TSTP Solution File: GRP181-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP181-1 : 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 : n028.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 01:17:35 EDT 2023
% Result : Unsatisfiable 32.17s 4.48s
% Output : Proof 32.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP181-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 22:35:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 32.17/4.48 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 32.17/4.48
% 32.17/4.48 % SZS status Unsatisfiable
% 32.17/4.48
% 32.91/4.54 % SZS output start Proof
% 32.91/4.54 Axiom 1 (left_identity): multiply(identity, X) = X.
% 32.91/4.54 Axiom 2 (idempotence_of_gld): greatest_lower_bound(X, X) = X.
% 32.91/4.54 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 32.91/4.54 Axiom 4 (p12_1): greatest_lower_bound(a, c) = greatest_lower_bound(b, c).
% 32.91/4.54 Axiom 5 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 32.91/4.54 Axiom 6 (p12_2): least_upper_bound(a, c) = least_upper_bound(b, c).
% 32.91/4.54 Axiom 7 (left_inverse): multiply(inverse(X), X) = identity.
% 32.91/4.54 Axiom 8 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 32.91/4.54 Axiom 9 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 32.91/4.54 Axiom 10 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 32.91/4.54 Axiom 11 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 32.91/4.54 Axiom 12 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 32.91/4.54 Axiom 13 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 32.91/4.54 Axiom 14 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 32.91/4.54 Axiom 15 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 32.91/4.54 Axiom 16 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 32.91/4.54
% 32.91/4.54 Lemma 17: multiply(inverse(X), multiply(X, Y)) = Y.
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(inverse(X), multiply(X, Y))
% 32.91/4.54 = { by axiom 8 (associativity) R->L }
% 32.91/4.54 multiply(multiply(inverse(X), X), Y)
% 32.91/4.54 = { by axiom 7 (left_inverse) }
% 32.91/4.54 multiply(identity, Y)
% 32.91/4.54 = { by axiom 1 (left_identity) }
% 32.91/4.54 Y
% 32.91/4.54
% 32.91/4.54 Lemma 18: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(inverse(inverse(X)), Y)
% 32.91/4.54 = { by lemma 17 R->L }
% 32.91/4.54 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 32.91/4.54 = { by lemma 17 }
% 32.91/4.54 multiply(X, Y)
% 32.91/4.54
% 32.91/4.54 Lemma 19: multiply(inverse(inverse(X)), identity) = X.
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(inverse(inverse(X)), identity)
% 32.91/4.54 = { by axiom 7 (left_inverse) R->L }
% 32.91/4.54 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 32.91/4.54 = { by lemma 17 }
% 32.91/4.54 X
% 32.91/4.54
% 32.91/4.54 Lemma 20: multiply(X, identity) = X.
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(X, identity)
% 32.91/4.54 = { by lemma 18 R->L }
% 32.91/4.54 multiply(inverse(inverse(X)), identity)
% 32.91/4.54 = { by lemma 19 }
% 32.91/4.54 X
% 32.91/4.54
% 32.91/4.54 Lemma 21: inverse(inverse(X)) = X.
% 32.91/4.54 Proof:
% 32.91/4.54 inverse(inverse(X))
% 32.91/4.54 = { by lemma 20 R->L }
% 32.91/4.54 multiply(inverse(inverse(X)), identity)
% 32.91/4.54 = { by lemma 19 }
% 32.91/4.54 X
% 32.91/4.54
% 32.91/4.54 Lemma 22: multiply(X, inverse(X)) = identity.
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(X, inverse(X))
% 32.91/4.54 = { by lemma 18 R->L }
% 32.91/4.54 multiply(inverse(inverse(X)), inverse(X))
% 32.91/4.54 = { by axiom 7 (left_inverse) }
% 32.91/4.54 identity
% 32.91/4.54
% 32.91/4.54 Lemma 23: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(X, inverse(multiply(Y, X)))
% 32.91/4.54 = { by lemma 17 R->L }
% 32.91/4.54 multiply(inverse(Y), multiply(Y, multiply(X, inverse(multiply(Y, X)))))
% 32.91/4.54 = { by axiom 8 (associativity) R->L }
% 32.91/4.54 multiply(inverse(Y), multiply(multiply(Y, X), inverse(multiply(Y, X))))
% 32.91/4.54 = { by lemma 22 }
% 32.91/4.54 multiply(inverse(Y), identity)
% 32.91/4.54 = { by lemma 20 }
% 32.91/4.54 inverse(Y)
% 32.91/4.54
% 32.91/4.54 Lemma 24: multiply(inverse(X), inverse(Y)) = inverse(multiply(Y, X)).
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(inverse(X), inverse(Y))
% 32.91/4.54 = { by lemma 23 R->L }
% 32.91/4.54 multiply(inverse(X), multiply(X, inverse(multiply(Y, X))))
% 32.91/4.54 = { by lemma 17 }
% 32.91/4.54 inverse(multiply(Y, X))
% 32.91/4.54
% 32.91/4.54 Lemma 25: multiply(X, multiply(inverse(X), Y)) = Y.
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(X, multiply(inverse(X), Y))
% 32.91/4.54 = { by lemma 18 R->L }
% 32.91/4.54 multiply(inverse(inverse(X)), multiply(inverse(X), Y))
% 32.91/4.54 = { by lemma 17 }
% 32.91/4.54 Y
% 32.91/4.54
% 32.91/4.54 Lemma 26: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 32.91/4.54 Proof:
% 32.91/4.54 inverse(multiply(X, inverse(Y)))
% 32.91/4.54 = { by lemma 25 R->L }
% 32.91/4.54 multiply(Y, multiply(inverse(Y), inverse(multiply(X, inverse(Y)))))
% 32.91/4.54 = { by lemma 23 }
% 32.91/4.54 multiply(Y, inverse(X))
% 32.91/4.54
% 32.91/4.54 Lemma 27: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 32.91/4.54 Proof:
% 32.91/4.54 inverse(multiply(inverse(X), Y))
% 32.91/4.54 = { by lemma 24 R->L }
% 32.91/4.54 multiply(inverse(Y), inverse(inverse(X)))
% 32.91/4.54 = { by lemma 21 }
% 32.91/4.54 multiply(inverse(Y), X)
% 32.91/4.54
% 32.91/4.54 Lemma 28: greatest_lower_bound(X, multiply(Y, X)) = multiply(greatest_lower_bound(Y, identity), X).
% 32.91/4.54 Proof:
% 32.91/4.54 greatest_lower_bound(X, multiply(Y, X))
% 32.91/4.54 = { by axiom 1 (left_identity) R->L }
% 32.91/4.54 greatest_lower_bound(multiply(identity, X), multiply(Y, X))
% 32.91/4.54 = { by axiom 14 (monotony_glb2) R->L }
% 32.91/4.54 multiply(greatest_lower_bound(identity, Y), X)
% 32.91/4.54 = { by axiom 3 (symmetry_of_glb) }
% 32.91/4.54 multiply(greatest_lower_bound(Y, identity), X)
% 32.91/4.54
% 32.91/4.54 Lemma 29: greatest_lower_bound(X, least_upper_bound(Y, X)) = X.
% 32.91/4.54 Proof:
% 32.91/4.54 greatest_lower_bound(X, least_upper_bound(Y, X))
% 32.91/4.54 = { by axiom 5 (symmetry_of_lub) R->L }
% 32.91/4.54 greatest_lower_bound(X, least_upper_bound(X, Y))
% 32.91/4.54 = { by axiom 9 (glb_absorbtion) }
% 32.91/4.54 X
% 32.91/4.54
% 32.91/4.54 Lemma 30: least_upper_bound(X, multiply(Y, X)) = multiply(least_upper_bound(Y, identity), X).
% 32.91/4.54 Proof:
% 32.91/4.54 least_upper_bound(X, multiply(Y, X))
% 32.91/4.54 = { by axiom 1 (left_identity) R->L }
% 32.91/4.54 least_upper_bound(multiply(identity, X), multiply(Y, X))
% 32.91/4.54 = { by axiom 16 (monotony_lub2) R->L }
% 32.91/4.54 multiply(least_upper_bound(identity, Y), X)
% 32.91/4.54 = { by axiom 5 (symmetry_of_lub) }
% 32.91/4.54 multiply(least_upper_bound(Y, identity), X)
% 32.91/4.54
% 32.91/4.54 Lemma 31: greatest_lower_bound(identity, multiply(inverse(X), Y)) = multiply(inverse(X), greatest_lower_bound(X, Y)).
% 32.91/4.54 Proof:
% 32.91/4.54 greatest_lower_bound(identity, multiply(inverse(X), Y))
% 32.91/4.54 = { by axiom 7 (left_inverse) R->L }
% 32.91/4.54 greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 32.91/4.54 = { by axiom 13 (monotony_glb1) R->L }
% 32.91/4.54 multiply(inverse(X), greatest_lower_bound(X, Y))
% 32.91/4.54
% 32.91/4.54 Lemma 32: multiply(inverse(X), greatest_lower_bound(X, identity)) = greatest_lower_bound(identity, inverse(X)).
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(inverse(X), greatest_lower_bound(X, identity))
% 32.91/4.54 = { by lemma 31 R->L }
% 32.91/4.54 greatest_lower_bound(identity, multiply(inverse(X), identity))
% 32.91/4.54 = { by lemma 28 }
% 32.91/4.54 multiply(greatest_lower_bound(inverse(X), identity), identity)
% 32.91/4.54 = { by lemma 20 }
% 32.91/4.54 greatest_lower_bound(inverse(X), identity)
% 32.91/4.54 = { by axiom 3 (symmetry_of_glb) }
% 32.91/4.54 greatest_lower_bound(identity, inverse(X))
% 32.91/4.54
% 32.91/4.54 Lemma 33: multiply(inverse(multiply(X, Y)), X) = inverse(Y).
% 32.91/4.54 Proof:
% 32.91/4.54 multiply(inverse(multiply(X, Y)), X)
% 32.91/4.54 = { by lemma 27 R->L }
% 32.91/4.54 inverse(multiply(inverse(X), multiply(X, Y)))
% 32.91/4.54 = { by lemma 24 R->L }
% 32.91/4.54 multiply(inverse(multiply(X, Y)), inverse(inverse(X)))
% 32.91/4.54 = { by lemma 23 R->L }
% 32.91/4.54 multiply(inverse(multiply(X, Y)), inverse(multiply(Y, inverse(multiply(X, Y)))))
% 32.91/4.54 = { by lemma 23 }
% 32.91/4.54 inverse(Y)
% 32.91/4.54
% 32.91/4.54 Lemma 34: greatest_lower_bound(identity, multiply(X, inverse(Y))) = multiply(greatest_lower_bound(Y, X), inverse(Y)).
% 32.91/4.54 Proof:
% 32.91/4.54 greatest_lower_bound(identity, multiply(X, inverse(Y)))
% 32.91/4.54 = { by lemma 22 R->L }
% 32.91/4.54 greatest_lower_bound(multiply(Y, inverse(Y)), multiply(X, inverse(Y)))
% 32.91/4.54 = { by axiom 14 (monotony_glb2) R->L }
% 32.91/4.54 multiply(greatest_lower_bound(Y, X), inverse(Y))
% 32.91/4.54
% 32.91/4.54 Lemma 35: least_upper_bound(identity, multiply(X, inverse(Y))) = multiply(least_upper_bound(Y, X), inverse(Y)).
% 32.91/4.54 Proof:
% 32.91/4.54 least_upper_bound(identity, multiply(X, inverse(Y)))
% 32.91/4.54 = { by lemma 22 R->L }
% 32.91/4.54 least_upper_bound(multiply(Y, inverse(Y)), multiply(X, inverse(Y)))
% 32.91/4.54 = { by axiom 16 (monotony_lub2) R->L }
% 32.91/4.54 multiply(least_upper_bound(Y, X), inverse(Y))
% 32.91/4.54
% 32.91/4.54 Lemma 36: least_upper_bound(identity, multiply(inverse(X), Y)) = multiply(inverse(X), least_upper_bound(Y, X)).
% 32.91/4.54 Proof:
% 32.91/4.54 least_upper_bound(identity, multiply(inverse(X), Y))
% 32.91/4.54 = { by axiom 7 (left_inverse) R->L }
% 32.91/4.54 least_upper_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 32.91/4.54 = { by axiom 15 (monotony_lub1) R->L }
% 32.91/4.54 multiply(inverse(X), least_upper_bound(X, Y))
% 32.91/4.54 = { by axiom 5 (symmetry_of_lub) }
% 32.91/4.54 multiply(inverse(X), least_upper_bound(Y, X))
% 32.91/4.54
% 32.91/4.54 Lemma 37: greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(identity, inverse(X))) = multiply(greatest_lower_bound(X, identity), least_upper_bound(identity, inverse(X))).
% 32.91/4.54 Proof:
% 32.91/4.54 greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(identity, inverse(X)))
% 32.91/4.54 = { by axiom 5 (symmetry_of_lub) R->L }
% 32.91/4.54 greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity))
% 32.91/4.54 = { by lemma 22 R->L }
% 32.91/4.54 greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), multiply(X, inverse(X))))
% 32.91/4.54 = { by lemma 30 }
% 32.91/4.54 greatest_lower_bound(least_upper_bound(X, identity), multiply(least_upper_bound(X, identity), inverse(X)))
% 32.91/4.54 = { by lemma 20 R->L }
% 32.91/4.54 greatest_lower_bound(multiply(least_upper_bound(X, identity), identity), multiply(least_upper_bound(X, identity), inverse(X)))
% 32.91/4.55 = { by axiom 13 (monotony_glb1) R->L }
% 32.91/4.55 multiply(least_upper_bound(X, identity), greatest_lower_bound(identity, inverse(X)))
% 32.91/4.55 = { by lemma 32 R->L }
% 32.91/4.55 multiply(least_upper_bound(X, identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
% 32.91/4.55 = { by lemma 30 R->L }
% 32.91/4.55 least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), multiply(X, multiply(inverse(X), greatest_lower_bound(X, identity))))
% 32.91/4.55 = { by lemma 25 }
% 32.91/4.55 least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), greatest_lower_bound(X, identity))
% 32.91/4.55 = { by axiom 5 (symmetry_of_lub) }
% 32.91/4.55 least_upper_bound(greatest_lower_bound(X, identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
% 32.91/4.55 = { by lemma 32 }
% 32.91/4.55 least_upper_bound(greatest_lower_bound(X, identity), greatest_lower_bound(identity, inverse(X)))
% 32.91/4.55 = { by axiom 3 (symmetry_of_glb) R->L }
% 32.91/4.55 least_upper_bound(greatest_lower_bound(X, identity), greatest_lower_bound(inverse(X), identity))
% 32.91/4.55 = { by lemma 22 R->L }
% 32.91/4.55 least_upper_bound(greatest_lower_bound(X, identity), greatest_lower_bound(inverse(X), multiply(X, inverse(X))))
% 32.91/4.55 = { by lemma 28 }
% 32.91/4.55 least_upper_bound(greatest_lower_bound(X, identity), multiply(greatest_lower_bound(X, identity), inverse(X)))
% 32.91/4.55 = { by lemma 20 R->L }
% 32.91/4.55 least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), multiply(greatest_lower_bound(X, identity), inverse(X)))
% 32.91/4.55 = { by axiom 15 (monotony_lub1) R->L }
% 32.91/4.55 multiply(greatest_lower_bound(X, identity), least_upper_bound(identity, inverse(X)))
% 32.91/4.55
% 32.91/4.55 Lemma 38: multiply(X, inverse(least_upper_bound(X, inverse(Y)))) = greatest_lower_bound(identity, multiply(X, Y)).
% 32.91/4.55 Proof:
% 32.91/4.55 multiply(X, inverse(least_upper_bound(X, inverse(Y))))
% 32.91/4.55 = { by lemma 26 R->L }
% 32.91/4.55 inverse(multiply(least_upper_bound(X, inverse(Y)), inverse(X)))
% 32.91/4.55 = { by lemma 35 R->L }
% 32.91/4.55 inverse(least_upper_bound(identity, multiply(inverse(Y), inverse(X))))
% 32.91/4.55 = { by lemma 24 }
% 32.91/4.55 inverse(least_upper_bound(identity, inverse(multiply(X, Y))))
% 32.91/4.55 = { by lemma 33 R->L }
% 32.91/4.55 multiply(inverse(multiply(greatest_lower_bound(multiply(X, Y), identity), least_upper_bound(identity, inverse(multiply(X, Y))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by lemma 37 R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, inverse(multiply(X, Y))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 9 (glb_absorbtion) R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, inverse(multiply(X, Y)))), least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, inverse(multiply(X, Y)))), identity))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 10 (associativity_of_glb) R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), greatest_lower_bound(least_upper_bound(identity, inverse(multiply(X, Y))), least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, inverse(multiply(X, Y)))), identity)))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 5 (symmetry_of_lub) }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), greatest_lower_bound(least_upper_bound(identity, inverse(multiply(X, Y))), least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, inverse(multiply(X, Y)))))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 5 (symmetry_of_lub) R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), greatest_lower_bound(least_upper_bound(inverse(multiply(X, Y)), identity), least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, inverse(multiply(X, Y)))))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 5 (symmetry_of_lub) R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), greatest_lower_bound(least_upper_bound(inverse(multiply(X, Y)), identity), least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(inverse(multiply(X, Y)), identity)))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 3 (symmetry_of_glb) R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), greatest_lower_bound(least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(inverse(multiply(X, Y)), identity))), least_upper_bound(inverse(multiply(X, Y)), identity)))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 11 (lub_absorbtion) R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), greatest_lower_bound(least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(inverse(multiply(X, Y)), identity))), least_upper_bound(least_upper_bound(inverse(multiply(X, Y)), identity), greatest_lower_bound(least_upper_bound(inverse(multiply(X, Y)), identity), least_upper_bound(multiply(X, Y), identity)))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 12 (associativity_of_lub) R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), greatest_lower_bound(least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(inverse(multiply(X, Y)), identity))), least_upper_bound(inverse(multiply(X, Y)), least_upper_bound(identity, greatest_lower_bound(least_upper_bound(inverse(multiply(X, Y)), identity), least_upper_bound(multiply(X, Y), identity))))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 3 (symmetry_of_glb) }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), greatest_lower_bound(least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(inverse(multiply(X, Y)), identity))), least_upper_bound(inverse(multiply(X, Y)), least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(inverse(multiply(X, Y)), identity))))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by lemma 29 }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(inverse(multiply(X, Y)), identity))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 5 (symmetry_of_lub) }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, inverse(multiply(X, Y))))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by lemma 37 }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, multiply(greatest_lower_bound(multiply(X, Y), identity), least_upper_bound(identity, inverse(multiply(X, Y))))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 5 (symmetry_of_lub) R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, multiply(greatest_lower_bound(multiply(X, Y), identity), least_upper_bound(inverse(multiply(X, Y)), identity))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 15 (monotony_lub1) }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, least_upper_bound(multiply(greatest_lower_bound(multiply(X, Y), identity), inverse(multiply(X, Y))), multiply(greatest_lower_bound(multiply(X, Y), identity), identity))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by lemma 28 R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, least_upper_bound(multiply(greatest_lower_bound(multiply(X, Y), identity), inverse(multiply(X, Y))), greatest_lower_bound(identity, multiply(multiply(X, Y), identity)))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 5 (symmetry_of_lub) R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(identity, multiply(multiply(X, Y), identity)), multiply(greatest_lower_bound(multiply(X, Y), identity), inverse(multiply(X, Y))))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 12 (associativity_of_lub) }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(least_upper_bound(identity, greatest_lower_bound(identity, multiply(multiply(X, Y), identity))), multiply(greatest_lower_bound(multiply(X, Y), identity), inverse(multiply(X, Y)))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 11 (lub_absorbtion) }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, multiply(greatest_lower_bound(multiply(X, Y), identity), inverse(multiply(X, Y)))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by lemma 34 R->L }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), least_upper_bound(identity, greatest_lower_bound(identity, multiply(identity, inverse(multiply(X, Y))))))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 11 (lub_absorbtion) }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(X, Y), identity), identity)), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 3 (symmetry_of_glb) }
% 32.91/4.55 multiply(inverse(greatest_lower_bound(identity, least_upper_bound(multiply(X, Y), identity))), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by lemma 29 }
% 32.91/4.55 multiply(inverse(identity), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by lemma 20 R->L }
% 32.91/4.55 multiply(multiply(inverse(identity), identity), greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 7 (left_inverse) }
% 32.91/4.55 multiply(identity, greatest_lower_bound(multiply(X, Y), identity))
% 32.91/4.55 = { by axiom 1 (left_identity) }
% 32.91/4.55 greatest_lower_bound(multiply(X, Y), identity)
% 32.91/4.55 = { by axiom 3 (symmetry_of_glb) }
% 32.91/4.55 greatest_lower_bound(identity, multiply(X, Y))
% 32.91/4.55
% 32.91/4.55 Goal 1 (prove_p12): a = b.
% 32.91/4.55 Proof:
% 32.91/4.55 a
% 32.91/4.55 = { by lemma 21 R->L }
% 32.91/4.55 inverse(inverse(a))
% 32.91/4.55 = { by lemma 17 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), multiply(least_upper_bound(c, a), inverse(a))))
% 32.91/4.55 = { by lemma 26 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(a, inverse(least_upper_bound(c, a))))))
% 32.91/4.55 = { by lemma 21 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(a, inverse(least_upper_bound(inverse(inverse(c)), a))))))
% 32.91/4.55 = { by axiom 5 (symmetry_of_lub) R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(a, inverse(least_upper_bound(a, inverse(inverse(c))))))))
% 32.91/4.55 = { by lemma 26 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(inverse(multiply(least_upper_bound(a, inverse(inverse(c))), inverse(a))))))
% 32.91/4.55 = { by lemma 35 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(inverse(least_upper_bound(identity, multiply(inverse(inverse(c)), inverse(a)))))))
% 32.91/4.55 = { by lemma 36 }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(inverse(multiply(inverse(inverse(c)), least_upper_bound(inverse(a), inverse(c)))))))
% 32.91/4.55 = { by lemma 27 }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(a), inverse(c))), inverse(c)))))
% 32.91/4.55 = { by lemma 21 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(inverse(inverse(least_upper_bound(inverse(a), inverse(c))))), inverse(c)))))
% 32.91/4.55 = { by lemma 33 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(a), inverse(least_upper_bound(inverse(a), inverse(c))))), inverse(a))), inverse(c)))))
% 32.91/4.55 = { by lemma 38 }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(identity, multiply(inverse(a), c))), inverse(a))), inverse(c)))))
% 32.91/4.55 = { by lemma 21 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(inverse(greatest_lower_bound(identity, multiply(inverse(inverse(inverse(a))), c))), inverse(a))), inverse(c)))))
% 32.91/4.55 = { by lemma 20 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(multiply(inverse(greatest_lower_bound(identity, multiply(inverse(inverse(inverse(a))), c))), identity), inverse(a))), inverse(c)))))
% 32.91/4.55 = { by axiom 11 (lub_absorbtion) R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(multiply(inverse(greatest_lower_bound(identity, multiply(inverse(inverse(inverse(a))), c))), least_upper_bound(identity, greatest_lower_bound(identity, multiply(inverse(inverse(inverse(a))), c)))), inverse(a))), inverse(c)))))
% 32.91/4.55 = { by lemma 36 R->L }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(least_upper_bound(identity, multiply(inverse(greatest_lower_bound(identity, multiply(inverse(inverse(inverse(a))), c))), identity)), inverse(a))), inverse(c)))))
% 32.91/4.55 = { by lemma 31 }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(least_upper_bound(identity, multiply(inverse(multiply(inverse(inverse(inverse(a))), greatest_lower_bound(inverse(inverse(a)), c))), identity)), inverse(a))), inverse(c)))))
% 32.91/4.55 = { by axiom 3 (symmetry_of_glb) }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(least_upper_bound(identity, multiply(inverse(multiply(inverse(inverse(inverse(a))), greatest_lower_bound(c, inverse(inverse(a))))), identity)), inverse(a))), inverse(c)))))
% 32.91/4.55 = { by lemma 30 }
% 32.91/4.55 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(multiply(least_upper_bound(inverse(multiply(inverse(inverse(inverse(a))), greatest_lower_bound(c, inverse(inverse(a))))), identity), identity), inverse(a))), inverse(c)))))
% 32.91/4.55 = { by lemma 20 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(least_upper_bound(inverse(multiply(inverse(inverse(inverse(a))), greatest_lower_bound(c, inverse(inverse(a))))), identity), inverse(a))), inverse(c)))))
% 32.91/4.56 = { by lemma 27 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(multiply(least_upper_bound(multiply(inverse(greatest_lower_bound(c, inverse(inverse(a)))), inverse(inverse(a))), identity), inverse(a))), inverse(c)))))
% 32.91/4.56 = { by axiom 16 (monotony_lub2) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(multiply(multiply(inverse(greatest_lower_bound(c, inverse(inverse(a)))), inverse(inverse(a))), inverse(a)), multiply(identity, inverse(a)))), inverse(c)))))
% 32.91/4.56 = { by axiom 8 (associativity) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(multiply(inverse(greatest_lower_bound(c, inverse(inverse(a)))), multiply(inverse(inverse(a)), inverse(a))), multiply(identity, inverse(a)))), inverse(c)))))
% 32.91/4.56 = { by axiom 7 (left_inverse) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(multiply(inverse(greatest_lower_bound(c, inverse(inverse(a)))), identity), multiply(identity, inverse(a)))), inverse(c)))))
% 32.91/4.56 = { by lemma 20 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), multiply(identity, inverse(a)))), inverse(c)))))
% 32.91/4.56 = { by axiom 1 (left_identity) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), inverse(a))), inverse(c)))))
% 32.91/4.56 = { by lemma 21 R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), inverse(inverse(inverse(a))))), inverse(c)))))
% 32.91/4.56 = { by lemma 20 R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), multiply(inverse(inverse(inverse(a))), identity))), inverse(c)))))
% 32.91/4.56 = { by lemma 22 R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), multiply(inverse(inverse(inverse(a))), multiply(greatest_lower_bound(inverse(inverse(a)), c), inverse(greatest_lower_bound(inverse(inverse(a)), c)))))), inverse(c)))))
% 32.91/4.56 = { by axiom 8 (associativity) R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), multiply(multiply(inverse(inverse(inverse(a))), greatest_lower_bound(inverse(inverse(a)), c)), inverse(greatest_lower_bound(inverse(inverse(a)), c))))), inverse(c)))))
% 32.91/4.56 = { by axiom 2 (idempotence_of_gld) R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), multiply(multiply(inverse(inverse(inverse(a))), greatest_lower_bound(greatest_lower_bound(inverse(inverse(a)), inverse(inverse(a))), c)), inverse(greatest_lower_bound(inverse(inverse(a)), c))))), inverse(c)))))
% 32.91/4.56 = { by axiom 10 (associativity_of_glb) R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), multiply(multiply(inverse(inverse(inverse(a))), greatest_lower_bound(inverse(inverse(a)), greatest_lower_bound(inverse(inverse(a)), c))), inverse(greatest_lower_bound(inverse(inverse(a)), c))))), inverse(c)))))
% 32.91/4.56 = { by lemma 31 R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), multiply(greatest_lower_bound(identity, multiply(inverse(inverse(inverse(a))), greatest_lower_bound(inverse(inverse(a)), c))), inverse(greatest_lower_bound(inverse(inverse(a)), c))))), inverse(c)))))
% 32.91/4.56 = { by axiom 3 (symmetry_of_glb) R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), multiply(greatest_lower_bound(multiply(inverse(inverse(inverse(a))), greatest_lower_bound(inverse(inverse(a)), c)), identity), inverse(greatest_lower_bound(inverse(inverse(a)), c))))), inverse(c)))))
% 32.91/4.56 = { by lemma 28 R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), greatest_lower_bound(inverse(greatest_lower_bound(inverse(inverse(a)), c)), multiply(multiply(inverse(inverse(inverse(a))), greatest_lower_bound(inverse(inverse(a)), c)), inverse(greatest_lower_bound(inverse(inverse(a)), c)))))), inverse(c)))))
% 32.91/4.56 = { by axiom 8 (associativity) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), greatest_lower_bound(inverse(greatest_lower_bound(inverse(inverse(a)), c)), multiply(inverse(inverse(inverse(a))), multiply(greatest_lower_bound(inverse(inverse(a)), c), inverse(greatest_lower_bound(inverse(inverse(a)), c))))))), inverse(c)))))
% 32.91/4.56 = { by lemma 22 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), greatest_lower_bound(inverse(greatest_lower_bound(inverse(inverse(a)), c)), multiply(inverse(inverse(inverse(a))), identity)))), inverse(c)))))
% 32.91/4.56 = { by lemma 20 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), greatest_lower_bound(inverse(greatest_lower_bound(inverse(inverse(a)), c)), inverse(inverse(inverse(a)))))), inverse(c)))))
% 32.91/4.56 = { by axiom 3 (symmetry_of_glb) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), greatest_lower_bound(inverse(inverse(inverse(a))), inverse(greatest_lower_bound(inverse(inverse(a)), c))))), inverse(c)))))
% 32.91/4.56 = { by lemma 21 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), greatest_lower_bound(inverse(a), inverse(greatest_lower_bound(inverse(inverse(a)), c))))), inverse(c)))))
% 32.91/4.56 = { by axiom 3 (symmetry_of_glb) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), greatest_lower_bound(inverse(a), inverse(greatest_lower_bound(c, inverse(inverse(a))))))), inverse(c)))))
% 32.91/4.56 = { by axiom 3 (symmetry_of_glb) R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), greatest_lower_bound(inverse(greatest_lower_bound(c, inverse(inverse(a)))), inverse(a)))), inverse(c)))))
% 32.91/4.56 = { by axiom 11 (lub_absorbtion) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(inverse(greatest_lower_bound(c, inverse(inverse(a))))), inverse(c)))))
% 32.91/4.56 = { by lemma 21 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(inverse(inverse(greatest_lower_bound(c, a))), inverse(c)))))
% 32.91/4.56 = { by lemma 24 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(inverse(multiply(c, inverse(greatest_lower_bound(c, a)))))))
% 32.91/4.56 = { by lemma 26 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(greatest_lower_bound(c, a), inverse(c)))))
% 32.91/4.56 = { by axiom 3 (symmetry_of_glb) R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(greatest_lower_bound(a, c), inverse(c)))))
% 32.91/4.56 = { by axiom 4 (p12_1) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(greatest_lower_bound(b, c), inverse(c)))))
% 32.91/4.56 = { by axiom 3 (symmetry_of_glb) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(greatest_lower_bound(c, b), inverse(c)))))
% 32.91/4.56 = { by lemma 34 R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(greatest_lower_bound(identity, multiply(b, inverse(c))))))
% 32.91/4.56 = { by lemma 38 R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(b, inverse(least_upper_bound(b, inverse(inverse(c))))))))
% 32.91/4.56 = { by lemma 21 }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(b, inverse(least_upper_bound(b, c))))))
% 32.91/4.56 = { by axiom 6 (p12_2) R->L }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(b, inverse(least_upper_bound(a, c))))))
% 32.91/4.56 = { by axiom 5 (symmetry_of_lub) }
% 32.91/4.56 inverse(multiply(inverse(least_upper_bound(c, a)), inverse(multiply(b, inverse(least_upper_bound(c, a))))))
% 32.91/4.56 = { by lemma 23 }
% 32.91/4.56 inverse(inverse(b))
% 32.91/4.56 = { by lemma 21 }
% 32.91/4.56 b
% 32.91/4.56 % SZS output end Proof
% 32.91/4.56
% 32.91/4.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------