TSTP Solution File: GRP185-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP185-3 : 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 : n031.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 01:17:39 EDT 2023
% Result : Unsatisfiable 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP185-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 20:26:55 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.48
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.21/0.49 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.21/0.49 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.21/0.49 Axiom 4 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.21/0.49 Axiom 5 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 0.21/0.49 Axiom 6 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.21/0.49 Axiom 7 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.21/0.49 Axiom 8 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.21/0.49 Axiom 9 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.49
% 0.21/0.49 Lemma 10: greatest_lower_bound(X, least_upper_bound(Y, X)) = X.
% 0.21/0.49 Proof:
% 0.21/0.49 greatest_lower_bound(X, least_upper_bound(Y, X))
% 0.21/0.49 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.49 greatest_lower_bound(X, least_upper_bound(X, Y))
% 0.21/0.49 = { by axiom 6 (glb_absorbtion) }
% 0.21/0.49 X
% 0.21/0.49
% 0.21/0.49 Lemma 11: greatest_lower_bound(Y, greatest_lower_bound(Z, X)) = greatest_lower_bound(X, greatest_lower_bound(Y, Z)).
% 0.21/0.49 Proof:
% 0.21/0.49 greatest_lower_bound(Y, greatest_lower_bound(Z, X))
% 0.21/0.49 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.21/0.49 greatest_lower_bound(greatest_lower_bound(Z, X), Y)
% 0.21/0.49 = { by axiom 3 (symmetry_of_glb) }
% 0.21/0.49 greatest_lower_bound(greatest_lower_bound(X, Z), Y)
% 0.21/0.49 = { by axiom 7 (associativity_of_glb) R->L }
% 0.21/0.49 greatest_lower_bound(X, greatest_lower_bound(Z, Y))
% 0.21/0.49 = { by axiom 3 (symmetry_of_glb) }
% 0.21/0.49 greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 0.21/0.49
% 0.21/0.49 Lemma 12: least_upper_bound(X, greatest_lower_bound(Y, X)) = X.
% 0.21/0.49 Proof:
% 0.21/0.49 least_upper_bound(X, greatest_lower_bound(Y, X))
% 0.21/0.49 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.21/0.49 least_upper_bound(X, greatest_lower_bound(X, Y))
% 0.21/0.49 = { by axiom 4 (lub_absorbtion) }
% 0.21/0.49 X
% 0.21/0.49
% 0.21/0.49 Lemma 13: least_upper_bound(Y, least_upper_bound(Z, X)) = least_upper_bound(X, least_upper_bound(Y, Z)).
% 0.21/0.49 Proof:
% 0.21/0.49 least_upper_bound(Y, least_upper_bound(Z, X))
% 0.21/0.49 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.21/0.49 least_upper_bound(least_upper_bound(Z, X), Y)
% 0.21/0.49 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.49 least_upper_bound(least_upper_bound(X, Z), Y)
% 0.21/0.49 = { by axiom 5 (associativity_of_lub) R->L }
% 0.21/0.49 least_upper_bound(X, least_upper_bound(Z, Y))
% 0.21/0.49 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.49 least_upper_bound(X, least_upper_bound(Y, Z))
% 0.21/0.49
% 0.21/0.49 Lemma 14: least_upper_bound(Z, least_upper_bound(Y, X)) = least_upper_bound(X, least_upper_bound(Y, Z)).
% 0.21/0.49 Proof:
% 0.21/0.49 least_upper_bound(Z, least_upper_bound(Y, X))
% 0.21/0.49 = { by lemma 13 }
% 0.21/0.49 least_upper_bound(X, least_upper_bound(Z, Y))
% 0.21/0.49 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.49 least_upper_bound(X, least_upper_bound(Y, Z))
% 0.21/0.49
% 0.21/0.49 Lemma 15: least_upper_bound(multiply(X, Y), multiply(Z, Y)) = multiply(least_upper_bound(Z, X), Y).
% 0.21/0.49 Proof:
% 0.21/0.49 least_upper_bound(multiply(X, Y), multiply(Z, Y))
% 0.21/0.49 = { by axiom 9 (monotony_lub2) R->L }
% 0.21/0.49 multiply(least_upper_bound(X, Z), Y)
% 0.21/0.49 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.49 multiply(least_upper_bound(Z, X), Y)
% 0.21/0.49
% 0.21/0.49 Lemma 16: least_upper_bound(multiply(least_upper_bound(X, identity), Y), Y) = multiply(least_upper_bound(X, identity), Y).
% 0.21/0.49 Proof:
% 0.21/0.49 least_upper_bound(multiply(least_upper_bound(X, identity), Y), Y)
% 0.21/0.49 = { by axiom 1 (left_identity) R->L }
% 0.21/0.49 least_upper_bound(multiply(least_upper_bound(X, identity), Y), multiply(identity, Y))
% 0.21/0.49 = { by lemma 15 }
% 0.21/0.49 multiply(least_upper_bound(identity, least_upper_bound(X, identity)), Y)
% 0.21/0.49 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.21/0.49 multiply(least_upper_bound(least_upper_bound(X, identity), identity), Y)
% 0.21/0.49 = { by lemma 10 R->L }
% 0.21/0.49 multiply(least_upper_bound(least_upper_bound(X, identity), greatest_lower_bound(identity, least_upper_bound(X, identity))), Y)
% 0.21/0.49 = { by lemma 12 }
% 0.21/0.49 multiply(least_upper_bound(X, identity), Y)
% 0.21/0.49
% 0.21/0.49 Lemma 17: greatest_lower_bound(X, multiply(least_upper_bound(Y, identity), least_upper_bound(Z, X))) = X.
% 0.21/0.49 Proof:
% 0.21/0.49 greatest_lower_bound(X, multiply(least_upper_bound(Y, identity), least_upper_bound(Z, X)))
% 0.21/0.50 = { by lemma 16 R->L }
% 0.21/0.50 greatest_lower_bound(X, least_upper_bound(multiply(least_upper_bound(Y, identity), least_upper_bound(Z, X)), least_upper_bound(Z, X)))
% 0.21/0.50 = { by lemma 13 }
% 0.21/0.50 greatest_lower_bound(X, least_upper_bound(X, least_upper_bound(multiply(least_upper_bound(Y, identity), least_upper_bound(Z, X)), Z)))
% 0.21/0.50 = { by axiom 6 (glb_absorbtion) }
% 0.21/0.50 X
% 0.21/0.50
% 0.21/0.50 Goal 1 (prove_p22b): greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))) = least_upper_bound(multiply(a, b), identity).
% 0.21/0.50 Proof:
% 0.21/0.50 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))
% 0.21/0.50 = { by lemma 12 R->L }
% 0.21/0.50 least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))))
% 0.21/0.50 = { by lemma 11 }
% 0.21/0.50 least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(identity, least_upper_bound(multiply(a, b), identity))))
% 0.21/0.50 = { by lemma 10 }
% 0.21/0.50 least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), identity))
% 0.21/0.50 = { by axiom 3 (symmetry_of_glb) }
% 0.21/0.50 least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(identity, multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))
% 0.21/0.50 = { by lemma 17 }
% 0.21/0.50 least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), identity)
% 0.21/0.50 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.50 least_upper_bound(identity, greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))
% 0.21/0.50 = { by lemma 12 R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))))
% 0.21/0.50 = { by lemma 11 }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(multiply(a, b), least_upper_bound(multiply(a, b), identity)))))
% 0.21/0.50 = { by axiom 6 (glb_absorbtion) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(a, b))))
% 0.21/0.50 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))))
% 0.21/0.50 = { by lemma 12 R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(identity, multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))))))
% 0.21/0.50 = { by lemma 17 }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), identity))))
% 0.21/0.50 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))))
% 0.21/0.50 = { by lemma 12 R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, multiply(least_upper_bound(a, identity), least_upper_bound(least_upper_bound(b, identity), greatest_lower_bound(b, least_upper_bound(b, identity))))))))
% 0.21/0.50 = { by axiom 6 (glb_absorbtion) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, multiply(least_upper_bound(a, identity), least_upper_bound(least_upper_bound(b, identity), b))))))
% 0.21/0.50 = { by axiom 8 (monotony_lub1) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(least_upper_bound(a, identity), b))))))
% 0.21/0.50 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(least_upper_bound(identity, a), b))))))
% 0.21/0.50 = { by lemma 15 R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), least_upper_bound(multiply(a, b), multiply(identity, b)))))))
% 0.21/0.50 = { by axiom 1 (left_identity) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), least_upper_bound(multiply(a, b), b))))))
% 0.21/0.50 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), least_upper_bound(b, multiply(a, b)))))))
% 0.21/0.50 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, least_upper_bound(least_upper_bound(b, multiply(a, b)), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))))))
% 0.21/0.50 = { by axiom 5 (associativity_of_lub) R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, least_upper_bound(b, least_upper_bound(multiply(a, b), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))))))
% 0.21/0.50 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(identity, least_upper_bound(b, least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(a, b)))))))
% 0.21/0.50 = { by lemma 14 R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(a, b)), least_upper_bound(b, identity)))))
% 0.21/0.50 = { by axiom 5 (associativity_of_lub) R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), least_upper_bound(multiply(a, b), least_upper_bound(b, identity))))))
% 0.21/0.50 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), least_upper_bound(least_upper_bound(b, identity), multiply(a, b))))))
% 0.21/0.50 = { by axiom 5 (associativity_of_lub) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), least_upper_bound(b, identity)), multiply(a, b)))))
% 0.21/0.50 = { by lemma 16 }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), greatest_lower_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(a, b)))))
% 0.21/0.50 = { by lemma 10 }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), multiply(a, b)))
% 0.21/0.50 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.50 least_upper_bound(identity, least_upper_bound(multiply(a, b), greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))))
% 0.21/0.50 = { by lemma 14 R->L }
% 0.21/0.50 least_upper_bound(greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))), least_upper_bound(multiply(a, b), identity))
% 0.21/0.50 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.21/0.50 least_upper_bound(least_upper_bound(multiply(a, b), identity), greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))
% 0.21/0.50 = { by axiom 3 (symmetry_of_glb) }
% 0.21/0.50 least_upper_bound(least_upper_bound(multiply(a, b), identity), greatest_lower_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), least_upper_bound(multiply(a, b), identity)))
% 0.21/0.50 = { by lemma 12 }
% 0.21/0.50 least_upper_bound(multiply(a, b), identity)
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50
% 0.21/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------