TSTP Solution File: GRP177-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP177-2 : 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 : n024.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 01:17:33 EDT 2023
% Result : Unsatisfiable 28.67s 4.04s
% Output : Proof 29.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP177-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 21:40:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 28.67/4.04 Command-line arguments: --ground-connectedness --complete-subsets
% 28.67/4.04
% 28.67/4.04 % SZS status Unsatisfiable
% 28.67/4.04
% 29.06/4.05 % SZS output start Proof
% 29.06/4.05 Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 29.06/4.05 Axiom 2 (left_identity): multiply(identity, X) = X.
% 29.06/4.05 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 29.06/4.05 Axiom 4 (p08b_2): greatest_lower_bound(identity, b) = identity.
% 29.06/4.05 Axiom 5 (p08b_3): greatest_lower_bound(identity, c) = identity.
% 29.06/4.05 Axiom 6 (p08b_1): greatest_lower_bound(identity, a) = identity.
% 29.06/4.05 Axiom 7 (left_inverse): multiply(inverse(X), X) = identity.
% 29.06/4.05 Axiom 8 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 29.06/4.05 Axiom 9 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 29.06/4.05 Axiom 10 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 29.06/4.05 Axiom 11 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 29.06/4.05 Axiom 12 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 29.06/4.05 Axiom 13 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 29.06/4.05 Axiom 14 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 29.06/4.05 Axiom 15 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 29.06/4.05 Axiom 16 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 29.06/4.05
% 29.06/4.05 Lemma 17: multiply(inverse(X), multiply(X, Y)) = Y.
% 29.06/4.05 Proof:
% 29.06/4.05 multiply(inverse(X), multiply(X, Y))
% 29.06/4.05 = { by axiom 10 (associativity) R->L }
% 29.06/4.05 multiply(multiply(inverse(X), X), Y)
% 29.06/4.05 = { by axiom 7 (left_inverse) }
% 29.06/4.05 multiply(identity, Y)
% 29.06/4.05 = { by axiom 2 (left_identity) }
% 29.06/4.05 Y
% 29.06/4.05
% 29.06/4.05 Lemma 18: multiply(X, identity) = X.
% 29.06/4.05 Proof:
% 29.06/4.05 multiply(X, identity)
% 29.06/4.05 = { by lemma 17 R->L }
% 29.06/4.05 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, identity)))
% 29.06/4.05 = { by lemma 17 }
% 29.06/4.05 multiply(inverse(inverse(X)), identity)
% 29.06/4.05 = { by axiom 7 (left_inverse) R->L }
% 29.06/4.05 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 29.06/4.05 = { by lemma 17 }
% 29.06/4.05 X
% 29.06/4.05
% 29.06/4.05 Lemma 19: greatest_lower_bound(X, least_upper_bound(Y, X)) = X.
% 29.06/4.05 Proof:
% 29.06/4.05 greatest_lower_bound(X, least_upper_bound(Y, X))
% 29.06/4.05 = { by axiom 1 (symmetry_of_lub) R->L }
% 29.06/4.05 greatest_lower_bound(X, least_upper_bound(X, Y))
% 29.06/4.05 = { by axiom 11 (glb_absorbtion) }
% 29.06/4.05 X
% 29.06/4.05
% 29.06/4.05 Lemma 20: greatest_lower_bound(Y, greatest_lower_bound(Z, X)) = greatest_lower_bound(X, greatest_lower_bound(Y, Z)).
% 29.06/4.05 Proof:
% 29.06/4.05 greatest_lower_bound(Y, greatest_lower_bound(Z, X))
% 29.06/4.05 = { by axiom 3 (symmetry_of_glb) R->L }
% 29.06/4.05 greatest_lower_bound(greatest_lower_bound(Z, X), Y)
% 29.06/4.05 = { by axiom 3 (symmetry_of_glb) }
% 29.06/4.05 greatest_lower_bound(greatest_lower_bound(X, Z), Y)
% 29.06/4.05 = { by axiom 12 (associativity_of_glb) R->L }
% 29.06/4.05 greatest_lower_bound(X, greatest_lower_bound(Z, Y))
% 29.06/4.05 = { by axiom 3 (symmetry_of_glb) }
% 29.06/4.05 greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 29.06/4.05
% 29.06/4.05 Lemma 21: greatest_lower_bound(Z, greatest_lower_bound(Y, X)) = greatest_lower_bound(X, greatest_lower_bound(Y, Z)).
% 29.06/4.05 Proof:
% 29.06/4.05 greatest_lower_bound(Z, greatest_lower_bound(Y, X))
% 29.06/4.05 = { by lemma 20 }
% 29.06/4.05 greatest_lower_bound(X, greatest_lower_bound(Z, Y))
% 29.06/4.05 = { by axiom 3 (symmetry_of_glb) }
% 29.06/4.05 greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 29.06/4.05
% 29.06/4.05 Lemma 22: least_upper_bound(X, greatest_lower_bound(Y, X)) = X.
% 29.06/4.05 Proof:
% 29.06/4.05 least_upper_bound(X, greatest_lower_bound(Y, X))
% 29.06/4.05 = { by axiom 3 (symmetry_of_glb) R->L }
% 29.06/4.05 least_upper_bound(X, greatest_lower_bound(X, Y))
% 29.06/4.05 = { by axiom 8 (lub_absorbtion) }
% 29.06/4.05 X
% 29.06/4.05
% 29.06/4.05 Lemma 23: least_upper_bound(multiply(X, c), X) = multiply(X, c).
% 29.06/4.05 Proof:
% 29.06/4.06 least_upper_bound(multiply(X, c), X)
% 29.06/4.06 = { by lemma 18 R->L }
% 29.06/4.06 least_upper_bound(multiply(X, c), multiply(X, identity))
% 29.06/4.06 = { by axiom 13 (monotony_lub1) R->L }
% 29.06/4.06 multiply(X, least_upper_bound(c, identity))
% 29.06/4.06 = { by axiom 5 (p08b_3) R->L }
% 29.06/4.06 multiply(X, least_upper_bound(c, greatest_lower_bound(identity, c)))
% 29.06/4.06 = { by lemma 22 }
% 29.06/4.06 multiply(X, c)
% 29.06/4.06
% 29.06/4.06 Lemma 24: least_upper_bound(multiply(b, X), X) = multiply(b, X).
% 29.06/4.06 Proof:
% 29.06/4.06 least_upper_bound(multiply(b, X), X)
% 29.06/4.06 = { by axiom 2 (left_identity) R->L }
% 29.06/4.06 least_upper_bound(multiply(b, X), multiply(identity, X))
% 29.06/4.06 = { by axiom 14 (monotony_lub2) R->L }
% 29.06/4.06 multiply(least_upper_bound(b, identity), X)
% 29.06/4.06 = { by axiom 4 (p08b_2) R->L }
% 29.06/4.06 multiply(least_upper_bound(b, greatest_lower_bound(identity, b)), X)
% 29.06/4.06 = { by lemma 22 }
% 29.06/4.06 multiply(b, X)
% 29.06/4.06
% 29.06/4.06 Lemma 25: least_upper_bound(greatest_lower_bound(X, Y), Y) = Y.
% 29.06/4.06 Proof:
% 29.06/4.06 least_upper_bound(greatest_lower_bound(X, Y), Y)
% 29.06/4.06 = { by axiom 1 (symmetry_of_lub) R->L }
% 29.06/4.06 least_upper_bound(Y, greatest_lower_bound(X, Y))
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) }
% 29.06/4.06 least_upper_bound(Y, greatest_lower_bound(Y, X))
% 29.06/4.06 = { by axiom 8 (lub_absorbtion) }
% 29.06/4.06 Y
% 29.06/4.06
% 29.06/4.06 Lemma 26: least_upper_bound(greatest_lower_bound(X, Y), least_upper_bound(Z, Y)) = least_upper_bound(Z, Y).
% 29.06/4.06 Proof:
% 29.06/4.06 least_upper_bound(greatest_lower_bound(X, Y), least_upper_bound(Z, Y))
% 29.06/4.06 = { by axiom 1 (symmetry_of_lub) R->L }
% 29.06/4.06 least_upper_bound(greatest_lower_bound(X, Y), least_upper_bound(Y, Z))
% 29.06/4.06 = { by axiom 9 (associativity_of_lub) }
% 29.06/4.06 least_upper_bound(least_upper_bound(greatest_lower_bound(X, Y), Y), Z)
% 29.06/4.06 = { by lemma 25 }
% 29.06/4.06 least_upper_bound(Y, Z)
% 29.06/4.06 = { by axiom 1 (symmetry_of_lub) }
% 29.06/4.06 least_upper_bound(Z, Y)
% 29.06/4.06
% 29.06/4.06 Lemma 27: greatest_lower_bound(multiply(Y, Z), greatest_lower_bound(W, multiply(X, Z))) = greatest_lower_bound(multiply(greatest_lower_bound(X, Y), Z), W).
% 29.06/4.06 Proof:
% 29.06/4.06 greatest_lower_bound(multiply(Y, Z), greatest_lower_bound(W, multiply(X, Z)))
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) R->L }
% 29.06/4.06 greatest_lower_bound(multiply(Y, Z), greatest_lower_bound(multiply(X, Z), W))
% 29.06/4.06 = { by axiom 12 (associativity_of_glb) }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(multiply(Y, Z), multiply(X, Z)), W)
% 29.06/4.06 = { by axiom 16 (monotony_glb2) R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(Y, X), Z), W)
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(X, Y), Z), W)
% 29.06/4.06
% 29.06/4.06 Goal 1 (prove_p08b): greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, c))) = greatest_lower_bound(a, multiply(b, c)).
% 29.06/4.06 Proof:
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, c)))
% 29.06/4.06 = { by lemma 19 R->L }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(greatest_lower_bound(a, c), least_upper_bound(multiply(b, c), greatest_lower_bound(a, c)))))
% 29.06/4.06 = { by axiom 1 (symmetry_of_lub) R->L }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(greatest_lower_bound(a, c), least_upper_bound(greatest_lower_bound(a, c), multiply(b, c)))))
% 29.06/4.06 = { by lemma 24 R->L }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(greatest_lower_bound(a, c), least_upper_bound(greatest_lower_bound(a, c), least_upper_bound(multiply(b, c), c)))))
% 29.06/4.06 = { by lemma 26 }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(greatest_lower_bound(a, c), least_upper_bound(multiply(b, c), c))))
% 29.06/4.06 = { by lemma 24 }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(greatest_lower_bound(a, c), multiply(b, c))))
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(multiply(b, c), greatest_lower_bound(a, c))))
% 29.06/4.06 = { by lemma 20 }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(c, greatest_lower_bound(multiply(b, c), a))))
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) R->L }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(c, greatest_lower_bound(a, multiply(b, c)))))
% 29.06/4.06 = { by axiom 15 (monotony_glb1) }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(multiply(greatest_lower_bound(a, b), c), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, multiply(b, c)))))
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) R->L }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, multiply(b, c))), multiply(greatest_lower_bound(a, b), c)))
% 29.06/4.06 = { by axiom 12 (associativity_of_glb) }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, multiply(b, c)))), multiply(greatest_lower_bound(a, b), c))
% 29.06/4.06 = { by axiom 2 (left_identity) R->L }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(multiply(identity, greatest_lower_bound(a, multiply(b, c))), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, multiply(b, c)))), multiply(greatest_lower_bound(a, b), c))
% 29.06/4.06 = { by axiom 16 (monotony_glb2) R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(identity, greatest_lower_bound(a, b)), greatest_lower_bound(a, multiply(b, c))), multiply(greatest_lower_bound(a, b), c))
% 29.06/4.06 = { by axiom 12 (associativity_of_glb) }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(identity, a), b), greatest_lower_bound(a, multiply(b, c))), multiply(greatest_lower_bound(a, b), c))
% 29.06/4.06 = { by axiom 6 (p08b_1) }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(identity, b), greatest_lower_bound(a, multiply(b, c))), multiply(greatest_lower_bound(a, b), c))
% 29.06/4.06 = { by axiom 4 (p08b_2) }
% 29.06/4.06 greatest_lower_bound(multiply(identity, greatest_lower_bound(a, multiply(b, c))), multiply(greatest_lower_bound(a, b), c))
% 29.06/4.06 = { by axiom 2 (left_identity) }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), c))
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(a, b), c), greatest_lower_bound(a, multiply(b, c)))
% 29.06/4.06 = { by lemma 21 }
% 29.06/4.06 greatest_lower_bound(multiply(b, c), greatest_lower_bound(a, multiply(greatest_lower_bound(a, b), c)))
% 29.06/4.06 = { by lemma 27 }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, b), b), c), a)
% 29.06/4.06 = { by lemma 25 R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, b), least_upper_bound(greatest_lower_bound(a, b), b)), c), a)
% 29.06/4.06 = { by axiom 11 (glb_absorbtion) }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(a, b), c), a)
% 29.06/4.06 = { by lemma 19 R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, b), least_upper_bound(multiply(b, c), greatest_lower_bound(a, b))), c), a)
% 29.06/4.06 = { by axiom 1 (symmetry_of_lub) R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, b), least_upper_bound(greatest_lower_bound(a, b), multiply(b, c))), c), a)
% 29.06/4.06 = { by lemma 23 R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, b), least_upper_bound(greatest_lower_bound(a, b), least_upper_bound(multiply(b, c), b))), c), a)
% 29.06/4.06 = { by lemma 26 }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, b), least_upper_bound(multiply(b, c), b)), c), a)
% 29.06/4.06 = { by lemma 23 }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, b), multiply(b, c)), c), a)
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(multiply(b, c), greatest_lower_bound(a, b)), c), a)
% 29.06/4.06 = { by lemma 20 }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(b, greatest_lower_bound(multiply(b, c), a)), c), a)
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(b, greatest_lower_bound(a, multiply(b, c))), c), a)
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), a)
% 29.06/4.06 = { by lemma 27 R->L }
% 29.06/4.06 greatest_lower_bound(multiply(b, c), greatest_lower_bound(a, multiply(greatest_lower_bound(a, multiply(b, c)), c)))
% 29.06/4.06 = { by lemma 21 R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(a, multiply(b, c)), c), greatest_lower_bound(a, multiply(b, c)))
% 29.06/4.06 = { by axiom 3 (symmetry_of_glb) }
% 29.06/4.06 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c))
% 29.06/4.06 = { by lemma 18 R->L }
% 29.06/4.06 greatest_lower_bound(multiply(greatest_lower_bound(a, multiply(b, c)), identity), multiply(greatest_lower_bound(a, multiply(b, c)), c))
% 29.06/4.06 = { by axiom 15 (monotony_glb1) R->L }
% 29.06/4.06 multiply(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(identity, c))
% 29.06/4.06 = { by axiom 5 (p08b_3) }
% 29.06/4.06 multiply(greatest_lower_bound(a, multiply(b, c)), identity)
% 29.06/4.06 = { by lemma 18 }
% 29.06/4.06 greatest_lower_bound(a, multiply(b, c))
% 29.06/4.06 % SZS output end Proof
% 29.06/4.06
% 29.06/4.06 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------