TSTP Solution File: GRP179-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP179-1 : 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 : n032.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 0.13s 0.50s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08 % Problem : GRP179-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.05/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Mon Aug 28 20:49:30 EDT 2023
% 0.08/0.28 % CPUTime :
% 0.13/0.50 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.13/0.50
% 0.13/0.50 % SZS status Unsatisfiable
% 0.13/0.50
% 0.13/0.53 % SZS output start Proof
% 0.13/0.53 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.13/0.53 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.13/0.53 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.13/0.53 Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 0.13/0.53 Axiom 5 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.13/0.53 Axiom 6 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.13/0.53 Axiom 7 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 0.13/0.53 Axiom 8 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.13/0.53 Axiom 9 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.13/0.53 Axiom 10 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.13/0.53 Axiom 11 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.13/0.53 Axiom 12 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.13/0.53 Axiom 13 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.13/0.53
% 0.13/0.53 Lemma 14: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.13/0.53 Proof:
% 0.13/0.53 multiply(inverse(X), multiply(X, Y))
% 0.13/0.53 = { by axiom 5 (associativity) R->L }
% 0.13/0.53 multiply(multiply(inverse(X), X), Y)
% 0.13/0.53 = { by axiom 4 (left_inverse) }
% 0.13/0.53 multiply(identity, Y)
% 0.13/0.53 = { by axiom 1 (left_identity) }
% 0.13/0.53 Y
% 0.13/0.53
% 0.13/0.53 Lemma 15: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.13/0.53 Proof:
% 0.13/0.53 multiply(inverse(inverse(X)), Y)
% 0.13/0.53 = { by lemma 14 R->L }
% 0.13/0.53 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 0.13/0.53 = { by lemma 14 }
% 0.13/0.53 multiply(X, Y)
% 0.13/0.53
% 0.13/0.53 Lemma 16: multiply(inverse(inverse(X)), identity) = X.
% 0.13/0.53 Proof:
% 0.13/0.53 multiply(inverse(inverse(X)), identity)
% 0.13/0.53 = { by axiom 4 (left_inverse) R->L }
% 0.13/0.53 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 0.13/0.53 = { by lemma 14 }
% 0.13/0.53 X
% 0.13/0.53
% 0.13/0.53 Lemma 17: multiply(X, identity) = X.
% 0.13/0.53 Proof:
% 0.13/0.53 multiply(X, identity)
% 0.13/0.53 = { by lemma 15 R->L }
% 0.13/0.53 multiply(inverse(inverse(X)), identity)
% 0.13/0.53 = { by lemma 16 }
% 0.13/0.53 X
% 0.13/0.53
% 0.13/0.53 Lemma 18: multiply(X, inverse(X)) = identity.
% 0.13/0.53 Proof:
% 0.13/0.53 multiply(X, inverse(X))
% 0.13/0.53 = { by lemma 15 R->L }
% 0.13/0.53 multiply(inverse(inverse(X)), inverse(X))
% 0.13/0.53 = { by axiom 4 (left_inverse) }
% 0.13/0.53 identity
% 0.13/0.53
% 0.13/0.53 Lemma 19: greatest_lower_bound(X, least_upper_bound(Y, X)) = X.
% 0.13/0.53 Proof:
% 0.13/0.53 greatest_lower_bound(X, least_upper_bound(Y, X))
% 0.13/0.53 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.13/0.53 greatest_lower_bound(X, least_upper_bound(X, Y))
% 0.13/0.53 = { by axiom 8 (glb_absorbtion) }
% 0.13/0.53 X
% 0.13/0.53
% 0.13/0.53 Lemma 20: least_upper_bound(X, greatest_lower_bound(Y, X)) = X.
% 0.13/0.53 Proof:
% 0.13/0.53 least_upper_bound(X, greatest_lower_bound(Y, X))
% 0.13/0.53 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.13/0.53 least_upper_bound(X, greatest_lower_bound(X, Y))
% 0.13/0.53 = { by axiom 6 (lub_absorbtion) }
% 0.13/0.53 X
% 0.13/0.53
% 0.13/0.53 Lemma 21: multiply(greatest_lower_bound(X, inverse(Y)), Y) = greatest_lower_bound(identity, multiply(X, Y)).
% 0.13/0.53 Proof:
% 0.13/0.53 multiply(greatest_lower_bound(X, inverse(Y)), Y)
% 0.13/0.53 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.13/0.53 multiply(greatest_lower_bound(inverse(Y), X), Y)
% 0.13/0.53 = { by axiom 13 (monotony_glb2) }
% 0.13/0.53 greatest_lower_bound(multiply(inverse(Y), Y), multiply(X, Y))
% 0.13/0.53 = { by axiom 4 (left_inverse) }
% 0.13/0.54 greatest_lower_bound(identity, multiply(X, Y))
% 0.13/0.54
% 0.13/0.54 Lemma 22: greatest_lower_bound(identity, multiply(X, inverse(Y))) = multiply(greatest_lower_bound(X, Y), inverse(Y)).
% 0.13/0.54 Proof:
% 0.13/0.54 greatest_lower_bound(identity, multiply(X, inverse(Y)))
% 0.13/0.54 = { by lemma 18 R->L }
% 0.13/0.54 greatest_lower_bound(multiply(Y, inverse(Y)), multiply(X, inverse(Y)))
% 0.13/0.54 = { by axiom 13 (monotony_glb2) R->L }
% 0.13/0.54 multiply(greatest_lower_bound(Y, X), inverse(Y))
% 0.13/0.54 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.54 multiply(greatest_lower_bound(X, Y), inverse(Y))
% 0.13/0.54
% 0.13/0.54 Lemma 23: greatest_lower_bound(identity, multiply(inverse(X), Y)) = multiply(inverse(X), greatest_lower_bound(Y, X)).
% 0.13/0.54 Proof:
% 0.13/0.54 greatest_lower_bound(identity, multiply(inverse(X), Y))
% 0.13/0.54 = { by axiom 4 (left_inverse) R->L }
% 0.13/0.54 greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 0.13/0.54 = { by axiom 12 (monotony_glb1) R->L }
% 0.13/0.54 multiply(inverse(X), greatest_lower_bound(X, Y))
% 0.13/0.54 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.54 multiply(inverse(X), greatest_lower_bound(Y, X))
% 0.13/0.54
% 0.13/0.54 Goal 1 (prove_p10): inverse(least_upper_bound(a, b)) = greatest_lower_bound(inverse(a), inverse(b)).
% 0.13/0.54 Proof:
% 0.13/0.54 inverse(least_upper_bound(a, b))
% 0.13/0.54 = { by lemma 17 R->L }
% 0.13/0.54 multiply(inverse(least_upper_bound(a, b)), identity)
% 0.13/0.54 = { by lemma 14 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(greatest_lower_bound(inverse(a), inverse(b)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 20 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(least_upper_bound(a, b)), greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(greatest_lower_bound(inverse(a), inverse(b)), inverse(least_upper_bound(a, b)))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 9 (associativity_of_glb) R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), greatest_lower_bound(inverse(b), inverse(least_upper_bound(a, b))))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b)))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 16 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), multiply(inverse(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b)))), identity))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 17 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b))), identity)), identity))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 4 (left_inverse) R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b))), multiply(inverse(b), b))), identity))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 19 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b))), multiply(inverse(b), greatest_lower_bound(b, least_upper_bound(a, b))))), identity))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b))), multiply(inverse(b), greatest_lower_bound(least_upper_bound(a, b), b)))), identity))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 23 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b))), greatest_lower_bound(identity, multiply(inverse(b), least_upper_bound(a, b))))), identity))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 21 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b))), multiply(greatest_lower_bound(inverse(b), inverse(least_upper_bound(a, b))), least_upper_bound(a, b)))), identity))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b))), multiply(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(b)), least_upper_bound(a, b)))), identity))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 14 }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), multiply(inverse(least_upper_bound(a, b)), identity))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 17 }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(a), inverse(least_upper_bound(a, b)))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 16 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), multiply(inverse(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a)))), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 17 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a))), identity)), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 4 (left_inverse) R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a))), multiply(inverse(a), a))), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 8 (glb_absorbtion) R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a))), multiply(inverse(a), greatest_lower_bound(a, least_upper_bound(a, b))))), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a))), multiply(inverse(a), greatest_lower_bound(least_upper_bound(a, b), a)))), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 23 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a))), greatest_lower_bound(identity, multiply(inverse(a), least_upper_bound(a, b))))), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 21 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a))), multiply(greatest_lower_bound(inverse(a), inverse(least_upper_bound(a, b))), least_upper_bound(a, b)))), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a))), multiply(greatest_lower_bound(inverse(least_upper_bound(a, b)), inverse(a)), least_upper_bound(a, b)))), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 14 }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), multiply(inverse(least_upper_bound(a, b)), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 17 }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(greatest_lower_bound(inverse(a), inverse(b)), inverse(least_upper_bound(a, b))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 2 (symmetry_of_lub) }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(inverse(least_upper_bound(a, b)), greatest_lower_bound(inverse(a), inverse(b))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 16 R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(inverse(least_upper_bound(a, b)), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), identity)), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by lemma 17 }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(least_upper_bound(inverse(least_upper_bound(a, b)), inverse(inverse(greatest_lower_bound(inverse(a), inverse(b))))), least_upper_bound(a, b)))), identity)
% 0.13/0.54 = { by axiom 11 (monotony_lub2) }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), least_upper_bound(multiply(inverse(least_upper_bound(a, b)), least_upper_bound(a, b)), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, b))))), identity)
% 0.13/0.54 = { by axiom 4 (left_inverse) }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), least_upper_bound(identity, multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, b))))), identity)
% 0.13/0.54 = { by axiom 4 (left_inverse) R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), least_upper_bound(multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), inverse(greatest_lower_bound(inverse(a), inverse(b)))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, b))))), identity)
% 0.13/0.54 = { by axiom 10 (monotony_lub1) R->L }
% 0.13/0.54 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), least_upper_bound(a, b))))), identity)
% 0.13/0.55 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(least_upper_bound(a, b), inverse(greatest_lower_bound(inverse(a), inverse(b))))))), identity)
% 0.13/0.55 = { by axiom 7 (associativity_of_lub) R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(b, inverse(greatest_lower_bound(inverse(a), inverse(b)))))))), identity)
% 0.13/0.55 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), b))))), identity)
% 0.13/0.55 = { by lemma 16 R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(b)), identity)))))), identity)
% 0.13/0.55 = { by lemma 18 R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(b)), multiply(greatest_lower_bound(inverse(a), inverse(b)), inverse(greatest_lower_bound(inverse(a), inverse(b)))))))))), identity)
% 0.13/0.55 = { by lemma 19 R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(b)), multiply(greatest_lower_bound(greatest_lower_bound(inverse(a), inverse(b)), least_upper_bound(inverse(b), greatest_lower_bound(inverse(a), inverse(b)))), inverse(greatest_lower_bound(inverse(a), inverse(b)))))))))), identity)
% 0.13/0.55 = { by lemma 20 }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(b)), multiply(greatest_lower_bound(greatest_lower_bound(inverse(a), inverse(b)), inverse(b)), inverse(greatest_lower_bound(inverse(a), inverse(b)))))))))), identity)
% 0.13/0.55 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(b)), multiply(greatest_lower_bound(inverse(b), greatest_lower_bound(inverse(a), inverse(b))), inverse(greatest_lower_bound(inverse(a), inverse(b)))))))))), identity)
% 0.13/0.55 = { by lemma 22 R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(b)), greatest_lower_bound(identity, multiply(inverse(b), inverse(greatest_lower_bound(inverse(a), inverse(b))))))))))), identity)
% 0.13/0.55 = { by lemma 23 }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(b)), multiply(inverse(b), greatest_lower_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), b)))))))), identity)
% 0.13/0.55 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(b)), multiply(inverse(b), greatest_lower_bound(b, inverse(greatest_lower_bound(inverse(a), inverse(b))))))))))), identity)
% 0.13/0.55 = { by lemma 14 }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), greatest_lower_bound(b, inverse(greatest_lower_bound(inverse(a), inverse(b))))))))), identity)
% 0.13/0.55 = { by lemma 20 }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(a, inverse(greatest_lower_bound(inverse(a), inverse(b))))))), identity)
% 0.13/0.55 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), a)))), identity)
% 0.13/0.55 = { by lemma 16 R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(a)), identity))))), identity)
% 0.13/0.55 = { by lemma 18 R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(a)), multiply(greatest_lower_bound(inverse(a), inverse(b)), inverse(greatest_lower_bound(inverse(a), inverse(b))))))))), identity)
% 0.13/0.55 = { by lemma 19 R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(a)), multiply(greatest_lower_bound(greatest_lower_bound(inverse(a), inverse(b)), least_upper_bound(inverse(a), greatest_lower_bound(inverse(a), inverse(b)))), inverse(greatest_lower_bound(inverse(a), inverse(b))))))))), identity)
% 0.13/0.55 = { by axiom 6 (lub_absorbtion) }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(a)), multiply(greatest_lower_bound(greatest_lower_bound(inverse(a), inverse(b)), inverse(a)), inverse(greatest_lower_bound(inverse(a), inverse(b))))))))), identity)
% 0.13/0.55 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(a)), multiply(greatest_lower_bound(inverse(a), greatest_lower_bound(inverse(a), inverse(b))), inverse(greatest_lower_bound(inverse(a), inverse(b))))))))), identity)
% 0.13/0.55 = { by lemma 22 R->L }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(a)), greatest_lower_bound(identity, multiply(inverse(a), inverse(greatest_lower_bound(inverse(a), inverse(b)))))))))), identity)
% 0.13/0.55 = { by lemma 23 }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(a)), multiply(inverse(a), greatest_lower_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), a))))))), identity)
% 0.13/0.55 = { by axiom 3 (symmetry_of_glb) }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(a)), multiply(inverse(a), greatest_lower_bound(a, inverse(greatest_lower_bound(inverse(a), inverse(b)))))))))), identity)
% 0.13/0.55 = { by lemma 14 }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), least_upper_bound(inverse(greatest_lower_bound(inverse(a), inverse(b))), greatest_lower_bound(a, inverse(greatest_lower_bound(inverse(a), inverse(b)))))))), identity)
% 0.13/0.55 = { by lemma 20 }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), inverse(greatest_lower_bound(inverse(a), inverse(b)))))), identity)
% 0.13/0.55 = { by lemma 15 }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(greatest_lower_bound(inverse(a), inverse(b)), inverse(greatest_lower_bound(inverse(a), inverse(b)))))), identity)
% 0.13/0.55 = { by lemma 18 }
% 0.13/0.55 multiply(inverse(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), identity)), identity)
% 0.13/0.55 = { by lemma 17 }
% 0.13/0.55 multiply(inverse(inverse(greatest_lower_bound(inverse(a), inverse(b)))), identity)
% 0.13/0.55 = { by lemma 16 }
% 0.13/0.55 greatest_lower_bound(inverse(a), inverse(b))
% 0.13/0.55 % SZS output end Proof
% 0.13/0.55
% 0.13/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------