TSTP Solution File: GRP178-2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP178-2 : 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 : n008.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 01:17:34 EDT 2023
% Result : Unsatisfiable 5.62s 1.15s
% Output : Proof 5.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP178-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14 % 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 : n008.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 20:30:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.62/1.15 Command-line arguments: --ground-connectedness --complete-subsets
% 5.62/1.15
% 5.62/1.15 % SZS status Unsatisfiable
% 5.62/1.15
% 5.62/1.17 % SZS output start Proof
% 5.62/1.17 Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 5.62/1.17 Axiom 2 (left_identity): multiply(identity, X) = X.
% 5.62/1.17 Axiom 3 (idempotence_of_gld): greatest_lower_bound(X, X) = X.
% 5.62/1.17 Axiom 4 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 5.62/1.17 Axiom 5 (p09b_4): greatest_lower_bound(a, b) = identity.
% 5.62/1.17 Axiom 6 (p09b_3): greatest_lower_bound(identity, c) = identity.
% 5.62/1.17 Axiom 7 (left_inverse): multiply(inverse(X), X) = identity.
% 5.62/1.17 Axiom 8 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 5.62/1.17 Axiom 9 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 5.62/1.17 Axiom 10 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 5.62/1.17 Axiom 11 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 5.62/1.17 Axiom 12 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 5.62/1.17 Axiom 13 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 5.62/1.17 Axiom 14 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 5.62/1.17 Axiom 15 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 5.62/1.17
% 5.62/1.17 Lemma 16: multiply(inverse(X), multiply(X, Y)) = Y.
% 5.62/1.17 Proof:
% 5.62/1.17 multiply(inverse(X), multiply(X, Y))
% 5.62/1.17 = { by axiom 10 (associativity) R->L }
% 5.62/1.17 multiply(multiply(inverse(X), X), Y)
% 5.62/1.17 = { by axiom 7 (left_inverse) }
% 5.62/1.17 multiply(identity, Y)
% 5.62/1.17 = { by axiom 2 (left_identity) }
% 5.62/1.17 Y
% 5.62/1.17
% 5.62/1.17 Lemma 17: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 5.62/1.17 Proof:
% 5.62/1.17 multiply(inverse(inverse(X)), Y)
% 5.62/1.17 = { by lemma 16 R->L }
% 5.62/1.17 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 5.62/1.17 = { by lemma 16 }
% 5.62/1.17 multiply(X, Y)
% 5.62/1.17
% 5.62/1.17 Lemma 18: multiply(X, identity) = X.
% 5.62/1.17 Proof:
% 5.62/1.17 multiply(X, identity)
% 5.62/1.17 = { by lemma 17 R->L }
% 5.62/1.17 multiply(inverse(inverse(X)), identity)
% 5.62/1.17 = { by axiom 7 (left_inverse) R->L }
% 5.62/1.17 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 5.62/1.17 = { by lemma 16 }
% 5.62/1.17 X
% 5.62/1.17
% 5.62/1.17 Lemma 19: greatest_lower_bound(b, a) = identity.
% 5.62/1.17 Proof:
% 5.62/1.17 greatest_lower_bound(b, a)
% 5.62/1.17 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.62/1.17 greatest_lower_bound(a, b)
% 5.62/1.17 = { by axiom 5 (p09b_4) }
% 5.62/1.17 identity
% 5.62/1.17
% 5.62/1.17 Lemma 20: greatest_lower_bound(c, identity) = identity.
% 5.62/1.17 Proof:
% 5.62/1.17 greatest_lower_bound(c, identity)
% 5.62/1.17 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.62/1.17 greatest_lower_bound(identity, c)
% 5.62/1.17 = { by axiom 6 (p09b_3) }
% 5.62/1.17 identity
% 5.62/1.17
% 5.62/1.17 Lemma 21: least_upper_bound(b, identity) = b.
% 5.62/1.17 Proof:
% 5.62/1.17 least_upper_bound(b, identity)
% 5.62/1.17 = { by lemma 19 R->L }
% 5.62/1.17 least_upper_bound(b, greatest_lower_bound(b, a))
% 5.62/1.17 = { by axiom 8 (lub_absorbtion) }
% 5.62/1.17 b
% 5.62/1.17
% 5.62/1.17 Lemma 22: multiply(X, inverse(X)) = identity.
% 5.62/1.17 Proof:
% 5.62/1.17 multiply(X, inverse(X))
% 5.62/1.17 = { by lemma 17 R->L }
% 5.62/1.17 multiply(inverse(inverse(X)), inverse(X))
% 5.62/1.17 = { by axiom 7 (left_inverse) }
% 5.62/1.17 identity
% 5.62/1.17
% 5.62/1.17 Lemma 23: multiply(least_upper_bound(X, identity), Y) = least_upper_bound(Y, multiply(X, Y)).
% 5.62/1.17 Proof:
% 5.62/1.17 multiply(least_upper_bound(X, identity), Y)
% 5.62/1.17 = { by axiom 1 (symmetry_of_lub) R->L }
% 5.62/1.17 multiply(least_upper_bound(identity, X), Y)
% 5.62/1.17 = { by axiom 13 (monotony_lub2) }
% 5.62/1.17 least_upper_bound(multiply(identity, Y), multiply(X, Y))
% 5.62/1.17 = { by axiom 2 (left_identity) }
% 5.62/1.17 least_upper_bound(Y, multiply(X, Y))
% 5.62/1.17
% 5.62/1.17 Lemma 24: greatest_lower_bound(X, greatest_lower_bound(X, Y)) = greatest_lower_bound(X, Y).
% 5.62/1.17 Proof:
% 5.62/1.17 greatest_lower_bound(X, greatest_lower_bound(X, Y))
% 5.62/1.17 = { by axiom 12 (associativity_of_glb) }
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(X, X), Y)
% 5.62/1.17 = { by axiom 3 (idempotence_of_gld) }
% 5.62/1.17 greatest_lower_bound(X, Y)
% 5.62/1.17
% 5.62/1.17 Lemma 25: greatest_lower_bound(X, least_upper_bound(Y, X)) = X.
% 5.62/1.17 Proof:
% 5.62/1.17 greatest_lower_bound(X, least_upper_bound(Y, X))
% 5.62/1.17 = { by axiom 1 (symmetry_of_lub) R->L }
% 5.62/1.17 greatest_lower_bound(X, least_upper_bound(X, Y))
% 5.62/1.17 = { by axiom 11 (glb_absorbtion) }
% 5.62/1.17 X
% 5.62/1.17
% 5.62/1.17 Lemma 26: greatest_lower_bound(multiply(b, c), identity) = identity.
% 5.62/1.17 Proof:
% 5.62/1.17 greatest_lower_bound(multiply(b, c), identity)
% 5.62/1.17 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.62/1.17 greatest_lower_bound(identity, multiply(b, c))
% 5.62/1.17 = { by lemma 21 R->L }
% 5.62/1.17 greatest_lower_bound(identity, multiply(least_upper_bound(b, identity), c))
% 5.62/1.17 = { by lemma 22 R->L }
% 5.62/1.17 greatest_lower_bound(identity, multiply(least_upper_bound(b, multiply(c, inverse(c))), c))
% 5.62/1.17 = { by axiom 8 (lub_absorbtion) R->L }
% 5.62/1.17 greatest_lower_bound(identity, multiply(least_upper_bound(b, multiply(least_upper_bound(c, greatest_lower_bound(c, identity)), inverse(c))), c))
% 5.62/1.17 = { by lemma 20 }
% 5.62/1.17 greatest_lower_bound(identity, multiply(least_upper_bound(b, multiply(least_upper_bound(c, identity), inverse(c))), c))
% 5.62/1.17 = { by lemma 23 }
% 5.62/1.17 greatest_lower_bound(identity, multiply(least_upper_bound(b, least_upper_bound(inverse(c), multiply(c, inverse(c)))), c))
% 5.62/1.17 = { by lemma 22 }
% 5.62/1.17 greatest_lower_bound(identity, multiply(least_upper_bound(b, least_upper_bound(inverse(c), identity)), c))
% 5.62/1.17 = { by axiom 1 (symmetry_of_lub) R->L }
% 5.62/1.17 greatest_lower_bound(identity, multiply(least_upper_bound(b, least_upper_bound(identity, inverse(c))), c))
% 5.62/1.17 = { by axiom 9 (associativity_of_lub) }
% 5.62/1.17 greatest_lower_bound(identity, multiply(least_upper_bound(least_upper_bound(b, identity), inverse(c)), c))
% 5.62/1.17 = { by lemma 21 }
% 5.62/1.17 greatest_lower_bound(identity, multiply(least_upper_bound(b, inverse(c)), c))
% 5.62/1.17 = { by axiom 13 (monotony_lub2) }
% 5.62/1.17 greatest_lower_bound(identity, least_upper_bound(multiply(b, c), multiply(inverse(c), c)))
% 5.62/1.17 = { by axiom 7 (left_inverse) }
% 5.62/1.17 greatest_lower_bound(identity, least_upper_bound(multiply(b, c), identity))
% 5.62/1.17 = { by lemma 25 }
% 5.62/1.17 identity
% 5.62/1.17
% 5.62/1.17 Lemma 27: greatest_lower_bound(greatest_lower_bound(a, X), b) = greatest_lower_bound(X, identity).
% 5.62/1.17 Proof:
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(a, X), b)
% 5.62/1.17 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.62/1.17 greatest_lower_bound(b, greatest_lower_bound(a, X))
% 5.62/1.17 = { by axiom 12 (associativity_of_glb) }
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(b, a), X)
% 5.62/1.17 = { by lemma 19 }
% 5.62/1.17 greatest_lower_bound(identity, X)
% 5.62/1.17 = { by axiom 4 (symmetry_of_glb) }
% 5.62/1.17 greatest_lower_bound(X, identity)
% 5.62/1.17
% 5.62/1.17 Lemma 28: greatest_lower_bound(multiply(X, Y), multiply(Z, Y)) = multiply(greatest_lower_bound(Z, X), Y).
% 5.62/1.17 Proof:
% 5.62/1.17 greatest_lower_bound(multiply(X, Y), multiply(Z, Y))
% 5.62/1.17 = { by axiom 15 (monotony_glb2) R->L }
% 5.62/1.17 multiply(greatest_lower_bound(X, Z), Y)
% 5.62/1.17 = { by axiom 4 (symmetry_of_glb) }
% 5.62/1.17 multiply(greatest_lower_bound(Z, X), Y)
% 5.62/1.17
% 5.62/1.17 Lemma 29: greatest_lower_bound(multiply(Y, Z), greatest_lower_bound(W, multiply(X, Z))) = greatest_lower_bound(multiply(greatest_lower_bound(X, Y), Z), W).
% 5.62/1.17 Proof:
% 5.62/1.17 greatest_lower_bound(multiply(Y, Z), greatest_lower_bound(W, multiply(X, Z)))
% 5.62/1.17 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.62/1.17 greatest_lower_bound(multiply(Y, Z), greatest_lower_bound(multiply(X, Z), W))
% 5.62/1.17 = { by axiom 12 (associativity_of_glb) }
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(multiply(Y, Z), multiply(X, Z)), W)
% 5.62/1.17 = { by lemma 28 }
% 5.62/1.17 greatest_lower_bound(multiply(greatest_lower_bound(X, Y), Z), W)
% 5.62/1.17
% 5.62/1.17 Goal 1 (prove_p09b): greatest_lower_bound(a, multiply(b, c)) = greatest_lower_bound(a, c).
% 5.62/1.17 Proof:
% 5.62/1.17 greatest_lower_bound(a, multiply(b, c))
% 5.62/1.17 = { by axiom 11 (glb_absorbtion) R->L }
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(greatest_lower_bound(a, multiply(b, c)), c))
% 5.62/1.17 = { by axiom 1 (symmetry_of_lub) R->L }
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(c, greatest_lower_bound(a, multiply(b, c))))
% 5.62/1.17 = { by lemma 18 R->L }
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(c, multiply(greatest_lower_bound(a, multiply(b, c)), identity)))
% 5.62/1.17 = { by lemma 20 R->L }
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(c, multiply(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(c, identity))))
% 5.62/1.17 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(c, multiply(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(identity, c))))
% 5.62/1.17 = { by axiom 14 (monotony_glb1) }
% 5.62/1.17 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(c, greatest_lower_bound(multiply(greatest_lower_bound(a, multiply(b, c)), identity), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by lemma 18 }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(c, greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by axiom 2 (left_identity) R->L }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(identity, c), greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by lemma 26 R->L }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(greatest_lower_bound(multiply(b, c), identity), c), greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by lemma 27 R->L }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by lemma 25 R->L }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(b, c), greatest_lower_bound(a, multiply(b, c)))), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by axiom 4 (symmetry_of_glb) }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(b, c), greatest_lower_bound(multiply(b, c), a))), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by axiom 8 (lub_absorbtion) }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by axiom 4 (symmetry_of_glb) }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), greatest_lower_bound(greatest_lower_bound(multiply(b, c), greatest_lower_bound(a, multiply(b, c))), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by axiom 12 (associativity_of_glb) R->L }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), greatest_lower_bound(multiply(b, c), greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c)))))
% 5.62/1.18 = { by lemma 28 R->L }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(greatest_lower_bound(multiply(b, c), multiply(greatest_lower_bound(a, multiply(b, c)), c)), greatest_lower_bound(multiply(b, c), greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c)))))
% 5.62/1.18 = { by lemma 24 R->L }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(greatest_lower_bound(multiply(b, c), greatest_lower_bound(multiply(b, c), multiply(greatest_lower_bound(a, multiply(b, c)), c))), greatest_lower_bound(multiply(b, c), greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c)))))
% 5.62/1.18 = { by lemma 29 }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), multiply(b, c)), greatest_lower_bound(multiply(b, c), greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, multiply(b, c)), c)))))
% 5.62/1.18 = { by lemma 29 }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), multiply(b, c)), greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), greatest_lower_bound(a, multiply(b, c)))))
% 5.62/1.18 = { by axiom 4 (symmetry_of_glb) }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), multiply(b, c)), greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), greatest_lower_bound(multiply(b, c), a))))
% 5.62/1.18 = { by axiom 12 (associativity_of_glb) }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), least_upper_bound(greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), multiply(b, c)), greatest_lower_bound(greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), multiply(b, c)), a)))
% 5.62/1.18 = { by axiom 8 (lub_absorbtion) }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c), multiply(b, c)))
% 5.62/1.18 = { by lemma 29 R->L }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(multiply(b, c), greatest_lower_bound(multiply(b, c), multiply(greatest_lower_bound(a, multiply(b, c)), c))))
% 5.62/1.18 = { by lemma 24 }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(multiply(b, c), multiply(greatest_lower_bound(a, multiply(b, c)), c)))
% 5.62/1.18 = { by lemma 28 }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), b), c))
% 5.62/1.18 = { by lemma 27 }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(multiply(b, c), identity), c))
% 5.62/1.18 = { by lemma 26 }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(identity, c))
% 5.62/1.18 = { by axiom 2 (left_identity) }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), c)
% 5.62/1.18 = { by axiom 4 (symmetry_of_glb) }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(multiply(b, c), a), c)
% 5.62/1.18 = { by axiom 12 (associativity_of_glb) R->L }
% 5.62/1.18 greatest_lower_bound(multiply(b, c), greatest_lower_bound(a, c))
% 5.62/1.18 = { by axiom 4 (symmetry_of_glb) R->L }
% 5.62/1.18 greatest_lower_bound(greatest_lower_bound(a, c), multiply(b, c))
% 5.62/1.18 = { by axiom 12 (associativity_of_glb) R->L }
% 5.62/1.18 greatest_lower_bound(a, greatest_lower_bound(c, multiply(b, c)))
% 5.62/1.18 = { by lemma 21 R->L }
% 5.62/1.18 greatest_lower_bound(a, greatest_lower_bound(c, multiply(least_upper_bound(b, identity), c)))
% 5.62/1.18 = { by lemma 23 }
% 5.62/1.18 greatest_lower_bound(a, greatest_lower_bound(c, least_upper_bound(c, multiply(b, c))))
% 5.62/1.18 = { by axiom 1 (symmetry_of_lub) }
% 5.62/1.18 greatest_lower_bound(a, greatest_lower_bound(c, least_upper_bound(multiply(b, c), c)))
% 5.62/1.18 = { by lemma 25 }
% 5.62/1.18 greatest_lower_bound(a, c)
% 5.62/1.18 % SZS output end Proof
% 5.62/1.18
% 5.62/1.18 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------