TSTP Solution File: GRP059-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP059-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n001.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 01:16:49 EDT 2023
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP059-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.32 % Computer : n001.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon Aug 28 21:45:21 EDT 2023
% 0.14/0.32 % CPUTime :
% 0.14/0.39 Command-line arguments: --no-flatten-goal
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39
% 0.16/0.42 % SZS output start Proof
% 0.16/0.42 Take the following subset of the input axioms:
% 0.16/0.42 fof(prove_these_axioms, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1) | (multiply(multiply(inverse(b2), b2), a2)!=a2 | multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3)))).
% 0.16/0.42 fof(single_axiom, axiom, ![X, Y, Z, U]: inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), Z)), X), Y), multiply(U, inverse(U))))=Z).
% 0.16/0.42
% 0.16/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.42 fresh(y, y, x1...xn) = u
% 0.16/0.42 C => fresh(s, t, x1...xn) = v
% 0.16/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.42 variables of u and v.
% 0.16/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.42 input problem has no model of domain size 1).
% 0.16/0.42
% 0.16/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.42
% 0.16/0.42 Axiom 1 (single_axiom): inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), Z)), X), Y), multiply(W, inverse(W)))) = Z.
% 0.16/0.42
% 0.16/0.42 Lemma 2: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.16/0.42 Proof:
% 0.16/0.42 multiply(Y, inverse(Y))
% 0.16/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.16/0.42 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), V)), Z), W), multiply(Y, inverse(Y)))), multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.16/0.42 = { by axiom 1 (single_axiom) }
% 0.16/0.42 inverse(multiply(multiply(multiply(V, multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.16/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.16/0.42 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), V)), Z), W), multiply(X, inverse(X)))), multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.16/0.42 = { by axiom 1 (single_axiom) }
% 0.16/0.42 multiply(X, inverse(X))
% 0.16/0.42
% 0.16/0.42 Lemma 3: inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(X))), Y), Z), multiply(W, inverse(W)))) = inverse(multiply(Y, Z)).
% 0.16/0.42 Proof:
% 0.16/0.42 inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(X))), Y), Z), multiply(W, inverse(W))))
% 0.16/0.42 = { by lemma 2 }
% 0.16/0.42 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, Z), inverse(multiply(Y, Z)))), Y), Z), multiply(W, inverse(W))))
% 0.16/0.42 = { by axiom 1 (single_axiom) }
% 0.16/0.42 inverse(multiply(Y, Z))
% 0.16/0.42
% 0.16/0.42 Lemma 4: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z)))) = inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), Y)).
% 0.16/0.42 Proof:
% 0.16/0.42 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z))))
% 0.16/0.42 = { by lemma 2 }
% 0.16/0.42 inverse(multiply(multiply(multiply(inverse(multiply(W, inverse(W))), inverse(inverse(multiply(W, inverse(W))))), Y), multiply(Z, inverse(Z))))
% 0.16/0.42 = { by lemma 3 }
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), Y))
% 0.16/0.43
% 0.16/0.43 Lemma 5: inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y)) = multiply(W, inverse(W)).
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y))
% 0.16/0.43 = { by lemma 3 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X)), Y), multiply(V, inverse(V))))
% 0.16/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y), multiply(W, inverse(W)))), multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X)), Y), multiply(V, inverse(V))))
% 0.16/0.43 = { by axiom 1 (single_axiom) }
% 0.16/0.43 multiply(W, inverse(W))
% 0.16/0.43
% 0.16/0.43 Lemma 6: inverse(multiply(multiply(inverse(multiply(X, inverse(X))), Y), inverse(Y))) = multiply(Z, inverse(Z)).
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(multiply(inverse(multiply(X, inverse(X))), Y), inverse(Y)))
% 0.16/0.43 = { by lemma 2 }
% 0.16/0.43 inverse(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y))))), Y), inverse(Y)))
% 0.16/0.43 = { by lemma 5 }
% 0.16/0.43 multiply(Z, inverse(Z))
% 0.16/0.43
% 0.16/0.43 Lemma 7: inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), Y)) = inverse(Y).
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), Y))
% 0.16/0.43 = { by lemma 4 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))), Y), multiply(W, inverse(W))))
% 0.16/0.43 = { by lemma 6 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(Z, inverse(Z))), Y), inverse(Y))), inverse(multiply(Z, inverse(Z)))), Y), multiply(W, inverse(W))))
% 0.16/0.43 = { by axiom 1 (single_axiom) }
% 0.16/0.43 inverse(Y)
% 0.16/0.43
% 0.16/0.43 Lemma 8: inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), inverse(multiply(Y, inverse(Y))))) = inverse(multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W)))).
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), inverse(multiply(Y, inverse(Y)))))
% 0.16/0.43 = { by lemma 4 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), multiply(W, inverse(W))))
% 0.16/0.43 = { by lemma 2 R->L }
% 0.16/0.43 inverse(multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W))))
% 0.16/0.43
% 0.16/0.43 Lemma 9: inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))) = multiply(Z, inverse(Z)).
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))))
% 0.16/0.43 = { by lemma 8 R->L }
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(multiply(V, inverse(V)))))
% 0.16/0.43 = { by lemma 4 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(U, inverse(U)), inverse(multiply(V, inverse(V)))), multiply(T, inverse(T))))
% 0.16/0.43 = { by lemma 6 R->L }
% 0.16/0.43 inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(V, inverse(V))), multiply(T, inverse(T))), inverse(multiply(T, inverse(T))))), inverse(multiply(V, inverse(V)))), multiply(T, inverse(T))))
% 0.16/0.43 = { by lemma 5 }
% 0.16/0.43 multiply(Z, inverse(Z))
% 0.16/0.43
% 0.16/0.43 Lemma 10: inverse(inverse(multiply(X, inverse(X)))) = multiply(Y, inverse(Y)).
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(inverse(multiply(X, inverse(X))))
% 0.16/0.43 = { by lemma 7 R->L }
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(multiply(X, inverse(X)))))
% 0.16/0.43 = { by lemma 8 }
% 0.16/0.43 inverse(multiply(multiply(W, inverse(W)), multiply(V, inverse(V))))
% 0.16/0.43 = { by lemma 9 }
% 0.16/0.43 multiply(Y, inverse(Y))
% 0.16/0.43
% 0.16/0.43 Lemma 11: inverse(multiply(multiply(X, inverse(X)), Y)) = inverse(Y).
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(multiply(X, inverse(X)), Y))
% 0.16/0.43 = { by lemma 10 R->L }
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), Y))
% 0.16/0.43 = { by lemma 7 }
% 0.16/0.43 inverse(Y)
% 0.16/0.43
% 0.16/0.43 Lemma 12: inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, inverse(X)), Y)), Z), inverse(Z)), multiply(W, inverse(W)))) = Y.
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, inverse(X)), Y)), Z), inverse(Z)), multiply(W, inverse(W))))
% 0.16/0.43 = { by lemma 2 }
% 0.16/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, inverse(Z)), Y)), Z), inverse(Z)), multiply(W, inverse(W))))
% 0.16/0.43 = { by axiom 1 (single_axiom) }
% 0.16/0.43 Y
% 0.16/0.43
% 0.16/0.43 Lemma 13: inverse(inverse(inverse(inverse(X)))) = X.
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(inverse(inverse(inverse(X))))
% 0.16/0.43 = { by lemma 7 R->L }
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(X)))))
% 0.16/0.43 = { by lemma 11 R->L }
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(multiply(multiply(Z, inverse(Z)), X))))))
% 0.16/0.43 = { by lemma 4 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, inverse(Z)), X)), inverse(inverse(multiply(multiply(Z, inverse(Z)), X)))), inverse(inverse(inverse(multiply(multiply(Z, inverse(Z)), X))))), multiply(W, inverse(W))))
% 0.16/0.43 = { by lemma 12 }
% 0.16/0.43 X
% 0.16/0.43
% 0.16/0.43 Lemma 14: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.16/0.43 Proof:
% 0.16/0.43 multiply(multiply(X, inverse(X)), Y)
% 0.16/0.43 = { by lemma 10 R->L }
% 0.16/0.43 multiply(inverse(inverse(multiply(Z, inverse(Z)))), Y)
% 0.16/0.43 = { by lemma 13 R->L }
% 0.16/0.43 inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), Y)))))
% 0.16/0.43 = { by lemma 7 }
% 0.16/0.43 inverse(inverse(inverse(inverse(Y))))
% 0.16/0.43 = { by lemma 13 }
% 0.16/0.43 Y
% 0.16/0.43
% 0.16/0.43 Lemma 15: inverse(multiply(X, multiply(Y, inverse(Y)))) = inverse(X).
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(X, multiply(Y, inverse(Y))))
% 0.16/0.43 = { by lemma 14 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(Z, inverse(Z)), X), multiply(Y, inverse(Y))))
% 0.16/0.43 = { by lemma 4 }
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), X))
% 0.16/0.43 = { by lemma 7 }
% 0.16/0.43 inverse(X)
% 0.16/0.43
% 0.16/0.43 Lemma 16: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(X, inverse(X)))
% 0.16/0.43 = { by lemma 2 }
% 0.16/0.43 inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))))
% 0.16/0.43 = { by lemma 10 R->L }
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(multiply(Z, inverse(Z)))))
% 0.16/0.43 = { by lemma 8 }
% 0.16/0.43 inverse(multiply(multiply(V, inverse(V)), multiply(U, inverse(U))))
% 0.16/0.43 = { by lemma 9 }
% 0.16/0.43 multiply(Y, inverse(Y))
% 0.16/0.43
% 0.16/0.43 Lemma 17: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.16/0.43 Proof:
% 0.16/0.43 multiply(inverse(X), X)
% 0.16/0.43 = { by lemma 13 R->L }
% 0.16/0.43 inverse(inverse(inverse(inverse(multiply(inverse(X), X)))))
% 0.16/0.43 = { by lemma 15 R->L }
% 0.16/0.43 inverse(inverse(inverse(inverse(multiply(inverse(multiply(X, multiply(Z, inverse(Z)))), X)))))
% 0.16/0.43 = { by lemma 15 R->L }
% 0.16/0.43 inverse(inverse(inverse(inverse(multiply(inverse(multiply(multiply(X, multiply(Z, inverse(Z))), multiply(W, inverse(W)))), X)))))
% 0.16/0.43 = { by lemma 16 R->L }
% 0.16/0.43 inverse(inverse(inverse(inverse(multiply(inverse(multiply(multiply(X, multiply(Z, inverse(Z))), inverse(multiply(V, inverse(V))))), X)))))
% 0.16/0.43 = { by lemma 15 R->L }
% 0.16/0.43 inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(multiply(X, multiply(Z, inverse(Z))), inverse(multiply(V, inverse(V))))), X), multiply(Z, inverse(Z)))))))
% 0.16/0.43 = { by lemma 5 }
% 0.16/0.43 inverse(inverse(inverse(multiply(U, inverse(U)))))
% 0.16/0.43 = { by lemma 10 }
% 0.16/0.43 inverse(multiply(T, inverse(T)))
% 0.16/0.43 = { by lemma 16 }
% 0.16/0.43 multiply(Y, inverse(Y))
% 0.16/0.43
% 0.16/0.43 Lemma 18: inverse(inverse(X)) = X.
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(inverse(X))
% 0.16/0.43 = { by lemma 11 R->L }
% 0.16/0.43 inverse(inverse(multiply(multiply(Y, inverse(Y)), X)))
% 0.16/0.43 = { by lemma 7 R->L }
% 0.16/0.43 inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(multiply(multiply(Y, inverse(Y)), X))))
% 0.16/0.43 = { by lemma 4 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(multiply(Y, inverse(Y)), X))), multiply(V, inverse(V))))
% 0.16/0.43 = { by lemma 17 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), X)), multiply(multiply(Y, inverse(Y)), X)), inverse(multiply(multiply(Y, inverse(Y)), X))), multiply(V, inverse(V))))
% 0.16/0.43 = { by lemma 12 }
% 0.16/0.43 X
% 0.16/0.43
% 0.16/0.43 Lemma 19: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.16/0.43 Proof:
% 0.16/0.43 multiply(X, multiply(Y, inverse(Y)))
% 0.16/0.43 = { by lemma 13 R->L }
% 0.16/0.43 inverse(inverse(inverse(inverse(multiply(X, multiply(Y, inverse(Y)))))))
% 0.16/0.43 = { by lemma 15 }
% 0.16/0.43 inverse(inverse(inverse(inverse(X))))
% 0.16/0.43 = { by lemma 13 }
% 0.16/0.43 X
% 0.16/0.43
% 0.16/0.43 Lemma 20: inverse(multiply(inverse(multiply(X, Y)), X)) = Y.
% 0.16/0.43 Proof:
% 0.16/0.43 inverse(multiply(inverse(multiply(X, Y)), X))
% 0.16/0.43 = { by lemma 15 R->L }
% 0.16/0.43 inverse(multiply(multiply(inverse(multiply(X, Y)), X), multiply(Z, inverse(Z))))
% 0.16/0.43 = { by lemma 19 R->L }
% 0.16/0.43 inverse(multiply(multiply(inverse(multiply(multiply(X, multiply(W, inverse(W))), Y)), X), multiply(Z, inverse(Z))))
% 0.16/0.43 = { by lemma 19 R->L }
% 0.16/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, multiply(W, inverse(W))), Y)), X), multiply(W, inverse(W))), multiply(Z, inverse(Z))))
% 0.16/0.43 = { by axiom 1 (single_axiom) }
% 0.16/0.43 Y
% 0.16/0.43
% 0.16/0.43 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 0.16/0.43 Proof:
% 0.16/0.43 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.16/0.43 = { by lemma 17 }
% 0.16/0.43 tuple(multiply(X, inverse(X)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.16/0.43 = { by lemma 17 }
% 0.16/0.43 tuple(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), a2), multiply(multiply(a3, b3), c3))
% 0.16/0.44 = { by lemma 14 }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 0.16/0.44 = { by lemma 13 R->L }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, inverse(inverse(inverse(inverse(multiply(multiply(a3, b3), c3))))))
% 0.16/0.44 = { by lemma 15 R->L }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, inverse(inverse(inverse(inverse(multiply(multiply(multiply(a3, b3), c3), multiply(Z, inverse(Z))))))))
% 0.16/0.44 = { by lemma 18 R->L }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, inverse(inverse(inverse(inverse(multiply(multiply(multiply(inverse(inverse(a3)), b3), c3), multiply(Z, inverse(Z))))))))
% 0.16/0.44 = { by lemma 18 R->L }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, inverse(inverse(inverse(inverse(multiply(multiply(multiply(inverse(inverse(inverse(inverse(a3)))), b3), c3), multiply(Z, inverse(Z))))))))
% 0.16/0.44 = { by lemma 20 R->L }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, inverse(inverse(inverse(inverse(multiply(multiply(multiply(inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), a3)), inverse(multiply(a3, multiply(b3, c3))))))))), b3), c3), multiply(Z, inverse(Z))))))))
% 0.16/0.44 = { by lemma 13 }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, inverse(inverse(inverse(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), a3)), inverse(multiply(a3, multiply(b3, c3))))), b3), c3), multiply(Z, inverse(Z))))))))
% 0.16/0.44 = { by lemma 20 }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, inverse(inverse(inverse(inverse(multiply(multiply(multiply(inverse(multiply(multiply(b3, c3), inverse(multiply(a3, multiply(b3, c3))))), b3), c3), multiply(Z, inverse(Z))))))))
% 0.16/0.44 = { by axiom 1 (single_axiom) }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, inverse(inverse(inverse(inverse(multiply(a3, multiply(b3, c3)))))))
% 0.16/0.44 = { by lemma 13 }
% 0.16/0.44 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 0.16/0.44 = { by lemma 17 R->L }
% 0.16/0.44 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 0.16/0.44 % SZS output end Proof
% 0.16/0.44
% 0.16/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------