TSTP Solution File: GRP186-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP186-1 : 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 : n022.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 7.18s 1.31s
% Output : Proof 7.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP186-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Tue Aug 29 00:54:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 7.18/1.31 Command-line arguments: --flatten
% 7.18/1.31
% 7.18/1.31 % SZS status Unsatisfiable
% 7.18/1.31
% 7.52/1.33 % SZS output start Proof
% 7.52/1.33 Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 7.52/1.33 Axiom 2 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 7.52/1.33 Axiom 3 (left_identity): multiply(identity, X) = X.
% 7.52/1.33 Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 7.52/1.33 Axiom 5 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 7.52/1.33 Axiom 6 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 7.52/1.33 Axiom 7 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 7.52/1.33 Axiom 8 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 7.52/1.33 Axiom 9 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 7.52/1.33 Axiom 10 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 7.52/1.33 Axiom 11 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 7.52/1.33 Axiom 12 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 7.52/1.33
% 7.52/1.33 Lemma 13: multiply(inverse(X), multiply(X, Y)) = Y.
% 7.52/1.33 Proof:
% 7.52/1.33 multiply(inverse(X), multiply(X, Y))
% 7.52/1.33 = { by axiom 9 (associativity) R->L }
% 7.52/1.33 multiply(multiply(inverse(X), X), Y)
% 7.52/1.33 = { by axiom 4 (left_inverse) }
% 7.52/1.33 multiply(identity, Y)
% 7.52/1.33 = { by axiom 3 (left_identity) }
% 7.52/1.33 Y
% 7.52/1.33
% 7.52/1.33 Lemma 14: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 7.52/1.33 Proof:
% 7.52/1.33 multiply(inverse(inverse(X)), Y)
% 7.52/1.33 = { by lemma 13 R->L }
% 7.52/1.33 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 7.52/1.33 = { by lemma 13 }
% 7.52/1.33 multiply(X, Y)
% 7.52/1.33
% 7.52/1.33 Lemma 15: multiply(inverse(inverse(X)), identity) = X.
% 7.52/1.33 Proof:
% 7.52/1.33 multiply(inverse(inverse(X)), identity)
% 7.52/1.33 = { by axiom 4 (left_inverse) R->L }
% 7.52/1.33 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 7.52/1.33 = { by lemma 13 }
% 7.52/1.33 X
% 7.52/1.33
% 7.52/1.33 Lemma 16: multiply(X, identity) = X.
% 7.52/1.33 Proof:
% 7.52/1.33 multiply(X, identity)
% 7.52/1.33 = { by lemma 14 R->L }
% 7.52/1.33 multiply(inverse(inverse(X)), identity)
% 7.52/1.33 = { by lemma 15 }
% 7.52/1.33 X
% 7.52/1.33
% 7.52/1.33 Lemma 17: multiply(X, inverse(X)) = identity.
% 7.52/1.33 Proof:
% 7.52/1.33 multiply(X, inverse(X))
% 7.52/1.33 = { by lemma 14 R->L }
% 7.52/1.33 multiply(inverse(inverse(X)), inverse(X))
% 7.52/1.33 = { by axiom 4 (left_inverse) }
% 7.52/1.33 identity
% 7.52/1.33
% 7.52/1.33 Lemma 18: multiply(greatest_lower_bound(X, identity), Y) = greatest_lower_bound(Y, multiply(X, Y)).
% 7.52/1.33 Proof:
% 7.52/1.33 multiply(greatest_lower_bound(X, identity), Y)
% 7.52/1.33 = { by axiom 2 (symmetry_of_glb) R->L }
% 7.52/1.33 multiply(greatest_lower_bound(identity, X), Y)
% 7.52/1.33 = { by axiom 12 (monotony_glb2) }
% 7.52/1.33 greatest_lower_bound(multiply(identity, Y), multiply(X, Y))
% 7.52/1.33 = { by axiom 3 (left_identity) }
% 7.52/1.33 greatest_lower_bound(Y, multiply(X, Y))
% 7.52/1.33
% 7.52/1.33 Lemma 19: least_upper_bound(X, greatest_lower_bound(Y, X)) = X.
% 7.52/1.33 Proof:
% 7.52/1.33 least_upper_bound(X, greatest_lower_bound(Y, X))
% 7.52/1.33 = { by axiom 2 (symmetry_of_glb) R->L }
% 7.52/1.33 least_upper_bound(X, greatest_lower_bound(X, Y))
% 7.52/1.33 = { by axiom 5 (lub_absorbtion) }
% 7.52/1.33 X
% 7.52/1.33
% 7.52/1.33 Lemma 20: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 7.52/1.33 Proof:
% 7.52/1.33 multiply(X, inverse(multiply(Y, X)))
% 7.52/1.33 = { by lemma 13 R->L }
% 7.52/1.33 multiply(inverse(Y), multiply(Y, multiply(X, inverse(multiply(Y, X)))))
% 7.52/1.33 = { by axiom 9 (associativity) R->L }
% 7.52/1.33 multiply(inverse(Y), multiply(multiply(Y, X), inverse(multiply(Y, X))))
% 7.52/1.33 = { by lemma 17 }
% 7.52/1.33 multiply(inverse(Y), identity)
% 7.52/1.33 = { by lemma 16 }
% 7.52/1.33 inverse(Y)
% 7.52/1.33
% 7.52/1.33 Lemma 21: multiply(inverse(X), least_upper_bound(X, Y)) = least_upper_bound(identity, multiply(inverse(X), Y)).
% 7.52/1.33 Proof:
% 7.52/1.33 multiply(inverse(X), least_upper_bound(X, Y))
% 7.52/1.33 = { by axiom 10 (monotony_lub1) }
% 7.52/1.33 least_upper_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 7.52/1.33 = { by axiom 4 (left_inverse) }
% 7.52/1.33 least_upper_bound(identity, multiply(inverse(X), Y))
% 7.52/1.33
% 7.52/1.33 Lemma 22: multiply(greatest_lower_bound(X, inverse(Y)), Y) = greatest_lower_bound(multiply(X, Y), identity).
% 7.52/1.33 Proof:
% 7.52/1.33 multiply(greatest_lower_bound(X, inverse(Y)), Y)
% 7.52/1.33 = { by axiom 12 (monotony_glb2) }
% 7.52/1.33 greatest_lower_bound(multiply(X, Y), multiply(inverse(Y), Y))
% 7.52/1.33 = { by axiom 4 (left_inverse) }
% 7.52/1.33 greatest_lower_bound(multiply(X, Y), identity)
% 7.52/1.33
% 7.52/1.33 Goal 1 (prove_p23): least_upper_bound(multiply(a, b), identity) = multiply(a, inverse(greatest_lower_bound(a, inverse(b)))).
% 7.52/1.33 Proof:
% 7.52/1.33 least_upper_bound(multiply(a, b), identity)
% 7.52/1.33 = { by lemma 13 R->L }
% 7.52/1.33 multiply(inverse(inverse(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)))
% 7.52/1.33 = { by lemma 19 R->L }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)))))
% 7.52/1.33 = { by lemma 13 R->L }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, multiply(multiply(inverse(inverse(greatest_lower_bound(a, inverse(b)))), multiply(inverse(greatest_lower_bound(a, inverse(b))), inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))), least_upper_bound(multiply(a, b), identity)))))
% 7.52/1.33 = { by lemma 20 }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, multiply(multiply(inverse(inverse(greatest_lower_bound(a, inverse(b)))), inverse(a)), least_upper_bound(multiply(a, b), identity)))))
% 7.52/1.33 = { by lemma 14 }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, multiply(multiply(greatest_lower_bound(a, inverse(b)), inverse(a)), least_upper_bound(multiply(a, b), identity)))))
% 7.52/1.33 = { by lemma 20 R->L }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), 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)))))
% 7.52/1.33 = { by axiom 9 (associativity) R->L }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), 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)))))
% 7.52/1.33 = { by lemma 22 }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, multiply(multiply(greatest_lower_bound(multiply(a, b), identity), inverse(multiply(a, b))), least_upper_bound(multiply(a, b), identity)))))
% 7.52/1.33 = { by lemma 18 }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), 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)))))
% 7.52/1.33 = { by lemma 17 }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, multiply(greatest_lower_bound(inverse(multiply(a, b)), identity), least_upper_bound(multiply(a, b), identity)))))
% 7.52/1.33 = { by lemma 18 }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), 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))))))
% 7.52/1.33 = { by lemma 21 }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(identity, multiply(inverse(multiply(a, b)), identity))))))
% 7.52/1.33 = { by lemma 16 }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(identity, inverse(multiply(a, b)))))))
% 7.52/1.33 = { by axiom 2 (symmetry_of_glb) R->L }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(identity, inverse(multiply(a, b))), least_upper_bound(multiply(a, b), identity)))))
% 7.52/1.33 = { by axiom 8 (associativity_of_glb) }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(greatest_lower_bound(identity, least_upper_bound(identity, inverse(multiply(a, b)))), least_upper_bound(multiply(a, b), identity))))
% 7.52/1.33 = { by axiom 7 (glb_absorbtion) }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, least_upper_bound(multiply(a, b), identity))))
% 7.52/1.33 = { by axiom 1 (symmetry_of_lub) R->L }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), greatest_lower_bound(identity, least_upper_bound(identity, multiply(a, b)))))
% 7.52/1.33 = { by axiom 7 (glb_absorbtion) }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity)), identity))
% 7.52/1.33 = { by axiom 1 (symmetry_of_lub) }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(identity, multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(multiply(a, b), identity))))
% 7.52/1.33 = { by lemma 21 R->L }
% 7.52/1.33 multiply(inverse(inverse(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, inverse(greatest_lower_bound(a, inverse(b)))), least_upper_bound(multiply(a, b), identity))))
% 7.52/1.33 = { by axiom 1 (symmetry_of_lub) R->L }
% 7.52/1.33 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), least_upper_bound(least_upper_bound(multiply(a, b), identity), multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))))
% 7.52/1.33 = { by axiom 6 (associativity_of_lub) R->L }
% 7.52/1.33 multiply(inverse(inverse(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), least_upper_bound(identity, multiply(a, inverse(greatest_lower_bound(a, inverse(b))))))))
% 7.52/1.33 = { by axiom 1 (symmetry_of_lub) }
% 7.52/1.33 multiply(inverse(inverse(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), least_upper_bound(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))), identity))))
% 7.52/1.33 = { by lemma 17 R->L }
% 7.52/1.33 multiply(inverse(inverse(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), 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))))))))
% 7.52/1.33 = { by axiom 11 (monotony_lub2) R->L }
% 7.52/1.33 multiply(inverse(inverse(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), multiply(least_upper_bound(a, greatest_lower_bound(a, inverse(b))), inverse(greatest_lower_bound(a, inverse(b)))))))
% 7.52/1.33 = { by axiom 2 (symmetry_of_glb) }
% 7.52/1.33 multiply(inverse(inverse(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), multiply(least_upper_bound(a, greatest_lower_bound(inverse(b), a)), inverse(greatest_lower_bound(a, inverse(b)))))))
% 7.52/1.33 = { by lemma 19 }
% 7.52/1.33 multiply(inverse(inverse(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), multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))))
% 7.52/1.34 = { by axiom 1 (symmetry_of_lub) }
% 7.52/1.34 multiply(inverse(inverse(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, inverse(greatest_lower_bound(a, inverse(b)))), multiply(a, b))))
% 7.52/1.34 = { by lemma 21 }
% 7.52/1.34 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(identity, multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), multiply(a, b))))
% 7.52/1.34 = { by lemma 13 R->L }
% 7.52/1.34 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(identity, multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), multiply(a, multiply(inverse(greatest_lower_bound(a, inverse(b))), multiply(greatest_lower_bound(a, inverse(b)), b))))))
% 7.52/1.34 = { by lemma 22 }
% 7.52/1.34 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(identity, multiply(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b))))), multiply(a, multiply(inverse(greatest_lower_bound(a, inverse(b))), greatest_lower_bound(multiply(a, b), identity))))))
% 7.52/1.34 = { by axiom 9 (associativity) R->L }
% 7.52/1.34 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(identity, multiply(inverse(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)))))
% 7.52/1.34 = { by lemma 13 }
% 7.52/1.34 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), least_upper_bound(identity, greatest_lower_bound(multiply(a, b), identity)))
% 7.52/1.34 = { by lemma 19 }
% 7.52/1.34 multiply(inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, inverse(b)))))), identity)
% 7.52/1.34 = { by lemma 15 }
% 7.52/1.34 multiply(a, inverse(greatest_lower_bound(a, inverse(b))))
% 7.52/1.34 % SZS output end Proof
% 7.52/1.34
% 7.52/1.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------