TSTP Solution File: GRP197-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP197-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n018.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 01:17:44 EDT 2023
% Result : Unsatisfiable 201.29s 25.97s
% Output : Proof 201.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP197-1 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % 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 : n018.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 20:07:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 201.29/25.97 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 201.29/25.97
% 201.29/25.97 % SZS status Unsatisfiable
% 201.29/25.97
% 201.94/26.04 % SZS output start Proof
% 201.94/26.04 Take the following subset of the input axioms:
% 201.94/26.04 fof(associativity_of_multiply, axiom, ![X, Y, Z]: multiply(multiply(X, Y), Z)=multiply(X, multiply(Y, Z))).
% 201.94/26.04 fof(condition, hypothesis, ![X2, Y2]: multiply(X2, multiply(X2, multiply(X2, multiply(Y2, Y2))))=multiply(Y2, multiply(X2, multiply(X2, multiply(Y2, X2))))).
% 201.94/26.04 fof(left_cancellation, axiom, ![A, B, C]: (multiply(A, B)!=multiply(A, C) | B=C)).
% 201.94/26.04 fof(prove_this, negated_conjecture, multiply(b, multiply(b, multiply(a, multiply(a, a))))!=multiply(a, multiply(b, multiply(a, multiply(a, b))))).
% 201.94/26.04 fof(right_cancellation, axiom, ![A2, B2, C2]: (multiply(A2, B2)!=multiply(C2, B2) | A2=C2)).
% 201.94/26.04
% 201.94/26.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 201.94/26.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 201.94/26.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 201.94/26.04 fresh(y, y, x1...xn) = u
% 201.94/26.04 C => fresh(s, t, x1...xn) = v
% 201.94/26.04 where fresh is a fresh function symbol and x1..xn are the free
% 201.94/26.04 variables of u and v.
% 201.94/26.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 201.94/26.04 input problem has no model of domain size 1).
% 201.94/26.04
% 201.94/26.04 The encoding turns the above axioms into the following unit equations and goals:
% 201.94/26.04
% 201.94/26.04 Axiom 1 (associativity_of_multiply): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 201.94/26.04 Axiom 2 (left_cancellation): fresh(X, X, Y, Z) = Z.
% 201.94/26.04 Axiom 3 (right_cancellation): fresh2(X, X, Y, Z) = Z.
% 201.94/26.04 Axiom 4 (condition): multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))).
% 201.94/26.04 Axiom 5 (left_cancellation): fresh(multiply(X, Y), multiply(X, Z), Y, Z) = Y.
% 201.94/26.04 Axiom 6 (right_cancellation): fresh2(multiply(X, Y), multiply(Z, Y), X, Z) = X.
% 201.94/26.04
% 201.94/26.04 Lemma 7: multiply(multiply(X, Y), multiply(Z, W)) = multiply(X, multiply(multiply(Y, Z), W)).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(X, Y), multiply(Z, W))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(Y, multiply(Z, W)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(X, multiply(multiply(Y, Z), W))
% 201.94/26.04
% 201.94/26.04 Lemma 8: multiply(multiply(X, multiply(Y, Z)), W) = multiply(X, multiply(Y, multiply(Z, W))).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(X, multiply(Y, Z)), W)
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(multiply(Y, Z), W))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(Y, multiply(Z, W)))
% 201.94/26.04
% 201.94/26.04 Lemma 9: multiply(multiply(X, multiply(Y, Z)), W) = multiply(multiply(X, Y), multiply(Z, W)).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(X, multiply(Y, Z)), W)
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(multiply(Y, Z), W))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(Y, multiply(Z, W)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(X, Y), multiply(Z, W))
% 201.94/26.04
% 201.94/26.04 Lemma 10: multiply(multiply(X, multiply(Y, Z)), multiply(W, V)) = multiply(X, multiply(multiply(Y, multiply(Z, W)), V)).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(X, multiply(Y, Z)), multiply(W, V))
% 201.94/26.04 = { by lemma 9 }
% 201.94/26.04 multiply(multiply(X, Y), multiply(Z, multiply(W, V)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(X, Y), multiply(multiply(Z, W), V))
% 201.94/26.04 = { by lemma 7 }
% 201.94/26.04 multiply(X, multiply(multiply(Y, multiply(Z, W)), V))
% 201.94/26.04
% 201.94/26.04 Lemma 11: multiply(multiply(X, multiply(Y, Z)), multiply(W, V)) = multiply(multiply(X, Y), multiply(multiply(Z, W), V)).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(X, multiply(Y, Z)), multiply(W, V))
% 201.94/26.04 = { by lemma 9 }
% 201.94/26.04 multiply(multiply(X, Y), multiply(Z, multiply(W, V)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(X, Y), multiply(multiply(Z, W), V))
% 201.94/26.04
% 201.94/26.04 Lemma 12: multiply(multiply(X, multiply(Y, multiply(Z, W))), V) = multiply(X, multiply(Y, multiply(Z, multiply(W, V)))).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(X, multiply(Y, multiply(Z, W))), V)
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(multiply(Y, multiply(Z, W)), V))
% 201.94/26.04 = { by lemma 8 }
% 201.94/26.04 multiply(X, multiply(Y, multiply(Z, multiply(W, V))))
% 201.94/26.04
% 201.94/26.04 Lemma 13: multiply(multiply(Y, multiply(X, multiply(X, Y))), X) = multiply(X, multiply(multiply(X, multiply(X, Y)), Y)).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(Y, multiply(X, multiply(X, Y))), X)
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(Y, multiply(multiply(X, multiply(X, Y)), X))
% 201.94/26.04 = { by lemma 9 }
% 201.94/26.04 multiply(Y, multiply(multiply(X, X), multiply(Y, X)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(Y, multiply(X, multiply(X, multiply(Y, X))))
% 201.94/26.04 = { by axiom 4 (condition) R->L }
% 201.94/26.04 multiply(X, multiply(X, multiply(X, multiply(Y, Y))))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(X, multiply(X, multiply(multiply(X, Y), Y)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(X, X), multiply(multiply(X, Y), Y))
% 201.94/26.04 = { by lemma 7 }
% 201.94/26.04 multiply(X, multiply(multiply(X, multiply(X, Y)), Y))
% 201.94/26.04
% 201.94/26.04 Lemma 14: multiply(Y, multiply(X, multiply(X, multiply(Y, multiply(X, Z))))) = multiply(X, multiply(X, multiply(X, multiply(Y, multiply(Y, Z))))).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(Y, multiply(X, multiply(X, multiply(Y, multiply(X, Z)))))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(Y, multiply(X, multiply(X, multiply(multiply(Y, X), Z))))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(Y, multiply(X, multiply(multiply(X, multiply(Y, X)), Z)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(Y, multiply(multiply(X, multiply(X, multiply(Y, X))), Z))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(Y, multiply(X, multiply(X, multiply(Y, X)))), Z)
% 201.94/26.04 = { by axiom 4 (condition) R->L }
% 201.94/26.04 multiply(multiply(X, multiply(X, multiply(X, multiply(Y, Y)))), Z)
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(multiply(X, multiply(X, multiply(Y, Y))), Z))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(X, multiply(multiply(X, multiply(Y, Y)), Z)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(X, multiply(X, multiply(multiply(Y, Y), Z))))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(X, multiply(X, multiply(Y, multiply(Y, Z)))))
% 201.94/26.04
% 201.94/26.04 Lemma 15: multiply(multiply(Y, X), multiply(X, multiply(multiply(Y, X), Z))) = multiply(X, multiply(X, multiply(X, multiply(multiply(Y, Y), Z)))).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(Y, X), multiply(X, multiply(multiply(Y, X), Z)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(Y, X), multiply(multiply(X, multiply(Y, X)), Z))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(multiply(Y, X), multiply(X, multiply(Y, X))), Z)
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(multiply(Y, multiply(X, multiply(X, multiply(Y, X)))), Z)
% 201.94/26.04 = { by axiom 4 (condition) R->L }
% 201.94/26.04 multiply(multiply(X, multiply(X, multiply(X, multiply(Y, Y)))), Z)
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(multiply(X, multiply(X, multiply(Y, Y))), Z))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(X, multiply(multiply(X, multiply(Y, Y)), Z)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(X, multiply(X, multiply(multiply(Y, Y), Z))))
% 201.94/26.04
% 201.94/26.04 Lemma 16: multiply(multiply(X, multiply(X, X)), multiply(Y, multiply(Y, Z))) = multiply(Y, multiply(multiply(X, X), multiply(Y, multiply(X, Z)))).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(X, multiply(X, X)), multiply(Y, multiply(Y, Z)))
% 201.94/26.04 = { by lemma 9 }
% 201.94/26.04 multiply(multiply(X, X), multiply(X, multiply(Y, multiply(Y, Z))))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(X, multiply(X, multiply(Y, multiply(Y, Z)))))
% 201.94/26.04 = { by lemma 14 R->L }
% 201.94/26.04 multiply(Y, multiply(X, multiply(X, multiply(Y, multiply(X, Z)))))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(Y, multiply(multiply(X, X), multiply(Y, multiply(X, Z))))
% 201.94/26.04
% 201.94/26.04 Lemma 17: multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, Z)) = multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, Z))).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, Z))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(multiply(Y, multiply(X, multiply(X, Y))), X), Z)
% 201.94/26.04 = { by lemma 13 }
% 201.94/26.04 multiply(multiply(X, multiply(multiply(X, multiply(X, Y)), Y)), Z)
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(multiply(multiply(X, multiply(X, Y)), Y), Z))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, Z)))
% 201.94/26.04
% 201.94/26.04 Lemma 18: multiply(multiply(X, multiply(Z, multiply(Y, multiply(Y, Z)))), Y) = multiply(multiply(X, Y), multiply(multiply(Y, multiply(Y, Z)), Z)).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(X, multiply(Z, multiply(Y, multiply(Y, Z)))), Y)
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(multiply(Z, multiply(Y, multiply(Y, Z))), Y))
% 201.94/26.04 = { by lemma 13 }
% 201.94/26.04 multiply(X, multiply(Y, multiply(multiply(Y, multiply(Y, Z)), Z)))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(X, Y), multiply(multiply(Y, multiply(Y, Z)), Z))
% 201.94/26.04
% 201.94/26.04 Lemma 19: multiply(multiply(X, multiply(Z, multiply(Y, multiply(Y, Z)))), multiply(Y, W)) = multiply(multiply(X, multiply(Y, Y)), multiply(multiply(Y, Z), multiply(Z, W))).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(X, multiply(Z, multiply(Y, multiply(Y, Z)))), multiply(Y, W))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.04 multiply(X, multiply(multiply(Z, multiply(Y, multiply(Y, Z))), multiply(Y, W)))
% 201.94/26.04 = { by lemma 17 }
% 201.94/26.04 multiply(X, multiply(Y, multiply(multiply(Y, multiply(Y, Z)), multiply(Z, W))))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.04 multiply(multiply(X, Y), multiply(multiply(Y, multiply(Y, Z)), multiply(Z, W)))
% 201.94/26.04 = { by lemma 11 R->L }
% 201.94/26.04 multiply(multiply(X, multiply(Y, Y)), multiply(multiply(Y, Z), multiply(Z, W)))
% 201.94/26.04
% 201.94/26.04 Lemma 20: multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(multiply(X, multiply(Z, W)), multiply(V, U))) = multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(Z, multiply(W, V)))), U)).
% 201.94/26.04 Proof:
% 201.94/26.04 multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(multiply(X, multiply(Z, W)), multiply(V, U)))
% 201.94/26.04 = { by lemma 9 }
% 201.94/26.04 multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(multiply(X, Z), multiply(W, multiply(V, U))))
% 201.94/26.04 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.05 multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(Z, multiply(W, multiply(V, U)))))
% 201.94/26.05 = { by lemma 17 }
% 201.94/26.05 multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(Z, multiply(W, multiply(V, U))))))
% 201.94/26.05 = { by lemma 12 R->L }
% 201.94/26.05 multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(multiply(Y, multiply(Z, multiply(W, V))), U)))
% 201.94/26.05 = { by lemma 7 R->L }
% 201.94/26.05 multiply(multiply(X, X), multiply(multiply(X, Y), multiply(multiply(Y, multiply(Z, multiply(W, V))), U)))
% 201.94/26.05 = { by lemma 7 }
% 201.94/26.05 multiply(multiply(X, X), multiply(X, multiply(multiply(Y, multiply(Y, multiply(Z, multiply(W, V)))), U)))
% 201.94/26.05 = { by lemma 9 R->L }
% 201.94/26.05 multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(Z, multiply(W, V)))), U))
% 201.94/26.05
% 201.94/26.05 Lemma 21: multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), multiply(X, Z)) = multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(X, Z)).
% 201.94/26.05 Proof:
% 201.94/26.05 multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), multiply(X, Z))
% 201.94/26.05 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.05 multiply(multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), Z)
% 201.94/26.05 = { by axiom 5 (left_cancellation) R->L }
% 201.94/26.05 multiply(fresh(multiply(multiply(multiply(X, multiply(X, X)), X), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(multiply(X, multiply(X, X)), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.05 multiply(fresh(multiply(multiply(X, multiply(X, X)), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(multiply(X, multiply(X, X)), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.05 multiply(fresh(multiply(multiply(X, multiply(X, X)), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X)))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.05 multiply(fresh(multiply(multiply(X, multiply(X, X)), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, Y)), multiply(multiply(X, multiply(X, Y)), X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 16 }
% 201.94/26.05 multiply(fresh(multiply(multiply(X, multiply(X, X)), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, multiply(X, Y)), multiply(multiply(X, X), multiply(multiply(X, multiply(X, Y)), multiply(X, X)))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 10 }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, multiply(X, Y)), multiply(multiply(X, X), multiply(multiply(X, multiply(X, Y)), multiply(X, X)))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 16 R->L }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, Y)), multiply(multiply(X, multiply(X, Y)), X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 10 }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 10 }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 18 }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(X, X), multiply(multiply(X, multiply(X, Y)), Y)))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 11 }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, Y)), Y)))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 9 }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), multiply(multiply(X, X), multiply(X, multiply(multiply(X, multiply(X, Y)), Y))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 13 R->L }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X)))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by axiom 2 (left_cancellation) R->L }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 11 }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(multiply(X, X), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(X, multiply(X, multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(Y, multiply(X, multiply(X, Y)))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 10 R->L }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(X, multiply(X, Y)))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(multiply(X, X), Y))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by lemma 9 }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(multiply(X, X), multiply(Y, multiply(Y, multiply(multiply(X, X), Y)))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.05 = { by axiom 4 (condition) R->L }
% 201.94/26.05 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(Y, multiply(Y, multiply(multiply(X, X), multiply(X, X))))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(Y, multiply(Y, multiply(X, multiply(X, multiply(X, X)))))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by lemma 12 R->L }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(Y, multiply(multiply(Y, multiply(X, multiply(X, X))), X))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by lemma 17 R->L }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by lemma 9 }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, X), multiply(X, multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y)))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(X, multiply(X, multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(Y, multiply(X, multiply(X, Y))))))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by axiom 4 (condition) }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(X, multiply(multiply(Y, multiply(X, multiply(X, Y))), X)))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), fresh(multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)), multiply(multiply(X, X), multiply(multiply(Y, multiply(X, multiply(X, Y))), X))))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by axiom 5 (left_cancellation) }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X)))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by lemma 9 R->L }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by lemma 20 R->L }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(X, multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(multiply(X, multiply(X, X)), multiply(X, X)))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(multiply(X, multiply(X, X)), multiply(X, X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), X))), Z)
% 201.94/26.06 = { by lemma 9 R->L }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X))), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(multiply(X, multiply(X, X)), multiply(X, X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), X)), Z)
% 201.94/26.06 = { by lemma 20 R->L }
% 201.94/26.06 multiply(fresh(multiply(X, multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(multiply(X, multiply(X, X)), multiply(X, X)))), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(multiply(X, multiply(X, X)), multiply(X, X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), X)), Z)
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.06 multiply(fresh(multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(multiply(X, multiply(X, X)), multiply(X, X))), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(multiply(X, multiply(X, X)), multiply(X, X))), multiply(multiply(Y, multiply(Y, multiply(X, multiply(X, X)))), X), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), X)), Z)
% 201.94/26.06 = { by axiom 2 (left_cancellation) }
% 201.94/26.06 multiply(multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), X), Z)
% 201.94/26.06 = { by lemma 18 }
% 201.94/26.06 multiply(multiply(multiply(X, X), multiply(multiply(X, multiply(X, Y)), Y)), Z)
% 201.94/26.06 = { by lemma 11 R->L }
% 201.94/26.06 multiply(multiply(multiply(X, multiply(X, X)), multiply(multiply(X, Y), Y)), Z)
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.06 multiply(multiply(X, multiply(X, X)), multiply(multiply(multiply(X, Y), Y), Z))
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.06 multiply(multiply(X, multiply(X, X)), multiply(multiply(X, Y), multiply(Y, Z)))
% 201.94/26.06 = { by lemma 19 R->L }
% 201.94/26.06 multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(X, Z))
% 201.94/26.06
% 201.94/26.06 Lemma 22: multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(X, multiply(X, Y)))) = multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(Y, multiply(X, multiply(X, Y)))))).
% 201.94/26.06 Proof:
% 201.94/26.06 multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(X, multiply(X, Y))))
% 201.94/26.06 = { by lemma 9 }
% 201.94/26.06 multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), multiply(X, multiply(X, Y)))))
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.06 multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(X, multiply(Y, multiply(multiply(X, multiply(X, Y)), multiply(X, multiply(X, Y))))))
% 201.94/26.06 = { by lemma 19 }
% 201.94/26.06 multiply(multiply(X, multiply(X, X)), multiply(multiply(X, Y), multiply(Y, multiply(Y, multiply(multiply(X, multiply(X, Y)), multiply(X, multiply(X, Y)))))))
% 201.94/26.06 = { by lemma 11 }
% 201.94/26.06 multiply(multiply(X, X), multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(Y, multiply(multiply(X, multiply(X, Y)), multiply(X, multiply(X, Y)))))))
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.06 multiply(X, multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(Y, multiply(multiply(X, multiply(X, Y)), multiply(X, multiply(X, Y))))))))
% 201.94/26.06 = { by lemma 10 R->L }
% 201.94/26.06 multiply(X, multiply(multiply(X, multiply(X, X)), multiply(Y, multiply(Y, multiply(Y, multiply(multiply(X, multiply(X, Y)), multiply(X, multiply(X, Y))))))))
% 201.94/26.06 = { by axiom 4 (condition) }
% 201.94/26.06 multiply(X, multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(Y, multiply(multiply(X, multiply(X, Y)), Y))))))
% 201.94/26.06 = { by lemma 7 R->L }
% 201.94/26.06 multiply(multiply(X, X), multiply(multiply(X, X), multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(Y, multiply(multiply(X, multiply(X, Y)), Y))))))
% 201.94/26.06 = { by lemma 9 }
% 201.94/26.06 multiply(multiply(X, X), multiply(multiply(X, X), multiply(multiply(X, X), multiply(Y, multiply(Y, multiply(Y, multiply(multiply(X, multiply(X, Y)), Y)))))))
% 201.94/26.06 = { by lemma 14 R->L }
% 201.94/26.06 multiply(Y, multiply(multiply(X, X), multiply(multiply(X, X), multiply(Y, multiply(multiply(X, X), multiply(Y, multiply(multiply(X, multiply(X, Y)), Y)))))))
% 201.94/26.06 = { by lemma 7 }
% 201.94/26.06 multiply(Y, multiply(X, multiply(multiply(X, multiply(X, X)), multiply(Y, multiply(multiply(X, X), multiply(Y, multiply(multiply(X, multiply(X, Y)), Y)))))))
% 201.94/26.06 = { by lemma 10 R->L }
% 201.94/26.06 multiply(Y, multiply(multiply(X, multiply(X, X)), multiply(X, multiply(Y, multiply(multiply(X, X), multiply(Y, multiply(multiply(X, multiply(X, Y)), Y)))))))
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(X, multiply(Y, multiply(multiply(X, X), multiply(Y, multiply(multiply(X, multiply(X, Y)), Y))))))
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(multiply(X, Y), multiply(multiply(X, X), multiply(Y, multiply(multiply(X, multiply(X, Y)), Y)))))
% 201.94/26.06 = { by lemma 9 R->L }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(multiply(X, Y), multiply(multiply(X, multiply(X, Y)), multiply(multiply(X, multiply(X, Y)), Y))))
% 201.94/26.06 = { by lemma 9 R->L }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(multiply(X, multiply(Y, multiply(X, multiply(X, Y)))), multiply(multiply(X, multiply(X, Y)), Y)))
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(X, multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(multiply(X, multiply(X, Y)), Y))))
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(X, multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(multiply(X, Y), Y)))))
% 201.94/26.06 = { by lemma 17 }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(X, multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(multiply(X, Y), Y))))))
% 201.94/26.06 = { by lemma 7 R->L }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(X, multiply(multiply(X, X), multiply(multiply(X, Y), multiply(Y, multiply(multiply(X, Y), Y))))))
% 201.94/26.06 = { by lemma 15 }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(X, multiply(multiply(X, X), multiply(Y, multiply(Y, multiply(Y, multiply(multiply(X, X), Y)))))))
% 201.94/26.06 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(X, multiply(multiply(X, X), multiply(Y, multiply(Y, multiply(Y, multiply(X, multiply(X, Y))))))))
% 201.94/26.06 = { by lemma 9 R->L }
% 201.94/26.06 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(Y, multiply(Y, multiply(X, multiply(X, Y)))))))
% 201.94/26.06 = { by lemma 17 R->L }
% 201.94/26.07 multiply(multiply(Y, multiply(X, multiply(X, X))), multiply(multiply(Y, multiply(X, multiply(X, Y))), multiply(X, multiply(Y, multiply(X, multiply(X, Y))))))
% 201.94/26.07
% 201.94/26.07 Goal 1 (prove_this): multiply(b, multiply(b, multiply(a, multiply(a, a)))) = multiply(a, multiply(b, multiply(a, multiply(a, b)))).
% 201.94/26.07 Proof:
% 201.94/26.07 multiply(b, multiply(b, multiply(a, multiply(a, a))))
% 201.94/26.07 = { by axiom 6 (right_cancellation) R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, multiply(a, b)))), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, multiply(a, b)))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 22 }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, multiply(a, b)))), multiply(multiply(b, multiply(a, multiply(a, a))), multiply(multiply(b, multiply(a, multiply(a, b))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 21 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(b, multiply(a, multiply(a, a))), multiply(multiply(b, multiply(a, multiply(a, b))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 22 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, multiply(a, b)))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(a, multiply(multiply(b, multiply(a, multiply(a, b))), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, multiply(a, b))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(a, multiply(multiply(b, multiply(a, multiply(a, b))), multiply(a, multiply(multiply(b, multiply(a, multiply(a, b))), multiply(a, multiply(a, b)))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 17 }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(a, multiply(a, multiply(multiply(a, multiply(a, b)), multiply(b, multiply(multiply(b, multiply(a, multiply(a, b))), multiply(a, multiply(a, b))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 10 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(a, multiply(multiply(a, multiply(a, a)), multiply(b, multiply(b, multiply(multiply(b, multiply(a, multiply(a, b))), multiply(a, multiply(a, b))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 12 }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(a, multiply(multiply(a, multiply(a, a)), multiply(b, multiply(b, multiply(b, multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, b)))))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(a, multiply(multiply(a, multiply(a, a)), multiply(b, multiply(b, multiply(b, multiply(multiply(a, a), multiply(b, multiply(a, multiply(a, b))))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 15 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(a, multiply(multiply(a, multiply(a, a)), multiply(multiply(a, b), multiply(b, multiply(multiply(a, b), multiply(b, multiply(a, multiply(a, b)))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 19 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(a, multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, multiply(multiply(a, b), multiply(b, multiply(a, multiply(a, b))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(a, multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(multiply(a, multiply(a, b)), multiply(b, multiply(a, multiply(a, b)))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 7 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(a, a), multiply(multiply(b, multiply(a, multiply(a, b))), multiply(multiply(a, multiply(a, b)), multiply(b, multiply(a, multiply(a, b)))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(a, a), multiply(multiply(b, multiply(a, multiply(a, b))), multiply(a, multiply(multiply(a, b), multiply(b, multiply(a, multiply(a, b))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 17 }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(a, a), multiply(a, multiply(multiply(a, multiply(a, b)), multiply(b, multiply(multiply(a, b), multiply(b, multiply(a, multiply(a, b)))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 7 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(a, a), multiply(multiply(a, a), multiply(multiply(a, b), multiply(b, multiply(multiply(a, b), multiply(b, multiply(a, multiply(a, b)))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 15 }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(a, a), multiply(multiply(a, a), multiply(b, multiply(b, multiply(b, multiply(multiply(a, a), multiply(b, multiply(a, multiply(a, b))))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 9 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(a, a), multiply(multiply(a, multiply(a, b)), multiply(b, multiply(b, multiply(multiply(a, a), multiply(b, multiply(a, multiply(a, b)))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 11 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(a, multiply(a, a)), multiply(multiply(a, b), multiply(b, multiply(b, multiply(multiply(a, a), multiply(b, multiply(a, multiply(a, b)))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 19 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, multiply(b, multiply(multiply(a, a), multiply(b, multiply(a, multiply(a, b))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 21 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(multiply(a, a), multiply(b, multiply(a, multiply(a, b))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by axiom 1 (associativity_of_multiply) R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(a, b), multiply(multiply(a, a), multiply(b, multiply(a, multiply(a, b)))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by axiom 1 (associativity_of_multiply) }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(a, b), multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, b))))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 8 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(a, b), multiply(multiply(a, multiply(a, b)), multiply(a, multiply(a, b))))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 9 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, multiply(a, b)))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by lemma 21 R->L }
% 201.94/26.07 fresh2(multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(a, b)))), multiply(b, multiply(b, multiply(a, multiply(a, a)))), multiply(a, multiply(b, multiply(a, multiply(a, b)))))
% 201.94/26.07 = { by axiom 3 (right_cancellation) }
% 201.94/26.07 multiply(a, multiply(b, multiply(a, multiply(a, b))))
% 201.94/26.07 % SZS output end Proof
% 201.94/26.07
% 201.94/26.07 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------