%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP185-4 : 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 : n019.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 39.58s 17.14s
% Output : CNFRefutation 39.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 17
% Syntax : Number of formulae : 136 ( 136 unt; 0 def)
% Number of atoms : 136 ( 135 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 44 ( 44 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 210 ( 18 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(symmetry_of_glb,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,VAR_1) = greatest_lower_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_glb) ).
cnf(c_4,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_glb]) ).
fof(symmetry_of_lub,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,VAR_1) = least_upper_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_lub) ).
cnf(c_5,plain,
least_upper_bound(A,B) = least_upper_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_lub]) ).
fof(associativity_of_glb,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(greatest_lower_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_glb) ).
cnf(c_6,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_glb]) ).
cnf(c_7,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(associativity_of_lub,axiom,
! [VAR_0,VAR_1,VAR_2] : least_upper_bound(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(least_upper_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_lub) ).
cnf(c_8,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_lub]) ).
cnf(c_9,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(idempotence_of_lub,axiom,
! [VAR_0] : least_upper_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_lub) ).
cnf(c_10,plain,
least_upper_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_lub]) ).
fof(idempotence_of_gld,axiom,
! [VAR_0] : greatest_lower_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_gld) ).
cnf(c_11,plain,
greatest_lower_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_gld]) ).
fof(lub_absorbtion,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,greatest_lower_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',lub_absorbtion) ).
cnf(c_12,plain,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
inference(clausify,[status(thm)],[lub_absorbtion]) ).
fof(glb_absorbtion,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',glb_absorbtion) ).
cnf(c_13,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
inference(clausify,[status(thm)],[glb_absorbtion]) ).
fof(monotony_lub1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_lub1) ).
cnf(c_14,plain,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_lub1]) ).
cnf(c_15,plain,
least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_14]) ).
fof(monotony_glb1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_glb1) ).
cnf(c_16,plain,
multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_glb1]) ).
cnf(c_17,plain,
greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_16]) ).
fof(monotony_lub2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(least_upper_bound(VAR_0,VAR_1),VAR_2) = least_upper_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_lub2) ).
cnf(c_18,plain,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_lub2]) ).
cnf(c_19,plain,
least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B),
inference(copy,[status(thm)],[c_18]) ).
fof(p22b_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',p22b_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[p22b_2]) ).
fof(p22b_3,axiom,
! [VAR_0,VAR_1] : inverse(multiply(VAR_0,VAR_1)) = multiply(inverse(VAR_1),inverse(VAR_0)),
file('theBenchmark.p',p22b_3) ).
cnf(c_24,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(clausify,[status(thm)],[p22b_3]) ).
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_25,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_14871,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_25]) ).
cnf(c_14872,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_14871]) ).
cnf(c_14873,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_14872]) ).
cnf(c_14874,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_14873]) ).
cnf(c_26,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_14874]) ).
cnf(c_14875,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_14876,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_14875]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_14876]) ).
cnf(c_14877,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_31,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_14877]) ).
cnf(c_14878,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_34,plain,
least_upper_bound(A,least_upper_bound(B,A)) = least_upper_bound(B,A),
inference(paramod,[status(thm)],[c_5,c_14878]) ).
cnf(c_14879,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_14879]) ).
cnf(c_38,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
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_42,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_45,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_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_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_14880,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_53,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A),
inference(paramod,[status(thm)],[c_5,c_14880]) ).
cnf(c_14881,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_55,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_5,c_14881]) ).
cnf(c_66,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_14882,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_27]) ).
cnf(c_68,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_23,c_14882]) ).
cnf(c_77,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_23,c_27]) ).
cnf(c_78,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_68,c_15]) ).
cnf(c_14883,plain,
least_upper_bound(multiply(A,B),identity) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_66,c_15]) ).
cnf(c_83,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_5,c_14883]) ).
cnf(c_14884,plain,
least_upper_bound(multiply(A,inverse(B)),identity) = multiply(least_upper_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_66,c_19]) ).
cnf(c_87,plain,
least_upper_bound(identity,multiply(A,inverse(B))) = multiply(least_upper_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_5,c_14884]) ).
cnf(c_95,plain,
greatest_lower_bound(A,least_upper_bound(B,least_upper_bound(C,A))) = A,
inference(paramod,[status(thm)],[c_9,c_42]) ).
cnf(c_103,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_77,c_17]) ).
cnf(c_119,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_103,c_26]) ).
cnf(c_155,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_14885,plain,
greatest_lower_bound(multiply(A,B),least_upper_bound(C,multiply(least_upper_bound(identity,A),B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_52,c_95]) ).
cnf(c_195,plain,
multiply(A,greatest_lower_bound(B,multiply(inverse(A),least_upper_bound(C,multiply(least_upper_bound(identity,A),B))))) = multiply(A,B),
inference(paramod,[status(thm)],[c_103,c_14885]) ).
cnf(c_303,plain,
greatest_lower_bound(least_upper_bound(A,B),least_upper_bound(B,A)) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_34,c_45]) ).
cnf(c_14886,plain,
multiply(inverse(A),least_upper_bound(A,multiply(A,B))) = least_upper_bound(identity,B),
inference(paramod,[status(thm)],[c_78,c_27]) ).
cnf(c_347,plain,
least_upper_bound(identity,A) = multiply(inverse(B),least_upper_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_14886]) ).
cnf(c_14887,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(B,A))) = multiply(inverse(A),A),
inference(paramod,[status(thm)],[c_38,c_46]) ).
cnf(c_387,plain,
least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_2,c_14887]) ).
cnf(c_659,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity,
inference(paramod,[status(thm)],[c_55,c_13]) ).
cnf(c_716,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity,
inference(paramod,[status(thm)],[c_23,c_659]) ).
cnf(c_14888,plain,
least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(A,B),inverse(B))),identity)) = identity,
inference(paramod,[status(thm)],[c_716,c_387]) ).
cnf(c_14889,plain,
least_upper_bound(identity,multiply(multiply(inverse(inverse(B)),inverse(least_upper_bound(A,B))),identity)) = identity,
inference(paramod,[status(thm)],[c_24,c_14888]) ).
cnf(c_14890,plain,
least_upper_bound(identity,multiply(multiply(B,inverse(least_upper_bound(A,B))),identity)) = identity,
inference(paramod,[status(thm)],[c_23,c_14889]) ).
cnf(c_743,plain,
least_upper_bound(identity,multiply(A,inverse(least_upper_bound(B,A)))) = identity,
inference(paramod,[status(thm)],[c_68,c_14890]) ).
cnf(c_1603,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(greatest_lower_bound(B,A)))) = identity,
inference(paramod,[status(thm)],[c_155,c_743]) ).
cnf(c_14891,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_155,c_87]) ).
cnf(c_14892,plain,
identity = multiply(greatest_lower_bound(A,B),inverse(greatest_lower_bound(B,A))),
inference(paramod,[status(thm)],[c_1603,c_14891]) ).
cnf(c_1885,plain,
multiply(greatest_lower_bound(A,B),inverse(greatest_lower_bound(B,A))) = identity,
inference(copy,[status(thm)],[c_14892]) ).
cnf(c_14893,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_303,c_1885]) ).
cnf(c_2258,plain,
multiply(least_upper_bound(A,B),inverse(least_upper_bound(B,A))) = identity,
inference(paramod,[status(thm)],[c_303,c_14893]) ).
cnf(c_14894,plain,
multiply(identity,A) = multiply(least_upper_bound(B,C),multiply(inverse(least_upper_bound(C,B)),A)),
inference(paramod,[status(thm)],[c_2258,c_3]) ).
cnf(c_14895,plain,
A = multiply(least_upper_bound(B,C),multiply(inverse(least_upper_bound(C,B)),A)),
inference(paramod,[status(thm)],[c_1,c_14894]) ).
cnf(c_2272,plain,
multiply(least_upper_bound(A,B),multiply(inverse(least_upper_bound(B,A)),C)) = C,
inference(copy,[status(thm)],[c_14895]) ).
cnf(c_14896,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_347,c_119]) ).
cnf(c_14897,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_103,c_14896]) ).
cnf(c_5536,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_23,c_14897]) ).
cnf(c_14898,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_53,c_5536]) ).
cnf(c_14899,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_52,c_14898]) ).
cnf(c_14900,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_14899]) ).
cnf(c_14901,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_14900]) ).
cnf(c_14902,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_103,c_14901]) ).
cnf(c_14903,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_103,c_14902]) ).
cnf(c_14904,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_23,c_14903]) ).
cnf(c_14905,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_27,c_14904]) ).
cnf(c_11696,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_77,c_14905]) ).
cnf(c_14906,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_2272,c_11696]) ).
cnf(c_13056,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_31,c_14906]) ).
cnf(c_13116,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(inverse(A),least_upper_bound(A,multiply(A,least_upper_bound(a,multiply(least_upper_bound(identity,a),b)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_347,c_13056]) ).
cnf(c_14907,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(inverse(inverse(a)),least_upper_bound(inverse(a),least_upper_bound(identity,multiply(inverse(a),multiply(least_upper_bound(identity,a),b)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_46,c_13116]) ).
cnf(c_14908,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(inverse(a),least_upper_bound(identity,multiply(inverse(a),multiply(least_upper_bound(identity,a),b)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_23,c_14907]) ).
cnf(c_14909,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(identity,least_upper_bound(inverse(a),multiply(inverse(a),multiply(least_upper_bound(identity,a),b)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_31,c_14908]) ).
cnf(c_14067,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(identity,multiply(inverse(a),least_upper_bound(identity,multiply(least_upper_bound(identity,a),b)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_78,c_14909]) ).
cnf(c_14910,plain,
greatest_lower_bound(multiply(a,least_upper_bound(b,inverse(a))),multiply(a,least_upper_bound(identity,multiply(inverse(a),least_upper_bound(identity,multiply(least_upper_bound(identity,a),b)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_83,c_14067]) ).
cnf(c_14911,plain,
greatest_lower_bound(multiply(a,least_upper_bound(identity,multiply(inverse(a),least_upper_bound(identity,multiply(least_upper_bound(identity,a),b))))),multiply(a,least_upper_bound(b,inverse(a)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_4,c_14910]) ).
cnf(c_14912,plain,
multiply(a,greatest_lower_bound(least_upper_bound(identity,multiply(inverse(a),least_upper_bound(identity,multiply(least_upper_bound(identity,a),b)))),multiply(inverse(a),multiply(a,least_upper_bound(b,inverse(a)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_103,c_14911]) ).
cnf(c_14487,plain,
multiply(a,greatest_lower_bound(least_upper_bound(identity,multiply(inverse(a),least_upper_bound(identity,multiply(least_upper_bound(identity,a),b)))),least_upper_bound(b,inverse(a)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_27,c_14912]) ).
cnf(c_14913,plain,
multiply(a,greatest_lower_bound(least_upper_bound(identity,multiply(inverse(a),multiply(least_upper_bound(least_upper_bound(identity,a),inverse(b)),b))),least_upper_bound(b,inverse(a)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_55,c_14487]) ).
cnf(c_14914,plain,
multiply(a,greatest_lower_bound(least_upper_bound(identity,multiply(inverse(a),multiply(least_upper_bound(inverse(b),least_upper_bound(identity,a)),b))),least_upper_bound(b,inverse(a)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_5,c_14913]) ).
cnf(c_14915,plain,
multiply(a,greatest_lower_bound(least_upper_bound(identity,multiply(inverse(a),multiply(least_upper_bound(identity,least_upper_bound(inverse(b),a)),b))),least_upper_bound(b,inverse(a)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_31,c_14914]) ).
cnf(c_14506,plain,
multiply(a,greatest_lower_bound(least_upper_bound(identity,multiply(inverse(a),multiply(least_upper_bound(identity,least_upper_bound(a,inverse(b))),b))),least_upper_bound(b,inverse(a)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_5,c_14915]) ).
cnf(c_14916,plain,
multiply(a,greatest_lower_bound(multiply(inverse(a),least_upper_bound(a,multiply(least_upper_bound(identity,least_upper_bound(a,inverse(b))),b))),least_upper_bound(b,inverse(a)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_46,c_14506]) ).
cnf(c_14917,plain,
multiply(a,multiply(inverse(a),greatest_lower_bound(least_upper_bound(a,multiply(least_upper_bound(identity,least_upper_bound(a,inverse(b))),b)),multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_103,c_14916]) ).
cnf(c_14918,plain,
multiply(a,multiply(inverse(a),greatest_lower_bound(least_upper_bound(a,multiply(least_upper_bound(identity,least_upper_bound(a,inverse(b))),b)),multiply(a,least_upper_bound(b,inverse(a)))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_23,c_14917]) ).
cnf(c_14526,plain,
greatest_lower_bound(least_upper_bound(a,multiply(least_upper_bound(identity,least_upper_bound(a,inverse(b))),b)),multiply(a,least_upper_bound(b,inverse(a)))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_77,c_14918]) ).
cnf(c_14919,plain,
greatest_lower_bound(least_upper_bound(a,multiply(least_upper_bound(identity,least_upper_bound(a,inverse(b))),b)),least_upper_bound(identity,multiply(a,b))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_83,c_14526]) ).
cnf(c_14744,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(a,multiply(least_upper_bound(identity,least_upper_bound(a,inverse(b))),b))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_4,c_14919]) ).
cnf(c_14920,plain,
greatest_lower_bound(multiply(least_upper_bound(a,inverse(b)),b),least_upper_bound(a,multiply(least_upper_bound(identity,least_upper_bound(a,inverse(b))),b))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_55,c_14744]) ).
cnf(c_14921,plain,
multiply(least_upper_bound(a,inverse(b)),greatest_lower_bound(b,multiply(inverse(least_upper_bound(a,inverse(b))),least_upper_bound(a,multiply(least_upper_bound(identity,least_upper_bound(a,inverse(b))),b))))) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_103,c_14920]) ).
cnf(c_14869,plain,
multiply(least_upper_bound(a,inverse(b)),b) != least_upper_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_195,c_14921]) ).
cnf(c_14922,plain,
multiply(least_upper_bound(A,inverse(B)),B) = least_upper_bound(identity,multiply(A,B)),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_14870,plain,
$false,
inference(resolve,[status(thm)],[c_14869,c_14922]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n019.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Fri Sep 25 14:36:27 UTC 2026
% 0.15/5.40 % CPUTime :
% 0.15/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.40 % Process 2983924 was started by sandbox on n019,
% 0.15/5.40 % Fri Sep 25 14:36:27 2026
% 0.15/5.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.40
% 0.15/5.40 % From the command line: assign(max_seconds, 300).
% 39.58/17.14
% 39.58/17.14 % SZS status Unsatisfiable for theBenchmark
% 39.58/17.14
% 39.58/17.14 % Proof 1 at 4.83 (+ 0.79) seconds.
% 39.58/17.14 % Length of proof is 67.
% 39.58/17.14 % Level of proof is 18.
% 39.58/17.14 % Maximum clause weight is 31.000.
% 39.58/17.14 % Given clauses 471.
% 39.58/17.14
% 39.58/17.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------