TSTP Solution File: GRP180-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP180-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n016.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 : Thu Aug 31 01:17:34 EDT 2023
% Result : Unsatisfiable 70.05s 9.24s
% Output : Proof 70.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP180-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 03:12:45 EDT 2023
% 0.12/0.33 % CPUTime :
% 70.05/9.24 Command-line arguments: --flatten
% 70.05/9.24
% 70.05/9.24 % SZS status Unsatisfiable
% 70.05/9.24
% 70.47/9.26 % SZS output start Proof
% 70.47/9.26 Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 70.47/9.26 Axiom 2 (idempotence_of_gld): greatest_lower_bound(X, X) = X.
% 70.47/9.26 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 70.47/9.26 Axiom 4 (left_identity): multiply(identity, X) = X.
% 70.47/9.26 Axiom 5 (left_inverse): multiply(inverse(X), X) = identity.
% 70.47/9.26 Axiom 6 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 70.47/9.26 Axiom 7 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 70.47/9.26 Axiom 8 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 70.47/9.26 Axiom 9 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 70.47/9.26 Axiom 10 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 70.47/9.26 Axiom 11 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 70.47/9.26 Axiom 12 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 70.47/9.26 Axiom 13 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 70.47/9.26 Axiom 14 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 70.47/9.26
% 70.47/9.26 Lemma 15: multiply(inverse(X), multiply(X, Y)) = Y.
% 70.47/9.26 Proof:
% 70.47/9.26 multiply(inverse(X), multiply(X, Y))
% 70.47/9.26 = { by axiom 10 (associativity) R->L }
% 70.47/9.26 multiply(multiply(inverse(X), X), Y)
% 70.47/9.26 = { by axiom 5 (left_inverse) }
% 70.47/9.27 multiply(identity, Y)
% 70.47/9.27 = { by axiom 4 (left_identity) }
% 70.47/9.27 Y
% 70.47/9.27
% 70.47/9.27 Lemma 16: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(inverse(inverse(X)), Y)
% 70.47/9.27 = { by lemma 15 R->L }
% 70.47/9.27 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 70.47/9.27 = { by lemma 15 }
% 70.47/9.27 multiply(X, Y)
% 70.47/9.27
% 70.47/9.27 Lemma 17: multiply(inverse(inverse(X)), identity) = X.
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(inverse(inverse(X)), identity)
% 70.47/9.27 = { by axiom 5 (left_inverse) R->L }
% 70.47/9.27 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 70.47/9.27 = { by lemma 15 }
% 70.47/9.27 X
% 70.47/9.27
% 70.47/9.27 Lemma 18: multiply(X, identity) = X.
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(X, identity)
% 70.47/9.27 = { by lemma 16 R->L }
% 70.47/9.27 multiply(inverse(inverse(X)), identity)
% 70.47/9.27 = { by lemma 17 }
% 70.47/9.27 X
% 70.47/9.27
% 70.47/9.27 Lemma 19: inverse(inverse(X)) = X.
% 70.47/9.27 Proof:
% 70.47/9.27 inverse(inverse(X))
% 70.47/9.27 = { by lemma 18 R->L }
% 70.47/9.27 multiply(inverse(inverse(X)), identity)
% 70.47/9.27 = { by lemma 17 }
% 70.47/9.27 X
% 70.47/9.27
% 70.47/9.27 Lemma 20: multiply(X, inverse(X)) = identity.
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(X, inverse(X))
% 70.47/9.27 = { by lemma 16 R->L }
% 70.47/9.27 multiply(inverse(inverse(X)), inverse(X))
% 70.47/9.27 = { by axiom 5 (left_inverse) }
% 70.47/9.27 identity
% 70.47/9.27
% 70.47/9.27 Lemma 21: multiply(X, multiply(Y, inverse(multiply(X, Y)))) = identity.
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(X, multiply(Y, inverse(multiply(X, Y))))
% 70.47/9.27 = { by axiom 10 (associativity) R->L }
% 70.47/9.27 multiply(multiply(X, Y), inverse(multiply(X, Y)))
% 70.47/9.27 = { by lemma 20 }
% 70.47/9.27 identity
% 70.47/9.27
% 70.47/9.27 Lemma 22: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(X, inverse(multiply(Y, X)))
% 70.47/9.27 = { by lemma 15 R->L }
% 70.47/9.27 multiply(inverse(Y), multiply(Y, multiply(X, inverse(multiply(Y, X)))))
% 70.47/9.27 = { by lemma 21 }
% 70.47/9.27 multiply(inverse(Y), identity)
% 70.47/9.27 = { by lemma 18 }
% 70.47/9.27 inverse(Y)
% 70.47/9.27
% 70.47/9.27 Lemma 23: multiply(inverse(X), inverse(Y)) = inverse(multiply(Y, X)).
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(inverse(X), inverse(Y))
% 70.47/9.27 = { by lemma 22 R->L }
% 70.47/9.27 multiply(inverse(X), multiply(X, inverse(multiply(Y, X))))
% 70.47/9.27 = { by lemma 15 }
% 70.47/9.27 inverse(multiply(Y, X))
% 70.47/9.27
% 70.47/9.27 Lemma 24: multiply(X, multiply(inverse(X), Y)) = Y.
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(X, multiply(inverse(X), Y))
% 70.47/9.27 = { by lemma 16 R->L }
% 70.47/9.27 multiply(inverse(inverse(X)), multiply(inverse(X), Y))
% 70.47/9.27 = { by lemma 15 }
% 70.47/9.27 Y
% 70.47/9.27
% 70.47/9.27 Lemma 25: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 70.47/9.27 Proof:
% 70.47/9.27 inverse(multiply(X, inverse(Y)))
% 70.47/9.27 = { by lemma 24 R->L }
% 70.47/9.27 multiply(Y, multiply(inverse(Y), inverse(multiply(X, inverse(Y)))))
% 70.47/9.27 = { by lemma 22 }
% 70.47/9.27 multiply(Y, inverse(X))
% 70.47/9.27
% 70.47/9.27 Lemma 26: greatest_lower_bound(X, least_upper_bound(Y, X)) = X.
% 70.47/9.27 Proof:
% 70.47/9.27 greatest_lower_bound(X, least_upper_bound(Y, X))
% 70.47/9.27 = { by axiom 1 (symmetry_of_lub) R->L }
% 70.47/9.27 greatest_lower_bound(X, least_upper_bound(X, Y))
% 70.47/9.27 = { by axiom 8 (glb_absorbtion) }
% 70.47/9.27 X
% 70.47/9.27
% 70.47/9.27 Lemma 27: least_upper_bound(X, greatest_lower_bound(Y, X)) = X.
% 70.47/9.27 Proof:
% 70.47/9.27 least_upper_bound(X, greatest_lower_bound(Y, X))
% 70.47/9.27 = { by axiom 3 (symmetry_of_glb) R->L }
% 70.47/9.27 least_upper_bound(X, greatest_lower_bound(X, Y))
% 70.47/9.27 = { by axiom 6 (lub_absorbtion) }
% 70.47/9.27 X
% 70.47/9.27
% 70.47/9.27 Lemma 28: multiply(inverse(X), greatest_lower_bound(X, Y)) = greatest_lower_bound(identity, multiply(inverse(X), Y)).
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(inverse(X), greatest_lower_bound(X, Y))
% 70.47/9.27 = { by axiom 13 (monotony_glb1) }
% 70.47/9.27 greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 70.47/9.27 = { by axiom 5 (left_inverse) }
% 70.47/9.27 greatest_lower_bound(identity, multiply(inverse(X), Y))
% 70.47/9.27
% 70.47/9.27 Lemma 29: multiply(inverse(multiply(inverse(Y), X)), Z) = multiply(inverse(X), multiply(Y, Z)).
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(inverse(multiply(inverse(Y), X)), Z)
% 70.47/9.27 = { by lemma 15 R->L }
% 70.47/9.27 multiply(inverse(X), multiply(X, multiply(inverse(multiply(inverse(Y), X)), Z)))
% 70.47/9.27 = { by lemma 15 R->L }
% 70.47/9.27 multiply(inverse(X), multiply(inverse(inverse(Y)), multiply(inverse(Y), multiply(X, multiply(inverse(multiply(inverse(Y), X)), Z)))))
% 70.47/9.27 = { by axiom 10 (associativity) R->L }
% 70.47/9.27 multiply(inverse(X), multiply(inverse(inverse(Y)), multiply(multiply(inverse(Y), X), multiply(inverse(multiply(inverse(Y), X)), Z))))
% 70.47/9.27 = { by lemma 16 }
% 70.47/9.27 multiply(inverse(X), multiply(Y, multiply(multiply(inverse(Y), X), multiply(inverse(multiply(inverse(Y), X)), Z))))
% 70.47/9.27 = { by lemma 24 }
% 70.47/9.27 multiply(inverse(X), multiply(Y, Z))
% 70.47/9.27
% 70.47/9.27 Lemma 30: greatest_lower_bound(multiply(inverse(greatest_lower_bound(X, Y)), Y), multiply(inverse(greatest_lower_bound(X, Y)), X)) = identity.
% 70.47/9.27 Proof:
% 70.47/9.27 greatest_lower_bound(multiply(inverse(greatest_lower_bound(X, Y)), Y), multiply(inverse(greatest_lower_bound(X, Y)), X))
% 70.47/9.27 = { by axiom 13 (monotony_glb1) R->L }
% 70.47/9.27 multiply(inverse(greatest_lower_bound(X, Y)), greatest_lower_bound(Y, X))
% 70.47/9.27 = { by axiom 3 (symmetry_of_glb) }
% 70.47/9.27 multiply(inverse(greatest_lower_bound(X, Y)), greatest_lower_bound(X, Y))
% 70.47/9.27 = { by axiom 5 (left_inverse) }
% 70.47/9.27 identity
% 70.47/9.27
% 70.47/9.27 Lemma 31: multiply(inverse(multiply(X, multiply(inverse(greatest_lower_bound(X, Y)), Y))), Y) = inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)).
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(inverse(multiply(X, multiply(inverse(greatest_lower_bound(X, Y)), Y))), Y)
% 70.47/9.27 = { by lemma 23 R->L }
% 70.47/9.27 multiply(multiply(inverse(multiply(inverse(greatest_lower_bound(X, Y)), Y)), inverse(X)), Y)
% 70.47/9.27 = { by lemma 29 }
% 70.47/9.27 multiply(multiply(inverse(Y), multiply(greatest_lower_bound(X, Y), inverse(X))), Y)
% 70.47/9.27 = { by axiom 14 (monotony_glb2) }
% 70.47/9.27 multiply(multiply(inverse(Y), greatest_lower_bound(multiply(X, inverse(X)), multiply(Y, inverse(X)))), Y)
% 70.47/9.27 = { by lemma 20 }
% 70.47/9.27 multiply(multiply(inverse(Y), greatest_lower_bound(identity, multiply(Y, inverse(X)))), Y)
% 70.47/9.27 = { by axiom 3 (symmetry_of_glb) R->L }
% 70.47/9.27 multiply(multiply(inverse(Y), greatest_lower_bound(multiply(Y, inverse(X)), identity)), Y)
% 70.47/9.27 = { by axiom 13 (monotony_glb1) }
% 70.47/9.27 multiply(greatest_lower_bound(multiply(inverse(Y), multiply(Y, inverse(X))), multiply(inverse(Y), identity)), Y)
% 70.47/9.27 = { by lemma 15 }
% 70.47/9.27 multiply(greatest_lower_bound(inverse(X), multiply(inverse(Y), identity)), Y)
% 70.47/9.27 = { by lemma 18 }
% 70.47/9.27 multiply(greatest_lower_bound(inverse(X), inverse(Y)), Y)
% 70.47/9.27 = { by axiom 3 (symmetry_of_glb) R->L }
% 70.47/9.27 multiply(greatest_lower_bound(inverse(Y), inverse(X)), Y)
% 70.47/9.27 = { by axiom 14 (monotony_glb2) }
% 70.47/9.27 greatest_lower_bound(multiply(inverse(Y), Y), multiply(inverse(X), Y))
% 70.47/9.27 = { by axiom 5 (left_inverse) }
% 70.47/9.27 greatest_lower_bound(identity, multiply(inverse(X), Y))
% 70.47/9.27 = { by axiom 2 (idempotence_of_gld) R->L }
% 70.47/9.27 greatest_lower_bound(greatest_lower_bound(identity, identity), multiply(inverse(X), Y))
% 70.47/9.27 = { by axiom 9 (associativity_of_glb) R->L }
% 70.47/9.27 greatest_lower_bound(identity, greatest_lower_bound(identity, multiply(inverse(X), Y)))
% 70.47/9.27 = { by lemma 28 R->L }
% 70.47/9.27 greatest_lower_bound(identity, multiply(inverse(X), greatest_lower_bound(X, Y)))
% 70.47/9.27 = { by lemma 18 R->L }
% 70.47/9.27 greatest_lower_bound(identity, multiply(inverse(X), multiply(greatest_lower_bound(X, Y), identity)))
% 70.47/9.27 = { by lemma 21 R->L }
% 70.47/9.27 greatest_lower_bound(identity, multiply(inverse(X), multiply(greatest_lower_bound(X, Y), multiply(inverse(greatest_lower_bound(X, Y)), multiply(X, inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)))))))
% 70.47/9.27 = { by lemma 24 }
% 70.47/9.27 greatest_lower_bound(identity, multiply(inverse(X), multiply(X, inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)))))
% 70.47/9.27 = { by lemma 15 }
% 70.47/9.27 greatest_lower_bound(identity, inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)))
% 70.47/9.27 = { by lemma 18 R->L }
% 70.47/9.27 greatest_lower_bound(identity, multiply(inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)), identity))
% 70.47/9.27 = { by lemma 28 R->L }
% 70.47/9.27 multiply(inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)), greatest_lower_bound(multiply(inverse(greatest_lower_bound(X, Y)), X), identity))
% 70.47/9.27 = { by axiom 3 (symmetry_of_glb) }
% 70.47/9.27 multiply(inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)), greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X, Y)), X)))
% 70.47/9.27 = { by lemma 27 R->L }
% 70.47/9.27 multiply(inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)), greatest_lower_bound(identity, least_upper_bound(multiply(inverse(greatest_lower_bound(X, Y)), X), greatest_lower_bound(multiply(inverse(greatest_lower_bound(X, Y)), Y), multiply(inverse(greatest_lower_bound(X, Y)), X)))))
% 70.47/9.27 = { by lemma 30 }
% 70.47/9.27 multiply(inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)), greatest_lower_bound(identity, least_upper_bound(multiply(inverse(greatest_lower_bound(X, Y)), X), identity)))
% 70.47/9.27 = { by axiom 1 (symmetry_of_lub) }
% 70.47/9.27 multiply(inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)), greatest_lower_bound(identity, least_upper_bound(identity, multiply(inverse(greatest_lower_bound(X, Y)), X))))
% 70.47/9.27 = { by axiom 8 (glb_absorbtion) }
% 70.47/9.27 multiply(inverse(multiply(inverse(greatest_lower_bound(X, Y)), X)), identity)
% 70.47/9.27 = { by lemma 18 }
% 70.47/9.27 inverse(multiply(inverse(greatest_lower_bound(X, Y)), X))
% 70.47/9.27
% 70.47/9.27 Goal 1 (prove_p11): multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)) = least_upper_bound(a, b).
% 70.47/9.27 Proof:
% 70.47/9.27 multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))
% 70.47/9.27 = { by lemma 19 R->L }
% 70.47/9.27 inverse(inverse(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))))
% 70.47/9.27 = { by lemma 19 R->L }
% 70.47/9.27 inverse(inverse(inverse(inverse(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))))))
% 70.47/9.27 = { by lemma 22 R->L }
% 70.47/9.27 inverse(inverse(multiply(b, inverse(multiply(inverse(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))), b)))))
% 70.47/9.27 = { by lemma 31 }
% 70.47/9.27 inverse(inverse(multiply(b, inverse(inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.27 = { by lemma 19 }
% 70.47/9.27 inverse(inverse(multiply(b, multiply(inverse(greatest_lower_bound(a, b)), a))))
% 70.47/9.27 = { by axiom 10 (associativity) R->L }
% 70.47/9.27 inverse(inverse(multiply(multiply(b, inverse(greatest_lower_bound(a, b))), a)))
% 70.47/9.27 = { by lemma 23 R->L }
% 70.47/9.27 inverse(multiply(inverse(a), inverse(multiply(b, inverse(greatest_lower_bound(a, b))))))
% 70.47/9.27 = { by lemma 25 }
% 70.47/9.27 inverse(multiply(inverse(a), multiply(greatest_lower_bound(a, b), inverse(b))))
% 70.47/9.27 = { by lemma 29 R->L }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(b)))
% 70.47/9.27 = { by lemma 26 R->L }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(greatest_lower_bound(b, least_upper_bound(a, b)))))
% 70.47/9.27 = { by axiom 3 (symmetry_of_glb) }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(greatest_lower_bound(least_upper_bound(a, b), b))))
% 70.47/9.27 = { by lemma 15 R->L }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(greatest_lower_bound(least_upper_bound(a, b), multiply(inverse(inverse(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)))), multiply(inverse(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))), b))))))
% 70.47/9.27 = { by lemma 31 }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(greatest_lower_bound(least_upper_bound(a, b), multiply(inverse(inverse(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a)))))))
% 70.47/9.27 = { by lemma 23 }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(greatest_lower_bound(least_upper_bound(a, b), inverse(multiply(multiply(inverse(greatest_lower_bound(a, b)), a), inverse(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)))))))))
% 70.47/9.27 = { by lemma 25 }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(greatest_lower_bound(least_upper_bound(a, b), multiply(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), inverse(multiply(inverse(greatest_lower_bound(a, b)), a)))))))
% 70.47/9.27 = { by lemma 18 R->L }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(greatest_lower_bound(multiply(least_upper_bound(a, b), identity), multiply(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), inverse(multiply(inverse(greatest_lower_bound(a, b)), a)))))))
% 70.47/9.27 = { by lemma 20 R->L }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(greatest_lower_bound(multiply(least_upper_bound(a, b), multiply(multiply(inverse(greatest_lower_bound(a, b)), a), inverse(multiply(inverse(greatest_lower_bound(a, b)), a)))), multiply(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), inverse(multiply(inverse(greatest_lower_bound(a, b)), a)))))))
% 70.47/9.27 = { by axiom 10 (associativity) R->L }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(greatest_lower_bound(multiply(multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))), multiply(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), inverse(multiply(inverse(greatest_lower_bound(a, b)), a)))))))
% 70.47/9.27 = { by axiom 14 (monotony_glb2) R->L }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), a)), multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.27 = { by axiom 3 (symmetry_of_glb) R->L }
% 70.47/9.27 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), a))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 8 (glb_absorbtion) R->L }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(multiply(greatest_lower_bound(a, least_upper_bound(a, b)), multiply(inverse(greatest_lower_bound(a, b)), b)), multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), a))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 14 (monotony_glb2) }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(greatest_lower_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), b))), multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), a))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 9 (associativity_of_glb) R->L }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), greatest_lower_bound(multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), b)), multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), a)))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 3 (symmetry_of_glb) }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), greatest_lower_bound(multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), a)), multiply(least_upper_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), b)))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 13 (monotony_glb1) R->L }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), multiply(least_upper_bound(a, b), greatest_lower_bound(multiply(inverse(greatest_lower_bound(a, b)), a), multiply(inverse(greatest_lower_bound(a, b)), b)))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 3 (symmetry_of_glb) }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), multiply(least_upper_bound(a, b), greatest_lower_bound(multiply(inverse(greatest_lower_bound(a, b)), b), multiply(inverse(greatest_lower_bound(a, b)), a)))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by lemma 30 }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), multiply(least_upper_bound(a, b), identity)), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by lemma 18 }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), least_upper_bound(a, b)), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 3 (symmetry_of_glb) R->L }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by lemma 27 R->L }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), multiply(a, multiply(inverse(greatest_lower_bound(a, b)), least_upper_bound(b, greatest_lower_bound(a, b))))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 11 (monotony_lub1) }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), multiply(a, least_upper_bound(multiply(inverse(greatest_lower_bound(a, b)), b), multiply(inverse(greatest_lower_bound(a, b)), greatest_lower_bound(a, b))))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 5 (left_inverse) }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), multiply(a, least_upper_bound(multiply(inverse(greatest_lower_bound(a, b)), b), identity))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 11 (monotony_lub1) }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), least_upper_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), multiply(a, identity))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by lemma 18 }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), least_upper_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), a)), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 1 (symmetry_of_lub) R->L }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), least_upper_bound(a, multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 6 (lub_absorbtion) R->L }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), least_upper_bound(a, multiply(least_upper_bound(a, greatest_lower_bound(a, b)), multiply(inverse(greatest_lower_bound(a, b)), b)))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 12 (monotony_lub2) }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), least_upper_bound(a, least_upper_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), multiply(greatest_lower_bound(a, b), multiply(inverse(greatest_lower_bound(a, b)), b))))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by lemma 24 }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), least_upper_bound(a, least_upper_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), b))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 1 (symmetry_of_lub) R->L }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), least_upper_bound(a, least_upper_bound(b, multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 7 (associativity_of_lub) }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), least_upper_bound(least_upper_bound(a, b), multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by axiom 1 (symmetry_of_lub) }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(greatest_lower_bound(least_upper_bound(a, b), least_upper_bound(multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)), least_upper_bound(a, b))), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by lemma 26 }
% 70.47/9.28 inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(a, b)), a)), inverse(multiply(least_upper_bound(a, b), inverse(multiply(inverse(greatest_lower_bound(a, b)), a))))))
% 70.47/9.28 = { by lemma 22 }
% 70.47/9.28 inverse(inverse(least_upper_bound(a, b)))
% 70.47/9.28 = { by lemma 19 }
% 70.47/9.28 least_upper_bound(a, b)
% 70.47/9.28 % SZS output end Proof
% 70.47/9.28
% 70.47/9.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------