TSTP Solution File: GRP186-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP186-2 : 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 : n025.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 01:17:40 EDT 2023
% Result : Unsatisfiable 3.87s 0.92s
% Output : Proof 4.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP186-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:46:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.87/0.92 Command-line arguments: --ground-connectedness --complete-subsets
% 3.87/0.92
% 3.87/0.92 % SZS status Unsatisfiable
% 3.87/0.92
% 4.56/0.94 % SZS output start Proof
% 4.56/0.94 Axiom 1 (p23_1): inverse(identity) = identity.
% 4.56/0.94 Axiom 2 (p23_2): inverse(inverse(X)) = X.
% 4.56/0.94 Axiom 3 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 4.56/0.94 Axiom 4 (idempotence_of_gld): greatest_lower_bound(X, X) = X.
% 4.56/0.94 Axiom 5 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 4.56/0.94 Axiom 6 (left_identity): multiply(identity, X) = X.
% 4.56/0.94 Axiom 7 (left_inverse): multiply(inverse(X), X) = identity.
% 4.56/0.94 Axiom 8 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 4.56/0.94 Axiom 9 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 4.56/0.94 Axiom 10 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 4.56/0.94 Axiom 11 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 4.56/0.94 Axiom 12 (p23_3): inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 4.56/0.94 Axiom 13 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 4.56/0.94 Axiom 14 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 4.56/0.94 Axiom 15 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 4.56/0.94 Axiom 16 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 4.56/0.94 Axiom 17 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 4.56/0.94
% 4.56/0.94 Lemma 18: multiply(X, identity) = X.
% 4.56/0.94 Proof:
% 4.56/0.94 multiply(X, identity)
% 4.56/0.94 = { by axiom 2 (p23_2) R->L }
% 4.56/0.94 inverse(inverse(multiply(X, identity)))
% 4.56/0.94 = { by axiom 12 (p23_3) }
% 4.56/0.94 inverse(multiply(inverse(identity), inverse(X)))
% 4.56/0.94 = { by axiom 1 (p23_1) }
% 4.56/0.94 inverse(multiply(identity, inverse(X)))
% 4.56/0.94 = { by axiom 6 (left_identity) }
% 4.56/0.94 inverse(inverse(X))
% 4.56/0.94 = { by axiom 2 (p23_2) }
% 4.56/0.94 X
% 4.56/0.94
% 4.56/0.94 Lemma 19: multiply(X, inverse(X)) = identity.
% 4.56/0.94 Proof:
% 4.56/0.94 multiply(X, inverse(X))
% 4.56/0.94 = { by axiom 2 (p23_2) R->L }
% 4.56/0.94 multiply(inverse(inverse(X)), inverse(X))
% 4.56/0.94 = { by axiom 7 (left_inverse) }
% 4.56/0.94 identity
% 4.56/0.94
% 4.56/0.94 Lemma 20: multiply(greatest_lower_bound(X, identity), Y) = greatest_lower_bound(Y, multiply(X, Y)).
% 4.56/0.94 Proof:
% 4.56/0.94 multiply(greatest_lower_bound(X, identity), Y)
% 4.56/0.94 = { by axiom 5 (symmetry_of_glb) R->L }
% 4.56/0.94 multiply(greatest_lower_bound(identity, X), Y)
% 4.56/0.94 = { by axiom 17 (monotony_glb2) }
% 4.56/0.94 greatest_lower_bound(multiply(identity, Y), multiply(X, Y))
% 4.56/0.94 = { by axiom 6 (left_identity) }
% 4.56/0.94 greatest_lower_bound(Y, multiply(X, Y))
% 4.56/0.94
% 4.56/0.94 Lemma 21: inverse(multiply(Y, inverse(X))) = multiply(X, inverse(Y)).
% 4.56/0.94 Proof:
% 4.56/0.94 inverse(multiply(Y, inverse(X)))
% 4.56/0.94 = { by axiom 12 (p23_3) }
% 4.56/0.94 multiply(inverse(inverse(X)), inverse(Y))
% 4.56/0.94 = { by axiom 2 (p23_2) }
% 4.56/0.94 multiply(X, inverse(Y))
% 4.56/0.94
% 4.56/0.94 Lemma 22: greatest_lower_bound(X, least_upper_bound(Y, X)) = X.
% 4.56/0.94 Proof:
% 4.56/0.94 greatest_lower_bound(X, least_upper_bound(Y, X))
% 4.56/0.94 = { by axiom 3 (symmetry_of_lub) R->L }
% 4.56/0.94 greatest_lower_bound(X, least_upper_bound(X, Y))
% 4.56/0.94 = { by axiom 10 (glb_absorbtion) }
% 4.56/0.94 X
% 4.56/0.94
% 4.56/0.94 Lemma 23: multiply(inverse(X), multiply(X, Y)) = Y.
% 4.56/0.94 Proof:
% 4.56/0.94 multiply(inverse(X), multiply(X, Y))
% 4.56/0.94 = { by axiom 13 (associativity) R->L }
% 4.56/0.94 multiply(multiply(inverse(X), X), Y)
% 4.56/0.94 = { by axiom 7 (left_inverse) }
% 4.56/0.94 multiply(identity, Y)
% 4.56/0.94 = { by axiom 6 (left_identity) }
% 4.56/0.94 Y
% 4.56/0.94
% 4.56/0.94 Lemma 24: multiply(greatest_lower_bound(X, inverse(Y)), Y) = greatest_lower_bound(multiply(X, Y), identity).
% 4.56/0.94 Proof:
% 4.56/0.94 multiply(greatest_lower_bound(X, inverse(Y)), Y)
% 4.56/0.94 = { by axiom 17 (monotony_glb2) }
% 4.56/0.94 greatest_lower_bound(multiply(X, Y), multiply(inverse(Y), Y))
% 4.56/0.94 = { by axiom 7 (left_inverse) }
% 4.56/0.94 greatest_lower_bound(multiply(X, Y), identity)
% 4.56/0.94
% 4.56/0.94 Lemma 25: multiply(multiply(X, inverse(greatest_lower_bound(Y, inverse(Z)))), greatest_lower_bound(multiply(Y, Z), identity)) = multiply(X, Z).
% 4.56/0.94 Proof:
% 4.56/0.94 multiply(multiply(X, inverse(greatest_lower_bound(Y, inverse(Z)))), greatest_lower_bound(multiply(Y, Z), identity))
% 4.56/0.94 = { by axiom 13 (associativity) }
% 4.56/0.94 multiply(X, multiply(inverse(greatest_lower_bound(Y, inverse(Z))), greatest_lower_bound(multiply(Y, Z), identity)))
% 4.56/0.94 = { by lemma 24 R->L }
% 4.56/0.94 multiply(X, multiply(inverse(greatest_lower_bound(Y, inverse(Z))), multiply(greatest_lower_bound(Y, inverse(Z)), Z)))
% 4.56/0.94 = { by lemma 23 }
% 4.56/0.95 multiply(X, Z)
% 4.56/0.95
% 4.56/0.95 Goal 1 (prove_p23): least_upper_bound(multiply(a, b), identity) = multiply(a, inverse(greatest_lower_bound(a, inverse(b)))).
% 4.56/0.95 Proof:
% 4.56/0.95 least_upper_bound(multiply(a, b), identity)
% 4.56/0.95 = { by axiom 2 (p23_2) R->L }
% 4.56/0.95 inverse(inverse(least_upper_bound(multiply(a, b), identity)))
% 4.56/0.95 = { by lemma 18 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), identity)
% 4.56/0.95 = { by axiom 1 (p23_1) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(identity))
% 4.56/0.95 = { by lemma 22 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, least_upper_bound(multiply(a, b), identity))))
% 4.56/0.95 = { by axiom 10 (glb_absorbtion) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(greatest_lower_bound(identity, least_upper_bound(identity, inverse(multiply(a, b)))), least_upper_bound(multiply(a, b), identity))))
% 4.56/0.95 = { by axiom 11 (associativity_of_glb) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(identity, inverse(multiply(a, b))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 5 (symmetry_of_glb) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(identity, inverse(multiply(a, b)))))))
% 4.56/0.95 = { by lemma 18 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(identity, multiply(inverse(multiply(a, b)), identity))))))
% 4.56/0.95 = { by axiom 7 (left_inverse) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(inverse(multiply(a, b)), multiply(a, b)), multiply(inverse(multiply(a, b)), identity))))))
% 4.56/0.95 = { by axiom 14 (monotony_lub1) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(inverse(multiply(a, b)), least_upper_bound(multiply(a, b), identity))))))
% 4.56/0.95 = { by lemma 20 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(greatest_lower_bound(inverse(multiply(a, b)), identity), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by lemma 19 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(greatest_lower_bound(inverse(multiply(a, b)), multiply(multiply(a, b), inverse(multiply(a, b)))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by lemma 20 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(multiply(greatest_lower_bound(multiply(a, b), identity), inverse(multiply(a, b))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by lemma 24 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(multiply(multiply(greatest_lower_bound(a, inverse(b)), b), inverse(multiply(a, b))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 13 (associativity) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(multiply(greatest_lower_bound(a, inverse(b)), multiply(b, inverse(multiply(a, b)))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by lemma 21 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(multiply(greatest_lower_bound(a, inverse(b)), inverse(multiply(multiply(a, b), inverse(b)))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by lemma 21 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(inverse(multiply(multiply(multiply(a, b), inverse(b)), inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 13 (associativity) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(inverse(multiply(multiply(a, b), multiply(inverse(b), inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 12 (p23_3) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(inverse(multiply(multiply(a, b), inverse(multiply(greatest_lower_bound(a, inverse(b)), b)))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 13 (associativity) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(inverse(multiply(a, multiply(b, inverse(multiply(greatest_lower_bound(a, inverse(b)), b))))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by lemma 21 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(inverse(multiply(a, inverse(multiply(multiply(greatest_lower_bound(a, inverse(b)), b), inverse(b))))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 12 (p23_3) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(inverse(multiply(a, multiply(inverse(inverse(b)), inverse(multiply(greatest_lower_bound(a, inverse(b)), b))))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 12 (p23_3) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(inverse(multiply(a, multiply(inverse(inverse(b)), multiply(inverse(b), inverse(greatest_lower_bound(a, inverse(b))))))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by lemma 23 }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(identity, multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 7 (left_inverse) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(greatest_lower_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 16 (monotony_glb1) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), inverse(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), greatest_lower_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), least_upper_bound(multiply(a, b), identity)))))
% 4.56/0.95 = { by axiom 12 (p23_3) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), least_upper_bound(multiply(a, b), identity))), inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))))
% 4.56/0.95 = { by axiom 2 (p23_2) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), least_upper_bound(multiply(a, b), identity))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 5 (symmetry_of_glb) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 8 (lub_absorbtion) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), greatest_lower_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), multiply(a, b))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by lemma 25 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), greatest_lower_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), multiply(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), greatest_lower_bound(multiply(a, b), identity)))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by lemma 18 R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), greatest_lower_bound(multiply(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), identity), multiply(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), greatest_lower_bound(multiply(a, b), identity)))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 16 (monotony_glb1) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), multiply(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), greatest_lower_bound(identity, greatest_lower_bound(multiply(a, b), identity)))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 5 (symmetry_of_glb) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), multiply(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), greatest_lower_bound(greatest_lower_bound(multiply(a, b), identity), identity))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 11 (associativity_of_glb) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), multiply(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), greatest_lower_bound(multiply(a, b), greatest_lower_bound(identity, identity)))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 4 (idempotence_of_gld) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), multiply(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), greatest_lower_bound(multiply(a, b), identity))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by lemma 25 }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), multiply(a, b)))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 3 (symmetry_of_lub) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 8 (lub_absorbtion) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), multiply(least_upper_bound(a, greatest_lower_bound(a, inverse(b))), inverse(greatest_lower_bound(a, inverse(b))))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 15 (monotony_lub2) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), multiply(greatest_lower_bound(a, inverse(b)), inverse(greatest_lower_bound(a, inverse(b)))))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by lemma 19 }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), identity)))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 3 (symmetry_of_lub) R->L }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(identity, multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 9 (associativity_of_lub) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(least_upper_bound(multiply(a, b), identity), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by axiom 3 (symmetry_of_lub) }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), least_upper_bound(multiply(a, b), identity)))), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by lemma 22 }
% 4.56/0.95 multiply(inverse(inverse(least_upper_bound(multiply(a, b), identity))), multiply(inverse(least_upper_bound(multiply(a, b), identity)), multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))
% 4.56/0.95 = { by lemma 23 }
% 4.56/0.95 multiply(a, inverse(greatest_lower_bound(a, inverse(b))))
% 4.56/0.95 % SZS output end Proof
% 4.56/0.95
% 4.56/0.95 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------