TSTP Solution File: GRP179-1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP179-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:10:52 EDT 2023
% Result : Unsatisfiable 228.76s 29.19s
% Output : CNFRefutation 231.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 15
% Syntax : Number of formulae : 197 ( 197 unt; 0 def)
% Number of atoms : 197 ( 196 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 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 : 367 (; 367 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] : least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : greatest_lower_bound(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] : multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,Z,X] : multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Y,Z,X] : multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
inverse(least_upper_bound(a,b)) != greatest_lower_bound(inverse(a),inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f21,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f23,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f25,plain,
! [X0] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f26,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f27,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f29,plain,
! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f30,plain,
! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f31,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f32,plain,
inverse(least_upper_bound(a,b)) != greatest_lower_bound(inverse(a),inverse(b)),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f33,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f22]) ).
fof(f39,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X1,X0),X2),
inference(paramodulation,[status(thm)],[f20,f22]) ).
fof(f40,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)),
inference(forward_demodulation,[status(thm)],[f22,f39]) ).
fof(f43,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f25,f22]) ).
fof(f48,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f20,f26]) ).
fof(f51,plain,
! [X0,X1,X2] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f22,f48]) ).
fof(f58,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f65,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2),
inference(paramodulation,[status(thm)],[f27,f22]) ).
fof(f69,plain,
! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X0) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f26,f58]) ).
fof(f70,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f22,f69]) ).
fof(f75,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X1) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f58,f48]) ).
fof(f76,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X1,X0),
inference(forward_demodulation,[status(thm)],[f21,f75]) ).
fof(f191,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(greatest_lower_bound(X1,X0),X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
inference(paramodulation,[status(thm)],[f70,f22]) ).
fof(f192,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X2))) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f22,f191]) ).
fof(f193,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X2))) = greatest_lower_bound(X0,greatest_lower_bound(X1,X2)),
inference(forward_demodulation,[status(thm)],[f22,f192]) ).
fof(f220,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2),
inference(paramodulation,[status(thm)],[f26,f23]) ).
fof(f239,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f23,f58]) ).
fof(f240,plain,
! [X0,X1,X2] : greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,least_upper_bound(X1,X2))) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f272,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f273,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f21,f272]) ).
fof(f278,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f279,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f278]) ).
fof(f289,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X0))),
inference(paramodulation,[status(thm)],[f19,f279]) ).
fof(f290,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f279,f279]) ).
fof(f291,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f279]) ).
fof(f292,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f290,f291]) ).
fof(f297,plain,
! [X0,X1,X2] : multiply(inverse(X0),least_upper_bound(multiply(X0,X1),X2)) = least_upper_bound(X1,multiply(inverse(X0),X2)),
inference(paramodulation,[status(thm)],[f279,f28]) ).
fof(f312,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f279,f290]) ).
fof(f313,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f18,f290]) ).
fof(f314,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f292,f290]) ).
fof(f315,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f292,f314]) ).
fof(f456,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f70,f33]) ).
fof(f457,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X1,greatest_lower_bound(X0,X1))),
inference(forward_demodulation,[status(thm)],[f22,f456]) ).
fof(f458,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X0)),
inference(forward_demodulation,[status(thm)],[f70,f457]) ).
fof(f523,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X2))) = greatest_lower_bound(X0,greatest_lower_bound(X2,X1)),
inference(paramodulation,[status(thm)],[f33,f43]) ).
fof(f524,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X0,greatest_lower_bound(X2,X1)),
inference(forward_demodulation,[status(thm)],[f193,f523]) ).
fof(f748,plain,
! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X2),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f29]) ).
fof(f749,plain,
! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = multiply(X0,greatest_lower_bound(X2,X1)),
inference(forward_demodulation,[status(thm)],[f29,f748]) ).
fof(f767,plain,
! [X0,X1] : multiply(X0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f292,f29]) ).
fof(f773,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f18,f29]) ).
fof(f774,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f20,f773]) ).
fof(f817,plain,
! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f30]) ).
fof(f818,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f30]) ).
fof(f872,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X1,X2),multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f20,f31]) ).
fof(f873,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = multiply(greatest_lower_bound(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f31,f872]) ).
fof(f880,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f31]) ).
fof(f887,plain,
! [X0,X1,X2,X3] : multiply(greatest_lower_bound(X0,multiply(X1,X2)),X3) = greatest_lower_bound(multiply(X0,X3),multiply(X1,multiply(X2,X3))),
inference(paramodulation,[status(thm)],[f19,f31]) ).
fof(f1338,plain,
! [X0,X1] : identity = multiply(inverse(greatest_lower_bound(X0,X1)),greatest_lower_bound(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f749]) ).
fof(f2031,plain,
! [X0] : multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(inverse(X0),identity),
inference(paramodulation,[status(thm)],[f18,f767]) ).
fof(f2032,plain,
! [X0] : multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f20,f2031]) ).
fof(f2185,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X0),multiply(inverse(X0),X1)) = greatest_lower_bound(multiply(inverse(X0),X1),X1),
inference(paramodulation,[status(thm)],[f312,f880]) ).
fof(f2186,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X0),multiply(inverse(X0),X1)) = greatest_lower_bound(X1,multiply(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f20,f2185]) ).
fof(f2187,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X0),multiply(inverse(X0),X1)) = multiply(greatest_lower_bound(identity,inverse(X0)),X1),
inference(forward_demodulation,[status(thm)],[f880,f2186]) ).
fof(f2922,plain,
! [X0] : multiply(inverse(greatest_lower_bound(X0,identity)),greatest_lower_bound(identity,X0)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(X0,identity))),
inference(paramodulation,[status(thm)],[f70,f2032]) ).
fof(f2923,plain,
! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(X0,identity))),
inference(forward_demodulation,[status(thm)],[f1338,f2922]) ).
fof(f2924,plain,
! [X0] : multiply(inverse(greatest_lower_bound(identity,X0)),greatest_lower_bound(identity,X0)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X0))),
inference(paramodulation,[status(thm)],[f43,f2032]) ).
fof(f2925,plain,
! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X0))),
inference(forward_demodulation,[status(thm)],[f18,f2924]) ).
fof(f2930,plain,
! [X0] : multiply(inverse(least_upper_bound(X0,identity)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(X0,identity))),
inference(paramodulation,[status(thm)],[f58,f2032]) ).
fof(f2931,plain,
! [X0] : inverse(least_upper_bound(X0,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X0,identity))),
inference(forward_demodulation,[status(thm)],[f292,f2930]) ).
fof(f2932,plain,
! [X0] : multiply(inverse(least_upper_bound(identity,X0)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X0))),
inference(paramodulation,[status(thm)],[f27,f2032]) ).
fof(f2933,plain,
! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X0))),
inference(forward_demodulation,[status(thm)],[f292,f2932]) ).
fof(f2972,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,inverse(X0)),X1) = multiply(inverse(X0),multiply(greatest_lower_bound(identity,X0),X1)),
inference(paramodulation,[status(thm)],[f2032,f19]) ).
fof(f2977,plain,
! [X0] : inverse(least_upper_bound(X0,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X0))),
inference(paramodulation,[status(thm)],[f21,f2931]) ).
fof(f2978,plain,
! [X0] : inverse(least_upper_bound(X0,identity)) = inverse(least_upper_bound(identity,X0)),
inference(forward_demodulation,[status(thm)],[f2933,f2977]) ).
fof(f3000,plain,
! [X0,X1] : greatest_lower_bound(identity,greatest_lower_bound(X0,inverse(least_upper_bound(X1,identity)))) = greatest_lower_bound(X0,inverse(least_upper_bound(X1,identity))),
inference(paramodulation,[status(thm)],[f2931,f40]) ).
fof(f3129,plain,
! [X0] : least_upper_bound(identity,inverse(least_upper_bound(identity,X0))) = identity,
inference(paramodulation,[status(thm)],[f2933,f26]) ).
fof(f4084,plain,
! [X0,X1] : least_upper_bound(inverse(greatest_lower_bound(X0,identity)),greatest_lower_bound(X1,identity)) = inverse(greatest_lower_bound(X0,identity)),
inference(paramodulation,[status(thm)],[f2923,f51]) ).
fof(f4085,plain,
! [X0] : least_upper_bound(inverse(greatest_lower_bound(X0,identity)),identity) = inverse(greatest_lower_bound(X0,identity)),
inference(paramodulation,[status(thm)],[f2923,f48]) ).
fof(f4086,plain,
! [X0] : least_upper_bound(identity,inverse(greatest_lower_bound(X0,identity))) = inverse(greatest_lower_bound(X0,identity)),
inference(forward_demodulation,[status(thm)],[f21,f4085]) ).
fof(f4092,plain,
! [X0] : least_upper_bound(identity,inverse(greatest_lower_bound(identity,X0))) = inverse(greatest_lower_bound(X0,identity)),
inference(paramodulation,[status(thm)],[f20,f4086]) ).
fof(f4138,plain,
! [X0] : least_upper_bound(identity,inverse(multiply(greatest_lower_bound(identity,X0),identity))) = inverse(greatest_lower_bound(multiply(X0,identity),identity)),
inference(paramodulation,[status(thm)],[f880,f4092]) ).
fof(f4139,plain,
! [X0] : least_upper_bound(identity,inverse(greatest_lower_bound(identity,X0))) = inverse(greatest_lower_bound(multiply(X0,identity),identity)),
inference(forward_demodulation,[status(thm)],[f292,f4138]) ).
fof(f4140,plain,
! [X0] : inverse(greatest_lower_bound(X0,identity)) = inverse(greatest_lower_bound(multiply(X0,identity),identity)),
inference(forward_demodulation,[status(thm)],[f4092,f4139]) ).
fof(f4141,plain,
! [X0] : inverse(greatest_lower_bound(X0,identity)) = inverse(greatest_lower_bound(identity,multiply(X0,identity))),
inference(forward_demodulation,[status(thm)],[f20,f4140]) ).
fof(f4142,plain,
! [X0] : inverse(greatest_lower_bound(X0,identity)) = inverse(multiply(greatest_lower_bound(identity,X0),identity)),
inference(forward_demodulation,[status(thm)],[f880,f4141]) ).
fof(f4143,plain,
! [X0] : inverse(greatest_lower_bound(X0,identity)) = inverse(greatest_lower_bound(identity,X0)),
inference(forward_demodulation,[status(thm)],[f292,f4142]) ).
fof(f4772,plain,
! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f76,f240]) ).
fof(f6147,plain,
! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(identity,X0)),least_upper_bound(X1,identity)) = inverse(least_upper_bound(identity,X0)),
inference(paramodulation,[status(thm)],[f3129,f239]) ).
fof(f6583,plain,
! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,identity),inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)),
inference(paramodulation,[status(thm)],[f20,f6147]) ).
fof(f6771,plain,
! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,identity),inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(identity,X1)),
inference(paramodulation,[status(thm)],[f2978,f6583]) ).
fof(f7163,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X2,X1))) = greatest_lower_bound(X0,least_upper_bound(X2,X1)),
inference(paramodulation,[status(thm)],[f4772,f524]) ).
fof(f7164,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(X1,X2)) = greatest_lower_bound(X0,least_upper_bound(X2,X1)),
inference(forward_demodulation,[status(thm)],[f4772,f7163]) ).
fof(f7176,plain,
! [X0,X1,X2] : greatest_lower_bound(least_upper_bound(X0,X1),greatest_lower_bound(least_upper_bound(X1,X0),X2)) = greatest_lower_bound(X2,least_upper_bound(X1,X0)),
inference(paramodulation,[status(thm)],[f4772,f458]) ).
fof(f7228,plain,
! [X0,X1,X2] : greatest_lower_bound(least_upper_bound(X0,X1),greatest_lower_bound(least_upper_bound(X1,X0),X2)) = greatest_lower_bound(least_upper_bound(X0,X1),X2),
inference(paramodulation,[status(thm)],[f4772,f22]) ).
fof(f7229,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(X1,X2)) = greatest_lower_bound(least_upper_bound(X2,X1),X0),
inference(forward_demodulation,[status(thm)],[f7176,f7228]) ).
fof(f7674,plain,
! [X0] : multiply(inverse(X0),least_upper_bound(identity,X0)) = multiply(least_upper_bound(identity,inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f818,f273]) ).
fof(f7675,plain,
! [X0] : multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(identity,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f292,f7674]) ).
fof(f10788,plain,
! [X0,X1] : greatest_lower_bound(X0,inverse(least_upper_bound(identity,X1))) = greatest_lower_bound(X0,inverse(least_upper_bound(X1,identity))),
inference(paramodulation,[status(thm)],[f6771,f65]) ).
fof(f10899,plain,
! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(identity,X0)),X1) = greatest_lower_bound(X1,inverse(least_upper_bound(X0,identity))),
inference(paramodulation,[status(thm)],[f20,f10788]) ).
fof(f10910,plain,
! [X0,X1] : greatest_lower_bound(X0,inverse(least_upper_bound(identity,X1))) = greatest_lower_bound(inverse(least_upper_bound(X1,identity)),X0),
inference(paramodulation,[status(thm)],[f20,f10788]) ).
fof(f13119,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,greatest_lower_bound(identity,X1))) = greatest_lower_bound(identity,multiply(inverse(multiply(X0,X1)),X0)),
inference(paramodulation,[status(thm)],[f767,f774]) ).
fof(f15796,plain,
! [X0,X1] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),greatest_lower_bound(X1,identity)) = inverse(greatest_lower_bound(identity,X0)),
inference(paramodulation,[status(thm)],[f2925,f51]) ).
fof(f15806,plain,
! [X0,X1] : least_upper_bound(greatest_lower_bound(X0,identity),inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,X1)),
inference(paramodulation,[status(thm)],[f21,f15796]) ).
fof(f16501,plain,
! [X0,X1] : least_upper_bound(greatest_lower_bound(X0,identity),inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(identity,X1)),
inference(paramodulation,[status(thm)],[f4143,f15806]) ).
fof(f17087,plain,
! [X0,X1] : least_upper_bound(X0,inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(X0,inverse(greatest_lower_bound(X1,identity))),
inference(paramodulation,[status(thm)],[f16501,f220]) ).
fof(f17093,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(inverse(greatest_lower_bound(X1,identity)),greatest_lower_bound(X2,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X1)),X0),
inference(paramodulation,[status(thm)],[f16501,f7229]) ).
fof(f17094,plain,
! [X0,X1] : greatest_lower_bound(X0,inverse(greatest_lower_bound(X1,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X1)),X0),
inference(forward_demodulation,[status(thm)],[f4084,f17093]) ).
fof(f17112,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(inverse(greatest_lower_bound(X1,identity)),greatest_lower_bound(X2,identity))) = greatest_lower_bound(X0,inverse(greatest_lower_bound(identity,X1))),
inference(paramodulation,[status(thm)],[f16501,f7164]) ).
fof(f17113,plain,
! [X0,X1] : greatest_lower_bound(X0,inverse(greatest_lower_bound(X1,identity))) = greatest_lower_bound(X0,inverse(greatest_lower_bound(identity,X1))),
inference(forward_demodulation,[status(thm)],[f4084,f17112]) ).
fof(f17197,plain,
! [X0,X1] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),X1) = least_upper_bound(X1,inverse(greatest_lower_bound(X0,identity))),
inference(paramodulation,[status(thm)],[f21,f17087]) ).
fof(f22828,plain,
! [X0] : multiply(greatest_lower_bound(identity,inverse(X0)),inverse(greatest_lower_bound(identity,X0))) = multiply(inverse(X0),identity),
inference(paramodulation,[status(thm)],[f313,f2972]) ).
fof(f22829,plain,
! [X0] : multiply(greatest_lower_bound(identity,inverse(X0)),inverse(greatest_lower_bound(identity,X0))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f292,f22828]) ).
fof(f23163,plain,
! [X0] : multiply(greatest_lower_bound(identity,X0),inverse(greatest_lower_bound(identity,inverse(X0)))) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f315,f22829]) ).
fof(f23164,plain,
! [X0] : multiply(greatest_lower_bound(identity,X0),inverse(greatest_lower_bound(identity,inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f315,f23163]) ).
fof(f23327,plain,
! [X0] : multiply(greatest_lower_bound(X0,identity),inverse(greatest_lower_bound(identity,inverse(X0)))) = X0,
inference(paramodulation,[status(thm)],[f873,f23164]) ).
fof(f23575,plain,
! [X0] : multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,X0)),inverse(greatest_lower_bound(identity,inverse(X0)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X0))),X0),
inference(paramodulation,[status(thm)],[f23164,f880]) ).
fof(f23576,plain,
! [X0] : multiply(greatest_lower_bound(identity,X0),inverse(greatest_lower_bound(identity,inverse(X0)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X0))),X0),
inference(forward_demodulation,[status(thm)],[f43,f23575]) ).
fof(f23577,plain,
! [X0] : X0 = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X0))),X0),
inference(forward_demodulation,[status(thm)],[f23164,f23576]) ).
fof(f23578,plain,
! [X0] : X0 = greatest_lower_bound(X0,inverse(greatest_lower_bound(inverse(X0),identity))),
inference(forward_demodulation,[status(thm)],[f17094,f23577]) ).
fof(f23579,plain,
! [X0] : X0 = greatest_lower_bound(X0,inverse(greatest_lower_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f17113,f23578]) ).
fof(f23580,plain,
! [X0] : multiply(least_upper_bound(identity,greatest_lower_bound(identity,X0)),inverse(greatest_lower_bound(identity,inverse(X0)))) = least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X0))),X0),
inference(paramodulation,[status(thm)],[f23164,f818]) ).
fof(f23581,plain,
! [X0] : multiply(identity,inverse(greatest_lower_bound(identity,inverse(X0)))) = least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X0))),X0),
inference(forward_demodulation,[status(thm)],[f26,f23580]) ).
fof(f23582,plain,
! [X0] : inverse(greatest_lower_bound(identity,inverse(X0))) = least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X0))),X0),
inference(forward_demodulation,[status(thm)],[f17,f23581]) ).
fof(f23583,plain,
! [X0] : inverse(greatest_lower_bound(identity,inverse(X0))) = least_upper_bound(X0,inverse(greatest_lower_bound(inverse(X0),identity))),
inference(forward_demodulation,[status(thm)],[f17197,f23582]) ).
fof(f23584,plain,
! [X0] : inverse(greatest_lower_bound(identity,inverse(X0))) = least_upper_bound(X0,inverse(greatest_lower_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f17087,f23583]) ).
fof(f24101,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,multiply(X1,X2)),inverse(X2)) = greatest_lower_bound(multiply(X0,inverse(X2)),multiply(X1,identity)),
inference(paramodulation,[status(thm)],[f313,f887]) ).
fof(f24102,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,multiply(X1,X2)),inverse(X2)) = greatest_lower_bound(multiply(X0,inverse(X2)),X1),
inference(forward_demodulation,[status(thm)],[f292,f24101]) ).
fof(f26316,plain,
! [X0,X1] : greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X0))),greatest_lower_bound(X0,X1)) = greatest_lower_bound(X1,X0),
inference(paramodulation,[status(thm)],[f23579,f458]) ).
fof(f26317,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X0))),X1)) = greatest_lower_bound(X1,X0),
inference(forward_demodulation,[status(thm)],[f40,f26316]) ).
fof(f36184,plain,
! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,inverse(greatest_lower_bound(identity,inverse(X1))))) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f23584,f240]) ).
fof(f39417,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(inverse(multiply(X1,X0)),X1)),identity),
inference(paramodulation,[status(thm)],[f18,f289]) ).
fof(f39418,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(X1,X0)),X1)),
inference(forward_demodulation,[status(thm)],[f292,f39417]) ).
fof(f39480,plain,
! [X0,X1,X2] : multiply(inverse(X0),X1) = multiply(inverse(multiply(X2,X0)),multiply(X2,X1)),
inference(paramodulation,[status(thm)],[f312,f289]) ).
fof(f39585,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(identity,multiply(inverse(multiply(X1,X0)),X1)),
inference(backward_demodulation,[status(thm)],[f39480,f13119]) ).
fof(f39586,plain,
! [X0,X1] : greatest_lower_bound(identity,inverse(X0)) = greatest_lower_bound(identity,multiply(inverse(multiply(X1,X0)),X1)),
inference(forward_demodulation,[status(thm)],[f2032,f39585]) ).
fof(f39965,plain,
! [X0,X1] : multiply(inverse(X0),inverse(greatest_lower_bound(identity,inverse(multiply(X0,X1))))) = least_upper_bound(X1,multiply(inverse(X0),inverse(greatest_lower_bound(identity,inverse(multiply(X0,X1)))))),
inference(paramodulation,[status(thm)],[f23584,f297]) ).
fof(f45316,plain,
! [X0] : greatest_lower_bound(least_upper_bound(identity,X0),inverse(greatest_lower_bound(inverse(X0),identity))) = least_upper_bound(identity,X0),
inference(paramodulation,[status(thm)],[f4092,f36184]) ).
fof(f45317,plain,
! [X0] : greatest_lower_bound(least_upper_bound(identity,X0),inverse(greatest_lower_bound(identity,inverse(X0)))) = least_upper_bound(identity,X0),
inference(forward_demodulation,[status(thm)],[f17113,f45316]) ).
fof(f52425,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f312,f39418]) ).
fof(f52531,plain,
! [X0,X1] : multiply(greatest_lower_bound(multiply(inverse(multiply(X0,X1)),X0),identity),inverse(greatest_lower_bound(identity,X1))) = multiply(inverse(multiply(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f39418,f23327]) ).
fof(f52532,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X0,X1)),X0)),inverse(greatest_lower_bound(identity,X1))) = multiply(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[status(thm)],[f873,f52531]) ).
fof(f52533,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,inverse(X0)),inverse(greatest_lower_bound(identity,X0))) = multiply(inverse(multiply(X1,X0)),X1),
inference(forward_demodulation,[status(thm)],[f39586,f52532]) ).
fof(f52534,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),X1),
inference(forward_demodulation,[status(thm)],[f22829,f52533]) ).
fof(f52832,plain,
! [X0] : multiply(inverse(least_upper_bound(identity,X0)),X0) = inverse(least_upper_bound(identity,inverse(X0))),
inference(paramodulation,[status(thm)],[f7675,f52425]) ).
fof(f52942,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f315,f52425]) ).
fof(f53158,plain,
! [X0,X1] : multiply(inverse(X0),inverse(greatest_lower_bound(identity,inverse(multiply(X0,X1))))) = least_upper_bound(X1,inverse(multiply(greatest_lower_bound(identity,inverse(multiply(X0,X1))),X0))),
inference(backward_demodulation,[status(thm)],[f52942,f39965]) ).
fof(f53159,plain,
! [X0,X1] : inverse(multiply(greatest_lower_bound(identity,inverse(multiply(X0,X1))),X0)) = least_upper_bound(X1,inverse(multiply(greatest_lower_bound(identity,inverse(multiply(X0,X1))),X0))),
inference(forward_demodulation,[status(thm)],[f52942,f53158]) ).
fof(f53354,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f52942,f312]) ).
fof(f53906,plain,
! [X0] : multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,X0))),X0) = least_upper_bound(X0,inverse(least_upper_bound(identity,inverse(X0)))),
inference(paramodulation,[status(thm)],[f52832,f818]) ).
fof(f53907,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,inverse(least_upper_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f3129,f53906]) ).
fof(f53908,plain,
! [X0] : X0 = least_upper_bound(X0,inverse(least_upper_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f53907]) ).
fof(f54249,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,multiply(X0,X1)),inverse(X1)) = multiply(greatest_lower_bound(identity,inverse(multiply(X0,X1))),X0),
inference(paramodulation,[status(thm)],[f52534,f2187]) ).
fof(f54250,plain,
! [X0,X1] : greatest_lower_bound(multiply(identity,inverse(X0)),X1) = multiply(greatest_lower_bound(identity,inverse(multiply(X1,X0))),X1),
inference(forward_demodulation,[status(thm)],[f24102,f54249]) ).
fof(f54251,plain,
! [X0,X1] : greatest_lower_bound(inverse(X0),X1) = multiply(greatest_lower_bound(identity,inverse(multiply(X1,X0))),X1),
inference(forward_demodulation,[status(thm)],[f17,f54250]) ).
fof(f54335,plain,
! [X0,X1] : inverse(multiply(greatest_lower_bound(identity,inverse(multiply(X0,X1))),X0)) = least_upper_bound(X1,inverse(greatest_lower_bound(inverse(X1),X0))),
inference(backward_demodulation,[status(thm)],[f54251,f53159]) ).
fof(f54336,plain,
! [X0,X1] : inverse(greatest_lower_bound(inverse(X0),X1)) = least_upper_bound(X0,inverse(greatest_lower_bound(inverse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f54251,f54335]) ).
fof(f55112,plain,
! [X0] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(identity,X0))),
inference(paramodulation,[status(thm)],[f315,f53908]) ).
fof(f56210,plain,
! [X0] : greatest_lower_bound(inverse(least_upper_bound(identity,X0)),inverse(X0)) = inverse(least_upper_bound(identity,X0)),
inference(paramodulation,[status(thm)],[f55112,f58]) ).
fof(f56211,plain,
! [X0] : greatest_lower_bound(inverse(X0),inverse(least_upper_bound(X0,identity))) = inverse(least_upper_bound(identity,X0)),
inference(forward_demodulation,[status(thm)],[f10899,f56210]) ).
fof(f66024,plain,
! [X0,X1] : greatest_lower_bound(X0,inverse(greatest_lower_bound(inverse(X0),X1))) = X0,
inference(paramodulation,[status(thm)],[f54336,f27]) ).
fof(f66231,plain,
! [X0,X1] : greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1))) = inverse(X0),
inference(paramodulation,[status(thm)],[f315,f66024]) ).
fof(f66880,plain,
! [X0,X1] : greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X1,X0))) = inverse(X0),
inference(paramodulation,[status(thm)],[f26317,f66231]) ).
fof(f67186,plain,
! [X0] : greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X0)))),inverse(least_upper_bound(identity,X0))) = inverse(inverse(greatest_lower_bound(identity,inverse(X0)))),
inference(paramodulation,[status(thm)],[f45317,f66880]) ).
fof(f67187,plain,
! [X0] : greatest_lower_bound(inverse(least_upper_bound(X0,identity)),inverse(inverse(greatest_lower_bound(identity,inverse(X0))))) = inverse(inverse(greatest_lower_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f10910,f67186]) ).
fof(f67188,plain,
! [X0] : greatest_lower_bound(inverse(least_upper_bound(X0,identity)),greatest_lower_bound(identity,inverse(X0))) = inverse(inverse(greatest_lower_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f315,f67187]) ).
fof(f67189,plain,
! [X0] : greatest_lower_bound(inverse(X0),greatest_lower_bound(identity,inverse(least_upper_bound(X0,identity)))) = inverse(inverse(greatest_lower_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f458,f67188]) ).
fof(f67190,plain,
! [X0] : greatest_lower_bound(identity,greatest_lower_bound(inverse(X0),inverse(least_upper_bound(X0,identity)))) = inverse(inverse(greatest_lower_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f40,f67189]) ).
fof(f67191,plain,
! [X0] : greatest_lower_bound(inverse(X0),inverse(least_upper_bound(X0,identity))) = inverse(inverse(greatest_lower_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f3000,f67190]) ).
fof(f67192,plain,
! [X0] : inverse(least_upper_bound(identity,X0)) = inverse(inverse(greatest_lower_bound(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f56211,f67191]) ).
fof(f67193,plain,
! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f315,f67192]) ).
fof(f96215,plain,
! [X0,X1] : multiply(X0,inverse(least_upper_bound(identity,multiply(X1,X0)))) = inverse(least_upper_bound(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f817,f53354]) ).
fof(f96362,plain,
! [X0,X1] : multiply(X0,greatest_lower_bound(identity,inverse(multiply(X1,X0)))) = greatest_lower_bound(X0,inverse(X1)),
inference(paramodulation,[status(thm)],[f53354,f767]) ).
fof(f96363,plain,
! [X0,X1] : multiply(X0,inverse(least_upper_bound(identity,multiply(X1,X0)))) = greatest_lower_bound(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f67193,f96362]) ).
fof(f96364,plain,
! [X0,X1] : inverse(least_upper_bound(inverse(X0),X1)) = greatest_lower_bound(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f96215,f96363]) ).
fof(f100654,plain,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
inference(paramodulation,[status(thm)],[f315,f96364]) ).
fof(f100931,plain,
inverse(least_upper_bound(a,b)) != inverse(least_upper_bound(a,b)),
inference(backward_demodulation,[status(thm)],[f100654,f32]) ).
fof(f100932,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f100931]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : GRP179-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n009.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 11:24:01 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 228.76/29.19 % Refutation found
% 228.76/29.19 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 228.76/29.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 235.38/30.78 % Elapsed time: 30.234887 seconds
% 235.38/30.78 % CPU time: 216.765558 seconds
% 235.38/30.78 % Memory used: 1.641 GB
%------------------------------------------------------------------------------