TSTP Solution File: GRP183-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP183-2 : 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 : n010.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 01:17:37 EDT 2023
% Result : Unsatisfiable 5.23s 1.04s
% Output : Proof 5.23s
% 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 : GRP183-2 : 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
% 0.17/0.34 % Computer : n010.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 20:46:04 EDT 2023
% 0.17/0.35 % CPUTime :
% 5.23/1.04 Command-line arguments: --ground-connectedness --complete-subsets
% 5.23/1.04
% 5.23/1.04 % SZS status Unsatisfiable
% 5.23/1.04
% 5.23/1.06 % SZS output start Proof
% 5.23/1.06 Axiom 1 (p20_1): inverse(identity) = identity.
% 5.23/1.06 Axiom 2 (p20_2): inverse(inverse(X)) = X.
% 5.23/1.06 Axiom 3 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 5.23/1.06 Axiom 4 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 5.23/1.06 Axiom 5 (left_identity): multiply(identity, X) = X.
% 5.23/1.06 Axiom 6 (left_inverse): multiply(inverse(X), X) = identity.
% 5.23/1.06 Axiom 7 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 5.23/1.06 Axiom 8 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 5.23/1.06 Axiom 9 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 5.23/1.06 Axiom 10 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 5.23/1.06 Axiom 11 (p20_3): inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 5.23/1.06 Axiom 12 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 5.23/1.06 Axiom 13 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 5.23/1.06 Axiom 14 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 5.23/1.06 Axiom 15 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 5.23/1.06 Axiom 16 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 5.23/1.06
% 5.23/1.06 Lemma 17: multiply(X, identity) = X.
% 5.23/1.06 Proof:
% 5.23/1.06 multiply(X, identity)
% 5.23/1.06 = { by axiom 2 (p20_2) R->L }
% 5.23/1.06 inverse(inverse(multiply(X, identity)))
% 5.23/1.06 = { by axiom 11 (p20_3) }
% 5.23/1.06 inverse(multiply(inverse(identity), inverse(X)))
% 5.23/1.06 = { by axiom 1 (p20_1) }
% 5.23/1.06 inverse(multiply(identity, inverse(X)))
% 5.23/1.06 = { by axiom 5 (left_identity) }
% 5.23/1.06 inverse(inverse(X))
% 5.23/1.06 = { by axiom 2 (p20_2) }
% 5.23/1.06 X
% 5.23/1.06
% 5.23/1.06 Lemma 18: multiply(X, greatest_lower_bound(Y, identity)) = greatest_lower_bound(X, multiply(X, Y)).
% 5.23/1.06 Proof:
% 5.23/1.06 multiply(X, greatest_lower_bound(Y, identity))
% 5.23/1.06 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.23/1.06 multiply(X, greatest_lower_bound(identity, Y))
% 5.23/1.06 = { by axiom 15 (monotony_glb1) }
% 5.23/1.06 greatest_lower_bound(multiply(X, identity), multiply(X, Y))
% 5.23/1.06 = { by lemma 17 }
% 5.23/1.06 greatest_lower_bound(X, multiply(X, Y))
% 5.23/1.06
% 5.23/1.06 Lemma 19: multiply(greatest_lower_bound(X, identity), Y) = greatest_lower_bound(Y, multiply(X, Y)).
% 5.23/1.06 Proof:
% 5.23/1.06 multiply(greatest_lower_bound(X, identity), Y)
% 5.23/1.06 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.23/1.06 multiply(greatest_lower_bound(identity, X), Y)
% 5.23/1.06 = { by axiom 16 (monotony_glb2) }
% 5.23/1.06 greatest_lower_bound(multiply(identity, Y), multiply(X, Y))
% 5.23/1.06 = { by axiom 5 (left_identity) }
% 5.23/1.06 greatest_lower_bound(Y, multiply(X, Y))
% 5.23/1.06
% 5.23/1.06 Lemma 20: multiply(least_upper_bound(X, identity), Y) = least_upper_bound(Y, multiply(X, Y)).
% 5.23/1.06 Proof:
% 5.23/1.06 multiply(least_upper_bound(X, identity), Y)
% 5.23/1.06 = { by axiom 3 (symmetry_of_lub) R->L }
% 5.23/1.06 multiply(least_upper_bound(identity, X), Y)
% 5.23/1.06 = { by axiom 14 (monotony_lub2) }
% 5.23/1.06 least_upper_bound(multiply(identity, Y), multiply(X, Y))
% 5.23/1.06 = { by axiom 5 (left_identity) }
% 5.23/1.06 least_upper_bound(Y, multiply(X, Y))
% 5.23/1.06
% 5.23/1.06 Lemma 21: greatest_lower_bound(X, least_upper_bound(Y, X)) = X.
% 5.23/1.06 Proof:
% 5.23/1.06 greatest_lower_bound(X, least_upper_bound(Y, X))
% 5.23/1.06 = { by axiom 3 (symmetry_of_lub) R->L }
% 5.23/1.06 greatest_lower_bound(X, least_upper_bound(X, Y))
% 5.23/1.06 = { by axiom 9 (glb_absorbtion) }
% 5.23/1.06 X
% 5.23/1.06
% 5.23/1.06 Lemma 22: multiply(inverse(X), multiply(X, Y)) = Y.
% 5.23/1.06 Proof:
% 5.23/1.06 multiply(inverse(X), multiply(X, Y))
% 5.23/1.06 = { by axiom 12 (associativity) R->L }
% 5.23/1.06 multiply(multiply(inverse(X), X), Y)
% 5.23/1.06 = { by axiom 6 (left_inverse) }
% 5.23/1.06 multiply(identity, Y)
% 5.23/1.06 = { by axiom 5 (left_identity) }
% 5.23/1.06 Y
% 5.23/1.06
% 5.23/1.06 Goal 1 (prove_p20): greatest_lower_bound(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity))) = identity.
% 5.23/1.06 Proof:
% 5.23/1.06 greatest_lower_bound(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity)))
% 5.23/1.06 = { by axiom 4 (symmetry_of_glb) }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity))
% 5.23/1.06 = { by lemma 22 R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity))))
% 5.23/1.06 = { by lemma 21 R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(a, multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity))))))
% 5.23/1.06 = { by axiom 3 (symmetry_of_lub) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(a, multiply(greatest_lower_bound(a, identity), least_upper_bound(identity, a))))))
% 5.23/1.06 = { by axiom 13 (monotony_lub1) }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(a, identity), identity), multiply(greatest_lower_bound(a, identity), a))))))
% 5.23/1.06 = { by lemma 17 }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(a, least_upper_bound(greatest_lower_bound(a, identity), multiply(greatest_lower_bound(a, identity), a))))))
% 5.23/1.06 = { by axiom 3 (symmetry_of_lub) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(a, identity), a), greatest_lower_bound(a, identity))))))
% 5.23/1.06 = { by axiom 8 (associativity_of_lub) }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(least_upper_bound(a, multiply(greatest_lower_bound(a, identity), a)), greatest_lower_bound(a, identity)))))
% 5.23/1.06 = { by lemma 20 R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(multiply(least_upper_bound(greatest_lower_bound(a, identity), identity), a), greatest_lower_bound(a, identity)))))
% 5.23/1.06 = { by axiom 3 (symmetry_of_lub) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(multiply(least_upper_bound(identity, greatest_lower_bound(a, identity)), a), greatest_lower_bound(a, identity)))))
% 5.23/1.06 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(multiply(least_upper_bound(identity, greatest_lower_bound(identity, a)), a), greatest_lower_bound(a, identity)))))
% 5.23/1.06 = { by axiom 7 (lub_absorbtion) }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(multiply(identity, a), greatest_lower_bound(a, identity)))))
% 5.23/1.06 = { by axiom 5 (left_identity) }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), least_upper_bound(a, greatest_lower_bound(a, identity)))))
% 5.23/1.06 = { by axiom 7 (lub_absorbtion) }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)), a)))
% 5.23/1.06 = { by axiom 4 (symmetry_of_glb) }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(greatest_lower_bound(a, identity), least_upper_bound(a, identity)))))
% 5.23/1.06 = { by axiom 2 (p20_2) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(inverse(inverse(greatest_lower_bound(a, identity))), least_upper_bound(a, identity)))))
% 5.23/1.06 = { by axiom 3 (symmetry_of_lub) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(inverse(inverse(greatest_lower_bound(a, identity))), least_upper_bound(identity, a)))))
% 5.23/1.06 = { by lemma 22 R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(inverse(inverse(greatest_lower_bound(a, identity))), least_upper_bound(identity, multiply(inverse(greatest_lower_bound(a, identity)), multiply(greatest_lower_bound(a, identity), a)))))))
% 5.23/1.06 = { by lemma 19 }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(inverse(inverse(greatest_lower_bound(a, identity))), least_upper_bound(identity, multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(a, a))))))))
% 5.23/1.06 = { by lemma 18 R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(inverse(inverse(greatest_lower_bound(a, identity))), least_upper_bound(identity, multiply(inverse(greatest_lower_bound(a, identity)), multiply(a, greatest_lower_bound(a, identity))))))))
% 5.23/1.06 = { by axiom 6 (left_inverse) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(inverse(inverse(greatest_lower_bound(a, identity))), least_upper_bound(multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), multiply(a, greatest_lower_bound(a, identity))))))))
% 5.23/1.06 = { by axiom 13 (monotony_lub1) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(inverse(inverse(greatest_lower_bound(a, identity))), multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(greatest_lower_bound(a, identity), multiply(a, greatest_lower_bound(a, identity))))))))
% 5.23/1.06 = { by lemma 20 R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(inverse(inverse(greatest_lower_bound(a, identity))), multiply(inverse(greatest_lower_bound(a, identity)), multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))))))
% 5.23/1.06 = { by lemma 22 }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, multiply(least_upper_bound(a, identity), greatest_lower_bound(a, identity)))))
% 5.23/1.06 = { by lemma 18 }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, greatest_lower_bound(least_upper_bound(a, identity), multiply(least_upper_bound(a, identity), a)))))
% 5.23/1.06 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, greatest_lower_bound(multiply(least_upper_bound(a, identity), a), least_upper_bound(a, identity)))))
% 5.23/1.06 = { by axiom 10 (associativity_of_glb) }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(greatest_lower_bound(a, multiply(least_upper_bound(a, identity), a)), least_upper_bound(a, identity))))
% 5.23/1.06 = { by lemma 19 R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(least_upper_bound(a, identity), identity), a), least_upper_bound(a, identity))))
% 5.23/1.06 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.23/1.06 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(greatest_lower_bound(identity, least_upper_bound(a, identity)), a), least_upper_bound(a, identity))))
% 5.23/1.07 = { by lemma 21 }
% 5.23/1.07 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(multiply(identity, a), least_upper_bound(a, identity))))
% 5.23/1.07 = { by axiom 5 (left_identity) }
% 5.23/1.07 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, least_upper_bound(a, identity))))
% 5.23/1.07 = { by axiom 9 (glb_absorbtion) }
% 5.23/1.07 greatest_lower_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), a))
% 5.23/1.07 = { by lemma 18 R->L }
% 5.23/1.07 multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, identity))
% 5.23/1.07 = { by axiom 6 (left_inverse) }
% 5.23/1.07 identity
% 5.23/1.07 % SZS output end Proof
% 5.23/1.07
% 5.23/1.07 RESULT: Unsatisfiable (the axioms are contradictory).
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