%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:15 AM UTC 2026
% Result : Unsatisfiable 5.11s 1.15s
% Output : CNFRefutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 15
% Syntax : Number of formulae : 153 ( 153 unt; 0 def)
% Number of atoms : 153 ( 152 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 218 ( 11 sgn 25 !; 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(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(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_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_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(p12x_1,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('theBenchmark.p',p12x_1) ).
cnf(c_22,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
inference(clausify,[status(thm)],[p12x_1]) ).
cnf(c_3041,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(b,c),
inference(paramod,[status(thm)],[c_4,c_22]) ).
cnf(c_3042,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(paramod,[status(thm)],[c_4,c_3041]) ).
cnf(c_23,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(c,a),
inference(copy,[status(thm)],[c_3042]) ).
fof(p12x_2,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('theBenchmark.p',p12x_2) ).
cnf(c_24,plain,
least_upper_bound(a,c) = least_upper_bound(b,c),
inference(clausify,[status(thm)],[p12x_2]) ).
cnf(c_3043,plain,
least_upper_bound(c,a) = least_upper_bound(b,c),
inference(paramod,[status(thm)],[c_5,c_24]) ).
cnf(c_3044,plain,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(paramod,[status(thm)],[c_5,c_3043]) ).
cnf(c_25,plain,
least_upper_bound(c,b) = least_upper_bound(c,a),
inference(copy,[status(thm)],[c_3044]) ).
fof(p12x_3,axiom,
! [VAR_0,VAR_1] : inverse(greatest_lower_bound(VAR_0,VAR_1)) = least_upper_bound(inverse(VAR_0),inverse(VAR_1)),
file('theBenchmark.p',p12x_3) ).
cnf(c_26,plain,
inverse(greatest_lower_bound(A,B)) = least_upper_bound(inverse(A),inverse(B)),
inference(clausify,[status(thm)],[p12x_3]) ).
cnf(c_27,plain,
least_upper_bound(inverse(A),inverse(B)) = inverse(greatest_lower_bound(A,B)),
inference(copy,[status(thm)],[c_26]) ).
fof(p12x_4,axiom,
! [VAR_0,VAR_1] : inverse(least_upper_bound(VAR_0,VAR_1)) = greatest_lower_bound(inverse(VAR_0),inverse(VAR_1)),
file('theBenchmark.p',p12x_4) ).
cnf(c_28,plain,
inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)),
inference(clausify,[status(thm)],[p12x_4]) ).
fof(prove_p12x,axiom,
a != b,
file('theBenchmark.p',prove_p12x) ).
cnf(c_29,plain,
a != b,
inference(clausify,[status(thm)],[prove_p12x]) ).
cnf(c_30,plain,
b != a,
inference(copy,[status(thm)],[c_29]) ).
cnf(c_3045,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3046,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3045]) ).
cnf(c_31,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3046]) ).
cnf(c_3047,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_41,plain,
greatest_lower_bound(A,greatest_lower_bound(B,A)) = greatest_lower_bound(B,A),
inference(paramod,[status(thm)],[c_4,c_3047]) ).
cnf(c_54,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_3048,plain,
greatest_lower_bound(multiply(inverse(A),B),identity) = multiply(inverse(A),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_55,plain,
greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_4,c_3048]) ).
cnf(c_64,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_3049,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(inverse(B),A),B),
inference(paramod,[status(thm)],[c_2,c_21]) ).
cnf(c_66,plain,
multiply(greatest_lower_bound(inverse(A),B),A) = greatest_lower_bound(identity,multiply(B,A)),
inference(copy,[status(thm)],[c_3049]) ).
cnf(c_3050,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_67,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_4,c_3050]) ).
cnf(c_76,plain,
greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_27,c_13]) ).
cnf(c_3051,plain,
inverse(least_upper_bound(c,a)) = greatest_lower_bound(inverse(c),inverse(b)),
inference(paramod,[status(thm)],[c_25,c_28]) ).
cnf(c_3052,plain,
greatest_lower_bound(inverse(c),inverse(a)) = greatest_lower_bound(inverse(c),inverse(b)),
inference(paramod,[status(thm)],[c_28,c_3051]) ).
cnf(c_79,plain,
greatest_lower_bound(inverse(c),inverse(b)) = greatest_lower_bound(inverse(c),inverse(a)),
inference(copy,[status(thm)],[c_3052]) ).
cnf(c_84,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_31]) ).
cnf(c_95,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_31,c_31]) ).
cnf(c_96,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_95,c_84]) ).
cnf(c_100,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_96,c_17]) ).
cnf(c_144,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_95,c_2]) ).
cnf(c_150,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_95,c_31]) ).
cnf(c_3053,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_95,c_96]) ).
cnf(c_3054,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_96,c_3053]) ).
cnf(c_151,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_3054]) ).
cnf(c_214,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(A),B)),C) = multiply(inverse(A),multiply(greatest_lower_bound(A,B),C)),
inference(paramod,[status(thm)],[c_54,c_3]) ).
cnf(c_3055,plain,
multiply(inverse(inverse(A)),greatest_lower_bound(identity,multiply(inverse(A),B))) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_54,c_31]) ).
cnf(c_3056,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),B))) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_151,c_3055]) ).
cnf(c_226,plain,
greatest_lower_bound(A,B) = multiply(A,greatest_lower_bound(identity,multiply(inverse(A),B))),
inference(copy,[status(thm)],[c_3056]) ).
cnf(c_3057,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(inverse(inverse(A)),greatest_lower_bound(inverse(A),B)),
inference(paramod,[status(thm)],[c_151,c_54]) ).
cnf(c_3058,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(inverse(A),B)),
inference(paramod,[status(thm)],[c_151,c_3057]) ).
cnf(c_232,plain,
multiply(A,greatest_lower_bound(inverse(A),B)) = greatest_lower_bound(identity,multiply(A,B)),
inference(copy,[status(thm)],[c_3058]) ).
cnf(c_3059,plain,
identity = multiply(A,multiply(B,inverse(multiply(A,B)))),
inference(paramod,[status(thm)],[c_144,c_3]) ).
cnf(c_233,plain,
multiply(A,multiply(B,inverse(multiply(A,B)))) = identity,
inference(copy,[status(thm)],[c_3059]) ).
cnf(c_3060,plain,
greatest_lower_bound(multiply(A,inverse(B)),identity) = multiply(greatest_lower_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_144,c_21]) ).
cnf(c_236,plain,
greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_4,c_3060]) ).
cnf(c_3061,plain,
greatest_lower_bound(A,inverse(greatest_lower_bound(inverse(A),B))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_151,c_76]) ).
cnf(c_257,plain,
greatest_lower_bound(A,inverse(greatest_lower_bound(inverse(A),B))) = A,
inference(paramod,[status(thm)],[c_151,c_3061]) ).
cnf(c_264,plain,
greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(b),greatest_lower_bound(c,a)),
inference(paramod,[status(thm)],[c_23,c_55]) ).
cnf(c_3062,plain,
multiply(inverse(inverse(A)),greatest_lower_bound(identity,multiply(inverse(A),B))) = greatest_lower_bound(B,A),
inference(paramod,[status(thm)],[c_55,c_31]) ).
cnf(c_3063,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),B))) = greatest_lower_bound(B,A),
inference(paramod,[status(thm)],[c_151,c_3062]) ).
cnf(c_265,plain,
greatest_lower_bound(A,B) = multiply(B,greatest_lower_bound(identity,multiply(inverse(B),A))),
inference(copy,[status(thm)],[c_3063]) ).
cnf(c_3064,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),B)) = multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_41,c_55]) ).
cnf(c_270,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),B)) = identity,
inference(paramod,[status(thm)],[c_2,c_3064]) ).
cnf(c_321,plain,
greatest_lower_bound(A,inverse(multiply(greatest_lower_bound(identity,B),inverse(A)))) = A,
inference(paramod,[status(thm)],[c_64,c_257]) ).
cnf(c_3065,plain,
multiply(inverse(A),identity) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_233,c_31]) ).
cnf(c_3066,plain,
inverse(A) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_96,c_3065]) ).
cnf(c_328,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(copy,[status(thm)],[c_3066]) ).
cnf(c_3067,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_328,c_31]) ).
cnf(c_335,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_3067]) ).
cnf(c_3068,plain,
greatest_lower_bound(A,multiply(inverse(inverse(A)),inverse(greatest_lower_bound(identity,B)))) = A,
inference(paramod,[status(thm)],[c_335,c_321]) ).
cnf(c_341,plain,
greatest_lower_bound(A,multiply(A,inverse(greatest_lower_bound(identity,B)))) = A,
inference(paramod,[status(thm)],[c_151,c_3068]) ).
cnf(c_381,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(c,a)),b)) = identity,
inference(paramod,[status(thm)],[c_23,c_270]) ).
cnf(c_3069,plain,
greatest_lower_bound(A,multiply(A,inverse(multiply(inverse(B),greatest_lower_bound(C,B))))) = A,
inference(paramod,[status(thm)],[c_55,c_341]) ).
cnf(c_3070,plain,
greatest_lower_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(C,B)),inverse(inverse(B))))) = A,
inference(paramod,[status(thm)],[c_335,c_3069]) ).
cnf(c_452,plain,
greatest_lower_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(B,C)),C))) = A,
inference(paramod,[status(thm)],[c_151,c_3070]) ).
cnf(c_3071,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(c)),inverse(b))) = multiply(inverse(inverse(c)),greatest_lower_bound(inverse(c),inverse(a))),
inference(paramod,[status(thm)],[c_79,c_54]) ).
cnf(c_3072,plain,
greatest_lower_bound(identity,multiply(c,inverse(b))) = multiply(inverse(inverse(c)),greatest_lower_bound(inverse(c),inverse(a))),
inference(paramod,[status(thm)],[c_151,c_3071]) ).
cnf(c_3073,plain,
greatest_lower_bound(identity,multiply(c,inverse(b))) = multiply(c,greatest_lower_bound(inverse(c),inverse(a))),
inference(paramod,[status(thm)],[c_151,c_3072]) ).
cnf(c_504,plain,
greatest_lower_bound(identity,multiply(c,inverse(b))) = greatest_lower_bound(identity,multiply(c,inverse(a))),
inference(paramod,[status(thm)],[c_232,c_3073]) ).
cnf(c_3074,plain,
multiply(greatest_lower_bound(inverse(c),inverse(a)),c) = greatest_lower_bound(identity,multiply(inverse(b),c)),
inference(paramod,[status(thm)],[c_79,c_66]) ).
cnf(c_3075,plain,
greatest_lower_bound(identity,multiply(inverse(a),c)) = greatest_lower_bound(identity,multiply(inverse(b),c)),
inference(paramod,[status(thm)],[c_66,c_3074]) ).
cnf(c_506,plain,
greatest_lower_bound(identity,multiply(inverse(a),c)) = multiply(inverse(b),greatest_lower_bound(c,a)),
inference(paramod,[status(thm)],[c_264,c_3075]) ).
cnf(c_512,plain,
greatest_lower_bound(inverse(A),B) = multiply(inverse(A),greatest_lower_bound(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_31,c_100]) ).
cnf(c_3076,plain,
greatest_lower_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))) = multiply(A,identity),
inference(paramod,[status(thm)],[c_381,c_100]) ).
cnf(c_534,plain,
greatest_lower_bound(A,multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))) = A,
inference(paramod,[status(thm)],[c_96,c_3076]) ).
cnf(c_3077,plain,
greatest_lower_bound(A,B) = multiply(A,multiply(greatest_lower_bound(inverse(A),inverse(B)),B)),
inference(paramod,[status(thm)],[c_67,c_226]) ).
cnf(c_3078,plain,
greatest_lower_bound(A,B) = multiply(A,multiply(multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(B)))),B)),
inference(paramod,[status(thm)],[c_512,c_3077]) ).
cnf(c_3079,plain,
greatest_lower_bound(A,B) = multiply(A,multiply(inverse(A),multiply(greatest_lower_bound(identity,multiply(A,inverse(B))),B))),
inference(paramod,[status(thm)],[c_3,c_3078]) ).
cnf(c_779,plain,
greatest_lower_bound(A,B) = multiply(greatest_lower_bound(identity,multiply(A,inverse(B))),B),
inference(paramod,[status(thm)],[c_150,c_3079]) ).
cnf(c_3080,plain,
greatest_lower_bound(c,b) = multiply(a,greatest_lower_bound(identity,multiply(inverse(a),c))),
inference(paramod,[status(thm)],[c_265,c_23]) ).
cnf(c_3081,plain,
greatest_lower_bound(c,a) = multiply(a,greatest_lower_bound(identity,multiply(inverse(a),c))),
inference(paramod,[status(thm)],[c_23,c_3080]) ).
cnf(c_3082,plain,
greatest_lower_bound(c,a) = multiply(a,multiply(inverse(b),greatest_lower_bound(c,a))),
inference(paramod,[status(thm)],[c_506,c_3081]) ).
cnf(c_914,plain,
multiply(a,multiply(inverse(b),greatest_lower_bound(c,a))) = greatest_lower_bound(c,a),
inference(copy,[status(thm)],[c_3082]) ).
cnf(c_3083,plain,
multiply(greatest_lower_bound(identity,multiply(c,inverse(b))),b) = greatest_lower_bound(c,a),
inference(paramod,[status(thm)],[c_779,c_23]) ).
cnf(c_3084,plain,
multiply(greatest_lower_bound(identity,multiply(c,inverse(a))),b) = greatest_lower_bound(c,a),
inference(paramod,[status(thm)],[c_504,c_3083]) ).
cnf(c_3085,plain,
greatest_lower_bound(b,multiply(multiply(c,inverse(a)),b)) = greatest_lower_bound(c,a),
inference(paramod,[status(thm)],[c_64,c_3084]) ).
cnf(c_2274,plain,
greatest_lower_bound(b,multiply(c,multiply(inverse(a),b))) = greatest_lower_bound(c,a),
inference(paramod,[status(thm)],[c_3,c_3085]) ).
cnf(c_3086,plain,
multiply(greatest_lower_bound(identity,multiply(A,inverse(multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))))),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))) = A,
inference(paramod,[status(thm)],[c_779,c_534]) ).
cnf(c_3087,plain,
multiply(greatest_lower_bound(identity,multiply(A,multiply(inverse(multiply(inverse(greatest_lower_bound(c,a)),b)),inverse(A)))),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))) = A,
inference(paramod,[status(thm)],[c_335,c_3086]) ).
cnf(c_3088,plain,
multiply(greatest_lower_bound(identity,multiply(A,multiply(multiply(inverse(b),inverse(inverse(greatest_lower_bound(c,a)))),inverse(A)))),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))) = A,
inference(paramod,[status(thm)],[c_335,c_3087]) ).
cnf(c_3089,plain,
multiply(greatest_lower_bound(identity,multiply(A,multiply(multiply(inverse(b),greatest_lower_bound(c,a)),inverse(A)))),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))) = A,
inference(paramod,[status(thm)],[c_151,c_3088]) ).
cnf(c_2377,plain,
multiply(greatest_lower_bound(identity,multiply(A,multiply(inverse(b),multiply(greatest_lower_bound(c,a),inverse(A))))),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))) = A,
inference(paramod,[status(thm)],[c_3,c_3089]) ).
cnf(c_3090,plain,
multiply(inverse(a),greatest_lower_bound(c,a)) = multiply(inverse(b),greatest_lower_bound(c,a)),
inference(paramod,[status(thm)],[c_914,c_31]) ).
cnf(c_2384,plain,
multiply(inverse(b),greatest_lower_bound(c,a)) = multiply(inverse(a),greatest_lower_bound(c,a)),
inference(copy,[status(thm)],[c_3090]) ).
cnf(c_3091,plain,
greatest_lower_bound(identity,multiply(A,inverse(multiply(A,multiply(inverse(greatest_lower_bound(B,C)),C))))) = multiply(A,inverse(multiply(A,multiply(inverse(greatest_lower_bound(B,C)),C)))),
inference(paramod,[status(thm)],[c_452,c_236]) ).
cnf(c_3092,plain,
greatest_lower_bound(identity,multiply(A,multiply(inverse(multiply(inverse(greatest_lower_bound(B,C)),C)),inverse(A)))) = multiply(A,inverse(multiply(A,multiply(inverse(greatest_lower_bound(B,C)),C)))),
inference(paramod,[status(thm)],[c_335,c_3091]) ).
cnf(c_3093,plain,
greatest_lower_bound(identity,multiply(A,multiply(multiply(inverse(C),inverse(inverse(greatest_lower_bound(B,C)))),inverse(A)))) = multiply(A,inverse(multiply(A,multiply(inverse(greatest_lower_bound(B,C)),C)))),
inference(paramod,[status(thm)],[c_335,c_3092]) ).
cnf(c_3094,plain,
greatest_lower_bound(identity,multiply(A,multiply(multiply(inverse(C),greatest_lower_bound(B,C)),inverse(A)))) = multiply(A,inverse(multiply(A,multiply(inverse(greatest_lower_bound(B,C)),C)))),
inference(paramod,[status(thm)],[c_151,c_3093]) ).
cnf(c_3095,plain,
greatest_lower_bound(identity,multiply(A,multiply(inverse(C),multiply(greatest_lower_bound(B,C),inverse(A))))) = multiply(A,inverse(multiply(A,multiply(inverse(greatest_lower_bound(B,C)),C)))),
inference(paramod,[status(thm)],[c_3,c_3094]) ).
cnf(c_3096,plain,
greatest_lower_bound(identity,multiply(A,multiply(inverse(C),multiply(greatest_lower_bound(B,C),inverse(A))))) = multiply(A,multiply(inverse(multiply(inverse(greatest_lower_bound(B,C)),C)),inverse(A))),
inference(paramod,[status(thm)],[c_335,c_3095]) ).
cnf(c_3097,plain,
greatest_lower_bound(identity,multiply(A,multiply(inverse(C),multiply(greatest_lower_bound(B,C),inverse(A))))) = multiply(A,multiply(multiply(inverse(C),inverse(inverse(greatest_lower_bound(B,C)))),inverse(A))),
inference(paramod,[status(thm)],[c_335,c_3096]) ).
cnf(c_3098,plain,
greatest_lower_bound(identity,multiply(A,multiply(inverse(C),multiply(greatest_lower_bound(B,C),inverse(A))))) = multiply(A,multiply(multiply(inverse(C),greatest_lower_bound(B,C)),inverse(A))),
inference(paramod,[status(thm)],[c_151,c_3097]) ).
cnf(c_2822,plain,
greatest_lower_bound(identity,multiply(A,multiply(inverse(B),multiply(greatest_lower_bound(C,B),inverse(A))))) = multiply(A,multiply(inverse(B),multiply(greatest_lower_bound(C,B),inverse(A)))),
inference(paramod,[status(thm)],[c_3,c_3098]) ).
cnf(c_3099,plain,
greatest_lower_bound(identity,multiply(inverse(b),multiply(c,multiply(inverse(a),b)))) = multiply(inverse(b),greatest_lower_bound(c,a)),
inference(paramod,[status(thm)],[c_2274,c_54]) ).
cnf(c_2930,plain,
greatest_lower_bound(identity,multiply(inverse(b),multiply(c,multiply(inverse(a),b)))) = multiply(inverse(a),greatest_lower_bound(c,a)),
inference(paramod,[status(thm)],[c_2384,c_3099]) ).
cnf(c_3100,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(b),multiply(c,multiply(inverse(a),b)))),A) = multiply(inverse(b),multiply(greatest_lower_bound(c,a),A)),
inference(paramod,[status(thm)],[c_2274,c_214]) ).
cnf(c_3101,plain,
multiply(multiply(inverse(a),greatest_lower_bound(c,a)),A) = multiply(inverse(b),multiply(greatest_lower_bound(c,a),A)),
inference(paramod,[status(thm)],[c_2930,c_3100]) ).
cnf(c_3102,plain,
multiply(inverse(a),multiply(greatest_lower_bound(c,a),A)) = multiply(inverse(b),multiply(greatest_lower_bound(c,a),A)),
inference(paramod,[status(thm)],[c_3,c_3101]) ).
cnf(c_2937,plain,
multiply(inverse(b),multiply(greatest_lower_bound(c,a),A)) = multiply(inverse(a),multiply(greatest_lower_bound(c,a),A)),
inference(copy,[status(thm)],[c_3102]) ).
cnf(c_3103,plain,
multiply(greatest_lower_bound(identity,multiply(A,multiply(inverse(a),multiply(greatest_lower_bound(c,a),inverse(A))))),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))) = A,
inference(paramod,[status(thm)],[c_2937,c_2377]) ).
cnf(c_3104,plain,
multiply(multiply(A,multiply(inverse(a),multiply(greatest_lower_bound(c,a),inverse(A)))),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))) = A,
inference(paramod,[status(thm)],[c_2822,c_3103]) ).
cnf(c_3105,plain,
multiply(A,multiply(multiply(inverse(a),multiply(greatest_lower_bound(c,a),inverse(A))),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b)))) = A,
inference(paramod,[status(thm)],[c_3,c_3104]) ).
cnf(c_3106,plain,
multiply(A,multiply(inverse(a),multiply(multiply(greatest_lower_bound(c,a),inverse(A)),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b))))) = A,
inference(paramod,[status(thm)],[c_3,c_3105]) ).
cnf(c_3107,plain,
multiply(A,multiply(inverse(a),multiply(greatest_lower_bound(c,a),multiply(inverse(A),multiply(A,multiply(inverse(greatest_lower_bound(c,a)),b)))))) = A,
inference(paramod,[status(thm)],[c_3,c_3106]) ).
cnf(c_3108,plain,
multiply(A,multiply(inverse(a),multiply(greatest_lower_bound(c,a),multiply(inverse(greatest_lower_bound(c,a)),b)))) = A,
inference(paramod,[status(thm)],[c_31,c_3107]) ).
cnf(c_2954,plain,
multiply(A,multiply(inverse(a),b)) = A,
inference(paramod,[status(thm)],[c_150,c_3108]) ).
cnf(c_3109,plain,
inverse(inverse(a)) = b,
inference(paramod,[status(thm)],[c_2954,c_31]) ).
cnf(c_3110,plain,
a = b,
inference(paramod,[status(thm)],[c_151,c_3109]) ).
cnf(c_3039,plain,
b = a,
inference(copy,[status(thm)],[c_3110]) ).
cnf(c_3040,plain,
$false,
inference(resolve,[status(thm)],[c_3039,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/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 14:37:57 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 1603005 was started by sandbox on n015,
% 0.09/0.37 % Fri Sep 25 14:37:57 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 5.11/1.15
% 5.11/1.15 % SZS status Unsatisfiable for theBenchmark
% 5.11/1.15
% 5.11/1.15 % Proof 1 at 0.58 (+ 0.18) seconds.
% 5.11/1.15 % Length of proof is 68.
% 5.11/1.15 % Level of proof is 12.
% 5.11/1.15 % Maximum clause weight is 25.000.
% 5.11/1.15 % Given clauses 152.
% 5.11/1.15
% 5.11/1.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------