TSTP Solution File: GRP167-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP167-3 : 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 : n004.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 01:17:27 EDT 2023
% Result : Unsatisfiable 0.21s 0.70s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP167-3 : 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 : n004.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 21:19:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.70 Command-line arguments: --ground-connectedness --complete-subsets
% 0.21/0.70
% 0.21/0.70 % SZS status Unsatisfiable
% 0.21/0.70
% 0.21/0.72 % SZS output start Proof
% 0.21/0.72 Axiom 1 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.21/0.72 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.21/0.72 Axiom 3 (left_identity): multiply(identity, X) = X.
% 0.21/0.72 Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 0.21/0.72 Axiom 5 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.21/0.72 Axiom 6 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.21/0.72 Axiom 7 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.21/0.72 Axiom 8 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 0.21/0.72 Axiom 9 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.21/0.72 Axiom 10 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.21/0.72 Axiom 11 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.72 Axiom 12 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.21/0.72 Axiom 13 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.72
% 0.21/0.72 Lemma 14: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.21/0.72 Proof:
% 0.21/0.72 multiply(inverse(X), multiply(X, Y))
% 0.21/0.72 = { by axiom 9 (associativity) R->L }
% 0.21/0.72 multiply(multiply(inverse(X), X), Y)
% 0.21/0.72 = { by axiom 4 (left_inverse) }
% 0.21/0.72 multiply(identity, Y)
% 0.21/0.72 = { by axiom 3 (left_identity) }
% 0.21/0.72 Y
% 0.21/0.72
% 0.21/0.72 Lemma 15: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.21/0.72 Proof:
% 0.21/0.72 multiply(inverse(inverse(X)), Y)
% 0.21/0.72 = { by lemma 14 R->L }
% 0.21/0.72 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 0.21/0.72 = { by lemma 14 }
% 0.21/0.72 multiply(X, Y)
% 0.21/0.72
% 0.21/0.72 Lemma 16: multiply(inverse(inverse(X)), identity) = X.
% 0.21/0.72 Proof:
% 0.21/0.72 multiply(inverse(inverse(X)), identity)
% 0.21/0.72 = { by axiom 4 (left_inverse) R->L }
% 0.21/0.72 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 0.21/0.72 = { by lemma 14 }
% 0.21/0.72 X
% 0.21/0.72
% 0.21/0.72 Lemma 17: multiply(X, identity) = X.
% 0.21/0.72 Proof:
% 0.21/0.72 multiply(X, identity)
% 0.21/0.72 = { by lemma 15 R->L }
% 0.21/0.72 multiply(inverse(inverse(X)), identity)
% 0.21/0.72 = { by lemma 16 }
% 0.21/0.72 X
% 0.21/0.72
% 0.21/0.72 Lemma 18: multiply(least_upper_bound(X, identity), Y) = least_upper_bound(Y, multiply(X, Y)).
% 0.21/0.72 Proof:
% 0.21/0.72 multiply(least_upper_bound(X, identity), Y)
% 0.21/0.72 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.21/0.72 multiply(least_upper_bound(identity, X), Y)
% 0.21/0.72 = { by axiom 13 (monotony_lub2) }
% 0.21/0.72 least_upper_bound(multiply(identity, Y), multiply(X, Y))
% 0.21/0.72 = { by axiom 3 (left_identity) }
% 0.21/0.72 least_upper_bound(Y, multiply(X, Y))
% 0.21/0.72
% 0.21/0.72 Lemma 19: multiply(inverse(X), greatest_lower_bound(X, Y)) = greatest_lower_bound(identity, multiply(inverse(X), Y)).
% 0.21/0.72 Proof:
% 0.21/0.72 multiply(inverse(X), greatest_lower_bound(X, Y))
% 0.21/0.72 = { by axiom 10 (monotony_glb1) }
% 0.21/0.72 greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 0.21/0.72 = { by axiom 4 (left_inverse) }
% 0.21/0.72 greatest_lower_bound(identity, multiply(inverse(X), Y))
% 0.21/0.72
% 0.21/0.72 Lemma 20: multiply(inverse(X), least_upper_bound(X, Y)) = least_upper_bound(identity, multiply(inverse(X), Y)).
% 0.21/0.72 Proof:
% 0.21/0.72 multiply(inverse(X), least_upper_bound(X, Y))
% 0.21/0.72 = { by axiom 12 (monotony_lub1) }
% 0.21/0.72 least_upper_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 0.21/0.72 = { by axiom 4 (left_inverse) }
% 0.21/0.72 least_upper_bound(identity, multiply(inverse(X), Y))
% 0.21/0.72
% 0.21/0.72 Lemma 21: multiply(least_upper_bound(X, identity), multiply(X, inverse(least_upper_bound(X, identity)))) = X.
% 0.21/0.72 Proof:
% 0.21/0.72 multiply(least_upper_bound(X, identity), multiply(X, inverse(least_upper_bound(X, identity))))
% 0.21/0.72 = { by lemma 18 }
% 0.21/0.72 least_upper_bound(multiply(X, inverse(least_upper_bound(X, identity))), multiply(X, multiply(X, inverse(least_upper_bound(X, identity)))))
% 0.21/0.72 = { by axiom 12 (monotony_lub1) R->L }
% 0.21/0.72 multiply(X, least_upper_bound(inverse(least_upper_bound(X, identity)), multiply(X, inverse(least_upper_bound(X, identity)))))
% 0.21/0.72 = { by lemma 18 R->L }
% 0.21/0.72 multiply(X, multiply(least_upper_bound(X, identity), inverse(least_upper_bound(X, identity))))
% 0.21/0.72 = { by lemma 15 R->L }
% 0.21/0.72 multiply(X, multiply(inverse(inverse(least_upper_bound(X, identity))), inverse(least_upper_bound(X, identity))))
% 0.21/0.72 = { by axiom 4 (left_inverse) }
% 0.21/0.72 multiply(X, identity)
% 0.21/0.72 = { by lemma 17 }
% 0.21/0.72 X
% 0.21/0.72
% 0.21/0.72 Lemma 22: multiply(inverse(least_upper_bound(X, identity)), X) = multiply(X, inverse(least_upper_bound(X, identity))).
% 0.21/0.72 Proof:
% 0.21/0.72 multiply(inverse(least_upper_bound(X, identity)), X)
% 0.21/0.72 = { by lemma 21 R->L }
% 0.21/0.72 multiply(inverse(least_upper_bound(X, identity)), multiply(least_upper_bound(X, identity), multiply(X, inverse(least_upper_bound(X, identity)))))
% 0.21/0.72 = { by lemma 14 }
% 0.21/0.72 multiply(X, inverse(least_upper_bound(X, identity)))
% 0.21/0.72
% 0.21/0.72 Goal 1 (prove_p19): a = multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)).
% 0.21/0.72 Proof:
% 0.21/0.72 a
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), identity)
% 0.21/0.72 = { by axiom 7 (lub_absorbtion) R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, greatest_lower_bound(identity, a)))
% 0.21/0.72 = { by axiom 1 (symmetry_of_glb) }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, greatest_lower_bound(a, identity)))
% 0.21/0.72 = { by axiom 7 (lub_absorbtion) R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(least_upper_bound(identity, greatest_lower_bound(identity, inverse(a))), greatest_lower_bound(a, identity)))
% 0.21/0.72 = { by axiom 8 (associativity_of_lub) R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(identity, inverse(a)), greatest_lower_bound(a, identity))))
% 0.21/0.72 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a)))))
% 0.21/0.72 = { by lemma 17 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, multiply(inverse(a), identity)))))
% 0.21/0.72 = { by lemma 19 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), multiply(inverse(a), greatest_lower_bound(a, identity)))))
% 0.21/0.72 = { by lemma 18 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, multiply(least_upper_bound(inverse(a), identity), greatest_lower_bound(a, identity))))
% 0.21/0.72 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, multiply(least_upper_bound(identity, inverse(a)), greatest_lower_bound(a, identity))))
% 0.21/0.72 = { by lemma 17 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, multiply(least_upper_bound(identity, multiply(inverse(a), identity)), greatest_lower_bound(a, identity))))
% 0.21/0.72 = { by lemma 20 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, multiply(multiply(inverse(a), least_upper_bound(a, identity)), greatest_lower_bound(a, identity))))
% 0.21/0.72 = { by axiom 9 (associativity) }
% 0.21/0.72 multiply(inverse(inverse(a)), least_upper_bound(identity, multiply(inverse(a), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))))
% 0.21/0.72 = { by lemma 20 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(a, multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))))
% 0.21/0.72 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), a)))
% 0.21/0.72 = { by lemma 21 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(a, inverse(least_upper_bound(a, identity)))))))
% 0.21/0.72 = { by lemma 22 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(inverse(least_upper_bound(a, identity)), a)))))
% 0.21/0.72 = { by axiom 3 (left_identity) R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(identity, multiply(inverse(least_upper_bound(a, identity)), a))))))
% 0.21/0.72 = { by axiom 5 (glb_absorbtion) R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(greatest_lower_bound(identity, least_upper_bound(identity, a)), multiply(inverse(least_upper_bound(a, identity)), a))))))
% 0.21/0.72 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(greatest_lower_bound(identity, least_upper_bound(a, identity)), multiply(inverse(least_upper_bound(a, identity)), a))))))
% 0.21/0.72 = { by axiom 11 (monotony_glb2) }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(identity, multiply(inverse(least_upper_bound(a, identity)), a)), multiply(least_upper_bound(a, identity), multiply(inverse(least_upper_bound(a, identity)), a)))))))
% 0.21/0.72 = { by axiom 3 (left_identity) }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(inverse(least_upper_bound(a, identity)), a), multiply(least_upper_bound(a, identity), multiply(inverse(least_upper_bound(a, identity)), a)))))))
% 0.21/0.72 = { by lemma 15 R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(inverse(least_upper_bound(a, identity)), a), multiply(inverse(inverse(least_upper_bound(a, identity))), multiply(inverse(least_upper_bound(a, identity)), a)))))))
% 0.21/0.72 = { by lemma 14 }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(inverse(least_upper_bound(a, identity)), a), a)))))
% 0.21/0.72 = { by axiom 1 (symmetry_of_glb) }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, multiply(inverse(least_upper_bound(a, identity)), a))))))
% 0.21/0.72 = { by axiom 5 (glb_absorbtion) R->L }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, multiply(inverse(least_upper_bound(a, identity)), greatest_lower_bound(a, least_upper_bound(a, identity))))))))
% 0.21/0.72 = { by axiom 1 (symmetry_of_glb) }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, multiply(inverse(least_upper_bound(a, identity)), greatest_lower_bound(least_upper_bound(a, identity), a)))))))
% 0.21/0.72 = { by lemma 19 }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, greatest_lower_bound(identity, multiply(inverse(least_upper_bound(a, identity)), a)))))))
% 0.21/0.72 = { by axiom 6 (associativity_of_glb) }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(greatest_lower_bound(a, identity), multiply(inverse(least_upper_bound(a, identity)), a))))))
% 0.21/0.72 = { by axiom 1 (symmetry_of_glb) }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(inverse(least_upper_bound(a, identity)), a), greatest_lower_bound(a, identity))))))
% 0.21/0.72 = { by lemma 22 }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(multiply(a, inverse(least_upper_bound(a, identity))), greatest_lower_bound(a, identity))))))
% 0.21/0.72 = { by axiom 1 (symmetry_of_glb) }
% 0.21/0.72 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(greatest_lower_bound(a, identity), multiply(a, inverse(least_upper_bound(a, identity))))))))
% 0.21/0.72 = { by axiom 10 (monotony_glb1) }
% 0.21/0.73 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), multiply(a, inverse(least_upper_bound(a, identity))))))))
% 0.21/0.73 = { by lemma 21 }
% 0.21/0.73 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)), a))))
% 0.21/0.73 = { by axiom 7 (lub_absorbtion) }
% 0.21/0.73 multiply(inverse(inverse(a)), multiply(inverse(a), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity))))
% 0.21/0.73 = { by lemma 14 }
% 0.21/0.73 multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity))
% 0.21/0.73 % SZS output end Proof
% 0.21/0.73
% 0.21/0.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------