TSTP Solution File: GRP184-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP184-1 : 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 : n021.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 01:17:38 EDT 2023
% Result : Unsatisfiable 0.20s 0.58s
% 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
% 0.07/0.12 % Problem : GRP184-1 : 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
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Mon Aug 28 21:33:43 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.58 Command-line arguments: --flatten
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% 0.20/0.58 % SZS status Unsatisfiable
% 0.20/0.58
% 0.20/0.59 % SZS output start Proof
% 0.20/0.59 Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.20/0.59 Axiom 2 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.20/0.59 Axiom 3 (left_identity): multiply(identity, X) = X.
% 0.20/0.59 Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 0.20/0.59 Axiom 5 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.20/0.59 Axiom 6 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.20/0.59 Axiom 7 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.59 Axiom 8 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.20/0.59 Axiom 9 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.59
% 0.20/0.59 Lemma 10: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(inverse(X), multiply(X, Y))
% 0.20/0.59 = { by axiom 5 (associativity) R->L }
% 0.20/0.59 multiply(multiply(inverse(X), X), Y)
% 0.20/0.59 = { by axiom 4 (left_inverse) }
% 0.20/0.59 multiply(identity, Y)
% 0.20/0.59 = { by axiom 3 (left_identity) }
% 0.20/0.59 Y
% 0.20/0.59
% 0.20/0.59 Lemma 11: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(inverse(inverse(X)), Y)
% 0.20/0.59 = { by lemma 10 R->L }
% 0.20/0.59 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 0.20/0.59 = { by lemma 10 }
% 0.20/0.59 multiply(X, Y)
% 0.20/0.59
% 0.20/0.59 Lemma 12: multiply(X, identity) = X.
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(X, identity)
% 0.20/0.59 = { by lemma 11 R->L }
% 0.20/0.59 multiply(inverse(inverse(X)), identity)
% 0.20/0.59 = { by axiom 4 (left_inverse) R->L }
% 0.20/0.59 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 0.20/0.59 = { by lemma 10 }
% 0.20/0.59 X
% 0.20/0.59
% 0.20/0.59 Lemma 13: multiply(X, least_upper_bound(Y, identity)) = least_upper_bound(X, multiply(X, Y)).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(X, least_upper_bound(Y, identity))
% 0.20/0.59 = { by axiom 1 (symmetry_of_lub) R->L }
% 0.20/0.59 multiply(X, least_upper_bound(identity, Y))
% 0.20/0.59 = { by axiom 6 (monotony_lub1) }
% 0.20/0.59 least_upper_bound(multiply(X, identity), multiply(X, Y))
% 0.20/0.59 = { by lemma 12 }
% 0.20/0.59 least_upper_bound(X, multiply(X, Y))
% 0.20/0.59
% 0.20/0.59 Lemma 14: multiply(greatest_lower_bound(X, identity), Y) = greatest_lower_bound(Y, multiply(X, Y)).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(greatest_lower_bound(X, identity), Y)
% 0.20/0.59 = { by axiom 2 (symmetry_of_glb) R->L }
% 0.20/0.59 multiply(greatest_lower_bound(identity, X), Y)
% 0.20/0.59 = { by axiom 9 (monotony_glb2) }
% 0.20/0.59 greatest_lower_bound(multiply(identity, Y), multiply(X, Y))
% 0.20/0.59 = { by axiom 3 (left_identity) }
% 0.20/0.59 greatest_lower_bound(Y, multiply(X, Y))
% 0.20/0.59
% 0.20/0.59 Goal 1 (prove_p21): multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity))) = multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity)).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity)))
% 0.20/0.59 = { by lemma 10 R->L }
% 0.20/0.59 multiply(inverse(X), multiply(X, multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity)))))
% 0.20/0.59 = { by axiom 5 (associativity) R->L }
% 0.20/0.59 multiply(inverse(X), multiply(multiply(X, least_upper_bound(a, identity)), inverse(greatest_lower_bound(a, identity))))
% 0.20/0.59 = { by lemma 13 }
% 0.20/0.59 multiply(inverse(X), multiply(least_upper_bound(X, multiply(X, a)), inverse(greatest_lower_bound(a, identity))))
% 0.20/0.59 = { by axiom 7 (monotony_lub2) }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(multiply(X, a), inverse(greatest_lower_bound(a, identity)))))
% 0.20/0.59 = { by axiom 5 (associativity) }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(X, multiply(a, inverse(greatest_lower_bound(a, identity))))))
% 0.20/0.59 = { by lemma 10 R->L }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(X, multiply(inverse(greatest_lower_bound(a, identity)), multiply(greatest_lower_bound(a, identity), multiply(a, inverse(greatest_lower_bound(a, identity))))))))
% 0.20/0.59 = { by lemma 14 }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(X, multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(a, inverse(greatest_lower_bound(a, identity))), multiply(a, multiply(a, inverse(greatest_lower_bound(a, identity)))))))))
% 0.20/0.59 = { by axiom 8 (monotony_glb1) R->L }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(X, multiply(inverse(greatest_lower_bound(a, identity)), multiply(a, greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(a, inverse(greatest_lower_bound(a, identity)))))))))
% 0.20/0.59 = { by lemma 14 R->L }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(X, multiply(inverse(greatest_lower_bound(a, identity)), multiply(a, multiply(greatest_lower_bound(a, identity), inverse(greatest_lower_bound(a, identity))))))))
% 0.20/0.59 = { by lemma 11 R->L }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(X, multiply(inverse(greatest_lower_bound(a, identity)), multiply(a, multiply(inverse(inverse(greatest_lower_bound(a, identity))), inverse(greatest_lower_bound(a, identity))))))))
% 0.20/0.59 = { by axiom 4 (left_inverse) }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(X, multiply(inverse(greatest_lower_bound(a, identity)), multiply(a, identity)))))
% 0.20/0.59 = { by lemma 12 }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(X, multiply(inverse(greatest_lower_bound(a, identity)), a))))
% 0.20/0.59 = { by axiom 5 (associativity) R->L }
% 0.20/0.59 multiply(inverse(X), least_upper_bound(multiply(X, inverse(greatest_lower_bound(a, identity))), multiply(multiply(X, inverse(greatest_lower_bound(a, identity))), a)))
% 0.20/0.59 = { by lemma 13 R->L }
% 0.20/0.59 multiply(inverse(X), multiply(multiply(X, inverse(greatest_lower_bound(a, identity))), least_upper_bound(a, identity)))
% 0.20/0.59 = { by axiom 5 (associativity) }
% 0.20/0.59 multiply(inverse(X), multiply(X, multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity))))
% 0.20/0.59 = { by lemma 10 }
% 0.20/0.59 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity))
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59
% 0.20/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
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