TSTP Solution File: GRP185-4 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP185-4 : 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 : n019.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 0.18s 0.47s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP185-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Aug 29 02:38:13 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.47 Command-line arguments: --flatten
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable
% 0.18/0.47
% 0.18/0.48 % SZS output start Proof
% 0.18/0.48 Axiom 1 (p22b_1): inverse(identity) = identity.
% 0.18/0.48 Axiom 2 (p22b_2): inverse(inverse(X)) = X.
% 0.18/0.48 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.18/0.48 Axiom 4 (idempotence_of_lub): least_upper_bound(X, X) = X.
% 0.18/0.48 Axiom 5 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.18/0.48 Axiom 6 (left_identity): multiply(identity, X) = X.
% 0.18/0.48 Axiom 7 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.18/0.48 Axiom 8 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.18/0.48 Axiom 9 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 0.18/0.48 Axiom 10 (p22b_3): inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 0.18/0.48 Axiom 11 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.18/0.48 Axiom 12 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.18/0.48 Axiom 13 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.18/0.48
% 0.18/0.48 Lemma 14: multiply(inverse(identity), X) = X.
% 0.18/0.48 Proof:
% 0.18/0.48 multiply(inverse(identity), X)
% 0.18/0.48 = { by axiom 1 (p22b_1) }
% 0.18/0.48 multiply(identity, X)
% 0.18/0.48 = { by axiom 6 (left_identity) }
% 0.18/0.48 X
% 0.18/0.48
% 0.18/0.48 Lemma 15: multiply(X, inverse(identity)) = X.
% 0.18/0.48 Proof:
% 0.18/0.48 multiply(X, inverse(identity))
% 0.18/0.48 = { by axiom 2 (p22b_2) R->L }
% 0.18/0.48 inverse(inverse(multiply(X, inverse(identity))))
% 0.18/0.48 = { by axiom 1 (p22b_1) }
% 0.18/0.48 inverse(inverse(multiply(X, identity)))
% 0.18/0.48 = { by axiom 10 (p22b_3) }
% 0.18/0.48 inverse(multiply(inverse(identity), inverse(X)))
% 0.18/0.48 = { by lemma 14 }
% 0.18/0.48 inverse(inverse(X))
% 0.18/0.48 = { by axiom 2 (p22b_2) }
% 0.18/0.48 X
% 0.18/0.48
% 0.18/0.48 Lemma 16: least_upper_bound(inverse(identity), X) = least_upper_bound(X, identity).
% 0.18/0.48 Proof:
% 0.18/0.48 least_upper_bound(inverse(identity), X)
% 0.18/0.48 = { by axiom 5 (symmetry_of_lub) R->L }
% 0.18/0.48 least_upper_bound(X, inverse(identity))
% 0.18/0.48 = { by axiom 1 (p22b_1) }
% 0.18/0.48 least_upper_bound(X, identity)
% 0.18/0.48
% 0.18/0.48 Lemma 17: least_upper_bound(inverse(identity), least_upper_bound(X, Y)) = least_upper_bound(X, least_upper_bound(Y, identity)).
% 0.18/0.48 Proof:
% 0.18/0.48 least_upper_bound(inverse(identity), least_upper_bound(X, Y))
% 0.18/0.48 = { by axiom 5 (symmetry_of_lub) R->L }
% 0.18/0.48 least_upper_bound(inverse(identity), least_upper_bound(Y, X))
% 0.18/0.48 = { by axiom 9 (associativity_of_lub) }
% 0.18/0.48 least_upper_bound(least_upper_bound(inverse(identity), Y), X)
% 0.18/0.48 = { by lemma 16 }
% 0.18/0.49 least_upper_bound(least_upper_bound(Y, identity), X)
% 0.18/0.49 = { by axiom 5 (symmetry_of_lub) }
% 0.18/0.49 least_upper_bound(X, least_upper_bound(Y, identity))
% 0.18/0.49
% 0.18/0.49 Lemma 18: least_upper_bound(multiply(X, Y), least_upper_bound(least_upper_bound(X, identity), Y)) = multiply(least_upper_bound(X, identity), least_upper_bound(Y, identity)).
% 0.18/0.49 Proof:
% 0.18/0.49 least_upper_bound(multiply(X, Y), least_upper_bound(least_upper_bound(X, identity), Y))
% 0.18/0.49 = { by axiom 5 (symmetry_of_lub) R->L }
% 0.18/0.49 least_upper_bound(multiply(X, Y), least_upper_bound(Y, least_upper_bound(X, identity)))
% 0.18/0.49 = { by lemma 17 R->L }
% 0.18/0.49 least_upper_bound(multiply(X, Y), least_upper_bound(inverse(identity), least_upper_bound(Y, X)))
% 0.18/0.49 = { by axiom 5 (symmetry_of_lub) }
% 0.18/0.49 least_upper_bound(multiply(X, Y), least_upper_bound(inverse(identity), least_upper_bound(X, Y)))
% 0.18/0.49 = { by lemma 17 }
% 0.18/0.49 least_upper_bound(multiply(X, Y), least_upper_bound(X, least_upper_bound(Y, identity)))
% 0.18/0.49 = { by axiom 9 (associativity_of_lub) }
% 0.18/0.49 least_upper_bound(least_upper_bound(multiply(X, Y), X), least_upper_bound(Y, identity))
% 0.18/0.49 = { by axiom 5 (symmetry_of_lub) }
% 0.18/0.49 least_upper_bound(least_upper_bound(Y, identity), least_upper_bound(multiply(X, Y), X))
% 0.18/0.49 = { by lemma 15 R->L }
% 0.18/0.49 least_upper_bound(least_upper_bound(Y, identity), least_upper_bound(multiply(X, Y), multiply(X, inverse(identity))))
% 0.18/0.49 = { by axiom 12 (monotony_lub1) R->L }
% 0.18/0.49 least_upper_bound(least_upper_bound(Y, identity), multiply(X, least_upper_bound(Y, inverse(identity))))
% 0.18/0.49 = { by axiom 5 (symmetry_of_lub) }
% 0.18/0.49 least_upper_bound(least_upper_bound(Y, identity), multiply(X, least_upper_bound(inverse(identity), Y)))
% 0.18/0.49 = { by lemma 16 }
% 0.18/0.49 least_upper_bound(least_upper_bound(Y, identity), multiply(X, least_upper_bound(Y, identity)))
% 0.18/0.49 = { by lemma 14 R->L }
% 0.18/0.49 least_upper_bound(multiply(inverse(identity), least_upper_bound(Y, identity)), multiply(X, least_upper_bound(Y, identity)))
% 0.18/0.49 = { by axiom 13 (monotony_lub2) R->L }
% 0.18/0.49 multiply(least_upper_bound(inverse(identity), X), least_upper_bound(Y, identity))
% 0.18/0.49 = { by lemma 16 }
% 0.18/0.49 multiply(least_upper_bound(X, identity), least_upper_bound(Y, identity))
% 0.18/0.49
% 0.18/0.49 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).
% 0.18/0.49 Proof:
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))
% 0.18/0.49 = { by lemma 18 R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(least_upper_bound(a, identity), b)))
% 0.18/0.49 = { by axiom 4 (idempotence_of_lub) R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(least_upper_bound(multiply(a, b), multiply(a, b)), least_upper_bound(least_upper_bound(a, identity), b)))
% 0.18/0.49 = { by axiom 9 (associativity_of_lub) R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(a, b), least_upper_bound(least_upper_bound(a, identity), b))))
% 0.18/0.49 = { by lemma 18 }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))
% 0.18/0.49 = { by axiom 8 (lub_absorbtion) R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(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)), inverse(identity)))))
% 0.18/0.49 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(inverse(identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))))
% 0.18/0.49 = { by axiom 8 (lub_absorbtion) R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(inverse(identity), least_upper_bound(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)), least_upper_bound(a, identity)))))))
% 0.18/0.49 = { by lemma 15 R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(inverse(identity), least_upper_bound(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(least_upper_bound(a, identity), inverse(identity))))))))
% 0.18/0.49 = { by axiom 11 (monotony_glb1) R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(inverse(identity), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(least_upper_bound(b, identity), inverse(identity))))))))
% 0.18/0.49 = { by axiom 3 (symmetry_of_glb) }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(inverse(identity), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(inverse(identity), least_upper_bound(b, identity))))))))
% 0.18/0.49 = { by lemma 16 R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(inverse(identity), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(inverse(identity), least_upper_bound(inverse(identity), b))))))))
% 0.18/0.49 = { by axiom 7 (glb_absorbtion) }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(inverse(identity), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(least_upper_bound(a, identity), inverse(identity)))))))
% 0.18/0.49 = { by lemma 15 }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(inverse(identity), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), least_upper_bound(a, identity))))))
% 0.18/0.49 = { by lemma 17 R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), greatest_lower_bound(inverse(identity), least_upper_bound(inverse(identity), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), a))))))
% 0.18/0.49 = { by axiom 7 (glb_absorbtion) }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), inverse(identity))))
% 0.18/0.49 = { by axiom 5 (symmetry_of_lub) R->L }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(multiply(a, b), least_upper_bound(inverse(identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))))
% 0.18/0.49 = { by axiom 9 (associativity_of_lub) }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(least_upper_bound(multiply(a, b), inverse(identity)), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))
% 0.18/0.49 = { by axiom 1 (p22b_1) }
% 0.18/0.49 greatest_lower_bound(least_upper_bound(multiply(a, b), identity), least_upper_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))
% 0.18/0.49 = { by axiom 7 (glb_absorbtion) }
% 0.18/0.49 least_upper_bound(multiply(a, b), identity)
% 0.18/0.49 % SZS output end Proof
% 0.18/0.49
% 0.18/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
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