TSTP Solution File: GRP179-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP179-2 : 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 : n011.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 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP179-2 : 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
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 00:52:56 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 Command-line arguments: --flatten
% 0.20/0.56
% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56
% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Axiom 1 (idempotence_of_lub): least_upper_bound(X, X) = X.
% 0.20/0.57 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.20/0.57 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.20/0.57 Axiom 4 (left_identity): multiply(identity, X) = X.
% 0.20/0.57 Axiom 5 (left_inverse): multiply(inverse(X), X) = identity.
% 0.20/0.57 Axiom 6 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.20/0.57 Axiom 7 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 0.20/0.57 Axiom 8 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.20/0.57 Axiom 9 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.20/0.57 Axiom 10 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.20/0.57 Axiom 11 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.20/0.57 Axiom 12 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.57 Axiom 13 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.57
% 0.20/0.57 Lemma 14: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(inverse(X), multiply(X, Y))
% 0.20/0.57 = { by axiom 10 (associativity) R->L }
% 0.20/0.57 multiply(multiply(inverse(X), X), Y)
% 0.20/0.57 = { by axiom 5 (left_inverse) }
% 0.20/0.57 multiply(identity, Y)
% 0.20/0.57 = { by axiom 4 (left_identity) }
% 0.20/0.57 Y
% 0.20/0.57
% 0.20/0.57 Lemma 15: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(inverse(inverse(X)), Y)
% 0.20/0.57 = { by lemma 14 R->L }
% 0.20/0.57 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 multiply(X, Y)
% 0.20/0.57
% 0.20/0.57 Lemma 16: multiply(X, identity) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(X, identity)
% 0.20/0.57 = { by lemma 15 R->L }
% 0.20/0.57 multiply(inverse(inverse(X)), identity)
% 0.20/0.57 = { by axiom 5 (left_inverse) R->L }
% 0.20/0.57 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 17: multiply(X, inverse(X)) = identity.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(X, inverse(X))
% 0.20/0.57 = { by lemma 15 R->L }
% 0.20/0.57 multiply(inverse(inverse(X)), inverse(X))
% 0.20/0.57 = { by axiom 5 (left_inverse) }
% 0.20/0.57 identity
% 0.20/0.57
% 0.20/0.57 Lemma 18: multiply(X, least_upper_bound(Y, identity)) = least_upper_bound(X, multiply(X, Y)).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(X, least_upper_bound(Y, identity))
% 0.20/0.57 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.20/0.57 multiply(X, least_upper_bound(identity, Y))
% 0.20/0.57 = { by axiom 11 (monotony_lub1) }
% 0.20/0.57 least_upper_bound(multiply(X, identity), multiply(X, Y))
% 0.20/0.57 = { by lemma 16 }
% 0.20/0.57 least_upper_bound(X, multiply(X, Y))
% 0.20/0.57
% 0.20/0.57 Lemma 19: multiply(greatest_lower_bound(X, identity), Y) = greatest_lower_bound(Y, multiply(X, Y)).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(greatest_lower_bound(X, identity), Y)
% 0.20/0.57 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.20/0.57 multiply(greatest_lower_bound(identity, X), Y)
% 0.20/0.57 = { by axiom 13 (monotony_glb2) }
% 0.20/0.57 greatest_lower_bound(multiply(identity, Y), multiply(X, Y))
% 0.20/0.57 = { by axiom 4 (left_identity) }
% 0.20/0.57 greatest_lower_bound(Y, multiply(X, Y))
% 0.20/0.57
% 0.20/0.57 Lemma 20: greatest_lower_bound(X, least_upper_bound(Y, X)) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 greatest_lower_bound(X, least_upper_bound(Y, X))
% 0.20/0.57 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.20/0.57 greatest_lower_bound(X, least_upper_bound(X, Y))
% 0.20/0.57 = { by axiom 8 (glb_absorbtion) }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 21: least_upper_bound(X, greatest_lower_bound(Y, X)) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 least_upper_bound(X, greatest_lower_bound(Y, X))
% 0.20/0.57 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.20/0.58 least_upper_bound(X, greatest_lower_bound(X, Y))
% 0.20/0.58 = { by axiom 6 (lub_absorbtion) }
% 0.20/0.58 X
% 0.20/0.58
% 0.20/0.58 Lemma 22: multiply(inverse(least_upper_bound(inverse(X), identity)), least_upper_bound(X, identity)) = X.
% 0.20/0.58 Proof:
% 0.20/0.58 multiply(inverse(least_upper_bound(inverse(X), identity)), least_upper_bound(X, identity))
% 0.20/0.58 = { by axiom 5 (left_inverse) R->L }
% 0.20/0.58 multiply(inverse(least_upper_bound(inverse(X), identity)), least_upper_bound(X, multiply(inverse(X), X)))
% 0.20/0.58 = { by axiom 4 (left_identity) R->L }
% 0.20/0.58 multiply(inverse(least_upper_bound(inverse(X), identity)), least_upper_bound(multiply(identity, X), multiply(inverse(X), X)))
% 0.20/0.58 = { by axiom 12 (monotony_lub2) R->L }
% 0.20/0.58 multiply(inverse(least_upper_bound(inverse(X), identity)), multiply(least_upper_bound(identity, inverse(X)), X))
% 0.20/0.58 = { by axiom 2 (symmetry_of_lub) }
% 0.20/0.58 multiply(inverse(least_upper_bound(inverse(X), identity)), multiply(least_upper_bound(inverse(X), identity), X))
% 0.20/0.58 = { by lemma 14 }
% 0.20/0.58 X
% 0.20/0.58
% 0.20/0.58 Goal 1 (prove_p18): least_upper_bound(inverse(a), identity) = inverse(greatest_lower_bound(a, identity)).
% 0.20/0.58 Proof:
% 0.20/0.58 least_upper_bound(inverse(a), identity)
% 0.20/0.58 = { by lemma 14 R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(greatest_lower_bound(a, identity), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 6 (lub_absorbtion) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(greatest_lower_bound(a, identity), inverse(least_upper_bound(inverse(a), identity)))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 9 (associativity_of_glb) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(a, greatest_lower_bound(identity, inverse(least_upper_bound(inverse(a), identity))))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(a, greatest_lower_bound(inverse(least_upper_bound(inverse(a), identity)), identity))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by lemma 17 R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(a, greatest_lower_bound(inverse(least_upper_bound(inverse(a), identity)), multiply(least_upper_bound(inverse(a), identity), inverse(least_upper_bound(inverse(a), identity)))))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by lemma 19 R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(a, multiply(greatest_lower_bound(least_upper_bound(inverse(a), identity), identity), inverse(least_upper_bound(inverse(a), identity))))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(a, multiply(greatest_lower_bound(identity, least_upper_bound(inverse(a), identity)), inverse(least_upper_bound(inverse(a), identity))))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by lemma 20 }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(a, multiply(identity, inverse(least_upper_bound(inverse(a), identity))))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 4 (left_identity) }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(a, inverse(least_upper_bound(inverse(a), identity)))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(least_upper_bound(inverse(a), identity)), a)), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by lemma 22 R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(least_upper_bound(inverse(a), identity)), multiply(inverse(least_upper_bound(inverse(a), identity)), least_upper_bound(a, identity)))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 1 (idempotence_of_lub) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(least_upper_bound(inverse(a), identity)), multiply(inverse(least_upper_bound(inverse(a), identity)), least_upper_bound(a, least_upper_bound(identity, identity))))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 7 (associativity_of_lub) }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(least_upper_bound(inverse(a), identity)), multiply(inverse(least_upper_bound(inverse(a), identity)), least_upper_bound(least_upper_bound(a, identity), identity)))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by lemma 18 }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(least_upper_bound(inverse(a), identity)), least_upper_bound(inverse(least_upper_bound(inverse(a), identity)), multiply(inverse(least_upper_bound(inverse(a), identity)), least_upper_bound(a, identity))))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by lemma 22 }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(least_upper_bound(inverse(a), identity)), least_upper_bound(inverse(least_upper_bound(inverse(a), identity)), a))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 2 (symmetry_of_lub) }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(least_upper_bound(inverse(a), identity)), least_upper_bound(a, inverse(least_upper_bound(inverse(a), identity))))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by lemma 20 }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(greatest_lower_bound(a, identity), inverse(least_upper_bound(inverse(a), identity))), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(inverse(least_upper_bound(inverse(a), identity)), greatest_lower_bound(a, identity)), least_upper_bound(inverse(a), identity)))
% 0.20/0.58 = { by axiom 12 (monotony_lub2) }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(multiply(inverse(least_upper_bound(inverse(a), identity)), least_upper_bound(inverse(a), identity)), multiply(greatest_lower_bound(a, identity), least_upper_bound(inverse(a), identity))))
% 0.20/0.58 = { by axiom 5 (left_inverse) }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(identity, multiply(greatest_lower_bound(a, identity), least_upper_bound(inverse(a), identity))))
% 0.20/0.58 = { by lemma 18 }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), multiply(greatest_lower_bound(a, identity), inverse(a)))))
% 0.20/0.58 = { by lemma 19 }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(a), multiply(a, inverse(a))))))
% 0.20/0.58 = { by lemma 17 }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(a), identity))))
% 0.20/0.58 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(inverse(a), identity)), identity))
% 0.20/0.58 = { by axiom 7 (associativity_of_lub) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(greatest_lower_bound(a, identity), least_upper_bound(greatest_lower_bound(inverse(a), identity), identity)))
% 0.20/0.58 = { by axiom 2 (symmetry_of_lub) }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(greatest_lower_bound(a, identity), least_upper_bound(identity, greatest_lower_bound(inverse(a), identity))))
% 0.20/0.58 = { by lemma 21 }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(greatest_lower_bound(a, identity), identity))
% 0.20/0.58 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(identity, greatest_lower_bound(a, identity)))
% 0.20/0.58 = { by lemma 21 }
% 0.20/0.58 multiply(inverse(greatest_lower_bound(a, identity)), identity)
% 0.20/0.58 = { by lemma 16 }
% 0.20/0.58 inverse(greatest_lower_bound(a, identity))
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58
% 0.20/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
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