TSTP Solution File: GRP183-4 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : GRP183-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 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 : Mon Jun 24 07:11:45 EDT 2024
% Result : Unsatisfiable 3.98s 0.92s
% Output : Proof 4.59s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP183-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 11:32:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 3.98/0.92 Command-line arguments: --ground-connectedness --complete-subsets
% 3.98/0.92
% 3.98/0.92 % SZS status Unsatisfiable
% 3.98/0.92
% 4.59/0.93 % SZS output start Proof
% 4.59/0.93 Axiom 1 (p20x_1): inverse(identity) = identity.
% 4.59/0.93 Axiom 2 (p20x_2): inverse(inverse(X)) = X.
% 4.59/0.93 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 4.59/0.93 Axiom 4 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 4.59/0.93 Axiom 5 (left_identity): multiply(identity, X) = X.
% 4.59/0.93 Axiom 6 (left_inverse): multiply(inverse(X), X) = identity.
% 4.59/0.93 Axiom 7 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 4.59/0.93 Axiom 8 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 4.59/0.93 Axiom 9 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 4.59/0.94 Axiom 10 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 4.59/0.94 Axiom 11 (p20x_3): inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 4.59/0.94 Axiom 12 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 4.59/0.94 Axiom 13 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 4.59/0.94 Axiom 14 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 4.59/0.94 Axiom 15 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 4.59/0.94
% 4.59/0.94 Lemma 16: multiply(least_upper_bound(X, identity), Y) = least_upper_bound(Y, multiply(X, Y)).
% 4.59/0.94 Proof:
% 4.59/0.94 multiply(least_upper_bound(X, identity), Y)
% 4.59/0.94 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.59/0.94 multiply(least_upper_bound(identity, X), Y)
% 4.59/0.94 = { by axiom 15 (monotony_lub2) }
% 4.59/0.94 least_upper_bound(multiply(identity, Y), multiply(X, Y))
% 4.59/0.94 = { by axiom 5 (left_identity) }
% 4.59/0.94 least_upper_bound(Y, multiply(X, Y))
% 4.59/0.94
% 4.59/0.94 Lemma 17: greatest_lower_bound(least_upper_bound(X, Y), Y) = Y.
% 4.59/0.94 Proof:
% 4.59/0.94 greatest_lower_bound(least_upper_bound(X, Y), Y)
% 4.59/0.94 = { by axiom 3 (symmetry_of_glb) R->L }
% 4.59/0.94 greatest_lower_bound(Y, least_upper_bound(X, Y))
% 4.59/0.94 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.59/0.94 greatest_lower_bound(Y, least_upper_bound(Y, X))
% 4.59/0.94 = { by axiom 7 (glb_absorbtion) }
% 4.59/0.94 Y
% 4.59/0.94
% 4.59/0.94 Lemma 18: multiply(inverse(X), multiply(X, Y)) = Y.
% 4.59/0.94 Proof:
% 4.59/0.94 multiply(inverse(X), multiply(X, Y))
% 4.59/0.94 = { by axiom 12 (associativity) R->L }
% 4.59/0.94 multiply(multiply(inverse(X), X), Y)
% 4.59/0.94 = { by axiom 6 (left_inverse) }
% 4.59/0.94 multiply(identity, Y)
% 4.59/0.94 = { by axiom 5 (left_identity) }
% 4.59/0.94 Y
% 4.59/0.94
% 4.59/0.94 Lemma 19: multiply(inverse(X), greatest_lower_bound(X, Y)) = greatest_lower_bound(identity, multiply(inverse(X), Y)).
% 4.59/0.94 Proof:
% 4.59/0.94 multiply(inverse(X), greatest_lower_bound(X, Y))
% 4.59/0.94 = { by axiom 13 (monotony_glb1) }
% 4.59/0.94 greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 4.59/0.94 = { by axiom 6 (left_inverse) }
% 4.59/0.94 greatest_lower_bound(identity, multiply(inverse(X), Y))
% 4.59/0.94
% 4.59/0.94 Lemma 20: multiply(least_upper_bound(inverse(X), identity), X) = least_upper_bound(X, identity).
% 4.59/0.94 Proof:
% 4.59/0.94 multiply(least_upper_bound(inverse(X), identity), X)
% 4.59/0.94 = { by lemma 16 }
% 4.59/0.94 least_upper_bound(X, multiply(inverse(X), X))
% 4.59/0.94 = { by axiom 6 (left_inverse) }
% 4.59/0.94 least_upper_bound(X, identity)
% 4.59/0.94
% 4.59/0.94 Lemma 21: multiply(inverse(least_upper_bound(inverse(X), identity)), greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity))) = greatest_lower_bound(X, identity).
% 4.59/0.94 Proof:
% 4.59/0.94 multiply(inverse(least_upper_bound(inverse(X), identity)), greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity)))
% 4.59/0.94 = { by axiom 3 (symmetry_of_glb) }
% 4.59/0.94 multiply(inverse(least_upper_bound(inverse(X), identity)), greatest_lower_bound(least_upper_bound(inverse(X), identity), least_upper_bound(X, identity)))
% 4.59/0.94 = { by lemma 19 }
% 4.59/0.94 greatest_lower_bound(identity, multiply(inverse(least_upper_bound(inverse(X), identity)), least_upper_bound(X, identity)))
% 4.59/0.94 = { by lemma 20 R->L }
% 4.59/0.94 greatest_lower_bound(identity, multiply(inverse(least_upper_bound(inverse(X), identity)), multiply(least_upper_bound(inverse(X), identity), X)))
% 4.59/0.94 = { by lemma 18 }
% 4.59/0.94 greatest_lower_bound(identity, X)
% 4.59/0.94 = { by axiom 3 (symmetry_of_glb) }
% 4.59/0.94 greatest_lower_bound(X, identity)
% 4.59/0.94
% 4.59/0.94 Lemma 22: multiply(greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity)), inverse(greatest_lower_bound(X, identity))) = least_upper_bound(inverse(X), identity).
% 4.59/0.94 Proof:
% 4.59/0.94 multiply(greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity)), inverse(greatest_lower_bound(X, identity)))
% 4.59/0.94 = { by lemma 21 R->L }
% 4.59/0.94 multiply(greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity)), inverse(multiply(inverse(least_upper_bound(inverse(X), identity)), greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity)))))
% 4.59/0.94 = { by axiom 2 (p20x_2) R->L }
% 4.59/0.94 multiply(inverse(inverse(greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity)))), inverse(multiply(inverse(least_upper_bound(inverse(X), identity)), greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity)))))
% 4.59/0.94 = { by axiom 11 (p20x_3) }
% 4.59/0.94 multiply(inverse(inverse(greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity)))), multiply(inverse(greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity))), inverse(inverse(least_upper_bound(inverse(X), identity)))))
% 4.59/0.94 = { by lemma 18 }
% 4.59/0.94 inverse(inverse(least_upper_bound(inverse(X), identity)))
% 4.59/0.94 = { by axiom 2 (p20x_2) }
% 4.59/0.94 least_upper_bound(inverse(X), identity)
% 4.59/0.94
% 4.59/0.94 Lemma 23: multiply(inverse(greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity))), least_upper_bound(inverse(X), identity)) = inverse(greatest_lower_bound(X, identity)).
% 4.59/0.94 Proof:
% 4.59/0.94 multiply(inverse(greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity))), least_upper_bound(inverse(X), identity))
% 4.59/0.94 = { by axiom 2 (p20x_2) R->L }
% 4.59/0.94 multiply(inverse(greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity))), inverse(inverse(least_upper_bound(inverse(X), identity))))
% 4.59/0.94 = { by axiom 11 (p20x_3) R->L }
% 4.59/0.94 inverse(multiply(inverse(least_upper_bound(inverse(X), identity)), greatest_lower_bound(least_upper_bound(X, identity), least_upper_bound(inverse(X), identity))))
% 4.59/0.94 = { by lemma 21 }
% 4.59/0.94 inverse(greatest_lower_bound(X, identity))
% 4.59/0.94
% 4.59/0.94 Goal 1 (prove_20x): greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)) = identity.
% 4.59/0.94 Proof:
% 4.59/0.94 greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))
% 4.59/0.94 = { by axiom 2 (p20x_2) R->L }
% 4.59/0.94 greatest_lower_bound(least_upper_bound(a, identity), inverse(inverse(least_upper_bound(inverse(a), identity))))
% 4.59/0.94 = { by axiom 5 (left_identity) R->L }
% 4.59/0.94 greatest_lower_bound(least_upper_bound(a, identity), inverse(multiply(identity, inverse(least_upper_bound(inverse(a), identity)))))
% 4.59/0.94 = { by axiom 1 (p20x_1) R->L }
% 4.59/0.94 greatest_lower_bound(least_upper_bound(a, identity), inverse(multiply(inverse(identity), inverse(least_upper_bound(inverse(a), identity)))))
% 4.59/0.94 = { by axiom 11 (p20x_3) R->L }
% 4.59/0.94 greatest_lower_bound(least_upper_bound(a, identity), inverse(inverse(multiply(least_upper_bound(inverse(a), identity), identity))))
% 4.59/0.94 = { by axiom 2 (p20x_2) }
% 4.59/0.94 greatest_lower_bound(least_upper_bound(a, identity), multiply(least_upper_bound(inverse(a), identity), identity))
% 4.59/0.94 = { by lemma 20 R->L }
% 4.59/0.94 greatest_lower_bound(multiply(least_upper_bound(inverse(a), identity), a), multiply(least_upper_bound(inverse(a), identity), identity))
% 4.59/0.94 = { by axiom 13 (monotony_glb1) R->L }
% 4.59/0.94 multiply(least_upper_bound(inverse(a), identity), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by lemma 22 R->L }
% 4.59/0.94 multiply(multiply(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)), inverse(greatest_lower_bound(a, identity))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 9 (lub_absorbtion) R->L }
% 4.59/0.94 multiply(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)), greatest_lower_bound(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)), identity)), inverse(greatest_lower_bound(a, identity))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 3 (symmetry_of_glb) }
% 4.59/0.94 multiply(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)), greatest_lower_bound(greatest_lower_bound(least_upper_bound(inverse(a), identity), least_upper_bound(a, identity)), identity)), inverse(greatest_lower_bound(a, identity))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 8 (associativity_of_glb) R->L }
% 4.59/0.94 multiply(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)), greatest_lower_bound(least_upper_bound(inverse(a), identity), greatest_lower_bound(least_upper_bound(a, identity), identity))), inverse(greatest_lower_bound(a, identity))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by lemma 17 }
% 4.59/0.94 multiply(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)), greatest_lower_bound(least_upper_bound(inverse(a), identity), identity)), inverse(greatest_lower_bound(a, identity))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by lemma 17 }
% 4.59/0.94 multiply(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)), identity), inverse(greatest_lower_bound(a, identity))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by lemma 16 }
% 4.59/0.94 multiply(least_upper_bound(inverse(greatest_lower_bound(a, identity)), multiply(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)), inverse(greatest_lower_bound(a, identity)))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by lemma 22 }
% 4.59/0.94 multiply(least_upper_bound(inverse(greatest_lower_bound(a, identity)), least_upper_bound(inverse(a), identity)), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.59/0.94 multiply(least_upper_bound(least_upper_bound(inverse(a), identity), inverse(greatest_lower_bound(a, identity))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 10 (associativity_of_lub) R->L }
% 4.59/0.94 multiply(least_upper_bound(inverse(a), least_upper_bound(identity, inverse(greatest_lower_bound(a, identity)))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by lemma 23 R->L }
% 4.59/0.94 multiply(least_upper_bound(inverse(a), least_upper_bound(identity, multiply(inverse(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))), least_upper_bound(inverse(a), identity)))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 6 (left_inverse) R->L }
% 4.59/0.94 multiply(least_upper_bound(inverse(a), least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))), greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))), multiply(inverse(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))), least_upper_bound(inverse(a), identity)))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 14 (monotony_lub1) R->L }
% 4.59/0.94 multiply(least_upper_bound(inverse(a), multiply(inverse(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))), least_upper_bound(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)), least_upper_bound(inverse(a), identity)))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.59/0.94 multiply(least_upper_bound(inverse(a), multiply(inverse(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))), least_upper_bound(least_upper_bound(inverse(a), identity), greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 3 (symmetry_of_glb) }
% 4.59/0.94 multiply(least_upper_bound(inverse(a), multiply(inverse(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))), least_upper_bound(least_upper_bound(inverse(a), identity), greatest_lower_bound(least_upper_bound(inverse(a), identity), least_upper_bound(a, identity))))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 9 (lub_absorbtion) }
% 4.59/0.94 multiply(least_upper_bound(inverse(a), multiply(inverse(greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))), least_upper_bound(inverse(a), identity))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by lemma 23 }
% 4.59/0.94 multiply(least_upper_bound(inverse(a), inverse(greatest_lower_bound(a, identity))), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 4 (symmetry_of_lub) R->L }
% 4.59/0.94 multiply(least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(a)), greatest_lower_bound(a, identity))
% 4.59/0.94 = { by axiom 15 (monotony_lub2) }
% 4.59/0.94 least_upper_bound(multiply(inverse(greatest_lower_bound(a, identity)), greatest_lower_bound(a, identity)), multiply(inverse(a), greatest_lower_bound(a, identity)))
% 4.59/0.94 = { by axiom 6 (left_inverse) }
% 4.59/0.94 least_upper_bound(identity, multiply(inverse(a), greatest_lower_bound(a, identity)))
% 4.59/0.94 = { by lemma 19 }
% 4.59/0.94 least_upper_bound(identity, greatest_lower_bound(identity, multiply(inverse(a), identity)))
% 4.59/0.94 = { by axiom 9 (lub_absorbtion) }
% 4.59/0.94 identity
% 4.59/0.94 % SZS output end Proof
% 4.59/0.94
% 4.59/0.94 RESULT: Unsatisfiable (the axioms are contradictory).
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