_9469]) ).
cnf(c_9471,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(inverse(multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_9470]) ).
cnf(c_9472,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(inverse(multiply(greatest_lower_bound(identity,A),inverse(C))),inverse(inverse(A))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_9471]) ).
cnf(c_9473,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(multiply(inverse(inverse(C)),inverse(greatest_lower_bound(identity,A))),inverse(inverse(A))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_9472]) ).
cnf(c_9474,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(multiply(C,inverse(greatest_lower_bound(identity,A))),inverse(inverse(A))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_23,c_9473]) ).
cnf(c_9475,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(multiply(C,inverse(greatest_lower_bound(identity,A))),A),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_23,c_9474]) ).
cnf(c_9476,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(C,multiply(inverse(greatest_lower_bound(identity,A)),A)),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_9475]) ).
cnf(c_9477,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(C,multiply(A,inverse(greatest_lower_bound(identity,A)))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_343,c_9476]) ).
cnf(c_9478,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(C,multiply(multiply(A,inverse(greatest_lower_bound(identity,A))),inverse(C))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_9477]) ).
cnf(c_9479,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(C,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),inverse(C)))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_9478]) ).
cnf(c_9480,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(C,multiply(multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),inverse(C))),multiply(C,B)))))))),
inference(paramod,[status(thm)],[c_3,c_9479]) ).
cnf(c_9481,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(C,multiply(A,multiply(multiply(inverse(greatest_lower_bound(identity,A)),inverse(C)),multiply(C,B))))))))),
inference(paramod,[status(thm)],[c_3,c_9480]) ).
cnf(c_9482,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(C,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(C),multiply(C,B)))))))))),
inference(paramod,[status(thm)],[c_3,c_9481]) ).
cnf(c_9483,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(C,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))))),
inference(paramod,[status(thm)],[c_27,c_9482]) ).
cnf(c_9484,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),multiply(C,least_upper_bound(A,multiply(inverse(C),multiply(C,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))))))),
inference(paramod,[status(thm)],[c_484,c_9483]) ).
cnf(c_9485,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),multiply(C,least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))))),
inference(paramod,[status(thm)],[c_27,c_9484]) ).
cnf(c_9486,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(C,multiply(multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C))),multiply(C,least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B))))))))),
inference(paramod,[status(thm)],[c_3,c_9485]) ).
cnf(c_9487,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(C,multiply(inverse(A),multiply(multiply(greatest_lower_bound(identity,A),inverse(C)),multiply(C,least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))))))),
inference(paramod,[status(thm)],[c_3,c_9486]) ).
cnf(c_9488,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),multiply(inverse(C),multiply(C,least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B))))))))))),
inference(paramod,[status(thm)],[c_3,c_9487]) ).
cnf(c_9489,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B))))))))),
inference(paramod,[status(thm)],[c_27,c_9488]) ).
cnf(c_9490,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B))))))),
inference(paramod,[status(thm)],[c_27,c_9489]) ).
cnf(c_7648,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))),
inference(paramod,[status(thm)],[c_35,c_9490]) ).
cnf(c_9491,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,identity))),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),greatest_lower_bound(A,identity)))))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_7648,c_376]) ).
cnf(c_9492,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),greatest_lower_bound(A,identity)))))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_1826,c_9491]) ).
cnf(c_9493,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,A)),greatest_lower_bound(A,identity)))))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_5867,c_9492]) ).
cnf(c_9494,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(A),identity)))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_5598,c_9493]) ).
cnf(c_9495,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,inverse(A)))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_89,c_9494]) ).
cnf(c_7723,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,identity)))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_66,c_9495]) ).
cnf(c_9496,plain,
greatest_lower_bound(A,multiply(inverse(B),greatest_lower_bound(least_upper_bound(C,A),multiply(B,least_upper_bound(C,A))))) = greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(C,A))),
inference(paramod,[status(thm)],[c_3039,c_80]) ).
cnf(c_9306,plain,
greatest_lower_bound(A,multiply(inverse(B),multiply(greatest_lower_bound(identity,B),least_upper_bound(C,A)))) = greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(C,A))),
inference(paramod,[status(thm)],[c_59,c_9496]) ).
cnf(c_9497,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,identity))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_9306,c_7723]) ).
cnf(c_9498,plain,
identity = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_1827,c_9497]) ).
cnf(c_9347,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))) = identity,
inference(copy,[status(thm)],[c_9498]) ).
cnf(c_9348,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))) = identity,
inference(paramod,[status(thm)],[c_9347,c_360]) ).
cnf(c_9499,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(A),least_upper_bound(A,identity))),least_upper_bound(identity,A))) = multiply(inverse(multiply(inverse(A),least_upper_bound(A,identity))),identity),
inference(paramod,[status(thm)],[c_9348,c_50]) ).
cnf(c_9500,plain,
greatest_lower_bound(identity,multiply(multiply(inverse(least_upper_bound(A,identity)),inverse(inverse(A))),least_upper_bound(identity,A))) = multiply(inverse(multiply(inverse(A),least_upper_bound(A,identity))),identity),
inference(paramod,[status(thm)],[c_24,c_9499]) ).
cnf(c_9501,plain,
greatest_lower_bound(identity,multiply(multiply(inverse(least_upper_bound(A,identity)),A),least_upper_bound(identity,A))) = multiply(inverse(multiply(inverse(A),least_upper_bound(A,identity))),identity),
inference(paramod,[status(thm)],[c_23,c_9500]) ).
cnf(c_9502,plain,
greatest_lower_bound(identity,multiply(multiply(A,inverse(least_upper_bound(A,identity))),least_upper_bound(identity,A))) = multiply(inverse(multiply(inverse(A),least_upper_bound(A,identity))),identity),
inference(paramod,[status(thm)],[c_387,c_9501]) ).
cnf(c_9503,plain,
greatest_lower_bound(identity,multiply(A,multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(identity,A)))) = multiply(inverse(multiply(inverse(A),least_upper_bound(A,identity))),identity),
inference(paramod,[status(thm)],[c_3,c_9502]) ).
cnf(c_9504,plain,
greatest_lower_bound(identity,multiply(A,identity)) = multiply(inverse(multiply(inverse(A),least_upper_bound(A,identity))),identity),
inference(paramod,[status(thm)],[c_5731,c_9503]) ).
cnf(c_9505,plain,
greatest_lower_bound(identity,A) = multiply(inverse(multiply(inverse(A),least_upper_bound(A,identity))),identity),
inference(paramod,[status(thm)],[c_89,c_9504]) ).
cnf(c_9506,plain,
greatest_lower_bound(identity,A) = multiply(multiply(inverse(least_upper_bound(A,identity)),inverse(inverse(A))),identity),
inference(paramod,[status(thm)],[c_24,c_9505]) ).
cnf(c_9507,plain,
greatest_lower_bound(identity,A) = multiply(multiply(inverse(least_upper_bound(A,identity)),A),identity),
inference(paramod,[status(thm)],[c_23,c_9506]) ).
cnf(c_9508,plain,
greatest_lower_bound(identity,A) = multiply(multiply(A,inverse(least_upper_bound(A,identity))),identity),
inference(paramod,[status(thm)],[c_387,c_9507]) ).
cnf(c_9509,plain,
greatest_lower_bound(identity,A) = multiply(A,inverse(least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_89,c_9508]) ).
cnf(c_9360,plain,
multiply(A,inverse(least_upper_bound(A,identity))) = greatest_lower_bound(identity,A),
inference(copy,[status(thm)],[c_9509]) ).
cnf(c_9510,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,A),inverse(multiply(inverse(A),least_upper_bound(A,identity))))) = multiply(identity,inverse(multiply(inverse(A),least_upper_bound(A,identity)))),
inference(paramod,[status(thm)],[c_9348,c_76]) ).
cnf(c_9511,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,A),multiply(inverse(least_upper_bound(A,identity)),inverse(inverse(A))))) = multiply(identity,inverse(multiply(inverse(A),least_upper_bound(A,identity)))),
inference(paramod,[status(thm)],[c_24,c_9510]) ).
cnf(c_9512,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,A),multiply(inverse(least_upper_bound(A,identity)),A))) = multiply(identity,inverse(multiply(inverse(A),least_upper_bound(A,identity)))),
inference(paramod,[status(thm)],[c_23,c_9511]) ).
cnf(c_9513,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,A),multiply(A,inverse(least_upper_bound(A,identity))))) = multiply(identity,inverse(multiply(inverse(A),least_upper_bound(A,identity)))),
inference(paramod,[status(thm)],[c_387,c_9512]) ).
cnf(c_9514,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A))) = multiply(identity,inverse(multiply(inverse(A),least_upper_bound(A,identity)))),
inference(paramod,[status(thm)],[c_9360,c_9513]) ).
cnf(c_9515,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))) = multiply(identity,inverse(multiply(inverse(A),least_upper_bound(A,identity)))),
inference(paramod,[status(thm)],[c_283,c_9514]) ).
cnf(c_9516,plain,
greatest_lower_bound(identity,multiply(A,least_upper_bound(identity,A))) = multiply(identity,inverse(multiply(inverse(A),least_upper_bound(A,identity)))),
inference(paramod,[status(thm)],[c_1460,c_9515]) ).
cnf(c_9517,plain,
greatest_lower_bound(identity,multiply(A,least_upper_bound(identity,A))) = multiply(identity,multiply(inverse(least_upper_bound(A,identity)),inverse(inverse(A)))),
inference(paramod,[status(thm)],[c_24,c_9516]) ).
cnf(c_9518,plain,
greatest_lower_bound(identity,multiply(A,least_upper_bound(identity,A))) = multiply(identity,multiply(inverse(least_upper_bound(A,identity)),A)),
inference(paramod,[status(thm)],[c_23,c_9517]) ).
cnf(c_9519,plain,
greatest_lower_bound(identity,multiply(A,least_upper_bound(identity,A))) = multiply(identity,multiply(A,inverse(least_upper_bound(A,identity)))),
inference(paramod,[status(thm)],[c_387,c_9518]) ).
cnf(c_9520,plain,
greatest_lower_bound(identity,multiply(A,least_upper_bound(identity,A))) = multiply(identity,greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_9360,c_9519]) ).
cnf(c_9361,plain,
greatest_lower_bound(identity,multiply(A,least_upper_bound(identity,A))) = greatest_lower_bound(identity,A),
inference(paramod,[status(thm)],[c_1,c_9520]) ).
cnf(c_9521,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(inverse(A),least_upper_bound(A,identity)),B),multiply(identity,greatest_lower_bound(identity,a)))),multiply(greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_9348,c_2412]) ).
cnf(c_9522,plain,
multiply(inverse(greatest_lower_bound(multiply(inverse(A),least_upper_bound(least_upper_bound(A,identity),multiply(inverse(inverse(A)),B))),multiply(identity,greatest_lower_bound(identity,a)))),multiply(greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_484,c_9521]) ).
cnf(c_9523,plain,
multiply(inverse(greatest_lower_bound(multiply(inverse(A),least_upper_bound(least_upper_bound(A,identity),multiply(A,B))),multiply(identity,greatest_lower_bound(identity,a)))),multiply(greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_23,c_9522]) ).
cnf(c_9524,plain,
multiply(inverse(greatest_lower_bound(multiply(inverse(A),least_upper_bound(A,least_upper_bound(identity,multiply(A,B)))),multiply(identity,greatest_lower_bound(identity,a)))),multiply(greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_9,c_9523]) ).
cnf(c_9525,plain,
multiply(inverse(greatest_lower_bound(multiply(inverse(A),least_upper_bound(A,least_upper_bound(identity,multiply(A,B)))),greatest_lower_bound(identity,a))),multiply(greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_1,c_9524]) ).
cnf(c_9526,plain,
multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,a),multiply(inverse(A),least_upper_bound(A,least_upper_bound(identity,multiply(A,B)))))),multiply(greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_4,c_9525]) ).
cnf(c_9527,plain,
multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,multiply(inverse(A),least_upper_bound(A,least_upper_bound(identity,multiply(A,B))))))),multiply(greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_7,c_9526]) ).
cnf(c_9528,plain,
multiply(inverse(greatest_lower_bound(a,identity)),multiply(greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_1931,c_9527]) ).
cnf(c_9529,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_4,c_9528]) ).
cnf(c_9530,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(identity,greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_9348,c_9529]) ).
cnf(c_9531,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(identity,greatest_lower_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_9361,c_9530]) ).
cnf(c_9532,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,a)) != identity,
inference(paramod,[status(thm)],[c_1,c_9531]) ).
cnf(c_9533,plain,
identity != identity,
inference(paramod,[status(thm)],[c_2,c_9532]) ).
cnf(c_9364,plain,
$false,
inference(copy,[status(thm)],[c_9533]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP183-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n003.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 14:37:39 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 403536 was started by sandbox2 on n003,
% 0.16/0.43 % Fri Sep 25 14:37:39 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 97.23/14.16
% 97.23/14.16 % SZS status Unsatisfiable for theBenchmark
% 97.23/14.16
% 97.23/14.16 % Proof 1 at 4.48 (+ 1.10) seconds.
% 97.23/14.16 % Length of proof is 114.
% 97.23/14.16 % Level of proof is 13.
% 97.23/14.16 % Maximum clause weight is 92.000.
% 97.23/14.16 % Given clauses 362.
% 97.23/14.16
% 97.23/14.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------