%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP185-3 : 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:18 AM UTC 2026
% Result : Unsatisfiable 75.98s 16.11s
% Output : CNFRefutation 75.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 15
% Syntax : Number of formulae : 145 ( 145 unt; 0 def)
% Number of atoms : 145 ( 144 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 37 ( 37 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 258 ( 18 sgn 30 !; 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(prove_p22b,axiom,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
file('theBenchmark.p',prove_p22b) ).
cnf(c_22,plain,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(clausify,[status(thm)],[prove_p22b]) ).
cnf(c_16043,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(paramod,[status(thm)],[c_5,c_22]) ).
cnf(c_16044,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,a),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(paramod,[status(thm)],[c_5,c_16043]) ).
cnf(c_16045,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,a),least_upper_bound(identity,b))) != least_upper_bound(multiply(a,b),identity),
inference(paramod,[status(thm)],[c_5,c_16044]) ).
cnf(c_16046,plain,
greatest_lower_bound(multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),least_upper_bound(identity,multiply(a,b))) != least_upper_bound(multiply(a,b),identity),
inference(paramod,[status(thm)],[c_4,c_16045]) ).
cnf(c_23,plain,
greatest_lower_bound(multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),least_upper_bound(identity,multiply(a,b))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_5,c_16046]) ).
cnf(c_16047,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_16048,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_16047]) ).
cnf(c_24,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_16048]) ).
cnf(c_16049,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(B,least_upper_bound(A,C)),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_28,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(B,least_upper_bound(A,C)),
inference(paramod,[status(thm)],[c_9,c_16049]) ).
cnf(c_16050,plain,
least_upper_bound(least_upper_bound(A,B),B) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_31,plain,
least_upper_bound(A,least_upper_bound(B,A)) = least_upper_bound(B,A),
inference(paramod,[status(thm)],[c_5,c_16050]) ).
cnf(c_16051,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_16051]) ).
cnf(c_35,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
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_39,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_42,plain,
greatest_lower_bound(least_upper_bound(A,B),least_upper_bound(A,least_upper_bound(B,C))) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_9,c_13]) ).
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_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_16052,plain,
least_upper_bound(multiply(A,B),B) = multiply(least_upper_bound(A,identity),B),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_50,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A),
inference(paramod,[status(thm)],[c_5,c_16052]) ).
cnf(c_16053,plain,
least_upper_bound(multiply(A,B),identity) = multiply(least_upper_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_2,c_19]) ).
cnf(c_52,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_5,c_16053]) ).
cnf(c_64,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_24]) ).
cnf(c_74,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_24,c_24]) ).
cnf(c_75,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_74,c_64]) ).
cnf(c_76,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_75,c_2]) ).
cnf(c_77,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_75,c_15]) ).
cnf(c_86,plain,
greatest_lower_bound(A,least_upper_bound(B,least_upper_bound(C,A))) = A,
inference(paramod,[status(thm)],[c_9,c_39]) ).
cnf(c_16054,plain,
least_upper_bound(A,multiply(B,least_upper_bound(C,D))) = least_upper_bound(multiply(B,C),least_upper_bound(A,multiply(B,D))),
inference(paramod,[status(thm)],[c_15,c_28]) ).
cnf(c_103,plain,
least_upper_bound(multiply(A,B),least_upper_bound(C,multiply(A,D))) = least_upper_bound(C,multiply(A,least_upper_bound(B,D))),
inference(copy,[status(thm)],[c_16054]) ).
cnf(c_16055,plain,
least_upper_bound(A,multiply(least_upper_bound(B,C),D)) = least_upper_bound(multiply(B,D),least_upper_bound(A,multiply(C,D))),
inference(paramod,[status(thm)],[c_19,c_28]) ).
cnf(c_104,plain,
least_upper_bound(multiply(A,B),least_upper_bound(C,multiply(D,B))) = least_upper_bound(C,multiply(least_upper_bound(A,D),B)),
inference(copy,[status(thm)],[c_16055]) ).
cnf(c_107,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_74,c_2]) ).
cnf(c_112,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_74,c_24]) ).
cnf(c_16056,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_74,c_75]) ).
cnf(c_16057,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_75,c_16056]) ).
cnf(c_113,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_16057]) ).
cnf(c_16058,plain,
identity = multiply(A,multiply(B,inverse(multiply(A,B)))),
inference(paramod,[status(thm)],[c_107,c_3]) ).
cnf(c_114,plain,
multiply(A,multiply(B,inverse(multiply(A,B)))) = identity,
inference(copy,[status(thm)],[c_16058]) ).
cnf(c_16059,plain,
least_upper_bound(multiply(A,B),identity) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_107,c_15]) ).
cnf(c_116,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_5,c_16059]) ).
cnf(c_16060,plain,
least_upper_bound(multiply(A,inverse(B)),identity) = multiply(least_upper_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_107,c_19]) ).
cnf(c_120,plain,
least_upper_bound(identity,multiply(A,inverse(B))) = multiply(least_upper_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_5,c_16060]) ).
cnf(c_124,plain,
least_upper_bound(multiply(A,B),C) = multiply(A,least_upper_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_112,c_15]) ).
cnf(c_125,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_112,c_17]) ).
cnf(c_16061,plain,
multiply(A,least_upper_bound(B,multiply(inverse(A),least_upper_bound(C,multiply(D,B))))) = least_upper_bound(C,multiply(least_upper_bound(A,D),B)),
inference(paramod,[status(thm)],[c_124,c_104]) ).
cnf(c_132,plain,
least_upper_bound(A,multiply(least_upper_bound(B,C),D)) = multiply(B,least_upper_bound(D,multiply(inverse(B),least_upper_bound(A,multiply(C,D))))),
inference(copy,[status(thm)],[c_16061]) ).
cnf(c_16062,plain,
multiply(A,least_upper_bound(B,multiply(inverse(A),least_upper_bound(C,multiply(A,D))))) = least_upper_bound(C,multiply(A,least_upper_bound(B,D))),
inference(paramod,[status(thm)],[c_124,c_103]) ).
cnf(c_133,plain,
least_upper_bound(A,multiply(B,least_upper_bound(C,D))) = multiply(B,least_upper_bound(C,multiply(inverse(B),least_upper_bound(A,multiply(B,D))))),
inference(copy,[status(thm)],[c_16062]) ).
cnf(c_143,plain,
multiply(least_upper_bound(identity,a),greatest_lower_bound(least_upper_bound(identity,b),multiply(inverse(least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,b))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_125,c_23]) ).
cnf(c_151,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_16063,plain,
multiply(inverse(A),identity) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_114,c_24]) ).
cnf(c_16064,plain,
inverse(A) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_75,c_16063]) ).
cnf(c_180,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(copy,[status(thm)],[c_16064]) ).
cnf(c_16065,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_180,c_24]) ).
cnf(c_184,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_16065]) ).
cnf(c_295,plain,
greatest_lower_bound(least_upper_bound(A,B),least_upper_bound(B,A)) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_31,c_42]) ).
cnf(c_364,plain,
least_upper_bound(identity,A) = multiply(inverse(B),least_upper_bound(B,multiply(B,A))),
inference(paramod,[status(thm)],[c_24,c_43]) ).
cnf(c_16066,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(B,A))) = multiply(inverse(A),A),
inference(paramod,[status(thm)],[c_35,c_43]) ).
cnf(c_366,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_2,c_16066]) ).
cnf(c_16067,plain,
greatest_lower_bound(multiply(A,B),least_upper_bound(C,multiply(A,least_upper_bound(identity,B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_77,c_86]) ).
cnf(c_552,plain,
multiply(A,greatest_lower_bound(B,multiply(inverse(A),least_upper_bound(C,multiply(A,least_upper_bound(identity,B)))))) = multiply(A,B),
inference(paramod,[status(thm)],[c_125,c_16067]) ).
cnf(c_676,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity,
inference(paramod,[status(thm)],[c_52,c_13]) ).
cnf(c_735,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity,
inference(paramod,[status(thm)],[c_113,c_676]) ).
cnf(c_16068,plain,
least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(A,B),inverse(B))),identity)) = identity,
inference(paramod,[status(thm)],[c_735,c_366]) ).
cnf(c_16069,plain,
least_upper_bound(identity,multiply(multiply(inverse(inverse(B)),inverse(least_upper_bound(A,B))),identity)) = identity,
inference(paramod,[status(thm)],[c_184,c_16068]) ).
cnf(c_16070,plain,
least_upper_bound(identity,multiply(multiply(B,inverse(least_upper_bound(A,B))),identity)) = identity,
inference(paramod,[status(thm)],[c_113,c_16069]) ).
cnf(c_762,plain,
least_upper_bound(identity,multiply(A,inverse(least_upper_bound(B,A)))) = identity,
inference(paramod,[status(thm)],[c_75,c_16070]) ).
cnf(c_1462,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(greatest_lower_bound(B,A)))) = identity,
inference(paramod,[status(thm)],[c_151,c_762]) ).
cnf(c_16071,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(greatest_lower_bound(B,A)))) = multiply(greatest_lower_bound(A,B),inverse(greatest_lower_bound(B,A))),
inference(paramod,[status(thm)],[c_151,c_120]) ).
cnf(c_16072,plain,
identity = multiply(greatest_lower_bound(A,B),inverse(greatest_lower_bound(B,A))),
inference(paramod,[status(thm)],[c_1462,c_16071]) ).
cnf(c_2907,plain,
multiply(greatest_lower_bound(A,B),inverse(greatest_lower_bound(B,A))) = identity,
inference(copy,[status(thm)],[c_16072]) ).
cnf(c_16073,plain,
multiply(least_upper_bound(A,B),inverse(greatest_lower_bound(least_upper_bound(B,A),least_upper_bound(A,B)))) = identity,
inference(paramod,[status(thm)],[c_295,c_2907]) ).
cnf(c_2961,plain,
multiply(least_upper_bound(A,B),inverse(least_upper_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_295,c_16073]) ).
cnf(c_16074,plain,
multiply(identity,A) = multiply(least_upper_bound(B,C),multiply(inverse(least_upper_bound(C,B)),A)),
inference(paramod,[status(thm)],[c_2961,c_3]) ).
cnf(c_16075,plain,
A = multiply(least_upper_bound(B,C),multiply(inverse(least_upper_bound(C,B)),A)),
inference(paramod,[status(thm)],[c_1,c_16074]) ).
cnf(c_2962,plain,
multiply(least_upper_bound(A,B),multiply(inverse(least_upper_bound(B,A)),C)) = C,
inference(copy,[status(thm)],[c_16075]) ).
cnf(c_16076,plain,
multiply(least_upper_bound(identity,a),greatest_lower_bound(multiply(inverse(A),least_upper_bound(A,multiply(A,b))),multiply(inverse(least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,b))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_364,c_143]) ).
cnf(c_16077,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(A),greatest_lower_bound(least_upper_bound(A,multiply(A,b)),multiply(inverse(inverse(A)),multiply(inverse(least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_125,c_16076]) ).
cnf(c_5199,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(A),greatest_lower_bound(least_upper_bound(A,multiply(A,b)),multiply(A,multiply(inverse(least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_113,c_16077]) ).
cnf(c_16078,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),greatest_lower_bound(least_upper_bound(least_upper_bound(A,identity),least_upper_bound(b,multiply(A,b))),multiply(least_upper_bound(A,identity),multiply(inverse(least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_50,c_5199]) ).
cnf(c_16079,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),greatest_lower_bound(least_upper_bound(least_upper_bound(A,identity),multiply(least_upper_bound(identity,A),b)),multiply(least_upper_bound(A,identity),multiply(inverse(least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_49,c_16078]) ).
cnf(c_16080,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),greatest_lower_bound(least_upper_bound(A,least_upper_bound(identity,multiply(least_upper_bound(identity,A),b))),multiply(least_upper_bound(A,identity),multiply(inverse(least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_9,c_16079]) ).
cnf(c_16081,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),greatest_lower_bound(multiply(least_upper_bound(A,identity),multiply(inverse(least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,b)))),least_upper_bound(A,least_upper_bound(identity,multiply(least_upper_bound(identity,A),b)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_4,c_16080]) ).
cnf(c_16082,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),multiply(least_upper_bound(A,identity),greatest_lower_bound(multiply(inverse(least_upper_bound(identity,a)),least_upper_bound(identity,multiply(a,b))),multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(A,least_upper_bound(identity,multiply(least_upper_bound(identity,A),b)))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_125,c_16081]) ).
cnf(c_16083,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),multiply(least_upper_bound(A,identity),multiply(inverse(least_upper_bound(identity,a)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(inverse(inverse(least_upper_bound(identity,a))),multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(A,least_upper_bound(identity,multiply(least_upper_bound(identity,A),b)))))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_125,c_16082]) ).
cnf(c_16084,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),multiply(least_upper_bound(A,identity),multiply(inverse(least_upper_bound(identity,a)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(A,least_upper_bound(identity,multiply(least_upper_bound(identity,A),b)))))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_113,c_16083]) ).
cnf(c_16085,plain,
multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(identity,a)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(A,least_upper_bound(identity,multiply(least_upper_bound(identity,A),b)))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_24,c_16084]) ).
cnf(c_12110,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,a),multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(A,least_upper_bound(identity,multiply(least_upper_bound(identity,A),b)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_112,c_16085]) ).
cnf(c_16086,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(a,least_upper_bound(identity,multiply(least_upper_bound(identity,a),b)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_2962,c_12110]) ).
cnf(c_13981,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,least_upper_bound(a,multiply(least_upper_bound(identity,a),b)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_28,c_16086]) ).
cnf(c_16087,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(identity,least_upper_bound(b,multiply(inverse(identity),least_upper_bound(a,multiply(a,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_132,c_13981]) ).
cnf(c_16088,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(identity,least_upper_bound(b,multiply(identity,least_upper_bound(a,multiply(a,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_76,c_16087]) ).
cnf(c_16089,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(identity,least_upper_bound(b,multiply(identity,multiply(a,least_upper_bound(identity,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_77,c_16088]) ).
cnf(c_16090,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(identity,least_upper_bound(b,multiply(a,least_upper_bound(identity,b)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_1,c_16089]) ).
cnf(c_14050,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,least_upper_bound(b,multiply(a,least_upper_bound(identity,b))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_1,c_16090]) ).
cnf(c_14063,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(inverse(A),least_upper_bound(A,multiply(A,least_upper_bound(b,multiply(a,least_upper_bound(identity,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_364,c_14050]) ).
cnf(c_16091,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(inverse(A),multiply(A,least_upper_bound(b,multiply(inverse(A),least_upper_bound(A,multiply(A,multiply(a,least_upper_bound(identity,b))))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_133,c_14063]) ).
cnf(c_14945,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(b,multiply(inverse(A),least_upper_bound(A,multiply(A,multiply(a,least_upper_bound(identity,b))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_24,c_16091]) ).
cnf(c_16092,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(b,multiply(inverse(inverse(a)),least_upper_bound(inverse(a),least_upper_bound(identity,b))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_24,c_14945]) ).
cnf(c_16093,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(b,multiply(a,least_upper_bound(inverse(a),least_upper_bound(identity,b))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_113,c_16092]) ).
cnf(c_16094,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(b,multiply(a,least_upper_bound(identity,least_upper_bound(inverse(a),b))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_28,c_16093]) ).
cnf(c_16001,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(b,multiply(a,least_upper_bound(identity,least_upper_bound(b,inverse(a)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_5,c_16094]) ).
cnf(c_16095,plain,
greatest_lower_bound(multiply(a,least_upper_bound(b,inverse(a))),least_upper_bound(b,multiply(a,least_upper_bound(identity,least_upper_bound(b,inverse(a)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_116,c_16001]) ).
cnf(c_16096,plain,
multiply(a,greatest_lower_bound(least_upper_bound(b,inverse(a)),multiply(inverse(a),least_upper_bound(b,multiply(a,least_upper_bound(identity,least_upper_bound(b,inverse(a)))))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_125,c_16095]) ).
cnf(c_16041,plain,
multiply(a,least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_552,c_16096]) ).
cnf(c_16097,plain,
multiply(A,least_upper_bound(B,inverse(A))) = least_upper_bound(identity,multiply(A,B)),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_16042,plain,
$false,
inference(resolve,[status(thm)],[c_16041,c_16097]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.43 % Computer : n006.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Fri Sep 25 14:35:50 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.44 % Process 3123857 was started by sandbox on n006,
% 0.17/5.44 % Fri Sep 25 14:35:50 2026
% 0.17/5.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.44
% 0.17/5.44 % From the command line: assign(max_seconds, 300).
% 75.98/16.11
% 75.98/16.11 % given #500 (T,wt=12): 3852 greatest_lower_bound(A,B) = multiply(greatest_lower_bound(identity,multiply(A,inverse(B))),B). [para(59(a,1),125(a,2,2)),rewrite([75(2),1010(4),3(8),112(9)])].
% 75.98/16.11
% 75.98/16.11 % SZS status Unsatisfiable for theBenchmark
% 75.98/16.11
% 75.98/16.11 % Proof 1 at 8.86 (+ 1.67) seconds.
% 75.98/16.11 % Length of proof is 75.
% 75.98/16.11 % Level of proof is 18.
% 75.98/16.11 % Maximum clause weight is 31.000.
% 75.98/16.11 % Given clauses 515.
% 75.98/16.11
% 75.98/16.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------