%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP183-1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:16 AM UTC 2026
% Result : Unsatisfiable 76.96s 11.23s
% Output : CNFRefutation 76.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 16
% Syntax : Number of formulae : 224 ( 224 unt; 0 def)
% Number of atoms : 224 ( 223 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 38 ( 38 ~; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 366 ( 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_p20,axiom,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity,
file('theBenchmark.p',prove_p20) ).
cnf(c_22,plain,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity,
inference(clausify,[status(thm)],[prove_p20]) ).
cnf(c_8028,plain,
greatest_lower_bound(least_upper_bound(identity,a),inverse(greatest_lower_bound(a,identity))) != identity,
inference(paramod,[status(thm)],[c_5,c_22]) ).
cnf(c_8029,plain,
greatest_lower_bound(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_4,c_8028]) ).
cnf(c_23,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != identity,
inference(paramod,[status(thm)],[c_4,c_8029]) ).
cnf(c_8030,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_8031,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_8030]) ).
cnf(c_24,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_8031]) ).
cnf(c_8032,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_8032]) ).
cnf(c_8033,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_8033]) ).
cnf(c_35,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
cnf(c_8034,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_8034]) ).
cnf(c_39,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_8035,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_8035]) ).
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_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_8036,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_8036]) ).
cnf(c_8037,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_8037]) ).
cnf(c_70,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,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_8038,plain,
least_upper_bound(multiply(A,B),A) = multiply(A,least_upper_bound(B,identity)),
inference(paramod,[status(thm)],[c_81,c_15]) ).
cnf(c_84,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(B,identity)),
inference(paramod,[status(thm)],[c_5,c_8038]) ).
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_8039,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_8039]) ).
cnf(c_143,plain,
multiply(inverse(greatest_lower_bound(identity,A)),greatest_lower_bound(B,multiply(A,B))) = B,
inference(paramod,[status(thm)],[c_56,c_24]) ).
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_8040,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_8040]) ).
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_8041,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_8041]) ).
cnf(c_8042,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_8042]) ).
cnf(c_8043,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_8043]) ).
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_234,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)))) != identity,
inference(paramod,[status(thm)],[c_220,c_23]) ).
cnf(c_8044,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_235,plain,
multiply(inverse(greatest_lower_bound(A,identity)),greatest_lower_bound(identity,A)) = identity,
inference(paramod,[status(thm)],[c_85,c_8044]) ).
cnf(c_8045,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_8046,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_8045]) ).
cnf(c_262,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_8046]) ).
cnf(c_8047,plain,
multiply(identity,A) = multiply(inverse(greatest_lower_bound(B,identity)),multiply(greatest_lower_bound(identity,B),A)),
inference(paramod,[status(thm)],[c_235,c_3]) ).
cnf(c_8048,plain,
A = multiply(inverse(greatest_lower_bound(B,identity)),multiply(greatest_lower_bound(identity,B),A)),
inference(paramod,[status(thm)],[c_1,c_8047]) ).
cnf(c_379,plain,
multiply(inverse(greatest_lower_bound(A,identity)),multiply(greatest_lower_bound(identity,A),B)) = B,
inference(copy,[status(thm)],[c_8048]) ).
cnf(c_457,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_80,c_2]) ).
cnf(c_462,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_80,c_24]) ).
cnf(c_8049,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_80,c_81]) ).
cnf(c_8050,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_81,c_8049]) ).
cnf(c_463,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_8050]) ).
cnf(c_8051,plain,
least_upper_bound(multiply(A,B),identity) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_457,c_15]) ).
cnf(c_465,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_5,c_8051]) ).
cnf(c_8052,plain,
greatest_lower_bound(multiply(A,B),identity) = multiply(A,greatest_lower_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_457,c_17]) ).
cnf(c_466,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_4,c_8052]) ).
cnf(c_469,plain,
greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_457,c_21]) ).
cnf(c_8053,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_457,c_56]) ).
cnf(c_8054,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_8053]) ).
cnf(c_8055,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_206,c_8054]) ).
cnf(c_474,plain,
multiply(greatest_lower_bound(identity,A),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_8055]) ).
cnf(c_8056,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_457,c_57]) ).
cnf(c_8057,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_8056]) ).
cnf(c_8058,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_206,c_8057]) ).
cnf(c_475,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_8058]) ).
cnf(c_8059,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_474,c_3]) ).
cnf(c_8060,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_8059]) ).
cnf(c_505,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_8060]) ).
cnf(c_518,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_4,c_475]) ).
cnf(c_8061,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_518,c_3]) ).
cnf(c_8062,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_8061]) ).
cnf(c_544,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_8062]) ).
cnf(c_557,plain,
least_upper_bound(multiply(A,B),C) = multiply(A,least_upper_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_462,c_15]) ).
cnf(c_558,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_462,c_17]) ).
cnf(c_8063,plain,
multiply(A,B) = multiply(inverse(greatest_lower_bound(identity,C)),multiply(greatest_lower_bound(A,multiply(C,A)),B)),
inference(paramod,[status(thm)],[c_143,c_3]) ).
cnf(c_831,plain,
multiply(inverse(greatest_lower_bound(identity,A)),multiply(greatest_lower_bound(B,multiply(A,B)),C)) = multiply(B,C),
inference(copy,[status(thm)],[c_8063]) ).
cnf(c_857,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_8064,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(multiply(inverse(A),greatest_lower_bound(A,multiply(A,a))),least_upper_bound(identity,a)))) != identity,
inference(paramod,[status(thm)],[c_219,c_234]) ).
cnf(c_946,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(A,multiply(A,a)),least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_3,c_8064]) ).
cnf(c_8065,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_1156,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_8065]) ).
cnf(c_1850,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_43,c_13]) ).
cnf(c_1962,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_5,c_1850]) ).
cnf(c_8066,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_462,c_145]) ).
cnf(c_8067,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_505,c_8066]) ).
cnf(c_8068,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_558,c_8067]) ).
cnf(c_8069,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_463,c_8068]) ).
cnf(c_8070,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_462,c_8069]) ).
cnf(c_8071,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_8070]) ).
cnf(c_8072,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_8071]) ).
cnf(c_2358,plain,
greatest_lower_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),greatest_lower_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_8072]) ).
cnf(c_8073,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_518,c_176]) ).
cnf(c_8074,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_8073]) ).
cnf(c_8075,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_544,c_8074]) ).
cnf(c_8076,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_8075]) ).
cnf(c_8077,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_8076]) ).
cnf(c_8078,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_8077]) ).
cnf(c_2582,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_262,c_8078]) ).
cnf(c_8079,plain,
greatest_lower_bound(identity,multiply(multiply(greatest_lower_bound(identity,A),B),inverse(B))) = multiply(greatest_lower_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_145,c_469]) ).
cnf(c_8080,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,A),multiply(B,inverse(B)))) = multiply(greatest_lower_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_3,c_8079]) ).
cnf(c_8081,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,A),identity)) = multiply(greatest_lower_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_457,c_8080]) ).
cnf(c_8082,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_81,c_8081]) ).
cnf(c_3670,plain,
greatest_lower_bound(identity,A) = multiply(greatest_lower_bound(B,multiply(A,B)),inverse(B)),
inference(paramod,[status(thm)],[c_32,c_8082]) ).
cnf(c_8083,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(inverse(identity),multiply(multiply(greatest_lower_bound(A,multiply(multiply(identity,a),A)),inverse(A)),least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_3670,c_946]) ).
cnf(c_8084,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(identity,multiply(multiply(greatest_lower_bound(A,multiply(multiply(identity,a),A)),inverse(A)),least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_82,c_8083]) ).
cnf(c_8085,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(identity,multiply(multiply(greatest_lower_bound(A,multiply(a,A)),inverse(A)),least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_1,c_8084]) ).
cnf(c_8086,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(identity,multiply(greatest_lower_bound(A,multiply(a,A)),multiply(inverse(A),least_upper_bound(identity,a)))))) != identity,
inference(paramod,[status(thm)],[c_3,c_8085]) ).
cnf(c_3743,plain,
multiply(inverse(greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(greatest_lower_bound(A,multiply(a,A)),multiply(inverse(A),least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_1,c_8086]) ).
cnf(c_8087,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(A,multiply(a,A)),greatest_lower_bound(multiply(inverse(A),least_upper_bound(identity,a)),inverse(greatest_lower_bound(A,multiply(a,A)))))) != identity,
inference(paramod,[status(thm)],[c_466,c_3743]) ).
cnf(c_8088,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(A,multiply(a,A)),multiply(inverse(A),greatest_lower_bound(least_upper_bound(identity,a),multiply(inverse(inverse(A)),inverse(greatest_lower_bound(A,multiply(a,A)))))))) != identity,
inference(paramod,[status(thm)],[c_558,c_8087]) ).
cnf(c_8089,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(greatest_lower_bound(A,multiply(a,A)),multiply(inverse(A),greatest_lower_bound(least_upper_bound(identity,a),multiply(A,inverse(greatest_lower_bound(A,multiply(a,A)))))))) != identity,
inference(paramod,[status(thm)],[c_463,c_8088]) ).
cnf(c_8090,plain,
multiply(A,multiply(inverse(A),greatest_lower_bound(least_upper_bound(identity,a),multiply(A,inverse(greatest_lower_bound(A,multiply(a,A))))))) != identity,
inference(paramod,[status(thm)],[c_831,c_8089]) ).
cnf(c_4037,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(A,inverse(greatest_lower_bound(A,multiply(a,A))))) != identity,
inference(paramod,[status(thm)],[c_462,c_8090]) ).
cnf(c_8091,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(A,identity),inverse(greatest_lower_bound(least_upper_bound(A,identity),least_upper_bound(a,multiply(a,A)))))) != identity,
inference(paramod,[status(thm)],[c_84,c_4037]) ).
cnf(c_4048,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(A,identity),inverse(greatest_lower_bound(least_upper_bound(A,identity),multiply(a,least_upper_bound(identity,A)))))) != identity,
inference(paramod,[status(thm)],[c_83,c_8091]) ).
cnf(c_8092,plain,
multiply(inverse(greatest_lower_bound(inverse(A),identity)),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_59,c_379]) ).
cnf(c_8093,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(A))),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_4,c_8092]) ).
cnf(c_8094,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_8093]) ).
cnf(c_4511,plain,
multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),greatest_lower_bound(identity,A)) = A,
inference(paramod,[status(thm)],[c_1,c_8094]) ).
cnf(c_8095,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_857,c_175]) ).
cnf(c_8096,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_463,c_8095]) ).
cnf(c_4638,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_463,c_8096]) ).
cnf(c_8097,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(inverse(a),identity),inverse(greatest_lower_bound(least_upper_bound(inverse(a),identity),least_upper_bound(identity,multiply(a,identity)))))) != identity,
inference(paramod,[status(thm)],[c_465,c_4048]) ).
cnf(c_8098,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(least_upper_bound(inverse(a),identity),least_upper_bound(identity,multiply(a,identity)))))) != identity,
inference(paramod,[status(thm)],[c_5,c_8097]) ).
cnf(c_8099,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(identity,a)),inverse(greatest_lower_bound(least_upper_bound(inverse(a),identity),least_upper_bound(identity,multiply(a,identity)))))) != identity,
inference(paramod,[status(thm)],[c_158,c_8098]) ).
cnf(c_8100,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(identity,a)),inverse(greatest_lower_bound(least_upper_bound(identity,inverse(a)),least_upper_bound(identity,multiply(a,identity)))))) != identity,
inference(paramod,[status(thm)],[c_5,c_8099]) ).
cnf(c_8101,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(identity,a)),inverse(greatest_lower_bound(multiply(inverse(a),least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,identity)))))) != identity,
inference(paramod,[status(thm)],[c_158,c_8100]) ).
cnf(c_8102,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(identity,a)),inverse(greatest_lower_bound(multiply(inverse(a),least_upper_bound(identity,a)),least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_81,c_8101]) ).
cnf(c_8103,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(identity,a)),inverse(greatest_lower_bound(least_upper_bound(identity,a),multiply(inverse(a),least_upper_bound(identity,a)))))) != identity,
inference(paramod,[status(thm)],[c_4,c_8102]) ).
cnf(c_8104,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(identity,a)),inverse(multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_56,c_8103]) ).
cnf(c_8105,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(identity,a)),inverse(multiply(multiply(inverse(a),greatest_lower_bound(identity,a)),least_upper_bound(identity,a))))) != identity,
inference(paramod,[status(thm)],[c_206,c_8104]) ).
cnf(c_8106,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(multiply(inverse(a),least_upper_bound(identity,a)),inverse(multiply(inverse(a),multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)))))) != identity,
inference(paramod,[status(thm)],[c_3,c_8105]) ).
cnf(c_5339,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(inverse(a),multiply(least_upper_bound(identity,a),inverse(multiply(inverse(a),multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_8106]) ).
cnf(c_8107,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_1156]) ).
cnf(c_6616,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_558,c_8107]) ).
cnf(c_8108,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_1156]) ).
cnf(c_8109,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_557,c_8108]) ).
cnf(c_6635,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_8109]) ).
cnf(c_8110,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_1156]) ).
cnf(c_8111,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_6635,c_8110]) ).
cnf(c_8112,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_8111]) ).
cnf(c_8113,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_8112]) ).
cnf(c_8114,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_8113]) ).
cnf(c_8115,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_8114]) ).
cnf(c_8116,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_557,c_8115]) ).
cnf(c_8117,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_463,c_8116]) ).
cnf(c_6671,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_8117]) ).
cnf(c_8118,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_6671,c_6616]) ).
cnf(c_8119,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_8118]) ).
cnf(c_6784,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_8119]) ).
cnf(c_8120,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_6784,c_4638]) ).
cnf(c_8121,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_8120]) ).
cnf(c_8122,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_8121]) ).
cnf(c_8123,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_8122]) ).
cnf(c_8124,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_8123]) ).
cnf(c_8125,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_8124]) ).
cnf(c_6940,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_4511,c_8125]) ).
cnf(c_8126,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_2358,c_40]) ).
cnf(c_7968,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_8126]) ).
cnf(c_8127,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_7968,c_6940]) ).
cnf(c_8128,plain,
multiply(A,identity) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_1962,c_8127]) ).
cnf(c_8129,plain,
A = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_8128]) ).
cnf(c_8023,plain,
multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)) = A,
inference(copy,[status(thm)],[c_8129]) ).
cnf(c_8130,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_8023,c_2582]) ).
cnf(c_8131,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_8130]) ).
cnf(c_8132,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_8131]) ).
cnf(c_8133,plain,
identity = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_35,c_8132]) ).
cnf(c_8026,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))) = identity,
inference(copy,[status(thm)],[c_8133]) ).
cnf(c_8134,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(inverse(a),multiply(least_upper_bound(identity,a),inverse(identity)))) != identity,
inference(paramod,[status(thm)],[c_8026,c_5339]) ).
cnf(c_8135,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(inverse(a),multiply(least_upper_bound(identity,a),identity))) != identity,
inference(paramod,[status(thm)],[c_82,c_8134]) ).
cnf(c_8136,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(inverse(a),least_upper_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_81,c_8135]) ).
cnf(c_8137,plain,
multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(identity,a)) != identity,
inference(paramod,[status(thm)],[c_56,c_8136]) ).
cnf(c_8138,plain,
multiply(multiply(inverse(a),greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != identity,
inference(paramod,[status(thm)],[c_206,c_8137]) ).
cnf(c_8139,plain,
multiply(inverse(a),multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_3,c_8138]) ).
cnf(c_8140,plain,
identity != identity,
inference(paramod,[status(thm)],[c_8026,c_8139]) ).
cnf(c_8027,plain,
$false,
inference(copy,[status(thm)],[c_8140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP183-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:38:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1603406 was started by sandbox on n015,
% 0.08/0.36 % Fri Sep 25 14:38:12 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.36
% 0.14/0.36 % From the command line: assign(max_seconds, 300).
% 76.96/11.23
% 76.96/11.23 % SZS status Unsatisfiable for theBenchmark
% 76.96/11.23
% 76.96/11.23 % Proof 1 at 2.19 (+ 0.56) seconds.
% 76.96/11.23 % Length of proof is 95.
% 76.96/11.23 % Level of proof is 12.
% 76.96/11.23 % Maximum clause weight is 100.000.
% 76.96/11.23 % Given clauses 329.
% 76.96/11.23
% 76.96/11.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------