%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP167-4 : 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 : n008.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 07:28:11 AM UTC 2026
% Result : Unsatisfiable 98.43s 12.89s
% Output : CNFRefutation 98.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 19
% Syntax : Number of formulae : 307 ( 307 unt; 0 def)
% Number of atoms : 307 ( 306 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 : 601 ( 31 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(p19_1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p19_1) ).
cnf(c_22,plain,
inverse(identity) = identity,
inference(clausify,[status(thm)],[p19_1]) ).
fof(p19_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',p19_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[p19_2]) ).
fof(p19_3,axiom,
! [VAR_0,VAR_1] : inverse(multiply(VAR_0,VAR_1)) = multiply(inverse(VAR_1),inverse(VAR_0)),
file('theBenchmark.p',p19_3) ).
cnf(c_24,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(clausify,[status(thm)],[p19_3]) ).
fof(prove_p19,axiom,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('theBenchmark.p',prove_p19) ).
cnf(c_25,plain,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(clausify,[status(thm)],[prove_p19]) ).
cnf(c_11690,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(a,identity)),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_11691,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)),
inference(paramod,[status(thm)],[c_4,c_11690]) ).
cnf(c_26,plain,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(copy,[status(thm)],[c_11691]) ).
cnf(c_11692,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_11693,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_11692]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_11693]) ).
cnf(c_11694,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_11694]) ).
cnf(c_11695,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_11695]) ).
cnf(c_11696,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_11696]) ).
cnf(c_11697,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_11697]) ).
cnf(c_11698,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_11698]) ).
cnf(c_38,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
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_11699,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_11699]) ).
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_11700,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_11700]) ).
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_11701,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_11701]) ).
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_11702,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_11702]) ).
cnf(c_66,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_11703,plain,
inverse(A) = multiply(inverse(A),inverse(identity)),
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_11704,plain,
inverse(A) = multiply(inverse(A),identity),
inference(paramod,[status(thm)],[c_22,c_11703]) ).
cnf(c_67,plain,
multiply(inverse(A),identity) = inverse(A),
inference(copy,[status(thm)],[c_11704]) ).
cnf(c_11705,plain,
multiply(identity,A) = multiply(B,multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_66,c_3]) ).
cnf(c_11706,plain,
A = multiply(B,multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_11705]) ).
cnf(c_68,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_11706]) ).
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_77,plain,
least_upper_bound(A,greatest_lower_bound(B,greatest_lower_bound(C,A))) = A,
inference(paramod,[status(thm)],[c_7,c_38]) ).
cnf(c_11707,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_11707]) ).
cnf(c_11708,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_11708]) ).
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_11709,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_11709]) ).
cnf(c_129,plain,
multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(B,multiply(A,B))) = B,
inference(paramod,[status(thm)],[c_52,c_27]) ).
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_11710,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_11710]) ).
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_11711,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_11712,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_11711]) ).
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_11712]) ).
cnf(c_194,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_11713,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_196,plain,
least_upper_bound(identity,A) = multiply(inverse(B),least_upper_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_11713]) ).
cnf(c_11714,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_11714]) ).
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_11715,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_11716,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_4,c_11715]) ).
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_11716]) ).
cnf(c_11717,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(identity,a),a)) != a,
inference(paramod,[status(thm)],[c_92,c_26]) ).
cnf(c_11718,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(a,least_upper_bound(identity,a))) != a,
inference(paramod,[status(thm)],[c_200,c_11717]) ).
cnf(c_243,plain,
multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)) != a,
inference(paramod,[status(thm)],[c_59,c_11718]) ).
cnf(c_11719,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_244,plain,
greatest_lower_bound(identity,A) = multiply(inverse(B),greatest_lower_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_11719]) ).
cnf(c_245,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_11720,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_251,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_11720]) ).
cnf(c_256,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_11721,plain,
inverse(multiply(A,least_upper_bound(identity,A))) = multiply(inverse(A),inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_200,c_24]) ).
cnf(c_280,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_11721]) ).
cnf(c_11722,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_11723,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_11722]) ).
cnf(c_282,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_11723]) ).
cnf(c_11724,plain,
inverse(multiply(A,greatest_lower_bound(identity,A))) = multiply(inverse(A),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_251,c_24]) ).
cnf(c_304,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_11724]) ).
cnf(c_11725,plain,
multiply(multiply(inverse(A),least_upper_bound(identity,A)),B) = multiply(least_upper_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_179,c_3]) ).
cnf(c_11726,plain,
multiply(inverse(A),multiply(least_upper_bound(identity,A),B)) = multiply(least_upper_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_3,c_11725]) ).
cnf(c_319,plain,
multiply(least_upper_bound(identity,A),multiply(inverse(A),B)) = multiply(inverse(A),multiply(least_upper_bound(identity,A),B)),
inference(copy,[status(thm)],[c_11726]) ).
cnf(c_320,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_11727,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_11728,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_11727]) ).
cnf(c_332,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_11728]) ).
cnf(c_333,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_11729,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_11730,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_11729]) ).
cnf(c_11731,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_11730]) ).
cnf(c_342,plain,
multiply(inverse(greatest_lower_bound(identity,A)),A) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_23,c_11731]) ).
cnf(c_347,plain,
multiply(least_upper_bound(A,identity),inverse(A)) = multiply(inverse(A),least_upper_bound(A,identity)),
inference(paramod,[status(thm)],[c_5,c_320]) ).
cnf(c_11732,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_320,c_59]) ).
cnf(c_11733,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_347,c_11732]) ).
cnf(c_11734,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_256,c_11733]) ).
cnf(c_359,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_11734]) ).
cnf(c_364,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_4,c_333]) ).
cnf(c_11735,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_333,c_52]) ).
cnf(c_11736,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_364,c_11735]) ).
cnf(c_11737,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_11736]) ).
cnf(c_11738,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_11737]) ).
cnf(c_375,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_282,c_11738]) ).
cnf(c_483,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_484,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_11739,plain,
multiply(A,B) = multiply(inverse(least_upper_bound(identity,C)),multiply(least_upper_bound(A,multiply(C,A)),B)),
inference(paramod,[status(thm)],[c_129,c_3]) ).
cnf(c_909,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(least_upper_bound(B,multiply(A,B)),C)) = multiply(B,C),
inference(copy,[status(thm)],[c_11739]) ).
cnf(c_980,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(A),least_upper_bound(A,multiply(A,a)))) != a,
inference(paramod,[status(thm)],[c_196,c_243]) ).
cnf(c_1036,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(least_upper_bound(A,B)),least_upper_bound(A,least_upper_bound(B,multiply(least_upper_bound(A,B),a))))) != a,
inference(paramod,[status(thm)],[c_9,c_980]) ).
cnf(c_11740,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,least_upper_bound(least_upper_bound(A,B),multiply(least_upper_bound(B,least_upper_bound(A,B)),a))))) != a,
inference(paramod,[status(thm)],[c_34,c_1036]) ).
cnf(c_11741,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,least_upper_bound(least_upper_bound(A,B),multiply(least_upper_bound(A,B),a))))) != a,
inference(paramod,[status(thm)],[c_34,c_11740]) ).
cnf(c_1055,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,multiply(least_upper_bound(A,B),least_upper_bound(identity,a))))) != a,
inference(paramod,[status(thm)],[c_90,c_11741]) ).
cnf(c_11742,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_1171,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_11742]) ).
cnf(c_11743,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(A),least_upper_bound(greatest_lower_bound(A,B),multiply(least_upper_bound(A,greatest_lower_bound(A,B)),least_upper_bound(identity,a))))) != a,
inference(paramod,[status(thm)],[c_12,c_1055]) ).
cnf(c_1653,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(A),least_upper_bound(greatest_lower_bound(A,B),multiply(A,least_upper_bound(identity,a))))) != a,
inference(paramod,[status(thm)],[c_12,c_11743]) ).
cnf(c_11744,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(identity,a),A),multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a))) != a,
inference(paramod,[status(thm)],[c_68,c_1653]) ).
cnf(c_1692,plain,
least_upper_bound(greatest_lower_bound(identity,greatest_lower_bound(a,A)),multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a))) != a,
inference(paramod,[status(thm)],[c_7,c_11744]) ).
cnf(c_1701,plain,
least_upper_bound(greatest_lower_bound(identity,greatest_lower_bound(A,a)),multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a))) != a,
inference(paramod,[status(thm)],[c_4,c_1692]) ).
cnf(c_1898,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a))) != a,
inference(paramod,[status(thm)],[c_29,c_1701]) ).
cnf(c_11745,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_1929,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_2,c_11745]) ).
cnf(c_1930,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_46,c_13]) ).
cnf(c_11746,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_11747,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_11746]) ).
cnf(c_2583,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_11747]) ).
cnf(c_11748,plain,
least_upper_bound(multiply(inverse(A),B),multiply(least_upper_bound(identity,A),multiply(inverse(A),B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_68,c_130]) ).
cnf(c_11749,plain,
least_upper_bound(multiply(inverse(A),B),multiply(inverse(A),multiply(least_upper_bound(identity,A),B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_319,c_11748]) ).
cnf(c_11750,plain,
multiply(inverse(A),least_upper_bound(B,multiply(inverse(inverse(A)),multiply(inverse(A),multiply(least_upper_bound(identity,A),B))))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_483,c_11749]) ).
cnf(c_11751,plain,
multiply(inverse(A),least_upper_bound(B,multiply(A,multiply(inverse(A),multiply(least_upper_bound(identity,A),B))))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_23,c_11750]) ).
cnf(c_11752,plain,
multiply(inverse(A),least_upper_bound(B,multiply(least_upper_bound(identity,A),B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_68,c_11751]) ).
cnf(c_11753,plain,
multiply(inverse(A),least_upper_bound(B,multiply(A,B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_130,c_11752]) ).
cnf(c_11754,plain,
multiply(inverse(A),least_upper_bound(B,multiply(A,B))) = least_upper_bound(B,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_5,c_11753]) ).
cnf(c_2845,plain,
least_upper_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_11754]) ).
cnf(c_11755,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_11756,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_11755]) ).
cnf(c_11757,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_11756]) ).
cnf(c_11758,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_11757]) ).
cnf(c_2860,plain,
least_upper_bound(identity,A) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_32,c_11758]) ).
cnf(c_2939,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(identity,a),multiply(least_upper_bound(B,multiply(a,B)),inverse(B)))) != a,
inference(paramod,[status(thm)],[c_2860,c_1898]) ).
cnf(c_11759,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_11760,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_332,c_11759]) ).
cnf(c_11761,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_484,c_11760]) ).
cnf(c_11762,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_11761]) ).
cnf(c_11763,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_11762]) ).
cnf(c_11764,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_11763]) ).
cnf(c_11765,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_11764]) ).
cnf(c_3006,plain,
greatest_lower_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),greatest_lower_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_11765]) ).
cnf(c_4707,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_194]) ).
cnf(c_5359,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_11766,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_5359,c_46]) ).
cnf(c_5429,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_11766]) ).
cnf(c_11767,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_5359,c_47]) ).
cnf(c_11768,plain,
identity = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_5429,c_11767]) ).
cnf(c_5431,plain,
multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)) = identity,
inference(copy,[status(thm)],[c_11768]) ).
cnf(c_5488,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_11769,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_5488,c_49]) ).
cnf(c_5624,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_11769]) ).
cnf(c_11770,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_5488,c_50]) ).
cnf(c_11771,plain,
identity = multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_5624,c_11770]) ).
cnf(c_5625,plain,
multiply(inverse(least_upper_bound(A,B)),least_upper_bound(B,A)) = identity,
inference(copy,[status(thm)],[c_11771]) ).
cnf(c_11772,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_280,c_3]) ).
cnf(c_11773,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_11772]) ).
cnf(c_5679,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_11773]) ).
cnf(c_11774,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_304,c_3]) ).
cnf(c_11775,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_11774]) ).
cnf(c_5838,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_11775]) ).
cnf(c_11776,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_1171]) ).
cnf(c_11777,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_483,c_11776]) ).
cnf(c_7484,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_11777]) ).
cnf(c_11778,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_244,c_1171]) ).
cnf(c_11779,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_483,c_11778]) ).
cnf(c_11780,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_11779]) ).
cnf(c_7493,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_11780]) ).
cnf(c_11781,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_1171]) ).
cnf(c_11782,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_7484,c_11781]) ).
cnf(c_11783,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_245,c_11782]) ).
cnf(c_11784,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_245,c_11783]) ).
cnf(c_11785,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_11784]) ).
cnf(c_11786,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_11785]) ).
cnf(c_11787,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_11786]) ).
cnf(c_11788,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_11787]) ).
cnf(c_11789,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_11788]) ).
cnf(c_11790,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_483,c_11789]) ).
cnf(c_11791,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_11790]) ).
cnf(c_7520,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_11791]) ).
cnf(c_11792,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_7520,c_7493]) ).
cnf(c_11793,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_11792]) ).
cnf(c_11794,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_2583,c_11793]) ).
cnf(c_11795,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_256,c_11794]) ).
cnf(c_11796,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_11795]) ).
cnf(c_11797,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_11796]) ).
cnf(c_11798,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_2583,c_11797]) ).
cnf(c_11799,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_256,c_11798]) ).
cnf(c_11800,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_11799]) ).
cnf(c_11801,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_11800]) ).
cnf(c_11802,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_11801]) ).
cnf(c_11803,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_11802]) ).
cnf(c_11804,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_11803]) ).
cnf(c_11805,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_11804]) ).
cnf(c_11806,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_11805]) ).
cnf(c_11807,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_342,c_11806]) ).
cnf(c_11808,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_11807]) ).
cnf(c_11809,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_11808]) ).
cnf(c_11810,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_11809]) ).
cnf(c_11811,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_11810]) ).
cnf(c_11812,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_11811]) ).
cnf(c_11813,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_11812]) ).
cnf(c_11814,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_483,c_11813]) ).
cnf(c_11815,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_11814]) ).
cnf(c_11816,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_11815]) ).
cnf(c_11817,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_11816]) ).
cnf(c_11818,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_11817]) ).
cnf(c_11819,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_11818]) ).
cnf(c_11820,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_11819]) ).
cnf(c_7698,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_11820]) ).
cnf(c_11821,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_7698,c_375]) ).
cnf(c_11822,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_1929,c_11821]) ).
cnf(c_11823,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_5838,c_11822]) ).
cnf(c_11824,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_5431,c_11823]) ).
cnf(c_11825,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_11824]) ).
cnf(c_7864,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_11825]) ).
cnf(c_11826,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(identity,a),multiply(least_upper_bound(multiply(inverse(a),B),B),inverse(multiply(inverse(a),B))))) != a,
inference(paramod,[status(thm)],[c_68,c_2939]) ).
cnf(c_11827,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(identity,a),multiply(least_upper_bound(B,multiply(inverse(a),B)),inverse(multiply(inverse(a),B))))) != a,
inference(paramod,[status(thm)],[c_5,c_11826]) ).
cnf(c_11828,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(B,multiply(a,B))),inverse(multiply(inverse(a),B))))) != a,
inference(paramod,[status(thm)],[c_2845,c_11827]) ).
cnf(c_11829,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(B,multiply(a,B))),multiply(inverse(B),inverse(inverse(a)))))) != a,
inference(paramod,[status(thm)],[c_24,c_11828]) ).
cnf(c_11830,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(B,multiply(a,B))),multiply(inverse(B),a)))) != a,
inference(paramod,[status(thm)],[c_23,c_11829]) ).
cnf(c_11831,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(identity,a),multiply(inverse(a),multiply(least_upper_bound(B,multiply(a,B)),multiply(inverse(B),a))))) != a,
inference(paramod,[status(thm)],[c_3,c_11830]) ).
cnf(c_8845,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(inverse(a),multiply(greatest_lower_bound(identity,a),multiply(least_upper_bound(B,multiply(a,B)),multiply(inverse(B),a))))) != a,
inference(paramod,[status(thm)],[c_332,c_11831]) ).
cnf(c_11832,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_3006,c_80]) ).
cnf(c_10267,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_11832]) ).
cnf(c_11833,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_10267,c_7864]) ).
cnf(c_11834,plain,
identity = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_1930,c_11833]) ).
cnf(c_10318,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))) = identity,
inference(copy,[status(thm)],[c_11834]) ).
cnf(c_10319,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(A,identity))) = identity,
inference(paramod,[status(thm)],[c_10318,c_359]) ).
cnf(c_11835,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_10319,c_49]) ).
cnf(c_11836,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_5679,c_11835]) ).
cnf(c_11837,plain,
greatest_lower_bound(identity,multiply(inverse(A),identity)) = multiply(inverse(least_upper_bound(identity,A)),identity),
inference(paramod,[status(thm)],[c_5625,c_11836]) ).
cnf(c_11838,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(least_upper_bound(identity,A)),identity),
inference(paramod,[status(thm)],[c_89,c_11837]) ).
cnf(c_11839,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),identity),
inference(paramod,[status(thm)],[c_256,c_11838]) ).
cnf(c_11840,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = inverse(least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_89,c_11839]) ).
cnf(c_10330,plain,
inverse(least_upper_bound(identity,A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_11840]) ).
cnf(c_11841,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_10330,c_4707]) ).
cnf(c_11842,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_11841]) ).
cnf(c_11843,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_11842]) ).
cnf(c_11844,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_11843]) ).
cnf(c_11845,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_11844]) ).
cnf(c_10704,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_11845]) ).
cnf(c_11846,plain,
multiply(multiply(inverse(A),multiply(identity,multiply(greatest_lower_bound(identity,multiply(inverse(identity),A)),inverse(identity)))),multiply(least_upper_bound(B,multiply(A,B)),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_10704,c_909]) ).
cnf(c_11847,plain,
multiply(multiply(inverse(A),multiply(identity,multiply(greatest_lower_bound(identity,multiply(identity,A)),inverse(identity)))),multiply(least_upper_bound(B,multiply(A,B)),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_22,c_11846]) ).
cnf(c_11848,plain,
multiply(multiply(inverse(A),multiply(identity,multiply(greatest_lower_bound(identity,A),inverse(identity)))),multiply(least_upper_bound(B,multiply(A,B)),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_1,c_11847]) ).
cnf(c_11849,plain,
multiply(multiply(inverse(A),multiply(identity,multiply(greatest_lower_bound(identity,A),identity))),multiply(least_upper_bound(B,multiply(A,B)),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_22,c_11848]) ).
cnf(c_11850,plain,
multiply(multiply(inverse(A),multiply(identity,greatest_lower_bound(identity,A))),multiply(least_upper_bound(B,multiply(A,B)),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_89,c_11849]) ).
cnf(c_11851,plain,
multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),multiply(least_upper_bound(B,multiply(A,B)),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_1,c_11850]) ).
cnf(c_10906,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(B,multiply(A,B)),C))) = multiply(B,C),
inference(paramod,[status(thm)],[c_3,c_11851]) ).
cnf(c_11852,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),multiply(B,multiply(inverse(B),a))) != a,
inference(paramod,[status(thm)],[c_10906,c_8845]) ).
cnf(c_11853,plain,
least_upper_bound(greatest_lower_bound(A,greatest_lower_bound(identity,a)),a) != a,
inference(paramod,[status(thm)],[c_68,c_11852]) ).
cnf(c_11854,plain,
least_upper_bound(a,greatest_lower_bound(A,greatest_lower_bound(identity,a))) != a,
inference(paramod,[status(thm)],[c_5,c_11853]) ).
cnf(c_11855,plain,
a != a,
inference(paramod,[status(thm)],[c_77,c_11854]) ).
cnf(c_11689,plain,
$false,
inference(copy,[status(thm)],[c_11855]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n008.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 25 14:33:54 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 1272027 was started by sandbox2 on n008,
% 0.12/0.37 % Fri Sep 25 14:33:54 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 98.43/12.89
% 98.43/12.89 % SZS status Unsatisfiable for theBenchmark
% 98.43/12.89
% 98.43/12.89 % Proof 1 at 3.65 (+ 0.79) seconds.
% 98.43/12.89 % Length of proof is 122.
% 98.43/12.89 % Level of proof is 15.
% 98.43/12.89 % Maximum clause weight is 92.000.
% 98.43/12.89 % Given clauses 359.
% 98.43/12.89
% 98.43/12.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------