%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP183-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 07:28:17 AM UTC 2026
% Result : Unsatisfiable 83.72s 12.00s
% Output : CNFRefutation 83.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 18
% Syntax : Number of formulae : 217 ( 217 unt; 0 def)
% Number of atoms : 217 ( 216 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 17 ( 17 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 417 ( 11 sgn 35 !; 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_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(p20x_1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p20x_1) ).
cnf(c_22,plain,
inverse(identity) = identity,
inference(clausify,[status(thm)],[p20x_1]) ).
fof(p20x_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',p20x_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[p20x_2]) ).
fof(p20x_3,axiom,
! [VAR_0,VAR_1] : inverse(multiply(VAR_0,VAR_1)) = multiply(inverse(VAR_1),inverse(VAR_0)),
file('theBenchmark.p',p20x_3) ).
cnf(c_24,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(clausify,[status(thm)],[p20x_3]) ).
fof(prove_20x,axiom,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
file('theBenchmark.p',prove_20x) ).
cnf(c_25,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
inference(clausify,[status(thm)],[prove_20x]) ).
cnf(c_10319,plain,
greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(inverse(a),identity)) != identity,
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_26,plain,
greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,inverse(a))) != identity,
inference(paramod,[status(thm)],[c_5,c_10319]) ).
cnf(c_10320,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_10321,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_10320]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_10321]) ).
cnf(c_10322,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_35,plain,
greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B),
inference(copy,[status(thm)],[c_10322]) ).
cnf(c_10323,plain,
greatest_lower_bound(greatest_lower_bound(A,B),B) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_37,plain,
greatest_lower_bound(A,greatest_lower_bound(B,A)) = greatest_lower_bound(B,A),
inference(paramod,[status(thm)],[c_4,c_10323]) ).
cnf(c_39,plain,
least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(A,greatest_lower_bound(B,C))) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_7,c_12]) ).
cnf(c_10324,plain,
least_upper_bound(A,B) = least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,C),B)),
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_40,plain,
least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,B),C)) = least_upper_bound(A,C),
inference(copy,[status(thm)],[c_10324]) ).
cnf(c_42,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_46,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_10325,plain,
least_upper_bound(multiply(inverse(A),B),identity) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_47,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_5,c_10325]) ).
cnf(c_49,plain,
greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_52,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_59,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_10326,plain,
greatest_lower_bound(multiply(A,B),identity) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_2,c_21]) ).
cnf(c_62,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_4,c_10326]) ).
cnf(c_66,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_10327,plain,
inverse(A) = multiply(inverse(A),inverse(identity)),
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_10328,plain,
inverse(A) = multiply(inverse(A),identity),
inference(paramod,[status(thm)],[c_22,c_10327]) ).
cnf(c_67,plain,
multiply(inverse(A),identity) = inverse(A),
inference(copy,[status(thm)],[c_10328]) ).
cnf(c_10329,plain,
multiply(identity,A) = multiply(B,multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_66,c_3]) ).
cnf(c_10330,plain,
A = multiply(B,multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_10329]) ).
cnf(c_68,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_10330]) ).
cnf(c_75,plain,
greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_66,c_21]) ).
cnf(c_10331,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(C,A),B)),
inference(paramod,[status(thm)],[c_42,c_7]) ).
cnf(c_80,plain,
greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(B,A),C)) = greatest_lower_bound(A,C),
inference(copy,[status(thm)],[c_10331]) ).
cnf(c_10332,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_23,c_67]) ).
cnf(c_89,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_23,c_10332]) ).
cnf(c_90,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_89,c_15]) ).
cnf(c_92,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_89,c_17]) ).
cnf(c_10333,plain,
least_upper_bound(inverse(A),identity) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_66,c_52]) ).
cnf(c_127,plain,
least_upper_bound(identity,inverse(A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_5,c_10333]) ).
cnf(c_10334,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(identity,a),inverse(a))) != identity,
inference(paramod,[status(thm)],[c_127,c_26]) ).
cnf(c_132,plain,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,inverse(a))) != identity,
inference(paramod,[status(thm)],[c_92,c_10334]) ).
cnf(c_10335,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_66,c_59]) ).
cnf(c_163,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_10335]) ).
cnf(c_165,plain,
greatest_lower_bound(A,multiply(greatest_lower_bound(identity,B),A)) = greatest_lower_bound(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_59,c_35]) ).
cnf(c_167,plain,
multiply(least_upper_bound(identity,a),multiply(greatest_lower_bound(identity,a),inverse(a))) != identity,
inference(paramod,[status(thm)],[c_163,c_132]) ).
cnf(c_10336,plain,
least_upper_bound(inverse(A),identity) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_90]) ).
cnf(c_10337,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_10336]) ).
cnf(c_181,plain,
multiply(least_upper_bound(identity,A),inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_127,c_10337]) ).
cnf(c_10338,plain,
multiply(A,least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),A),
inference(paramod,[status(thm)],[c_90,c_52]) ).
cnf(c_202,plain,
multiply(least_upper_bound(identity,A),A) = multiply(A,least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_10338]) ).
cnf(c_210,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_181,c_127]) ).
cnf(c_10339,plain,
greatest_lower_bound(inverse(A),identity) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_92]) ).
cnf(c_10340,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_4,c_10339]) ).
cnf(c_231,plain,
multiply(greatest_lower_bound(identity,A),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_163,c_10340]) ).
cnf(c_10341,plain,
multiply(inverse(A),greatest_lower_bound(A,multiply(A,B))) = greatest_lower_bound(identity,B),
inference(paramod,[status(thm)],[c_92,c_27]) ).
cnf(c_245,plain,
greatest_lower_bound(identity,A) = multiply(inverse(B),greatest_lower_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_10341]) ).
cnf(c_246,plain,
greatest_lower_bound(inverse(A),B) = multiply(inverse(A),greatest_lower_bound(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_27,c_92]) ).
cnf(c_10342,plain,
multiply(A,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),A),
inference(paramod,[status(thm)],[c_92,c_59]) ).
cnf(c_252,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_10342]) ).
cnf(c_257,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(a),greatest_lower_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_231,c_167]) ).
cnf(c_258,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_231,c_163]) ).
cnf(c_10343,plain,
least_upper_bound(multiply(inverse(a),greatest_lower_bound(identity,a)),multiply(a,multiply(inverse(a),greatest_lower_bound(identity,a)))) != identity,
inference(paramod,[status(thm)],[c_52,c_257]) ).
cnf(c_10344,plain,
least_upper_bound(multiply(inverse(a),greatest_lower_bound(identity,a)),greatest_lower_bound(identity,a)) != identity,
inference(paramod,[status(thm)],[c_68,c_10343]) ).
cnf(c_10345,plain,
least_upper_bound(greatest_lower_bound(identity,a),multiply(inverse(a),greatest_lower_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_5,c_10344]) ).
cnf(c_10346,plain,
multiply(least_upper_bound(identity,inverse(a)),greatest_lower_bound(identity,a)) != identity,
inference(paramod,[status(thm)],[c_52,c_10345]) ).
cnf(c_10347,plain,
multiply(multiply(inverse(a),least_upper_bound(identity,a)),greatest_lower_bound(identity,a)) != identity,
inference(paramod,[status(thm)],[c_210,c_10346]) ).
cnf(c_277,plain,
multiply(inverse(a),multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_3,c_10347]) ).
cnf(c_10348,plain,
multiply(inverse(a),greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(identity,a),a))) != identity,
inference(paramod,[status(thm)],[c_92,c_277]) ).
cnf(c_10349,plain,
multiply(inverse(a),greatest_lower_bound(least_upper_bound(identity,a),multiply(a,least_upper_bound(identity,a)))) != identity,
inference(paramod,[status(thm)],[c_202,c_10348]) ).
cnf(c_278,plain,
multiply(inverse(a),multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a))) != identity,
inference(paramod,[status(thm)],[c_59,c_10349]) ).
cnf(c_10350,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(A,least_upper_bound(identity,A))) = multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_202,c_92]) ).
cnf(c_10351,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_59,c_10350]) ).
cnf(c_286,plain,
multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_10351]) ).
cnf(c_10352,plain,
inverse(multiply(A,greatest_lower_bound(identity,A))) = multiply(inverse(A),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_252,c_24]) ).
cnf(c_308,plain,
multiply(inverse(greatest_lower_bound(identity,A)),inverse(A)) = multiply(inverse(A),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_24,c_10352]) ).
cnf(c_10353,plain,
multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),B) = multiply(greatest_lower_bound(identity,A),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_231,c_3]) ).
cnf(c_10354,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_10353]) ).
cnf(c_336,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_10354]) ).
cnf(c_337,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_4,c_231]) ).
cnf(c_10355,plain,
inverse(multiply(inverse(A),greatest_lower_bound(identity,A))) = multiply(inverse(inverse(A)),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_231,c_24]) ).
cnf(c_10356,plain,
multiply(inverse(greatest_lower_bound(identity,A)),inverse(inverse(A))) = multiply(inverse(inverse(A)),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_24,c_10355]) ).
cnf(c_10357,plain,
multiply(inverse(greatest_lower_bound(identity,A)),A) = multiply(inverse(inverse(A)),inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_23,c_10356]) ).
cnf(c_346,plain,
multiply(inverse(greatest_lower_bound(identity,A)),A) = multiply(A,inverse(greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_23,c_10357]) ).
cnf(c_368,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = multiply(inverse(A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_4,c_337]) ).
cnf(c_10358,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(greatest_lower_bound(A,identity),inverse(A))) = multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_337,c_52]) ).
cnf(c_10359,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(inverse(A),greatest_lower_bound(A,identity))) = multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_368,c_10358]) ).
cnf(c_10360,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(inverse(A),greatest_lower_bound(A,identity))) = multiply(multiply(inverse(A),least_upper_bound(identity,A)),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_210,c_10359]) ).
cnf(c_10361,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(inverse(A),greatest_lower_bound(A,identity))) = multiply(inverse(A),multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_3,c_10360]) ).
cnf(c_379,plain,
least_upper_bound(greatest_lower_bound(identity,A),multiply(inverse(A),greatest_lower_bound(A,identity))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_286,c_10361]) ).
cnf(c_487,plain,
least_upper_bound(multiply(A,B),C) = multiply(A,least_upper_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_68,c_15]) ).
cnf(c_488,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_68,c_17]) ).
cnf(c_10362,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(A,B),C),least_upper_bound(A,C)) = least_upper_bound(greatest_lower_bound(A,B),C),
inference(paramod,[status(thm)],[c_40,c_42]) ).
cnf(c_1138,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_10362]) ).
cnf(c_10363,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = multiply(inverse(A),A),
inference(paramod,[status(thm)],[c_12,c_46]) ).
cnf(c_1836,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_2,c_10363]) ).
cnf(c_1837,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity,
inference(paramod,[status(thm)],[c_46,c_13]) ).
cnf(c_10364,plain,
greatest_lower_bound(identity,multiply(multiply(A,B),inverse(A))) = multiply(multiply(A,greatest_lower_bound(identity,B)),inverse(A)),
inference(paramod,[status(thm)],[c_92,c_75]) ).
cnf(c_10365,plain,
greatest_lower_bound(identity,multiply(A,multiply(B,inverse(A)))) = multiply(multiply(A,greatest_lower_bound(identity,B)),inverse(A)),
inference(paramod,[status(thm)],[c_3,c_10364]) ).
cnf(c_2577,plain,
greatest_lower_bound(identity,multiply(A,multiply(B,inverse(A)))) = multiply(A,multiply(greatest_lower_bound(identity,B),inverse(A))),
inference(paramod,[status(thm)],[c_3,c_10365]) ).
cnf(c_10366,plain,
greatest_lower_bound(multiply(inverse(A),B),multiply(greatest_lower_bound(identity,A),multiply(inverse(A),B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_68,c_165]) ).
cnf(c_10367,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_336,c_10366]) ).
cnf(c_10368,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_488,c_10367]) ).
cnf(c_10369,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(A,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),B))))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_23,c_10368]) ).
cnf(c_10370,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(greatest_lower_bound(identity,A),B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_68,c_10369]) ).
cnf(c_10371,plain,
multiply(inverse(A),greatest_lower_bound(B,multiply(A,B))) = greatest_lower_bound(multiply(inverse(A),B),B),
inference(paramod,[status(thm)],[c_165,c_10370]) ).
cnf(c_10372,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_10371]) ).
cnf(c_3026,plain,
greatest_lower_bound(A,multiply(inverse(B),A)) = multiply(inverse(B),greatest_lower_bound(A,multiply(B,A))),
inference(copy,[status(thm)],[c_10372]) ).
cnf(c_5190,plain,
least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(B,A)) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_37,c_39]) ).
cnf(c_10373,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_5190,c_46]) ).
cnf(c_5292,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_10373]) ).
cnf(c_10374,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_5190,c_47]) ).
cnf(c_10375,plain,
identity = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_5292,c_10374]) ).
cnf(c_5294,plain,
multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(B,A)) = identity,
inference(copy,[status(thm)],[c_10375]) ).
cnf(c_10376,plain,
multiply(multiply(inverse(A),inverse(greatest_lower_bound(identity,A))),B) = multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_308,c_3]) ).
cnf(c_10377,plain,
multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,A)),B)) = multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_3,c_10376]) ).
cnf(c_5599,plain,
multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),B)) = multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,A)),B)),
inference(copy,[status(thm)],[c_10377]) ).
cnf(c_10378,plain,
greatest_lower_bound(least_upper_bound(identity,A),least_upper_bound(multiply(greatest_lower_bound(B,inverse(C)),C),A)) = least_upper_bound(greatest_lower_bound(identity,multiply(B,C)),A),
inference(paramod,[status(thm)],[c_62,c_1138]) ).
cnf(c_10379,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_487,c_10378]) ).
cnf(c_7256,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_10379]) ).
cnf(c_10380,plain,
greatest_lower_bound(least_upper_bound(identity,A),least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,multiply(B,C))),A)) = least_upper_bound(greatest_lower_bound(identity,C),A),
inference(paramod,[status(thm)],[c_245,c_1138]) ).
cnf(c_10381,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,multiply(B,C)),multiply(inverse(inverse(B)),A)))) = least_upper_bound(greatest_lower_bound(identity,C),A),
inference(paramod,[status(thm)],[c_487,c_10380]) ).
cnf(c_10382,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,multiply(B,C)),multiply(B,A)))) = least_upper_bound(greatest_lower_bound(identity,C),A),
inference(paramod,[status(thm)],[c_23,c_10381]) ).
cnf(c_7265,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),least_upper_bound(greatest_lower_bound(C,multiply(C,A)),multiply(C,B)))),
inference(copy,[status(thm)],[c_10382]) ).
cnf(c_10383,plain,
greatest_lower_bound(least_upper_bound(identity,A),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(B),C)),A)) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_49,c_1138]) ).
cnf(c_10384,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_7256,c_10383]) ).
cnf(c_10385,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C)))),least_upper_bound(C,multiply(inverse(greatest_lower_bound(inverse(B),inverse(C))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_246,c_10384]) ).
cnf(c_10386,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C)))),least_upper_bound(C,multiply(inverse(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C))))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_246,c_10385]) ).
cnf(c_10387,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C)))),least_upper_bound(C,multiply(multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(C)))),inverse(inverse(B))),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_24,c_10386]) ).
cnf(c_10388,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C)))),least_upper_bound(C,multiply(multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(C)))),B),A))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_23,c_10387]) ).
cnf(c_10389,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(multiply(inverse(B),greatest_lower_bound(identity,multiply(B,inverse(C)))),least_upper_bound(C,multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(C)))),multiply(B,A)))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_3,c_10388]) ).
cnf(c_10390,plain,
greatest_lower_bound(least_upper_bound(identity,A),greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(C)))),multiply(B,A))))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_3,c_10389]) ).
cnf(c_10391,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(C)))),multiply(B,A)))))) = least_upper_bound(multiply(inverse(B),greatest_lower_bound(B,C)),A),
inference(paramod,[status(thm)],[c_35,c_10390]) ).
cnf(c_10392,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(C)))),multiply(B,A)))))) = multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,C),multiply(inverse(inverse(B)),A))),
inference(paramod,[status(thm)],[c_487,c_10391]) ).
cnf(c_10393,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(inverse(B),multiply(greatest_lower_bound(identity,multiply(B,inverse(C))),least_upper_bound(C,multiply(inverse(greatest_lower_bound(identity,multiply(B,inverse(C)))),multiply(B,A)))))) = multiply(inverse(B),least_upper_bound(greatest_lower_bound(B,C),multiply(B,A))),
inference(paramod,[status(thm)],[c_23,c_10392]) ).
cnf(c_7292,plain,
multiply(inverse(A),least_upper_bound(greatest_lower_bound(A,B),multiply(A,C))) = greatest_lower_bound(least_upper_bound(identity,C),multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(B))),least_upper_bound(B,multiply(inverse(greatest_lower_bound(identity,multiply(A,inverse(B)))),multiply(A,C)))))),
inference(copy,[status(thm)],[c_10393]) ).
cnf(c_10394,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A)))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_7292,c_7265]) ).
cnf(c_10395,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(greatest_lower_bound(identity,multiply(C,multiply(inverse(A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_10394]) ).
cnf(c_10396,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(greatest_lower_bound(identity,inverse(A)),inverse(C))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_2577,c_10395]) ).
cnf(c_10397,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),inverse(C))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_258,c_10396]) ).
cnf(c_10398,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,inverse(multiply(C,A))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_10397]) ).
cnf(c_10399,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(greatest_lower_bound(identity,multiply(C,multiply(inverse(A),inverse(C))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_10398]) ).
cnf(c_10400,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(multiply(C,multiply(greatest_lower_bound(identity,inverse(A)),inverse(C)))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_2577,c_10399]) ).
cnf(c_10401,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(multiply(C,multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),inverse(C)))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_258,c_10400]) ).
cnf(c_10402,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(inverse(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C))))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_10401]) ).
cnf(c_10403,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(inverse(multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_10402]) ).
cnf(c_10404,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(inverse(multiply(greatest_lower_bound(identity,A),inverse(C))),inverse(inverse(A))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_10403]) ).
cnf(c_10405,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(multiply(inverse(inverse(C)),inverse(greatest_lower_bound(identity,A))),inverse(inverse(A))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_24,c_10404]) ).
cnf(c_10406,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(multiply(C,inverse(greatest_lower_bound(identity,A))),inverse(inverse(A))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_23,c_10405]) ).
cnf(c_10407,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(multiply(C,inverse(greatest_lower_bound(identity,A))),A),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_23,c_10406]) ).
cnf(c_10408,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(C,multiply(inverse(greatest_lower_bound(identity,A)),A)),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_10407]) ).
cnf(c_10409,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(multiply(C,multiply(A,inverse(greatest_lower_bound(identity,A)))),inverse(C)),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_346,c_10408]) ).
cnf(c_10410,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(C,multiply(multiply(A,inverse(greatest_lower_bound(identity,A))),inverse(C))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_10409]) ).
cnf(c_10411,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(multiply(C,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),inverse(C)))),multiply(C,B))))))),
inference(paramod,[status(thm)],[c_3,c_10410]) ).
cnf(c_10412,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(C,multiply(multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),inverse(C))),multiply(C,B)))))))),
inference(paramod,[status(thm)],[c_3,c_10411]) ).
cnf(c_10413,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(C,multiply(A,multiply(multiply(inverse(greatest_lower_bound(identity,A)),inverse(C)),multiply(C,B))))))))),
inference(paramod,[status(thm)],[c_3,c_10412]) ).
cnf(c_10414,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(C,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(C),multiply(C,B)))))))))),
inference(paramod,[status(thm)],[c_3,c_10413]) ).
cnf(c_10415,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),least_upper_bound(multiply(C,A),multiply(C,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))))),
inference(paramod,[status(thm)],[c_27,c_10414]) ).
cnf(c_10416,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),multiply(C,least_upper_bound(A,multiply(inverse(C),multiply(C,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))))))),
inference(paramod,[status(thm)],[c_487,c_10415]) ).
cnf(c_10417,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C)))),multiply(C,least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))))),
inference(paramod,[status(thm)],[c_27,c_10416]) ).
cnf(c_10418,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(C,multiply(multiply(inverse(A),multiply(greatest_lower_bound(identity,A),inverse(C))),multiply(C,least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B))))))))),
inference(paramod,[status(thm)],[c_3,c_10417]) ).
cnf(c_10419,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(C,multiply(inverse(A),multiply(multiply(greatest_lower_bound(identity,A),inverse(C)),multiply(C,least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))))))),
inference(paramod,[status(thm)],[c_3,c_10418]) ).
cnf(c_10420,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),multiply(inverse(C),multiply(C,least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B))))))))))),
inference(paramod,[status(thm)],[c_3,c_10419]) ).
cnf(c_10421,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(C),multiply(C,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B))))))))),
inference(paramod,[status(thm)],[c_27,c_10420]) ).
cnf(c_10422,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B))))))),
inference(paramod,[status(thm)],[c_27,c_10421]) ).
cnf(c_7425,plain,
least_upper_bound(greatest_lower_bound(identity,A),B) = greatest_lower_bound(least_upper_bound(identity,B),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),B)))))),
inference(paramod,[status(thm)],[c_35,c_10422]) ).
cnf(c_10423,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,identity))),multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),greatest_lower_bound(A,identity)))))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_7425,c_379]) ).
cnf(c_10424,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(identity,A)),multiply(inverse(A),greatest_lower_bound(A,identity)))))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_1836,c_10423]) ).
cnf(c_10425,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(A),multiply(inverse(greatest_lower_bound(identity,A)),greatest_lower_bound(A,identity)))))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_5599,c_10424]) ).
cnf(c_10426,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,multiply(inverse(A),identity)))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_5294,c_10425]) ).
cnf(c_10427,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,multiply(A,inverse(A)))))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_89,c_10426]) ).
cnf(c_7514,plain,
greatest_lower_bound(identity,multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(A,identity)))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_66,c_10427]) ).
cnf(c_10428,plain,
greatest_lower_bound(A,multiply(inverse(B),greatest_lower_bound(least_upper_bound(C,A),multiply(B,least_upper_bound(C,A))))) = greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(C,A))),
inference(paramod,[status(thm)],[c_3026,c_80]) ).
cnf(c_10274,plain,
greatest_lower_bound(A,multiply(inverse(B),multiply(greatest_lower_bound(identity,B),least_upper_bound(C,A)))) = greatest_lower_bound(A,multiply(inverse(B),least_upper_bound(C,A))),
inference(paramod,[status(thm)],[c_59,c_10428]) ).
cnf(c_10429,plain,
greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,identity))) = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_10274,c_7514]) ).
cnf(c_10430,plain,
identity = multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_1837,c_10429]) ).
cnf(c_10317,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))) = identity,
inference(copy,[status(thm)],[c_10430]) ).
cnf(c_10318,plain,
$false,
inference(resolve,[status(thm)],[c_10317,c_278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP183-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:38:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1604774 was started by sandbox2 on n015,
% 0.09/0.37 % Fri Sep 25 14:38:57 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 83.72/12.00
% 83.72/12.00 % SZS status Unsatisfiable for theBenchmark
% 83.72/12.00
% 83.72/12.00 % Proof 1 at 2.89 (+ 0.62) seconds.
% 83.72/12.00 % Length of proof is 87.
% 83.72/12.00 % Level of proof is 10.
% 83.72/12.00 % Maximum clause weight is 92.000.
% 83.72/12.00 % Given clauses 361.
% 83.72/12.00
% 83.72/12.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------