TSTP Solution File: ALG010-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG010-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n009.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 : Wed Aug 30 16:41:59 EDT 2023
% Result : Unsatisfiable 5.85s 1.08s
% Output : Proof 6.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : ALG010-1 : TPTP v8.1.2. Released v2.5.0.
% 0.02/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 05:35:35 EDT 2023
% 0.11/0.32 % CPUTime :
% 5.85/1.08 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 5.85/1.08
% 5.85/1.08 % SZS status Unsatisfiable
% 5.85/1.08
% 6.28/1.16 % SZS output start Proof
% 6.28/1.16 Take the following subset of the input axioms:
% 6.28/1.16 fof(h, axiom, ![A, B, C]: multiply(multiply(A, B), multiply(A, C))=multiply(multiply(B, A), multiply(B, C))).
% 6.28/1.16 fof(m3, axiom, ![A3]: multiply(A3, one)=one).
% 6.28/1.16 fof(m4, axiom, ![A3]: multiply(one, A3)=A3).
% 6.28/1.16 fof(m5, axiom, ![A3, B2, C2]: multiply(multiply(A3, B2), multiply(multiply(C2, A3), multiply(C2, B2)))=one).
% 6.28/1.16 fof(m7, axiom, ![A2, B2]: (multiply(A2, B2)!=one | (multiply(B2, A2)!=one | A2=B2))).
% 6.28/1.16 fof(m8, axiom, ![A3]: multiply(A3, A3)=one).
% 6.28/1.16 fof(m9, axiom, ![A3, B2, C2]: multiply(A3, multiply(B2, C2))=multiply(B2, multiply(A3, C2))).
% 6.28/1.16 fof(prove_j, negated_conjecture, multiply(multiply(multiply(multiply(a, b), b), a), a)!=multiply(multiply(multiply(multiply(b, a), a), b), b)).
% 6.28/1.16
% 6.28/1.16 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.28/1.16 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.28/1.16 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.28/1.16 fresh(y, y, x1...xn) = u
% 6.28/1.16 C => fresh(s, t, x1...xn) = v
% 6.28/1.16 where fresh is a fresh function symbol and x1..xn are the free
% 6.28/1.16 variables of u and v.
% 6.28/1.16 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.28/1.16 input problem has no model of domain size 1).
% 6.28/1.16
% 6.28/1.16 The encoding turns the above axioms into the following unit equations and goals:
% 6.28/1.16
% 6.28/1.16 Axiom 1 (m8): multiply(X, X) = one.
% 6.28/1.16 Axiom 2 (m3): multiply(X, one) = one.
% 6.28/1.16 Axiom 3 (m4): multiply(one, X) = X.
% 6.28/1.16 Axiom 4 (m9): multiply(X, multiply(Y, Z)) = multiply(Y, multiply(X, Z)).
% 6.28/1.16 Axiom 5 (m7): fresh(X, X, Y, Z) = Y.
% 6.28/1.16 Axiom 6 (m7): fresh2(X, X, Y, Z) = Z.
% 6.28/1.16 Axiom 7 (h): multiply(multiply(X, Y), multiply(X, Z)) = multiply(multiply(Y, X), multiply(Y, Z)).
% 6.28/1.16 Axiom 8 (m7): fresh(multiply(X, Y), one, Y, X) = fresh2(multiply(Y, X), one, Y, X).
% 6.28/1.16 Axiom 9 (m5): multiply(multiply(X, Y), multiply(multiply(Z, X), multiply(Z, Y))) = one.
% 6.28/1.16
% 6.28/1.16 Lemma 10: multiply(X, multiply(Y, X)) = one.
% 6.28/1.16 Proof:
% 6.28/1.16 multiply(X, multiply(Y, X))
% 6.28/1.16 = { by axiom 4 (m9) R->L }
% 6.28/1.16 multiply(Y, multiply(X, X))
% 6.28/1.16 = { by axiom 1 (m8) }
% 6.28/1.16 multiply(Y, one)
% 6.28/1.16 = { by axiom 2 (m3) }
% 6.28/1.16 one
% 6.28/1.16
% 6.28/1.16 Lemma 11: multiply(X, multiply(Y, multiply(Z, W))) = multiply(Y, multiply(Z, multiply(X, W))).
% 6.28/1.16 Proof:
% 6.28/1.16 multiply(X, multiply(Y, multiply(Z, W)))
% 6.28/1.16 = { by axiom 4 (m9) R->L }
% 6.28/1.16 multiply(Y, multiply(X, multiply(Z, W)))
% 6.28/1.16 = { by axiom 4 (m9) R->L }
% 6.28/1.16 multiply(Y, multiply(Z, multiply(X, W)))
% 6.28/1.16
% 6.28/1.16 Lemma 12: multiply(X, multiply(multiply(X, Y), Y)) = one.
% 6.28/1.16 Proof:
% 6.28/1.16 multiply(X, multiply(multiply(X, Y), Y))
% 6.28/1.16 = { by axiom 4 (m9) R->L }
% 6.28/1.16 multiply(multiply(X, Y), multiply(X, Y))
% 6.28/1.16 = { by axiom 1 (m8) }
% 6.28/1.16 one
% 6.28/1.16
% 6.28/1.16 Lemma 13: multiply(Y, multiply(multiply(Y, X), Z)) = multiply(X, multiply(multiply(X, Y), Z)).
% 6.28/1.16 Proof:
% 6.28/1.16 multiply(Y, multiply(multiply(Y, X), Z))
% 6.28/1.16 = { by axiom 4 (m9) R->L }
% 6.28/1.16 multiply(multiply(Y, X), multiply(Y, Z))
% 6.28/1.16 = { by axiom 7 (h) R->L }
% 6.28/1.16 multiply(multiply(X, Y), multiply(X, Z))
% 6.28/1.16 = { by axiom 4 (m9) }
% 6.28/1.16 multiply(X, multiply(multiply(X, Y), Z))
% 6.28/1.16
% 6.28/1.16 Lemma 14: multiply(multiply(Y, X), multiply(Y, Z)) = multiply(X, multiply(multiply(X, Y), Z)).
% 6.28/1.16 Proof:
% 6.28/1.16 multiply(multiply(Y, X), multiply(Y, Z))
% 6.28/1.16 = { by axiom 4 (m9) }
% 6.28/1.16 multiply(Y, multiply(multiply(Y, X), Z))
% 6.28/1.16 = { by lemma 13 R->L }
% 6.28/1.16 multiply(X, multiply(multiply(X, Y), Z))
% 6.28/1.16
% 6.28/1.16 Lemma 15: multiply(multiply(multiply(X, Y), Y), Y) = multiply(X, Y).
% 6.28/1.16 Proof:
% 6.28/1.16 multiply(multiply(multiply(X, Y), Y), Y)
% 6.28/1.16 = { by axiom 5 (m7) R->L }
% 6.28/1.16 fresh(one, one, multiply(multiply(multiply(X, Y), Y), Y), multiply(X, Y))
% 6.28/1.16 = { by axiom 1 (m8) R->L }
% 6.28/1.16 fresh(multiply(multiply(multiply(X, Y), Y), multiply(multiply(X, Y), Y)), one, multiply(multiply(multiply(X, Y), Y), Y), multiply(X, Y))
% 6.28/1.16 = { by axiom 4 (m9) }
% 6.28/1.16 fresh(multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), Y), Y)), one, multiply(multiply(multiply(X, Y), Y), Y), multiply(X, Y))
% 6.28/1.16 = { by axiom 8 (m7) }
% 6.28/1.16 fresh2(multiply(multiply(multiply(multiply(X, Y), Y), Y), multiply(X, Y)), one, multiply(multiply(multiply(X, Y), Y), Y), multiply(X, Y))
% 6.28/1.16 = { by axiom 3 (m4) R->L }
% 6.28/1.16 fresh2(multiply(multiply(multiply(multiply(X, Y), Y), Y), multiply(X, multiply(one, Y))), one, multiply(multiply(multiply(X, Y), Y), Y), multiply(X, Y))
% 6.28/1.16 = { by lemma 12 R->L }
% 6.28/1.16 fresh2(multiply(multiply(multiply(multiply(X, Y), Y), Y), multiply(X, multiply(multiply(X, multiply(multiply(X, Y), Y)), Y))), one, multiply(multiply(multiply(X, Y), Y), Y), multiply(X, Y))
% 6.28/1.16 = { by axiom 4 (m9) R->L }
% 6.28/1.16 fresh2(multiply(multiply(multiply(multiply(X, Y), Y), Y), multiply(multiply(X, multiply(multiply(X, Y), Y)), multiply(X, Y))), one, multiply(multiply(multiply(X, Y), Y), Y), multiply(X, Y))
% 6.28/1.16 = { by axiom 9 (m5) }
% 6.28/1.16 fresh2(one, one, multiply(multiply(multiply(X, Y), Y), Y), multiply(X, Y))
% 6.28/1.16 = { by axiom 6 (m7) }
% 6.28/1.16 multiply(X, Y)
% 6.28/1.16
% 6.28/1.16 Lemma 16: multiply(multiply(multiply(Y, Z), Z), multiply(X, Z)) = multiply(X, multiply(Y, Z)).
% 6.28/1.16 Proof:
% 6.28/1.16 multiply(multiply(multiply(Y, Z), Z), multiply(X, Z))
% 6.28/1.16 = { by axiom 4 (m9) }
% 6.28/1.16 multiply(X, multiply(multiply(multiply(Y, Z), Z), Z))
% 6.28/1.16 = { by lemma 15 }
% 6.28/1.16 multiply(X, multiply(Y, Z))
% 6.28/1.16
% 6.28/1.16 Lemma 17: multiply(multiply(multiply(X, Z), Z), multiply(Y, Z)) = multiply(X, multiply(Y, Z)).
% 6.28/1.16 Proof:
% 6.28/1.16 multiply(multiply(multiply(X, Z), Z), multiply(Y, Z))
% 6.28/1.16 = { by lemma 16 }
% 6.28/1.16 multiply(Y, multiply(X, Z))
% 6.28/1.16 = { by axiom 4 (m9) R->L }
% 6.28/1.16 multiply(X, multiply(Y, Z))
% 6.28/1.16
% 6.28/1.17 Lemma 18: multiply(multiply(multiply(X, Y), Y), multiply(multiply(X, Y), Z)) = multiply(Y, Z).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(multiply(X, Y), Y), multiply(multiply(X, Y), Z))
% 6.28/1.17 = { by axiom 4 (m9) R->L }
% 6.28/1.17 multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), Y), Z))
% 6.28/1.17 = { by lemma 13 }
% 6.28/1.17 multiply(Y, multiply(multiply(Y, multiply(X, Y)), Z))
% 6.28/1.17 = { by lemma 10 }
% 6.28/1.17 multiply(Y, multiply(one, Z))
% 6.28/1.17 = { by axiom 3 (m4) }
% 6.28/1.17 multiply(Y, Z)
% 6.28/1.17
% 6.28/1.17 Lemma 19: multiply(X, multiply(multiply(multiply(multiply(Y, X), X), Z), Z)) = one.
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(X, multiply(multiply(multiply(multiply(Y, X), X), Z), Z))
% 6.28/1.17 = { by lemma 18 R->L }
% 6.28/1.17 multiply(multiply(multiply(Y, X), X), multiply(multiply(Y, X), multiply(multiply(multiply(multiply(Y, X), X), Z), Z)))
% 6.28/1.17 = { by axiom 4 (m9) R->L }
% 6.28/1.17 multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), X), multiply(multiply(multiply(multiply(Y, X), X), Z), Z)))
% 6.28/1.17 = { by lemma 12 }
% 6.28/1.17 multiply(multiply(Y, X), one)
% 6.28/1.17 = { by axiom 2 (m3) }
% 6.28/1.17 one
% 6.28/1.17
% 6.28/1.17 Lemma 20: multiply(Y, multiply(multiply(multiply(X, W), W), multiply(Z, W))) = multiply(X, multiply(Y, multiply(Z, W))).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(Y, multiply(multiply(multiply(X, W), W), multiply(Z, W)))
% 6.28/1.17 = { by lemma 17 }
% 6.28/1.17 multiply(Y, multiply(X, multiply(Z, W)))
% 6.28/1.17 = { by axiom 4 (m9) }
% 6.28/1.17 multiply(X, multiply(Y, multiply(Z, W)))
% 6.28/1.17
% 6.28/1.17 Lemma 21: multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), Y), Z)) = multiply(Y, Z).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), Y), Z))
% 6.28/1.17 = { by axiom 4 (m9) }
% 6.28/1.17 multiply(multiply(multiply(X, Y), Y), multiply(multiply(X, Y), Z))
% 6.28/1.17 = { by lemma 18 }
% 6.28/1.17 multiply(Y, Z)
% 6.28/1.17
% 6.28/1.17 Lemma 22: multiply(multiply(multiply(X, W), W), multiply(Y, multiply(Z, W))) = multiply(X, multiply(Y, multiply(Z, W))).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(multiply(X, W), W), multiply(Y, multiply(Z, W)))
% 6.28/1.17 = { by axiom 4 (m9) R->L }
% 6.28/1.17 multiply(Y, multiply(multiply(multiply(X, W), W), multiply(Z, W)))
% 6.28/1.17 = { by lemma 20 }
% 6.28/1.17 multiply(X, multiply(Y, multiply(Z, W)))
% 6.28/1.17
% 6.28/1.17 Lemma 23: multiply(multiply(multiply(Z, W), W), multiply(Y, multiply(X, W))) = multiply(X, multiply(Y, multiply(Z, W))).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(multiply(Z, W), W), multiply(Y, multiply(X, W)))
% 6.28/1.17 = { by axiom 4 (m9) R->L }
% 6.28/1.17 multiply(Y, multiply(multiply(multiply(Z, W), W), multiply(X, W)))
% 6.28/1.17 = { by lemma 16 }
% 6.28/1.17 multiply(Y, multiply(X, multiply(Z, W)))
% 6.28/1.17 = { by axiom 4 (m9) }
% 6.28/1.17 multiply(X, multiply(Y, multiply(Z, W)))
% 6.28/1.17
% 6.28/1.17 Lemma 24: multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(X, Y)) = multiply(X, Y).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(X, Y))
% 6.28/1.17 = { by lemma 15 R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(multiply(multiply(X, Y), Y), Y))
% 6.28/1.17 = { by axiom 4 (m9) R->L }
% 6.28/1.17 multiply(multiply(multiply(X, Y), Y), multiply(multiply(multiply(multiply(X, Y), Y), X), Y))
% 6.28/1.17 = { by lemma 13 }
% 6.28/1.17 multiply(X, multiply(multiply(X, multiply(multiply(X, Y), Y)), Y))
% 6.28/1.17 = { by lemma 12 }
% 6.28/1.17 multiply(X, multiply(one, Y))
% 6.28/1.17 = { by axiom 3 (m4) }
% 6.28/1.17 multiply(X, Y)
% 6.28/1.17
% 6.28/1.17 Lemma 25: multiply(multiply(multiply(Z, W), W), multiply(multiply(Y, X), multiply(Y, W))) = multiply(X, multiply(multiply(X, Y), multiply(Z, W))).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(multiply(Z, W), W), multiply(multiply(Y, X), multiply(Y, W)))
% 6.28/1.17 = { by lemma 22 }
% 6.28/1.17 multiply(Z, multiply(multiply(Y, X), multiply(Y, W)))
% 6.28/1.17 = { by lemma 14 }
% 6.28/1.17 multiply(Z, multiply(X, multiply(multiply(X, Y), W)))
% 6.28/1.17 = { by lemma 11 }
% 6.28/1.17 multiply(X, multiply(multiply(X, Y), multiply(Z, W)))
% 6.28/1.17
% 6.28/1.17 Lemma 26: multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(multiply(X, Y), Z)) = multiply(multiply(X, Y), multiply(multiply(Y, X), Z)).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(multiply(X, Y), Z))
% 6.28/1.17 = { by lemma 24 R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(X, Y)), Z))
% 6.28/1.17 = { by lemma 13 R->L }
% 6.28/1.17 multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), Y), X)), Z))
% 6.28/1.17 = { by lemma 21 }
% 6.28/1.17 multiply(multiply(X, Y), multiply(multiply(Y, X), Z))
% 6.28/1.17
% 6.28/1.17 Lemma 27: multiply(multiply(X, Y), multiply(multiply(multiply(multiply(multiply(multiply(Z, X), X), Y), Y), multiply(multiply(X, Y), Y)), W)) = multiply(multiply(multiply(multiply(Z, X), X), Y), W).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(X, Y), multiply(multiply(multiply(multiply(multiply(multiply(Z, X), X), Y), Y), multiply(multiply(X, Y), Y)), W))
% 6.28/1.17 = { by lemma 17 }
% 6.28/1.17 multiply(multiply(X, Y), multiply(multiply(multiply(multiply(Z, X), X), multiply(multiply(X, Y), Y)), W))
% 6.28/1.17 = { by axiom 4 (m9) }
% 6.28/1.17 multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), multiply(multiply(multiply(Z, X), X), Y)), W))
% 6.28/1.17 = { by lemma 13 R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(Z, X), X), Y), multiply(multiply(multiply(multiply(multiply(Z, X), X), Y), multiply(X, Y)), W))
% 6.28/1.17 = { by lemma 21 R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(Z, X), X), Y), multiply(multiply(multiply(multiply(multiply(Z, X), X), Y), multiply(multiply(Z, X), multiply(multiply(multiply(Z, X), X), Y))), W))
% 6.28/1.17 = { by lemma 10 }
% 6.28/1.17 multiply(multiply(multiply(multiply(Z, X), X), Y), multiply(one, W))
% 6.28/1.17 = { by axiom 3 (m4) }
% 6.28/1.17 multiply(multiply(multiply(multiply(Z, X), X), Y), W)
% 6.28/1.17
% 6.28/1.17 Lemma 28: multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), W)) = multiply(multiply(multiply(Y, Z), Z), W).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), W))
% 6.28/1.17 = { by axiom 4 (m9) R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), W))
% 6.28/1.17 = { by axiom 3 (m4) R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), multiply(multiply(one, multiply(multiply(multiply(multiply(X, Y), Y), Z), Z)), W))
% 6.28/1.17 = { by lemma 19 R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), multiply(multiply(multiply(Y, multiply(multiply(multiply(multiply(X, Y), Y), Z), Z)), multiply(multiply(multiply(multiply(X, Y), Y), Z), Z)), W))
% 6.28/1.17 = { by axiom 4 (m9) }
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), multiply(multiply(Y, multiply(multiply(multiply(multiply(X, Y), Y), Z), Z)), Z)), W))
% 6.28/1.17 = { by axiom 4 (m9) R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), multiply(Y, Z)), Z)), W))
% 6.28/1.17 = { by lemma 14 R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), multiply(multiply(multiply(multiply(Y, Z), multiply(multiply(multiply(X, Y), Y), Z)), multiply(multiply(Y, Z), Z)), W))
% 6.28/1.17 = { by lemma 16 R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), multiply(multiply(Y, Z), Z)), W))
% 6.28/1.17 = { by lemma 13 R->L }
% 6.28/1.17 multiply(multiply(multiply(Y, Z), Z), multiply(multiply(multiply(multiply(Y, Z), Z), multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z))), W))
% 6.28/1.17 = { by lemma 10 }
% 6.28/1.17 multiply(multiply(multiply(Y, Z), Z), multiply(one, W))
% 6.28/1.17 = { by axiom 3 (m4) }
% 6.28/1.17 multiply(multiply(multiply(Y, Z), Z), W)
% 6.28/1.17
% 6.28/1.17 Lemma 29: multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), W) = multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(multiply(multiply(Y, Z), Z), Y), W)).
% 6.28/1.17 Proof:
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), W)
% 6.28/1.17 = { by axiom 3 (m4) R->L }
% 6.28/1.17 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), multiply(one, W))
% 6.57/1.17 = { by lemma 10 R->L }
% 6.57/1.17 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), multiply(multiply(multiply(Y, Z), multiply(multiply(Y, multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z))), multiply(Y, Z))), W))
% 6.57/1.17 = { by lemma 14 }
% 6.57/1.17 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), multiply(multiply(multiply(Y, Z), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), Z))), W))
% 6.57/1.17 = { by lemma 27 }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), Z)), W))
% 6.57/1.18 = { by axiom 4 (m9) R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y), multiply(multiply(multiply(multiply(X, Y), Y), Z), Z)), W))
% 6.57/1.18 = { by lemma 13 R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(Y, Z), Z)), Y)), W))
% 6.57/1.18 = { by lemma 28 }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), Z), Z), multiply(multiply(multiply(multiply(Y, Z), Z), Y), W))
% 6.57/1.18
% 6.57/1.18 Lemma 30: multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)) = one.
% 6.57/1.18 Proof:
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(Y, X), X), Y), Y))
% 6.57/1.18 = { by axiom 3 (m4) R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(one, multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))
% 6.57/1.18 = { by lemma 10 R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(X, Y), multiply(multiply(multiply(multiply(X, Y), Y), X), X))), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))
% 6.57/1.18 = { by axiom 4 (m9) }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(multiply(X, Y), X))), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))
% 6.57/1.18 = { by lemma 26 }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(X, Y), multiply(multiply(Y, X), X))), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))
% 6.57/1.18 = { by axiom 4 (m9) R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), multiply(multiply(X, Y), X))), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))
% 6.57/1.18 = { by lemma 21 R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), multiply(multiply(multiply(Y, X), X), Y)), X))), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))
% 6.57/1.18 = { by lemma 13 }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(Y, X), X), Y), multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), multiply(Y, X)), X))), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))
% 6.57/1.18 = { by lemma 24 }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(Y, X), X), Y), multiply(multiply(Y, X), X))), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))
% 6.57/1.18 = { by lemma 29 R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), Y), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))
% 6.57/1.18 = { by axiom 4 (m9) }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(Y, X), X), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), Y), multiply(multiply(Y, X), X)), Y)))
% 6.57/1.18 = { by lemma 29 R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), Y), multiply(multiply(Y, X), X)), Y))
% 6.57/1.18 = { by lemma 14 R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(Y, X), X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), Y)), multiply(multiply(multiply(Y, X), X), Y))
% 6.57/1.18 = { by axiom 4 (m9) R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(Y, X), X), Y))
% 6.57/1.18 = { by axiom 3 (m4) R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(one, multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.18 = { by axiom 2 (m3) R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(Y, X), one), multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.18 = { by axiom 2 (m3) R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(Y, X), multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X))), one)), multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.18 = { by lemma 19 R->L }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(Y, X), multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X))), multiply(X, multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))), multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.18 = { by axiom 4 (m9) }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(Y, X), multiply(X, multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X))), multiply(multiply(multiply(multiply(Y, X), X), Y), Y)))), multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.18 = { by lemma 14 }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(Y, X), multiply(X, multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), Y)))), multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.18 = { by lemma 11 }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(Y, X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(X, Y)))), multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.18 = { by lemma 27 }
% 6.57/1.18 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(X, Y))), multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.19 = { by axiom 4 (m9) R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(X, Y))), multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.19 = { by lemma 24 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y)), multiply(X, Y)), multiply(multiply(multiply(Y, X), X), Y)))
% 6.57/1.19 = { by lemma 25 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(X, Y), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 23 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(X, Y), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 22 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(Y, X), X), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(X, Y), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 20 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(X, Y), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 16 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(X, Y), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 15 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(X, Y), Y), Y), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 28 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(X, Y), Y)), Y)), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 16 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(X, Y), Y)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 17 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(Y, X), X), multiply(multiply(X, Y), Y)), multiply(multiply(multiply(Y, X), X), Y)), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 14 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(X, Y), Y), multiply(multiply(multiply(multiply(X, Y), Y), multiply(multiply(Y, X), X)), Y)), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 16 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(X, Y), Y), multiply(multiply(Y, X), X)), multiply(X, Y)), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 17 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(X, Y)), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 17 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(X, Y), Y), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(Y, X), X)), multiply(X, Y)), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 17 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(X, Y), Y), multiply(multiply(Y, X), X)), multiply(multiply(multiply(multiply(multiply(X, Y), Y), multiply(multiply(Y, X), X)), multiply(X, Y)), multiply(multiply(multiply(Y, X), X), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 25 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), Y), multiply(multiply(Y, X), X))), multiply(multiply(X, Y), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 11 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(Y, X), multiply(multiply(X, Y), multiply(multiply(multiply(X, Y), Y), X))), multiply(multiply(X, Y), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 23 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(X, Y), multiply(multiply(Y, X), X))), multiply(multiply(X, Y), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 26 R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(multiply(multiply(X, Y), Y), X), multiply(multiply(X, Y), X))), multiply(multiply(X, Y), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by axiom 4 (m9) R->L }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(X, Y), Y), X), X), multiply(multiply(X, Y), multiply(multiply(multiply(multiply(X, Y), Y), X), X))), multiply(multiply(X, Y), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 10 }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(one, multiply(multiply(X, Y), Y))), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by axiom 3 (m4) }
% 6.57/1.19 multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(multiply(multiply(multiply(multiply(Y, X), X), Y), Y), multiply(multiply(X, Y), Y)), multiply(multiply(X, Y), Y)))
% 6.57/1.19 = { by lemma 28 }
% 6.57/1.19 multiply(multiply(multiply(X, Y), Y), multiply(multiply(X, Y), Y))
% 6.57/1.19 = { by axiom 1 (m8) }
% 6.57/1.19 one
% 6.57/1.19
% 6.57/1.19 Goal 1 (prove_j): multiply(multiply(multiply(multiply(a, b), b), a), a) = multiply(multiply(multiply(multiply(b, a), a), b), b).
% 6.57/1.19 Proof:
% 6.57/1.19 multiply(multiply(multiply(multiply(a, b), b), a), a)
% 6.57/1.19 = { by axiom 5 (m7) R->L }
% 6.57/1.19 fresh(one, one, multiply(multiply(multiply(multiply(a, b), b), a), a), multiply(multiply(multiply(multiply(b, a), a), b), b))
% 6.57/1.19 = { by lemma 30 R->L }
% 6.57/1.19 fresh(multiply(multiply(multiply(multiply(multiply(b, a), a), b), b), multiply(multiply(multiply(multiply(a, b), b), a), a)), one, multiply(multiply(multiply(multiply(a, b), b), a), a), multiply(multiply(multiply(multiply(b, a), a), b), b))
% 6.57/1.19 = { by axiom 8 (m7) }
% 6.57/1.19 fresh2(multiply(multiply(multiply(multiply(multiply(a, b), b), a), a), multiply(multiply(multiply(multiply(b, a), a), b), b)), one, multiply(multiply(multiply(multiply(a, b), b), a), a), multiply(multiply(multiply(multiply(b, a), a), b), b))
% 6.57/1.19 = { by lemma 30 }
% 6.57/1.19 fresh2(one, one, multiply(multiply(multiply(multiply(a, b), b), a), a), multiply(multiply(multiply(multiply(b, a), a), b), b))
% 6.57/1.19 = { by axiom 6 (m7) }
% 6.57/1.19 multiply(multiply(multiply(multiply(b, a), a), b), b)
% 6.57/1.19 % SZS output end Proof
% 6.57/1.19
% 6.57/1.19 RESULT: Unsatisfiable (the axioms are contradictory).
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