%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP179-3 : 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 : n013.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 106.66s 25.61s
% Output : CNFRefutation 106.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 83
% Number of leaves : 19
% Syntax : Number of formulae : 283 ( 283 unt; 0 def)
% Number of atoms : 283 ( 282 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 28 ( 28 ~; 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 : 541 ( 12 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(p18_1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p18_1) ).
cnf(c_22,plain,
inverse(identity) = identity,
inference(clausify,[status(thm)],[p18_1]) ).
fof(p18_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',p18_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[p18_2]) ).
fof(p18_3,axiom,
! [VAR_0,VAR_1] : inverse(multiply(VAR_0,VAR_1)) = multiply(inverse(VAR_1),inverse(VAR_0)),
file('theBenchmark.p',p18_3) ).
cnf(c_24,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(clausify,[status(thm)],[p18_3]) ).
fof(prove_p18,axiom,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)),
file('theBenchmark.p',prove_p18) ).
cnf(c_25,plain,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)),
inference(clausify,[status(thm)],[prove_p18]) ).
cnf(c_10400,plain,
least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity)),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_26,plain,
least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(identity,a)),
inference(paramod,[status(thm)],[c_4,c_10400]) ).
cnf(c_10401,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_10402,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_10401]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_10402]) ).
cnf(c_10403,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_32,plain,
least_upper_bound(A,least_upper_bound(A,B)) = least_upper_bound(A,B),
inference(copy,[status(thm)],[c_10403]) ).
cnf(c_10404,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_10404]) ).
cnf(c_10405,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_10405]) ).
cnf(c_10406,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_10406]) ).
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_10407,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_10407]) ).
cnf(c_42,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
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_10408,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_10408]) ).
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_10409,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_10409]) ).
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_10410,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_10410]) ).
cnf(c_66,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_10411,plain,
inverse(A) = multiply(inverse(A),inverse(identity)),
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_10412,plain,
inverse(A) = multiply(inverse(A),identity),
inference(paramod,[status(thm)],[c_22,c_10411]) ).
cnf(c_67,plain,
multiply(inverse(A),identity) = inverse(A),
inference(copy,[status(thm)],[c_10412]) ).
cnf(c_10413,plain,
multiply(identity,A) = multiply(B,multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_66,c_3]) ).
cnf(c_10414,plain,
A = multiply(B,multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_10413]) ).
cnf(c_68,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_10414]) ).
cnf(c_73,plain,
least_upper_bound(identity,multiply(A,inverse(B))) = multiply(least_upper_bound(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_66,c_19]) ).
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_10415,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_10415]) ).
cnf(c_10416,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_10416]) ).
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_10417,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_10417]) ).
cnf(c_130,plain,
least_upper_bound(A,multiply(least_upper_bound(identity,B),A)) = least_upper_bound(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_52,c_32]) ).
cnf(c_132,plain,
multiply(least_upper_bound(identity,a),inverse(a)) != inverse(greatest_lower_bound(identity,a)),
inference(paramod,[status(thm)],[c_127,c_26]) ).
cnf(c_10418,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_163,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_10418]) ).
cnf(c_165,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_10419,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_10420,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_10419]) ).
cnf(c_180,plain,
multiply(least_upper_bound(identity,A),inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_127,c_10420]) ).
cnf(c_195,plain,
inverse(least_upper_bound(A,multiply(A,B))) = multiply(inverse(least_upper_bound(identity,B)),inverse(A)),
inference(paramod,[status(thm)],[c_90,c_24]) ).
cnf(c_10421,plain,
multiply(inverse(A),least_upper_bound(A,multiply(A,B))) = least_upper_bound(identity,B),
inference(paramod,[status(thm)],[c_90,c_27]) ).
cnf(c_197,plain,
least_upper_bound(identity,A) = multiply(inverse(B),least_upper_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_10421]) ).
cnf(c_10422,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_201,plain,
multiply(least_upper_bound(identity,A),A) = multiply(A,least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_10422]) ).
cnf(c_209,plain,
multiply(inverse(a),least_upper_bound(identity,a)) != inverse(greatest_lower_bound(identity,a)),
inference(paramod,[status(thm)],[c_180,c_132]) ).
cnf(c_210,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_180,c_127]) ).
cnf(c_10423,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_10424,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_4,c_10423]) ).
cnf(c_231,plain,
multiply(greatest_lower_bound(identity,A),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_163,c_10424]) ).
cnf(c_10425,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_245,plain,
greatest_lower_bound(identity,A) = multiply(inverse(B),greatest_lower_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_10425]) ).
cnf(c_246,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_10426,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_252,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_10426]) ).
cnf(c_257,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_231,c_163]) ).
cnf(c_10427,plain,
inverse(multiply(A,least_upper_bound(identity,A))) = multiply(inverse(A),inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_201,c_24]) ).
cnf(c_281,plain,
multiply(inverse(least_upper_bound(identity,A)),inverse(A)) = multiply(inverse(A),inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_24,c_10427]) ).
cnf(c_10428,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_201,c_92]) ).
cnf(c_10429,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_10428]) ).
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_10429]) ).
cnf(c_10430,plain,
inverse(multiply(A,greatest_lower_bound(identity,A))) = multiply(inverse(A),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_252,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_10430]) ).
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_180]) ).
cnf(c_10431,plain,
inverse(multiply(inverse(A),least_upper_bound(identity,A))) = multiply(inverse(inverse(A)),inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_180,c_24]) ).
cnf(c_10432,plain,
multiply(inverse(least_upper_bound(identity,A)),inverse(inverse(A))) = multiply(inverse(inverse(A)),inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_24,c_10431]) ).
cnf(c_10433,plain,
multiply(inverse(least_upper_bound(identity,A)),A) = multiply(inverse(inverse(A)),inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_23,c_10432]) ).
cnf(c_330,plain,
multiply(inverse(least_upper_bound(identity,A)),A) = multiply(A,inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_23,c_10433]) ).
cnf(c_10434,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_231,c_3]) ).
cnf(c_10435,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_10434]) ).
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_10435]) ).
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_231]) ).
cnf(c_10436,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_231,c_24]) ).
cnf(c_10437,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_10436]) ).
cnf(c_10438,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_10437]) ).
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_10438]) ).
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_10439,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_10440,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_10439]) ).
cnf(c_10441,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_257,c_10440]) ).
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_10441]) ).
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_10442,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_10443,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_10442]) ).
cnf(c_10444,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_210,c_10443]) ).
cnf(c_10445,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_10444]) ).
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_10445]) ).
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_10446,plain,
multiply(inverse(a),least_upper_bound(identity,a)) != inverse(multiply(inverse(A),greatest_lower_bound(A,multiply(A,a)))),
inference(paramod,[status(thm)],[c_245,c_209]) ).
cnf(c_10447,plain,
multiply(inverse(a),least_upper_bound(identity,a)) != multiply(inverse(greatest_lower_bound(A,multiply(A,a))),inverse(inverse(A))),
inference(paramod,[status(thm)],[c_24,c_10446]) ).
cnf(c_10448,plain,
multiply(inverse(a),least_upper_bound(identity,a)) != multiply(inverse(greatest_lower_bound(A,multiply(A,a))),A),
inference(paramod,[status(thm)],[c_23,c_10447]) ).
cnf(c_1052,plain,
multiply(inverse(greatest_lower_bound(A,multiply(A,a))),A) != multiply(inverse(a),least_upper_bound(identity,a)),
inference(copy,[status(thm)],[c_10448]) ).
cnf(c_10449,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_1133,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_10449]) ).
cnf(c_10450,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_1884,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_2,c_10450]) ).
cnf(c_1885,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_46,c_13]) ).
cnf(c_10451,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_10452,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_10451]) ).
cnf(c_2811,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_10452]) ).
cnf(c_10453,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_130,c_73]) ).
cnf(c_10454,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_10453]) ).
cnf(c_10455,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_66,c_10454]) ).
cnf(c_10456,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_89,c_10455]) ).
cnf(c_3046,plain,
least_upper_bound(identity,A) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_32,c_10456]) ).
cnf(c_3129,plain,
multiply(inverse(greatest_lower_bound(A,multiply(A,a))),A) != multiply(inverse(a),multiply(least_upper_bound(B,multiply(a,B)),inverse(B))),
inference(paramod,[status(thm)],[c_3046,c_1052]) ).
cnf(c_10457,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_165]) ).
cnf(c_10458,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_10457]) ).
cnf(c_10459,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_10458]) ).
cnf(c_10460,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_10459]) ).
cnf(c_10461,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_10460]) ).
cnf(c_10462,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(A,B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_165,c_10461]) ).
cnf(c_10463,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_10462]) ).
cnf(c_3223,plain,
greatest_lower_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),greatest_lower_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_10463]) ).
cnf(c_10464,plain,
multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,a)),multiply(a,inverse(least_upper_bound(identity,a))))),inverse(least_upper_bound(identity,a))) != multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))),
inference(paramod,[status(thm)],[c_330,c_3129]) ).
cnf(c_10465,plain,
multiply(inverse(multiply(greatest_lower_bound(identity,a),inverse(least_upper_bound(identity,a)))),inverse(least_upper_bound(identity,a))) != multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))),
inference(paramod,[status(thm)],[c_59,c_10464]) ).
cnf(c_10466,plain,
multiply(multiply(inverse(inverse(least_upper_bound(identity,a))),inverse(greatest_lower_bound(identity,a))),inverse(least_upper_bound(identity,a))) != multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))),
inference(paramod,[status(thm)],[c_24,c_10465]) ).
cnf(c_10467,plain,
multiply(multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),inverse(least_upper_bound(identity,a))) != multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))),
inference(paramod,[status(thm)],[c_23,c_10466]) ).
cnf(c_3945,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(greatest_lower_bound(identity,a)),inverse(least_upper_bound(identity,a)))) != multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))),
inference(paramod,[status(thm)],[c_3,c_10467]) ).
cnf(c_10468,plain,
multiply(multiply(inverse(A),least_upper_bound(A,multiply(A,a))),multiply(inverse(greatest_lower_bound(identity,a)),inverse(least_upper_bound(identity,a)))) != multiply(inverse(a),multiply(least_upper_bound(B,multiply(a,B)),inverse(B))),
inference(paramod,[status(thm)],[c_197,c_3945]) ).
cnf(c_10469,plain,
multiply(inverse(A),multiply(least_upper_bound(A,multiply(A,a)),multiply(inverse(greatest_lower_bound(identity,a)),inverse(least_upper_bound(identity,a))))) != multiply(inverse(a),multiply(least_upper_bound(B,multiply(a,B)),inverse(B))),
inference(paramod,[status(thm)],[c_3,c_10468]) ).
cnf(c_4868,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),multiply(inverse(greatest_lower_bound(identity,a)),inverse(least_upper_bound(identity,a))))),
inference(copy,[status(thm)],[c_10469]) ).
cnf(c_4969,plain,
inverse(least_upper_bound(A,B)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(A),B))),inverse(A)),
inference(paramod,[status(thm)],[c_68,c_195]) ).
cnf(c_5487,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_10470,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_5487,c_46]) ).
cnf(c_5621,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_10470]) ).
cnf(c_10471,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_5487,c_47]) ).
cnf(c_10472,plain,
identity = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_5621,c_10471]) ).
cnf(c_5624,plain,
multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)) = identity,
inference(copy,[status(thm)],[c_10472]) ).
cnf(c_5682,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_10473,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_5682,c_49]) ).
cnf(c_5758,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_10473]) ).
cnf(c_10474,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_5682,c_50]) ).
cnf(c_10475,plain,
identity = multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_5758,c_10474]) ).
cnf(c_5762,plain,
multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A)) = identity,
inference(copy,[status(thm)],[c_10475]) ).
cnf(c_10476,plain,
multiply(multiply(inverse(A),inverse(least_upper_bound(identity,A))),B) = multiply(inverse(least_upper_bound(identity,A)),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_281,c_3]) ).
cnf(c_10477,plain,
multiply(inverse(A),multiply(inverse(least_upper_bound(identity,A)),B)) = multiply(inverse(least_upper_bound(identity,A)),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_3,c_10476]) ).
cnf(c_5877,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(inverse(A),B)) = multiply(inverse(A),multiply(inverse(least_upper_bound(identity,A)),B)),
inference(copy,[status(thm)],[c_10477]) ).
cnf(c_10478,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_10479,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_10478]) ).
cnf(c_5922,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_10479]) ).
cnf(c_10480,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_1133]) ).
cnf(c_10481,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_10480]) ).
cnf(c_7829,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_10481]) ).
cnf(c_10482,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_245,c_1133]) ).
cnf(c_10483,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_10482]) ).
cnf(c_10484,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_10483]) ).
cnf(c_7838,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_10484]) ).
cnf(c_10485,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_1133]) ).
cnf(c_10486,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_7829,c_10485]) ).
cnf(c_10487,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_246,c_10486]) ).
cnf(c_10488,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_246,c_10487]) ).
cnf(c_10489,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_10488]) ).
cnf(c_10490,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_10489]) ).
cnf(c_10491,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_10490]) ).
cnf(c_10492,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_10491]) ).
cnf(c_10493,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_10492]) ).
cnf(c_10494,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_10493]) ).
cnf(c_10495,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_10494]) ).
cnf(c_7866,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_10495]) ).
cnf(c_10496,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_7866,c_7838]) ).
cnf(c_10497,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_10496]) ).
cnf(c_10498,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_2811,c_10497]) ).
cnf(c_10499,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_257,c_10498]) ).
cnf(c_10500,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_10499]) ).
cnf(c_10501,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_10500]) ).
cnf(c_10502,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_2811,c_10501]) ).
cnf(c_10503,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_257,c_10502]) ).
cnf(c_10504,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_10503]) ).
cnf(c_10505,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_10504]) ).
cnf(c_10506,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_10505]) ).
cnf(c_10507,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_10506]) ).
cnf(c_10508,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_10507]) ).
cnf(c_10509,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_10508]) ).
cnf(c_10510,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_10509]) ).
cnf(c_10511,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_10510]) ).
cnf(c_10512,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_10511]) ).
cnf(c_10513,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_10512]) ).
cnf(c_10514,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_10513]) ).
cnf(c_10515,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_10514]) ).
cnf(c_10516,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_10515]) ).
cnf(c_10517,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_10516]) ).
cnf(c_10518,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_10517]) ).
cnf(c_10519,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_10518]) ).
cnf(c_10520,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_10519]) ).
cnf(c_10521,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_10520]) ).
cnf(c_10522,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_10521]) ).
cnf(c_10523,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_10522]) ).
cnf(c_10524,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_10523]) ).
cnf(c_8011,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_10524]) ).
cnf(c_10525,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_8011,c_376]) ).
cnf(c_10526,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_1884,c_10525]) ).
cnf(c_10527,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_5922,c_10526]) ).
cnf(c_10528,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_5624,c_10527]) ).
cnf(c_10529,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_10528]) ).
cnf(c_8115,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_10529]) ).
cnf(c_10530,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_3223,c_80]) ).
cnf(c_10075,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_10530]) ).
cnf(c_10531,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_10075,c_8115]) ).
cnf(c_10532,plain,
identity = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_1885,c_10531]) ).
cnf(c_10122,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))) = identity,
inference(copy,[status(thm)],[c_10532]) ).
cnf(c_10123,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))) = identity,
inference(paramod,[status(thm)],[c_10122,c_360]) ).
cnf(c_10533,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,A)),multiply(inverse(A),least_upper_bound(A,identity)))) = multiply(inverse(least_upper_bound(identity,A)),identity),
inference(paramod,[status(thm)],[c_10123,c_49]) ).
cnf(c_10534,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(A,identity)))) = multiply(inverse(least_upper_bound(identity,A)),identity),
inference(paramod,[status(thm)],[c_5877,c_10533]) ).
cnf(c_10535,plain,
greatest_lower_bound(identity,multiply(inverse(A),identity)) = multiply(inverse(least_upper_bound(identity,A)),identity),
inference(paramod,[status(thm)],[c_5762,c_10534]) ).
cnf(c_10536,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(least_upper_bound(identity,A)),identity),
inference(paramod,[status(thm)],[c_89,c_10535]) ).
cnf(c_10537,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),identity),
inference(paramod,[status(thm)],[c_257,c_10536]) ).
cnf(c_10538,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = inverse(least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_89,c_10537]) ).
cnf(c_10134,plain,
inverse(least_upper_bound(identity,A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_10538]) ).
cnf(c_10539,plain,
inverse(least_upper_bound(A,B)) = multiply(multiply(inverse(multiply(inverse(A),B)),greatest_lower_bound(identity,multiply(inverse(A),B))),inverse(A)),
inference(paramod,[status(thm)],[c_10134,c_4969]) ).
cnf(c_10540,plain,
inverse(least_upper_bound(A,B)) = multiply(multiply(multiply(inverse(B),inverse(inverse(A))),greatest_lower_bound(identity,multiply(inverse(A),B))),inverse(A)),
inference(paramod,[status(thm)],[c_24,c_10539]) ).
cnf(c_10541,plain,
inverse(least_upper_bound(A,B)) = multiply(multiply(multiply(inverse(B),A),greatest_lower_bound(identity,multiply(inverse(A),B))),inverse(A)),
inference(paramod,[status(thm)],[c_23,c_10540]) ).
cnf(c_10542,plain,
inverse(least_upper_bound(A,B)) = multiply(multiply(inverse(B),multiply(A,greatest_lower_bound(identity,multiply(inverse(A),B)))),inverse(A)),
inference(paramod,[status(thm)],[c_3,c_10541]) ).
cnf(c_10543,plain,
inverse(least_upper_bound(A,B)) = multiply(inverse(B),multiply(multiply(A,greatest_lower_bound(identity,multiply(inverse(A),B))),inverse(A))),
inference(paramod,[status(thm)],[c_3,c_10542]) ).
cnf(c_10393,plain,
inverse(least_upper_bound(A,B)) = multiply(inverse(B),multiply(A,multiply(greatest_lower_bound(identity,multiply(inverse(A),B)),inverse(A)))),
inference(paramod,[status(thm)],[c_3,c_10543]) ).
cnf(c_10544,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(a),multiply(identity,multiply(greatest_lower_bound(identity,multiply(inverse(identity),a)),inverse(identity))))))),
inference(paramod,[status(thm)],[c_10393,c_4868]) ).
cnf(c_10545,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(a),multiply(identity,multiply(greatest_lower_bound(identity,multiply(identity,a)),inverse(identity))))))),
inference(paramod,[status(thm)],[c_22,c_10544]) ).
cnf(c_10546,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(a),multiply(identity,multiply(greatest_lower_bound(identity,a),inverse(identity))))))),
inference(paramod,[status(thm)],[c_1,c_10545]) ).
cnf(c_10547,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(a),multiply(identity,multiply(greatest_lower_bound(identity,a),identity)))))),
inference(paramod,[status(thm)],[c_22,c_10546]) ).
cnf(c_10548,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(a),multiply(identity,greatest_lower_bound(identity,a)))))),
inference(paramod,[status(thm)],[c_89,c_10547]) ).
cnf(c_10549,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(a),greatest_lower_bound(identity,a))))),
inference(paramod,[status(thm)],[c_1,c_10548]) ).
cnf(c_10550,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),multiply(inverse(a),multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,a))))),
inference(paramod,[status(thm)],[c_5922,c_10549]) ).
cnf(c_10551,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),multiply(inverse(a),identity))),
inference(paramod,[status(thm)],[c_2,c_10550]) ).
cnf(c_10552,plain,
multiply(inverse(a),multiply(least_upper_bound(A,multiply(a,A)),inverse(A))) != multiply(inverse(B),multiply(least_upper_bound(B,multiply(B,a)),inverse(a))),
inference(paramod,[status(thm)],[c_89,c_10551]) ).
cnf(c_10399,plain,
$false,
inference(copy,[status(thm)],[c_10552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP179-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/11.07 % Computer : n013.cluster.edu
% 0.17/11.07 % Model : x86_64 x86_64
% 0.17/11.07 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/11.07 % Memory : 8046.5625MB
% 0.17/11.07 % OS : Linux 6.8.0-71-generic
% 0.17/11.07 % CPULimit : 300
% 0.17/11.07 % WCLimit : 300
% 0.17/11.07 % DateTime : Fri Sep 25 14:34:04 UTC 2026
% 0.17/11.08 % CPUTime :
% 0.17/11.08 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/11.08 % Process 631821 was started by sandbox2 on n013,
% 0.17/11.08 % Fri Sep 25 14:34:04 2026
% 0.17/11.08 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/11.08
% 0.17/11.08 % From the command line: assign(max_seconds, 300).
% 106.66/25.61
% 106.66/25.61 % SZS status Unsatisfiable for theBenchmark
% 106.66/25.61
% 106.66/25.61 % Proof 1 at 5.20 (+ 1.20) seconds.
% 106.66/25.61 % Length of proof is 111.
% 106.66/25.61 % Level of proof is 13.
% 106.66/25.61 % Maximum clause weight is 92.000.
% 106.66/25.61 % Given clauses 360.
% 106.66/25.61
% 106.66/25.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------