%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP167-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:11 AM UTC 2026
% Result : Unsatisfiable 103.78s 14.32s
% Output : CNFRefutation 103.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 16
% Syntax : Number of formulae : 209 ( 209 unt; 0 def)
% Number of atoms : 209 ( 208 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 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 : 381 ( 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_p19,axiom,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('theBenchmark.p',prove_p19) ).
cnf(c_22,plain,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(clausify,[status(thm)],[prove_p19]) ).
cnf(c_9633,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(a,identity)),
inference(paramod,[status(thm)],[c_5,c_22]) ).
cnf(c_9634,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)),
inference(paramod,[status(thm)],[c_4,c_9633]) ).
cnf(c_23,plain,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(copy,[status(thm)],[c_9634]) ).
cnf(c_9635,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_9636,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_9635]) ).
cnf(c_24,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_9636]) ).
cnf(c_9637,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_9637]) ).
cnf(c_9638,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_9638]) ).
cnf(c_9639,plain,
greatest_lower_bound(greatest_lower_bound(A,B),B) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_34,plain,
greatest_lower_bound(A,greatest_lower_bound(B,A)) = greatest_lower_bound(B,A),
inference(paramod,[status(thm)],[c_4,c_9639]) ).
cnf(c_36,plain,
least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(A,greatest_lower_bound(B,C))) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_7,c_12]) ).
cnf(c_9640,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_9640]) ).
cnf(c_39,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_9641,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_9641]) ).
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_9642,plain,
least_upper_bound(multiply(inverse(A),B),identity) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_44,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_5,c_9642]) ).
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_9643,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_9643]) ).
cnf(c_9644,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_9644]) ).
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_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_9645,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_9645]) ).
cnf(c_112,plain,
multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(B,multiply(A,B))) = B,
inference(paramod,[status(thm)],[c_49,c_24]) ).
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_9646,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_9646]) ).
cnf(c_9647,plain,
multiply(inverse(A),least_upper_bound(A,multiply(A,B))) = least_upper_bound(identity,B),
inference(paramod,[status(thm)],[c_83,c_24]) ).
cnf(c_174,plain,
least_upper_bound(identity,A) = multiply(inverse(B),least_upper_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_9647]) ).
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_9648,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_9648]) ).
cnf(c_9649,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_9649]) ).
cnf(c_9650,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(identity,a),a)) != a,
inference(paramod,[status(thm)],[c_85,c_23]) ).
cnf(c_9651,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(a,least_upper_bound(identity,a))) != a,
inference(paramod,[status(thm)],[c_178,c_9650]) ).
cnf(c_219,plain,
multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)) != a,
inference(paramod,[status(thm)],[c_56,c_9651]) ).
cnf(c_221,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_9652,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_9652]) ).
cnf(c_9653,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_9654,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_9653]) ).
cnf(c_261,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_9654]) ).
cnf(c_9655,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_9656,plain,
A = multiply(inverse(greatest_lower_bound(B,identity)),multiply(greatest_lower_bound(identity,B),A)),
inference(paramod,[status(thm)],[c_1,c_9655]) ).
cnf(c_378,plain,
multiply(inverse(greatest_lower_bound(A,identity)),multiply(greatest_lower_bound(identity,A),B)) = B,
inference(copy,[status(thm)],[c_9656]) ).
cnf(c_456,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_80,c_2]) ).
cnf(c_461,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_80,c_24]) ).
cnf(c_9657,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_80,c_81]) ).
cnf(c_9658,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_81,c_9657]) ).
cnf(c_462,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_9658]) ).
cnf(c_9659,plain,
least_upper_bound(inverse(A),identity) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_456,c_49]) ).
cnf(c_9660,plain,
least_upper_bound(identity,inverse(A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_5,c_9659]) ).
cnf(c_9661,plain,
multiply(inverse(A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_158,c_9660]) ).
cnf(c_470,plain,
multiply(least_upper_bound(identity,A),inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_9661]) ).
cnf(c_9662,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_456,c_56]) ).
cnf(c_9663,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_9662]) ).
cnf(c_9664,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_206,c_9663]) ).
cnf(c_473,plain,
multiply(greatest_lower_bound(identity,A),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_9664]) ).
cnf(c_9665,plain,
multiply(multiply(inverse(A),least_upper_bound(identity,A)),B) = multiply(least_upper_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_470,c_3]) ).
cnf(c_9666,plain,
multiply(inverse(A),multiply(least_upper_bound(identity,A),B)) = multiply(least_upper_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_3,c_9665]) ).
cnf(c_476,plain,
multiply(least_upper_bound(identity,A),multiply(inverse(A),B)) = multiply(inverse(A),multiply(least_upper_bound(identity,A),B)),
inference(copy,[status(thm)],[c_9666]) ).
cnf(c_9667,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_473,c_3]) ).
cnf(c_9668,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_9667]) ).
cnf(c_504,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_9668]) ).
cnf(c_556,plain,
least_upper_bound(multiply(A,B),C) = multiply(A,least_upper_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_461,c_15]) ).
cnf(c_557,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_461,c_17]) ).
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_872,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(A),least_upper_bound(A,multiply(A,a)))) != a,
inference(paramod,[status(thm)],[c_174,c_219]) ).
cnf(c_9669,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(multiply(A,B)),least_upper_bound(multiply(A,B),multiply(A,multiply(B,a))))) != a,
inference(paramod,[status(thm)],[c_3,c_872]) ).
cnf(c_9670,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(multiply(A,B)),multiply(A,least_upper_bound(B,multiply(inverse(A),multiply(A,multiply(B,a))))))) != a,
inference(paramod,[status(thm)],[c_556,c_9669]) ).
cnf(c_991,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(multiply(A,B)),multiply(A,least_upper_bound(B,multiply(B,a))))) != a,
inference(paramod,[status(thm)],[c_24,c_9670]) ).
cnf(c_1030,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(multiply(inverse(least_upper_bound(identity,a)),a)),a)) != a,
inference(paramod,[status(thm)],[c_112,c_991]) ).
cnf(c_9671,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_1167,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_9671]) ).
cnf(c_1882,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_43,c_13]) ).
cnf(c_1959,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_5,c_1882]) ).
cnf(c_9672,plain,
least_upper_bound(multiply(inverse(A),B),multiply(least_upper_bound(identity,A),multiply(inverse(A),B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_461,c_114]) ).
cnf(c_9673,plain,
least_upper_bound(multiply(inverse(A),B),multiply(inverse(A),multiply(least_upper_bound(identity,A),B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_476,c_9672]) ).
cnf(c_9674,plain,
multiply(inverse(A),least_upper_bound(B,multiply(inverse(inverse(A)),multiply(inverse(A),multiply(least_upper_bound(identity,A),B))))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_556,c_9673]) ).
cnf(c_9675,plain,
multiply(inverse(A),least_upper_bound(B,multiply(A,multiply(inverse(A),multiply(least_upper_bound(identity,A),B))))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_462,c_9674]) ).
cnf(c_9676,plain,
multiply(inverse(A),least_upper_bound(B,multiply(least_upper_bound(identity,A),B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_461,c_9675]) ).
cnf(c_9677,plain,
multiply(inverse(A),least_upper_bound(B,multiply(A,B))) = least_upper_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_114,c_9676]) ).
cnf(c_9678,plain,
multiply(inverse(A),least_upper_bound(B,multiply(A,B))) = least_upper_bound(B,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_5,c_9677]) ).
cnf(c_2323,plain,
least_upper_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),least_upper_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_9678]) ).
cnf(c_9679,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_461,c_145]) ).
cnf(c_9680,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_504,c_9679]) ).
cnf(c_9681,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_557,c_9680]) ).
cnf(c_9682,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_462,c_9681]) ).
cnf(c_9683,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_461,c_9682]) ).
cnf(c_9684,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_9683]) ).
cnf(c_9685,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_9684]) ).
cnf(c_2390,plain,
greatest_lower_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),greatest_lower_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_9685]) ).
cnf(c_9686,plain,
multiply(inverse(greatest_lower_bound(inverse(A),identity)),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_59,c_378]) ).
cnf(c_9687,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(A))),greatest_lower_bound(identity,multiply(identity,A))) = A,
inference(paramod,[status(thm)],[c_4,c_9686]) ).
cnf(c_9688,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_9687]) ).
cnf(c_4743,plain,
multiply(inverse(multiply(inverse(A),greatest_lower_bound(identity,A))),greatest_lower_bound(identity,A)) = A,
inference(paramod,[status(thm)],[c_1,c_9688]) ).
cnf(c_9689,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_9690,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_462,c_9689]) ).
cnf(c_5051,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_462,c_9690]) ).
cnf(c_5108,plain,
least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(B,A)) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_34,c_36]) ).
cnf(c_9691,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A))) = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_5108,c_43]) ).
cnf(c_5180,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_2,c_9691]) ).
cnf(c_9692,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A))) = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_5108,c_44]) ).
cnf(c_9693,plain,
identity = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_5180,c_9692]) ).
cnf(c_5182,plain,
multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)) = identity,
inference(copy,[status(thm)],[c_9693]) ).
cnf(c_9694,plain,
multiply(identity,A) = multiply(inverse(greatest_lower_bound(B,C)),multiply(greatest_lower_bound(C,B),A)),
inference(paramod,[status(thm)],[c_5182,c_3]) ).
cnf(c_9695,plain,
A = multiply(inverse(greatest_lower_bound(B,C)),multiply(greatest_lower_bound(C,B),A)),
inference(paramod,[status(thm)],[c_1,c_9694]) ).
cnf(c_5324,plain,
multiply(inverse(greatest_lower_bound(A,B)),multiply(greatest_lower_bound(B,A),C)) = C,
inference(copy,[status(thm)],[c_9695]) ).
cnf(c_9696,plain,
least_upper_bound(inverse(inverse(greatest_lower_bound(A,B))),multiply(greatest_lower_bound(B,A),C)) = multiply(inverse(inverse(greatest_lower_bound(A,B))),least_upper_bound(identity,C)),
inference(paramod,[status(thm)],[c_5324,c_175]) ).
cnf(c_9697,plain,
least_upper_bound(greatest_lower_bound(A,B),multiply(greatest_lower_bound(B,A),C)) = multiply(inverse(inverse(greatest_lower_bound(A,B))),least_upper_bound(identity,C)),
inference(paramod,[status(thm)],[c_462,c_9696]) ).
cnf(c_5378,plain,
least_upper_bound(greatest_lower_bound(A,B),multiply(greatest_lower_bound(B,A),C)) = multiply(greatest_lower_bound(A,B),least_upper_bound(identity,C)),
inference(paramod,[status(thm)],[c_462,c_9697]) ).
cnf(c_9698,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_1167]) ).
cnf(c_7741,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_557,c_9698]) ).
cnf(c_9699,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_1167]) ).
cnf(c_9700,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_556,c_9699]) ).
cnf(c_7760,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_9700]) ).
cnf(c_9701,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_1167]) ).
cnf(c_9702,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_7760,c_9701]) ).
cnf(c_9703,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_221,c_9702]) ).
cnf(c_9704,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_221,c_9703]) ).
cnf(c_9705,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_9704]) ).
cnf(c_9706,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_9705]) ).
cnf(c_9707,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_556,c_9706]) ).
cnf(c_9708,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_462,c_9707]) ).
cnf(c_7796,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_9708]) ).
cnf(c_9709,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_7796,c_7741]) ).
cnf(c_9710,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_9709]) ).
cnf(c_7920,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_9710]) ).
cnf(c_9711,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_7920,c_5051]) ).
cnf(c_9712,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_9711]) ).
cnf(c_9713,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_9712]) ).
cnf(c_9714,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_9713]) ).
cnf(c_9715,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_9714]) ).
cnf(c_9716,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_9715]) ).
cnf(c_7962,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_4743,c_9716]) ).
cnf(c_9717,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(inverse(least_upper_bound(identity,A)),greatest_lower_bound(A,identity))) = multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_261,c_2323]) ).
cnf(c_9718,plain,
multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,A))),greatest_lower_bound(A,identity)) = multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_49,c_9717]) ).
cnf(c_9719,plain,
multiply(multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(identity,least_upper_bound(identity,A))),greatest_lower_bound(A,identity)) = multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_158,c_9718]) ).
cnf(c_9720,plain,
multiply(multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(identity,A)),greatest_lower_bound(A,identity)) = multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_29,c_9719]) ).
cnf(c_9721,plain,
multiply(identity,greatest_lower_bound(A,identity)) = multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_2,c_9720]) ).
cnf(c_9722,plain,
greatest_lower_bound(A,identity) = multiply(inverse(least_upper_bound(identity,A)),least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_1,c_9721]) ).
cnf(c_9723,plain,
greatest_lower_bound(A,identity) = multiply(inverse(least_upper_bound(identity,A)),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,least_upper_bound(identity,A)))),
inference(paramod,[status(thm)],[c_5378,c_9722]) ).
cnf(c_9724,plain,
greatest_lower_bound(A,identity) = multiply(inverse(least_upper_bound(identity,A)),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_29,c_9723]) ).
cnf(c_9035,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A))) = greatest_lower_bound(A,identity),
inference(copy,[status(thm)],[c_9724]) ).
cnf(c_9725,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_2390,c_40]) ).
cnf(c_9565,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_9725]) ).
cnf(c_9726,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_9565,c_7962]) ).
cnf(c_9727,plain,
multiply(A,identity) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_1959,c_9726]) ).
cnf(c_9728,plain,
A = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_81,c_9727]) ).
cnf(c_9626,plain,
multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,A)) = A,
inference(copy,[status(thm)],[c_9728]) ).
cnf(c_9628,plain,
multiply(inverse(least_upper_bound(identity,A)),A) = greatest_lower_bound(A,identity),
inference(paramod,[status(thm)],[c_9626,c_9035]) ).
cnf(c_9729,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(greatest_lower_bound(a,identity)),a)) != a,
inference(paramod,[status(thm)],[c_9628,c_1030]) ).
cnf(c_9730,plain,
multiply(greatest_lower_bound(identity,a),multiply(inverse(greatest_lower_bound(identity,a)),a)) != a,
inference(paramod,[status(thm)],[c_4,c_9729]) ).
cnf(c_9731,plain,
a != a,
inference(paramod,[status(thm)],[c_461,c_9730]) ).
cnf(c_9632,plain,
$false,
inference(copy,[status(thm)],[c_9731]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n009.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 14:33:00 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1818512 was started by sandbox2 on n009,
% 0.16/0.43 % Fri Sep 25 14:33:00 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 103.78/14.32
% 103.78/14.32 % SZS status Unsatisfiable for theBenchmark
% 103.78/14.32
% 103.78/14.32 % Proof 1 at 4.35 (+ 1.01) seconds.
% 103.78/14.32 % Length of proof is 94.
% 103.78/14.32 % Level of proof is 12.
% 103.78/14.32 % Maximum clause weight is 100.000.
% 103.78/14.32 % Given clauses 326.
% 103.78/14.32
% 103.78/14.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------