TSTP Solution File: GRP167-4 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP167-4 : 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 : 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 : Thu Aug 31 01:17:28 EDT 2023
% Result : Unsatisfiable 4.03s 0.87s
% Output : Proof 4.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP167-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.12 % 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 : n009.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 : Mon Aug 28 22:37:20 EDT 2023
% 0.12/0.33 % CPUTime :
% 4.03/0.87 Command-line arguments: --ground-connectedness --complete-subsets
% 4.03/0.87
% 4.03/0.87 % SZS status Unsatisfiable
% 4.03/0.87
% 4.29/0.91 % SZS output start Proof
% 4.29/0.91 Axiom 1 (p19_1): inverse(identity) = identity.
% 4.29/0.91 Axiom 2 (p19_2): inverse(inverse(X)) = X.
% 4.29/0.91 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 4.29/0.91 Axiom 4 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 4.29/0.91 Axiom 5 (left_identity): multiply(identity, X) = X.
% 4.29/0.91 Axiom 6 (left_inverse): multiply(inverse(X), X) = identity.
% 4.29/0.91 Axiom 7 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 4.29/0.91 Axiom 8 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 4.29/0.91 Axiom 9 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 4.29/0.91 Axiom 10 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 4.29/0.91 Axiom 11 (p19_3): inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 4.29/0.91 Axiom 12 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 4.29/0.91 Axiom 13 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 4.29/0.91 Axiom 14 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 4.29/0.91 Axiom 15 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 4.29/0.91 Axiom 16 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 4.29/0.91
% 4.29/0.91 Lemma 17: multiply(X, identity) = X.
% 4.29/0.91 Proof:
% 4.29/0.91 multiply(X, identity)
% 4.29/0.91 = { by axiom 2 (p19_2) R->L }
% 4.29/0.91 inverse(inverse(multiply(X, identity)))
% 4.29/0.91 = { by axiom 11 (p19_3) }
% 4.29/0.91 inverse(multiply(inverse(identity), inverse(X)))
% 4.29/0.91 = { by axiom 1 (p19_1) }
% 4.29/0.91 inverse(multiply(identity, inverse(X)))
% 4.29/0.91 = { by axiom 5 (left_identity) }
% 4.29/0.91 inverse(inverse(X))
% 4.29/0.91 = { by axiom 2 (p19_2) }
% 4.29/0.91 X
% 4.29/0.91
% 4.29/0.91 Lemma 18: multiply(X, inverse(X)) = identity.
% 4.29/0.91 Proof:
% 4.29/0.91 multiply(X, inverse(X))
% 4.29/0.91 = { by axiom 2 (p19_2) R->L }
% 4.29/0.91 multiply(inverse(inverse(X)), inverse(X))
% 4.29/0.91 = { by axiom 6 (left_inverse) }
% 4.29/0.91 identity
% 4.29/0.91
% 4.29/0.91 Lemma 19: multiply(greatest_lower_bound(X, identity), Y) = greatest_lower_bound(Y, multiply(X, Y)).
% 4.29/0.91 Proof:
% 4.29/0.91 multiply(greatest_lower_bound(X, identity), Y)
% 4.29/0.91 = { by axiom 3 (symmetry_of_glb) R->L }
% 4.29/0.91 multiply(greatest_lower_bound(identity, X), Y)
% 4.29/0.91 = { by axiom 14 (monotony_glb2) }
% 4.29/0.91 greatest_lower_bound(multiply(identity, Y), multiply(X, Y))
% 4.29/0.91 = { by axiom 5 (left_identity) }
% 4.29/0.91 greatest_lower_bound(Y, multiply(X, Y))
% 4.29/0.91
% 4.29/0.91 Lemma 20: multiply(least_upper_bound(X, identity), Y) = least_upper_bound(Y, multiply(X, Y)).
% 4.29/0.91 Proof:
% 4.29/0.91 multiply(least_upper_bound(X, identity), Y)
% 4.29/0.91 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.29/0.91 multiply(least_upper_bound(identity, X), Y)
% 4.29/0.91 = { by axiom 16 (monotony_lub2) }
% 4.29/0.91 least_upper_bound(multiply(identity, Y), multiply(X, Y))
% 4.29/0.91 = { by axiom 5 (left_identity) }
% 4.29/0.91 least_upper_bound(Y, multiply(X, Y))
% 4.29/0.91
% 4.29/0.91 Lemma 21: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 4.29/0.91 Proof:
% 4.29/0.91 inverse(multiply(X, inverse(Y)))
% 4.29/0.91 = { by axiom 11 (p19_3) }
% 4.29/0.91 multiply(inverse(inverse(Y)), inverse(X))
% 4.29/0.91 = { by axiom 2 (p19_2) }
% 4.29/0.91 multiply(Y, inverse(X))
% 4.29/0.91
% 4.29/0.91 Lemma 22: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 4.29/0.91 Proof:
% 4.29/0.91 inverse(multiply(inverse(X), Y))
% 4.29/0.91 = { by axiom 11 (p19_3) }
% 4.29/0.91 multiply(inverse(Y), inverse(inverse(X)))
% 4.29/0.91 = { by axiom 2 (p19_2) }
% 4.29/0.91 multiply(inverse(Y), X)
% 4.29/0.91
% 4.29/0.91 Lemma 23: multiply(inverse(X), greatest_lower_bound(X, Y)) = greatest_lower_bound(identity, multiply(inverse(X), Y)).
% 4.29/0.91 Proof:
% 4.29/0.91 multiply(inverse(X), greatest_lower_bound(X, Y))
% 4.29/0.91 = { by axiom 13 (monotony_glb1) }
% 4.29/0.91 greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 4.29/0.91 = { by axiom 6 (left_inverse) }
% 4.29/0.91 greatest_lower_bound(identity, multiply(inverse(X), Y))
% 4.29/0.91
% 4.29/0.91 Lemma 24: multiply(inverse(X), least_upper_bound(X, Y)) = least_upper_bound(identity, multiply(inverse(X), Y)).
% 4.29/0.91 Proof:
% 4.29/0.91 multiply(inverse(X), least_upper_bound(X, Y))
% 4.29/0.91 = { by axiom 15 (monotony_lub1) }
% 4.29/0.91 least_upper_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 4.29/0.91 = { by axiom 6 (left_inverse) }
% 4.29/0.91 least_upper_bound(identity, multiply(inverse(X), Y))
% 4.29/0.91
% 4.29/0.91 Lemma 25: multiply(inverse(X), least_upper_bound(X, identity)) = least_upper_bound(identity, inverse(X)).
% 4.29/0.91 Proof:
% 4.29/0.91 multiply(inverse(X), least_upper_bound(X, identity))
% 4.29/0.91 = { by lemma 24 }
% 4.29/0.91 least_upper_bound(identity, multiply(inverse(X), identity))
% 4.29/0.91 = { by lemma 17 }
% 4.29/0.92 least_upper_bound(identity, inverse(X))
% 4.29/0.92
% 4.29/0.92 Lemma 26: multiply(inverse(multiply(X, Y)), X) = inverse(Y).
% 4.29/0.92 Proof:
% 4.29/0.92 multiply(inverse(multiply(X, Y)), X)
% 4.29/0.92 = { by lemma 22 R->L }
% 4.29/0.92 inverse(multiply(inverse(X), multiply(X, Y)))
% 4.29/0.92 = { by axiom 12 (associativity) R->L }
% 4.29/0.92 inverse(multiply(multiply(inverse(X), X), Y))
% 4.29/0.92 = { by axiom 6 (left_inverse) }
% 4.29/0.92 inverse(multiply(identity, Y))
% 4.29/0.92 = { by axiom 5 (left_identity) }
% 4.29/0.92 inverse(Y)
% 4.29/0.92
% 4.29/0.92 Lemma 27: multiply(inverse(least_upper_bound(X, identity)), X) = multiply(X, inverse(least_upper_bound(X, identity))).
% 4.29/0.92 Proof:
% 4.29/0.92 multiply(inverse(least_upper_bound(X, identity)), X)
% 4.29/0.92 = { by lemma 22 R->L }
% 4.29/0.92 inverse(multiply(inverse(X), least_upper_bound(X, identity)))
% 4.29/0.92 = { by lemma 25 }
% 4.29/0.92 inverse(least_upper_bound(identity, inverse(X)))
% 4.29/0.92 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.29/0.92 inverse(least_upper_bound(inverse(X), identity))
% 4.29/0.92 = { by lemma 18 R->L }
% 4.29/0.92 inverse(least_upper_bound(inverse(X), multiply(X, inverse(X))))
% 4.29/0.92 = { by lemma 20 R->L }
% 4.29/0.92 inverse(multiply(least_upper_bound(X, identity), inverse(X)))
% 4.29/0.92 = { by lemma 21 }
% 4.29/0.92 multiply(X, inverse(least_upper_bound(X, identity)))
% 4.29/0.92
% 4.29/0.92 Lemma 28: multiply(least_upper_bound(X, identity), multiply(X, Y)) = multiply(X, multiply(least_upper_bound(X, identity), Y)).
% 4.29/0.92 Proof:
% 4.29/0.92 multiply(least_upper_bound(X, identity), multiply(X, Y))
% 4.29/0.92 = { by lemma 20 }
% 4.29/0.92 least_upper_bound(multiply(X, Y), multiply(X, multiply(X, Y)))
% 4.29/0.92 = { by axiom 15 (monotony_lub1) R->L }
% 4.29/0.92 multiply(X, least_upper_bound(Y, multiply(X, Y)))
% 4.29/0.92 = { by lemma 20 R->L }
% 4.29/0.92 multiply(X, multiply(least_upper_bound(X, identity), Y))
% 4.29/0.92
% 4.29/0.92 Lemma 29: multiply(least_upper_bound(X, identity), multiply(X, inverse(least_upper_bound(X, identity)))) = X.
% 4.29/0.92 Proof:
% 4.29/0.92 multiply(least_upper_bound(X, identity), multiply(X, inverse(least_upper_bound(X, identity))))
% 4.29/0.92 = { by lemma 28 }
% 4.29/0.92 multiply(X, multiply(least_upper_bound(X, identity), inverse(least_upper_bound(X, identity))))
% 4.29/0.92 = { by lemma 18 }
% 4.29/0.92 multiply(X, identity)
% 4.29/0.92 = { by lemma 17 }
% 4.29/0.92 X
% 4.29/0.92
% 4.29/0.92 Goal 1 (prove_p19): a = multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)).
% 4.29/0.92 Proof:
% 4.29/0.92 a
% 4.29/0.92 = { by axiom 2 (p19_2) R->L }
% 4.29/0.92 inverse(inverse(a))
% 4.29/0.92 = { by lemma 26 R->L }
% 4.29/0.92 multiply(inverse(multiply(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), inverse(a))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 21 R->L }
% 4.29/0.92 multiply(inverse(inverse(multiply(a, inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 26 R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(multiply(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(a, inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by axiom 12 (associativity) }
% 4.29/0.92 multiply(inverse(multiply(inverse(multiply(least_upper_bound(a, identity), multiply(greatest_lower_bound(a, identity), multiply(a, inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 19 }
% 4.29/0.92 multiply(inverse(multiply(inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(a, inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(a, multiply(a, inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by axiom 13 (monotony_glb1) R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(multiply(least_upper_bound(a, identity), multiply(a, greatest_lower_bound(inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity))), multiply(a, inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 19 R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(multiply(least_upper_bound(a, identity), multiply(a, multiply(greatest_lower_bound(a, identity), inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 28 }
% 4.29/0.92 multiply(inverse(multiply(inverse(multiply(a, multiply(least_upper_bound(a, identity), multiply(greatest_lower_bound(a, identity), inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by axiom 12 (associativity) R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(multiply(a, multiply(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), inverse(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 18 }
% 4.29/0.92 multiply(inverse(multiply(inverse(multiply(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 17 }
% 4.29/0.92 multiply(inverse(multiply(inverse(a), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by axiom 9 (lub_absorbtion) R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), a)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 29 R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(a, inverse(least_upper_bound(a, identity)))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by axiom 13 (monotony_glb1) R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(greatest_lower_bound(a, identity), multiply(a, inverse(least_upper_bound(a, identity)))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by axiom 3 (symmetry_of_glb) R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(a, inverse(least_upper_bound(a, identity))), greatest_lower_bound(a, identity)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 27 R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(inverse(least_upper_bound(a, identity)), a), greatest_lower_bound(a, identity)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by axiom 3 (symmetry_of_glb) R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(greatest_lower_bound(a, identity), multiply(inverse(least_upper_bound(a, identity)), a)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by axiom 8 (associativity_of_glb) R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, greatest_lower_bound(identity, multiply(inverse(least_upper_bound(a, identity)), a))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by lemma 23 R->L }
% 4.29/0.92 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, multiply(inverse(least_upper_bound(a, identity)), greatest_lower_bound(least_upper_bound(a, identity), a))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.92 = { by axiom 3 (symmetry_of_glb) R->L }
% 4.29/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, multiply(inverse(least_upper_bound(a, identity)), greatest_lower_bound(a, least_upper_bound(a, identity)))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.93 = { by axiom 7 (glb_absorbtion) }
% 4.29/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, multiply(inverse(least_upper_bound(a, identity)), a)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.29/0.93 = { by axiom 3 (symmetry_of_glb) R->L }
% 4.29/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(inverse(least_upper_bound(a, identity)), a), a))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 5 (left_identity) R->L }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(inverse(least_upper_bound(a, identity)), a), multiply(identity, a)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by lemma 18 R->L }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(inverse(least_upper_bound(a, identity)), a), multiply(multiply(least_upper_bound(a, identity), inverse(least_upper_bound(a, identity))), a)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 12 (associativity) }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(inverse(least_upper_bound(a, identity)), a), multiply(least_upper_bound(a, identity), multiply(inverse(least_upper_bound(a, identity)), a))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by lemma 19 R->L }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(greatest_lower_bound(least_upper_bound(a, identity), identity), multiply(inverse(least_upper_bound(a, identity)), a)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 3 (symmetry_of_glb) R->L }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(greatest_lower_bound(identity, least_upper_bound(a, identity)), multiply(inverse(least_upper_bound(a, identity)), a)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(greatest_lower_bound(identity, least_upper_bound(identity, a)), multiply(inverse(least_upper_bound(a, identity)), a)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 7 (glb_absorbtion) }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(identity, multiply(inverse(least_upper_bound(a, identity)), a)))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 5 (left_identity) }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(inverse(least_upper_bound(a, identity)), a))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by lemma 27 }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(a, inverse(least_upper_bound(a, identity))))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by lemma 29 }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), a))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.69/0.93 multiply(inverse(multiply(inverse(a), least_upper_bound(a, multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by lemma 24 }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, multiply(inverse(a), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 12 (associativity) R->L }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, multiply(multiply(inverse(a), least_upper_bound(a, identity)), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by lemma 25 }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, multiply(least_upper_bound(identity, inverse(a)), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, multiply(least_upper_bound(inverse(a), identity), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by lemma 20 }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), multiply(inverse(a), greatest_lower_bound(a, identity))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by lemma 23 }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, multiply(inverse(a), identity))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by lemma 17 }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, least_upper_bound(greatest_lower_bound(identity, inverse(a)), greatest_lower_bound(a, identity)))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 10 (associativity_of_lub) }
% 4.69/0.93 multiply(inverse(least_upper_bound(least_upper_bound(identity, greatest_lower_bound(identity, inverse(a))), greatest_lower_bound(a, identity))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 9 (lub_absorbtion) }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, greatest_lower_bound(a, identity))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 3 (symmetry_of_glb) R->L }
% 4.69/0.93 multiply(inverse(least_upper_bound(identity, greatest_lower_bound(identity, a))), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 9 (lub_absorbtion) }
% 4.69/0.93 multiply(inverse(identity), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 1 (p19_1) }
% 4.69/0.93 multiply(identity, multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))
% 4.69/0.93 = { by axiom 5 (left_identity) }
% 4.69/0.93 multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity))
% 4.69/0.93 % SZS output end Proof
% 4.69/0.93
% 4.69/0.93 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------