%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP186-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 07:28:18 AM UTC 2026
% Result : Unsatisfiable 99.31s 13.55s
% Output : CNFRefutation 99.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 16
% Syntax : Number of formulae : 257 ( 257 unt; 0 def)
% Number of atoms : 257 ( 256 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 20 ( 20 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 427 ( 10 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(symmetry_of_glb,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,VAR_1) = greatest_lower_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_glb) ).
cnf(c_4,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_glb]) ).
fof(symmetry_of_lub,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,VAR_1) = least_upper_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_lub) ).
cnf(c_5,plain,
least_upper_bound(A,B) = least_upper_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_lub]) ).
fof(associativity_of_glb,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(greatest_lower_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_glb) ).
cnf(c_6,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_glb]) ).
cnf(c_7,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(associativity_of_lub,axiom,
! [VAR_0,VAR_1,VAR_2] : least_upper_bound(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(least_upper_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_lub) ).
cnf(c_8,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_lub]) ).
cnf(c_9,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(idempotence_of_lub,axiom,
! [VAR_0] : least_upper_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_lub) ).
cnf(c_10,plain,
least_upper_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_lub]) ).
fof(idempotence_of_gld,axiom,
! [VAR_0] : greatest_lower_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_gld) ).
cnf(c_11,plain,
greatest_lower_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_gld]) ).
fof(lub_absorbtion,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,greatest_lower_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',lub_absorbtion) ).
cnf(c_12,plain,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
inference(clausify,[status(thm)],[lub_absorbtion]) ).
fof(glb_absorbtion,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',glb_absorbtion) ).
cnf(c_13,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
inference(clausify,[status(thm)],[glb_absorbtion]) ).
fof(monotony_lub1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_lub1) ).
cnf(c_14,plain,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_lub1]) ).
cnf(c_15,plain,
least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_14]) ).
fof(monotony_glb1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_glb1) ).
cnf(c_16,plain,
multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_glb1]) ).
cnf(c_17,plain,
greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_16]) ).
fof(monotony_lub2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(least_upper_bound(VAR_0,VAR_1),VAR_2) = least_upper_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_lub2) ).
cnf(c_18,plain,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_lub2]) ).
cnf(c_19,plain,
least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B),
inference(copy,[status(thm)],[c_18]) ).
fof(monotony_glb2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(greatest_lower_bound(VAR_0,VAR_1),VAR_2) = greatest_lower_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_glb2) ).
cnf(c_20,plain,
multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_glb2]) ).
cnf(c_21,plain,
greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B),
inference(copy,[status(thm)],[c_20]) ).
fof(prove_p23,axiom,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
file('theBenchmark.p',prove_p23) ).
cnf(c_22,plain,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(clausify,[status(thm)],[prove_p23]) ).
cnf(c_23,plain,
least_upper_bound(identity,multiply(a,b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_5,c_22]) ).
cnf(c_11394,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_11395,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_11394]) ).
cnf(c_24,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_11395]) ).
cnf(c_11396,plain,
least_upper_bound(A,B) = least_upper_bound(A,least_upper_bound(A,B)),
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_29,plain,
least_upper_bound(A,least_upper_bound(A,B)) = least_upper_bound(A,B),
inference(copy,[status(thm)],[c_11396]) ).
cnf(c_11397,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_32,plain,
greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B),
inference(copy,[status(thm)],[c_11397]) ).
cnf(c_35,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
cnf(c_11398,plain,
least_upper_bound(A,B) = least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,C),B)),
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_37,plain,
least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,B),C)) = least_upper_bound(A,C),
inference(copy,[status(thm)],[c_11398]) ).
cnf(c_39,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_11399,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(A,C),B)),
inference(paramod,[status(thm)],[c_13,c_7]) ).
cnf(c_40,plain,
greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(A,B),C)) = greatest_lower_bound(A,C),
inference(copy,[status(thm)],[c_11399]) ).
cnf(c_43,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_46,plain,
greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_49,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_11400,plain,
least_upper_bound(multiply(A,B),identity) = multiply(least_upper_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_2,c_19]) ).
cnf(c_52,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_5,c_11400]) ).
cnf(c_56,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_11401,plain,
greatest_lower_bound(multiply(A,B),B) = multiply(greatest_lower_bound(A,identity),B),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_57,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(B,identity),A),
inference(paramod,[status(thm)],[c_4,c_11401]) ).
cnf(c_11402,plain,
greatest_lower_bound(multiply(A,B),identity) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_2,c_21]) ).
cnf(c_59,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_4,c_11402]) ).
cnf(c_70,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_24]) ).
cnf(c_71,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_24]) ).
cnf(c_80,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_24,c_24]) ).
cnf(c_81,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_80,c_70]) ).
cnf(c_82,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_81,c_2]) ).
cnf(c_83,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_81,c_15]) ).
cnf(c_85,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_81,c_17]) ).
cnf(c_11403,plain,
greatest_lower_bound(multiply(A,B),A) = multiply(A,greatest_lower_bound(B,identity)),
inference(paramod,[status(thm)],[c_81,c_17]) ).
cnf(c_86,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(B,identity)),
inference(paramod,[status(thm)],[c_4,c_11403]) ).
cnf(c_114,plain,
least_upper_bound(A,multiply(least_upper_bound(identity,B),A)) = least_upper_bound(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_49,c_29]) ).
cnf(c_145,plain,
greatest_lower_bound(A,multiply(greatest_lower_bound(identity,B),A)) = greatest_lower_bound(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_56,c_32]) ).
cnf(c_157,plain,
multiply(inverse(greatest_lower_bound(A,identity)),greatest_lower_bound(B,multiply(A,B))) = B,
inference(paramod,[status(thm)],[c_57,c_24]) ).
cnf(c_11404,plain,
least_upper_bound(inverse(A),identity) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_83]) ).
cnf(c_158,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_11404]) ).
cnf(c_175,plain,
least_upper_bound(inverse(A),B) = multiply(inverse(A),least_upper_bound(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_24,c_83]) ).
cnf(c_176,plain,
least_upper_bound(A,multiply(A,least_upper_bound(identity,B))) = least_upper_bound(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_83,c_29]) ).
cnf(c_11405,plain,
multiply(A,least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),A),
inference(paramod,[status(thm)],[c_83,c_49]) ).
cnf(c_178,plain,
multiply(least_upper_bound(identity,A),A) = multiply(A,least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_11405]) ).
cnf(c_11406,plain,
greatest_lower_bound(inverse(A),identity) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_85]) ).
cnf(c_206,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_4,c_11406]) ).
cnf(c_11407,plain,
multiply(inverse(A),greatest_lower_bound(A,multiply(A,B))) = greatest_lower_bound(identity,B),
inference(paramod,[status(thm)],[c_85,c_24]) ).
cnf(c_219,plain,
greatest_lower_bound(identity,A) = multiply(inverse(B),greatest_lower_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_11407]) ).
cnf(c_220,plain,
greatest_lower_bound(inverse(A),B) = multiply(inverse(A),greatest_lower_bound(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_24,c_85]) ).
cnf(c_11408,plain,
multiply(A,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),A),
inference(paramod,[status(thm)],[c_85,c_56]) ).
cnf(c_226,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_11408]) ).
cnf(c_11409,plain,
greatest_lower_bound(inverse(greatest_lower_bound(A,identity)),multiply(inverse(greatest_lower_bound(A,identity)),A)) = identity,
inference(paramod,[status(thm)],[c_86,c_2]) ).
cnf(c_234,plain,
multiply(inverse(greatest_lower_bound(A,identity)),greatest_lower_bound(identity,A)) = identity,
inference(paramod,[status(thm)],[c_85,c_11409]) ).
cnf(c_258,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(A,least_upper_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_178,c_24]) ).
cnf(c_11410,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(A,least_upper_bound(identity,A))) = multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_178,c_85]) ).
cnf(c_11411,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_56,c_11410]) ).
cnf(c_259,plain,
multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_11411]) ).
cnf(c_11412,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(A,least_upper_bound(identity,A))) = multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_178,c_86]) ).
cnf(c_11413,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_56,c_11412]) ).
cnf(c_260,plain,
multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_11413]) ).
cnf(c_11414,plain,
multiply(multiply(A,greatest_lower_bound(identity,A)),B) = multiply(greatest_lower_bound(identity,A),multiply(A,B)),
inference(paramod,[status(thm)],[c_226,c_3]) ).
cnf(c_11415,plain,
multiply(A,multiply(greatest_lower_bound(identity,A),B)) = multiply(greatest_lower_bound(identity,A),multiply(A,B)),
inference(paramod,[status(thm)],[c_3,c_11414]) ).
cnf(c_275,plain,
multiply(greatest_lower_bound(identity,A),multiply(A,B)) = multiply(A,multiply(greatest_lower_bound(identity,A),B)),
inference(copy,[status(thm)],[c_11415]) ).
cnf(c_11416,plain,
multiply(identity,A) = multiply(inverse(greatest_lower_bound(B,identity)),multiply(greatest_lower_bound(identity,B),A)),
inference(paramod,[status(thm)],[c_234,c_3]) ).
cnf(c_11417,plain,
A = multiply(inverse(greatest_lower_bound(B,identity)),multiply(greatest_lower_bound(identity,B),A)),
inference(paramod,[status(thm)],[c_1,c_11416]) ).
cnf(c_377,plain,
multiply(inverse(greatest_lower_bound(A,identity)),multiply(greatest_lower_bound(identity,A),B)) = B,
inference(copy,[status(thm)],[c_11417]) ).
cnf(c_455,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_80,c_2]) ).
cnf(c_460,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_80,c_24]) ).
cnf(c_11418,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_80,c_81]) ).
cnf(c_11419,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_81,c_11418]) ).
cnf(c_461,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_11419]) ).
cnf(c_11420,plain,
least_upper_bound(multiply(A,B),identity) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_455,c_15]) ).
cnf(c_463,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_5,c_11420]) ).
cnf(c_11421,plain,
greatest_lower_bound(multiply(A,B),identity) = multiply(A,greatest_lower_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_455,c_17]) ).
cnf(c_464,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_4,c_11421]) ).
cnf(c_465,plain,
least_upper_bound(identity,multiply(A,inverse(B))) = multiply(least_upper_bound(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_455,c_19]) ).
cnf(c_11422,plain,
least_upper_bound(inverse(A),identity) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_455,c_49]) ).
cnf(c_11423,plain,
least_upper_bound(identity,inverse(A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_5,c_11422]) ).
cnf(c_11424,plain,
multiply(inverse(A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_158,c_11423]) ).
cnf(c_469,plain,
multiply(least_upper_bound(identity,A),inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_11424]) ).
cnf(c_11425,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_455,c_56]) ).
cnf(c_11426,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_11425]) ).
cnf(c_11427,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_206,c_11426]) ).
cnf(c_472,plain,
multiply(greatest_lower_bound(identity,A),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_11427]) ).
cnf(c_11428,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_455,c_57]) ).
cnf(c_11429,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_11428]) ).
cnf(c_11430,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_206,c_11429]) ).
cnf(c_473,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_11430]) ).
cnf(c_11431,plain,
multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),B) = multiply(greatest_lower_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_472,c_3]) ).
cnf(c_11432,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_11431]) ).
cnf(c_503,plain,
multiply(greatest_lower_bound(identity,A),multiply(inverse(A),B)) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B)),
inference(copy,[status(thm)],[c_11432]) ).
cnf(c_516,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_4,c_473]) ).
cnf(c_11433,plain,
multiply(multiply(inverse(A),greatest_lower_bound(A,identity)),B) = multiply(greatest_lower_bound(A,identity),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_516,c_3]) ).
cnf(c_11434,plain,
multiply(inverse(A),multiply(greatest_lower_bound(A,identity),B)) = multiply(greatest_lower_bound(A,identity),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_3,c_11433]) ).
cnf(c_542,plain,
multiply(greatest_lower_bound(A,identity),multiply(inverse(A),B)) = multiply(inverse(A),multiply(greatest_lower_bound(A,identity),B)),
inference(copy,[status(thm)],[c_11434]) ).
cnf(c_555,plain,
least_upper_bound(multiply(A,B),C) = multiply(A,least_upper_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_460,c_15]) ).
cnf(c_556,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_460,c_17]) ).
cnf(c_693,plain,
multiply(least_upper_bound(a,inverse(b)),b) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_52,c_23]) ).
cnf(c_853,plain,
multiply(inverse(greatest_lower_bound(A,identity)),multiply(A,greatest_lower_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_85,c_157]) ).
cnf(c_11435,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(least_upper_bound(identity,A)),greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_469,c_219]) ).
cnf(c_11436,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_206,c_11435]) ).
cnf(c_11437,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),multiply(greatest_lower_bound(identity,inverse(A)),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_56,c_11436]) ).
cnf(c_11438,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_206,c_11437]) ).
cnf(c_11439,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(inverse(least_upper_bound(identity,A)),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_3,c_11438]) ).
cnf(c_950,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_11439]) ).
cnf(c_11440,plain,
multiply(inverse(A),least_upper_bound(identity,multiply(A,B))) = least_upper_bound(B,inverse(A)),
inference(paramod,[status(thm)],[c_463,c_24]) ).
cnf(c_998,plain,
least_upper_bound(A,inverse(B)) = multiply(inverse(B),least_upper_bound(identity,multiply(B,A))),
inference(copy,[status(thm)],[c_11440]) ).
cnf(c_11441,plain,
multiply(A,least_upper_bound(B,inverse(A))) = multiply(least_upper_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_463,c_52]) ).
cnf(c_1039,plain,
multiply(least_upper_bound(A,inverse(B)),B) = multiply(A,least_upper_bound(B,inverse(A))),
inference(copy,[status(thm)],[c_11441]) ).
cnf(c_11442,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(A,B),C),least_upper_bound(A,C)) = least_upper_bound(greatest_lower_bound(A,B),C),
inference(paramod,[status(thm)],[c_37,c_39]) ).
cnf(c_1141,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_11442]) ).
cnf(c_1824,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_43,c_13]) ).
cnf(c_1938,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_5,c_1824]) ).
cnf(c_11443,plain,
greatest_lower_bound(multiply(inverse(A),B),multiply(greatest_lower_bound(identity,A),multiply(inverse(A),B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_460,c_145]) ).
cnf(c_11444,plain,
greatest_lower_bound(multiply(inverse(A),B),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_503,c_11443]) ).
cnf(c_11445,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(inverse(inverse(A)),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B))))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_556,c_11444]) ).
cnf(c_11446,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(A,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B))))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_461,c_11445]) ).
cnf(c_11447,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(greatest_lower_bound(identity,A),B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_460,c_11446]) ).
cnf(c_11448,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(A,B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_145,c_11447]) ).
cnf(c_11449,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_11448]) ).
cnf(c_2334,plain,
greatest_lower_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),greatest_lower_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_11449]) ).
cnf(c_11450,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,inverse(A)))) = least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),greatest_lower_bound(A,identity))),
inference(paramod,[status(thm)],[c_516,c_176]) ).
cnf(c_11451,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(A,identity),multiply(inverse(A),least_upper_bound(identity,A)))) = least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),greatest_lower_bound(A,identity))),
inference(paramod,[status(thm)],[c_158,c_11450]) ).
cnf(c_11452,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),greatest_lower_bound(A,identity))),
inference(paramod,[status(thm)],[c_542,c_11451]) ).
cnf(c_11453,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_49,c_11452]) ).
cnf(c_11454,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = multiply(multiply(inverse(A),least_upper_bound(identity,A)),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_158,c_11453]) ).
cnf(c_11455,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = multiply(inverse(A),multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity))),
inference(paramod,[status(thm)],[c_3,c_11454]) ).
cnf(c_2532,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_260,c_11455]) ).
cnf(c_11456,plain,
least_upper_bound(identity,multiply(multiply(least_upper_bound(identity,A),B),inverse(B))) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_114,c_465]) ).
cnf(c_11457,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_11456]) ).
cnf(c_11458,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,A),identity)) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_455,c_11457]) ).
cnf(c_11459,plain,
least_upper_bound(identity,least_upper_bound(identity,A)) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_81,c_11458]) ).
cnf(c_3045,plain,
least_upper_bound(identity,A) = multiply(least_upper_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_29,c_11459]) ).
cnf(c_11460,plain,
least_upper_bound(identity,least_upper_bound(identity,A)) = multiply(least_upper_bound(greatest_lower_bound(identity,A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_259,c_3045]) ).
cnf(c_11461,plain,
least_upper_bound(identity,A) = multiply(least_upper_bound(greatest_lower_bound(identity,A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_29,c_11460]) ).
cnf(c_11462,plain,
least_upper_bound(identity,A) = multiply(multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,least_upper_bound(identity,A))),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_83,c_11461]) ).
cnf(c_11463,plain,
least_upper_bound(identity,A) = multiply(multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_29,c_11462]) ).
cnf(c_11464,plain,
least_upper_bound(identity,A) = multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(identity,A),inverse(greatest_lower_bound(identity,A)))),
inference(paramod,[status(thm)],[c_3,c_11463]) ).
cnf(c_3239,plain,
multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(identity,A),inverse(greatest_lower_bound(identity,A)))) = least_upper_bound(identity,A),
inference(copy,[status(thm)],[c_11464]) ).
cnf(c_11465,plain,
multiply(multiply(inverse(b),least_upper_bound(identity,multiply(b,a))),b) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_998,c_693]) ).
cnf(c_3770,plain,
multiply(inverse(b),multiply(least_upper_bound(identity,multiply(b,a)),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_3,c_11465]) ).
cnf(c_11466,plain,
multiply(A,multiply(least_upper_bound(inverse(A),inverse(B)),B)) = least_upper_bound(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_1039,c_460]) ).
cnf(c_11467,plain,
multiply(A,multiply(multiply(inverse(A),least_upper_bound(identity,multiply(A,inverse(B)))),B)) = least_upper_bound(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_175,c_11466]) ).
cnf(c_11468,plain,
multiply(A,multiply(inverse(A),multiply(least_upper_bound(identity,multiply(A,inverse(B))),B))) = least_upper_bound(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_3,c_11467]) ).
cnf(c_11469,plain,
multiply(least_upper_bound(identity,multiply(A,inverse(B))),B) = least_upper_bound(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_460,c_11468]) ).
cnf(c_11470,plain,
multiply(least_upper_bound(identity,multiply(A,inverse(B))),B) = least_upper_bound(B,A),
inference(paramod,[status(thm)],[c_461,c_11469]) ).
cnf(c_3839,plain,
least_upper_bound(A,B) = multiply(least_upper_bound(identity,multiply(B,inverse(A))),A),
inference(copy,[status(thm)],[c_11470]) ).
cnf(c_11471,plain,
multiply(A,B) = multiply(inverse(least_upper_bound(identity,A)),multiply(multiply(A,least_upper_bound(identity,A)),B)),
inference(paramod,[status(thm)],[c_258,c_3]) ).
cnf(c_11472,plain,
multiply(A,B) = multiply(inverse(least_upper_bound(identity,A)),multiply(A,multiply(least_upper_bound(identity,A),B))),
inference(paramod,[status(thm)],[c_3,c_11471]) ).
cnf(c_4121,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(A,multiply(least_upper_bound(identity,A),B))) = multiply(A,B),
inference(copy,[status(thm)],[c_11472]) ).
cnf(c_11473,plain,
multiply(inverse(greatest_lower_bound(inverse(A),identity)),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_59,c_377]) ).
cnf(c_11474,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(A))),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_4,c_11473]) ).
cnf(c_11475,plain,
multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_206,c_11474]) ).
cnf(c_4239,plain,
multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),greatest_lower_bound(identity,A)) = A,
inference(paramod,[status(thm)],[c_1,c_11475]) ).
cnf(c_11476,plain,
least_upper_bound(inverse(inverse(greatest_lower_bound(A,identity))),multiply(A,greatest_lower_bound(identity,A))) = multiply(inverse(inverse(greatest_lower_bound(A,identity))),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_853,c_175]) ).
cnf(c_11477,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(A,greatest_lower_bound(identity,A))) = multiply(inverse(inverse(greatest_lower_bound(A,identity))),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_461,c_11476]) ).
cnf(c_4372,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(A,greatest_lower_bound(identity,A))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_461,c_11477]) ).
cnf(c_11478,plain,
greatest_lower_bound(multiply(A,least_upper_bound(identity,B)),least_upper_bound(greatest_lower_bound(A,C),multiply(A,B))) = least_upper_bound(greatest_lower_bound(A,C),multiply(A,B)),
inference(paramod,[status(thm)],[c_83,c_1141]) ).
cnf(c_6567,plain,
multiply(A,greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),least_upper_bound(greatest_lower_bound(A,C),multiply(A,B))))) = least_upper_bound(greatest_lower_bound(A,C),multiply(A,B)),
inference(paramod,[status(thm)],[c_556,c_11478]) ).
cnf(c_11479,plain,
greatest_lower_bound(least_upper_bound(identity,A),least_upper_bound(multiply(greatest_lower_bound(B,inverse(C)),C),A)) = least_upper_bound(greatest_lower_bound(identity,multiply(B,C)),A),
inference(paramod,[status(thm)],[c_59,c_1141]) ).
cnf(c_11480,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(greatest_lower_bound(B,inverse(C)),least_upper_bound(C,multiply(inverse(greatest_lower_bound(B,inverse(C))),A)))) = least_upper_bound(greatest_lower_bound(identity,multiply(B,C)),A),
inference(paramod,[status(thm)],[c_555,c_11479]) ).
cnf(c_6586,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_11480]) ).
cnf(c_11481,plain,
greatest_lower_bound(least_upper_bound(identity,A),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(B),C)),A)) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_46,c_1141]) ).
cnf(c_11482,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_6586,c_11481]) ).
cnf(c_11483,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C)))),least_upper_bound(C,multiply(inverse(greatest_lower_bound(inverse(B),inverse(C))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_220,c_11482]) ).
cnf(c_11484,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C)))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_220,c_11483]) ).
cnf(c_11485,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A)))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_3,c_11484]) ).
cnf(c_11486,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_32,c_11485]) ).
cnf(c_11487,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A))))) = multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,C),multiply(inverse(inverse(B)),A))),
inference(paramod,[status(thm)],[c_555,c_11486]) ).
cnf(c_11488,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A))))) = multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,C),multiply(B,A))),
inference(paramod,[status(thm)],[c_461,c_11487]) ).
cnf(c_6622,plain,
multiply(inverse(A),least_upper_bound(greatest_lower_bound(A,B),multiply(A,C))) = greatest_lower_bound(least_upper_bound(identity,C),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(B))),least_upper_bound(B,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(B))))),C))))),
inference(copy,[status(thm)],[c_11488]) ).
cnf(c_11489,plain,
multiply(A,greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(C))))),B))))))) = least_upper_bound(greatest_lower_bound(A,C),multiply(A,B)),
inference(paramod,[status(thm)],[c_6622,c_6567]) ).
cnf(c_11490,plain,
multiply(A,greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(C))),least_upper_bound(C,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(C))))),B)))))) = least_upper_bound(greatest_lower_bound(A,C),multiply(A,B)),
inference(paramod,[status(thm)],[c_32,c_11489]) ).
cnf(c_6757,plain,
least_upper_bound(greatest_lower_bound(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(least_upper_bound(identity,C),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(B))),least_upper_bound(B,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(B))))),C)))))),
inference(copy,[status(thm)],[c_11490]) ).
cnf(c_11491,plain,
multiply(A,greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,A)),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(identity))),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(identity))))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_6757,c_4372]) ).
cnf(c_11492,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(identity))),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(identity))))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_12,c_11491]) ).
cnf(c_11493,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,identity)),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(identity))))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_82,c_11492]) ).
cnf(c_11494,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(identity))))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_11493]) ).
cnf(c_11495,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,identity)))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_82,c_11494]) ).
cnf(c_11496,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),greatest_lower_bound(identity,A))))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_11495]) ).
cnf(c_6799,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_4239,c_11496]) ).
cnf(c_11497,plain,
greatest_lower_bound(A,multiply(inverse(B),greatest_lower_bound(least_upper_bound(A,C),multiply(B,least_upper_bound(A,C))))) = greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(A,C))),
inference(paramod,[status(thm)],[c_2334,c_40]) ).
cnf(c_8303,plain,
greatest_lower_bound(A,multiply(inverse(B),multiply(greatest_lower_bound(identity,B),least_upper_bound(A,C)))) = greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(A,C))),
inference(paramod,[status(thm)],[c_56,c_11497]) ).
cnf(c_11498,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(identity,A)))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_8303,c_6799]) ).
cnf(c_11499,plain,
multiply(A,identity) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_1938,c_11498]) ).
cnf(c_11500,plain,
A = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_11499]) ).
cnf(c_8370,plain,
multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)) = A,
inference(copy,[status(thm)],[c_11500]) ).
cnf(c_11501,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(A),A)) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_8370,c_2532]) ).
cnf(c_11502,plain,
least_upper_bound(greatest_lower_bound(A,identity),identity) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_2,c_11501]) ).
cnf(c_11503,plain,
least_upper_bound(identity,greatest_lower_bound(A,identity)) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_5,c_11502]) ).
cnf(c_11504,plain,
identity = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_35,c_11503]) ).
cnf(c_8373,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))) = identity,
inference(copy,[status(thm)],[c_11504]) ).
cnf(c_11505,plain,
multiply(inverse(least_upper_bound(identity,A)),identity) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_8373,c_950]) ).
cnf(c_8375,plain,
inverse(least_upper_bound(identity,A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_11505]) ).
cnf(c_11506,plain,
multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),multiply(A,multiply(least_upper_bound(identity,A),B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_8375,c_4121]) ).
cnf(c_11507,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),multiply(A,multiply(least_upper_bound(identity,A),B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_3,c_11506]) ).
cnf(c_11508,plain,
multiply(inverse(A),multiply(A,multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(identity,A),B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_275,c_11507]) ).
cnf(c_8660,plain,
multiply(greatest_lower_bound(identity,A),multiply(least_upper_bound(identity,A),B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_24,c_11508]) ).
cnf(c_11509,plain,
multiply(A,inverse(greatest_lower_bound(identity,A))) = least_upper_bound(identity,A),
inference(paramod,[status(thm)],[c_8660,c_3239]) ).
cnf(c_8924,plain,
least_upper_bound(identity,A) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(copy,[status(thm)],[c_11509]) ).
cnf(c_11510,plain,
least_upper_bound(A,B) = multiply(multiply(multiply(B,inverse(A)),inverse(greatest_lower_bound(identity,multiply(B,inverse(A))))),A),
inference(paramod,[status(thm)],[c_8924,c_3839]) ).
cnf(c_11511,plain,
least_upper_bound(A,B) = multiply(multiply(B,multiply(inverse(A),inverse(greatest_lower_bound(identity,multiply(B,inverse(A)))))),A),
inference(paramod,[status(thm)],[c_3,c_11510]) ).
cnf(c_11512,plain,
least_upper_bound(A,B) = multiply(B,multiply(multiply(inverse(A),inverse(greatest_lower_bound(identity,multiply(B,inverse(A))))),A)),
inference(paramod,[status(thm)],[c_3,c_11511]) ).
cnf(c_10411,plain,
least_upper_bound(A,B) = multiply(B,multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(A)))),A))),
inference(paramod,[status(thm)],[c_3,c_11512]) ).
cnf(c_11513,plain,
multiply(inverse(b),multiply(multiply(multiply(b,a),multiply(inverse(identity),multiply(inverse(greatest_lower_bound(identity,multiply(multiply(b,a),inverse(identity)))),identity))),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_10411,c_3770]) ).
cnf(c_11514,plain,
multiply(inverse(b),multiply(multiply(multiply(b,a),multiply(identity,multiply(inverse(greatest_lower_bound(identity,multiply(multiply(b,a),inverse(identity)))),identity))),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_82,c_11513]) ).
cnf(c_11515,plain,
multiply(inverse(b),multiply(multiply(multiply(b,a),multiply(identity,multiply(inverse(greatest_lower_bound(identity,multiply(multiply(b,a),identity))),identity))),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_82,c_11514]) ).
cnf(c_11516,plain,
multiply(inverse(b),multiply(multiply(multiply(b,a),multiply(identity,multiply(inverse(greatest_lower_bound(identity,multiply(b,a))),identity))),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_81,c_11515]) ).
cnf(c_11517,plain,
multiply(inverse(b),multiply(multiply(multiply(b,a),multiply(identity,inverse(greatest_lower_bound(identity,multiply(b,a))))),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_81,c_11516]) ).
cnf(c_11518,plain,
multiply(inverse(b),multiply(multiply(multiply(b,a),inverse(greatest_lower_bound(identity,multiply(b,a)))),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_1,c_11517]) ).
cnf(c_11519,plain,
multiply(inverse(b),multiply(multiply(b,multiply(a,inverse(greatest_lower_bound(identity,multiply(b,a))))),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_3,c_11518]) ).
cnf(c_11520,plain,
multiply(inverse(b),multiply(b,multiply(multiply(a,inverse(greatest_lower_bound(identity,multiply(b,a)))),b))) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_3,c_11519]) ).
cnf(c_11521,plain,
multiply(inverse(b),multiply(b,multiply(a,multiply(inverse(greatest_lower_bound(identity,multiply(b,a))),b)))) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_3,c_11520]) ).
cnf(c_11522,plain,
multiply(a,multiply(inverse(greatest_lower_bound(identity,multiply(b,a))),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_24,c_11521]) ).
cnf(c_10423,plain,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != multiply(a,multiply(inverse(greatest_lower_bound(identity,multiply(b,a))),b)),
inference(copy,[status(thm)],[c_11522]) ).
cnf(c_11523,plain,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != multiply(a,multiply(inverse(multiply(b,greatest_lower_bound(a,inverse(b)))),b)),
inference(paramod,[status(thm)],[c_464,c_10423]) ).
cnf(c_11235,plain,
multiply(a,multiply(inverse(multiply(b,greatest_lower_bound(a,inverse(b)))),b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(copy,[status(thm)],[c_11523]) ).
cnf(c_11524,plain,
multiply(inverse(multiply(A,B)),multiply(A,identity)) = inverse(B),
inference(paramod,[status(thm)],[c_455,c_71]) ).
cnf(c_11376,plain,
multiply(inverse(multiply(A,B)),A) = inverse(B),
inference(paramod,[status(thm)],[c_81,c_11524]) ).
cnf(c_11525,plain,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(paramod,[status(thm)],[c_11376,c_11235]) ).
cnf(c_11393,plain,
$false,
inference(copy,[status(thm)],[c_11525]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP186-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:36:07 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.35 % Process 3395982 was started by sandbox on n004,
% 0.12/0.35 % Fri Sep 25 14:36:07 2026
% 0.12/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 99.31/13.55
% 99.31/13.55 % SZS status Unsatisfiable for theBenchmark
% 99.31/13.55
% 99.31/13.55 % Proof 1 at 4.35 (+ 0.77) seconds.
% 99.31/13.55 % Length of proof is 109.
% 99.31/13.55 % Level of proof is 18.
% 99.31/13.55 % Maximum clause weight is 100.000.
% 99.31/13.55 % Given clauses 345.
% 99.31/13.55
% 99.31/13.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------