TSTP Solution File: GRP058-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP058-1 : 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 : n011.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 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP058-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 00:36:26 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.43 Command-line arguments: --no-flatten-goal
% 0.19/0.43
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 Take the following subset of the input axioms:
% 0.19/0.48 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)))).
% 0.19/0.48 fof(single_axiom, axiom, ![X, Y, Z, U]: multiply(X, inverse(multiply(Y, multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(U, Y))), X))))=U).
% 0.19/0.48
% 0.19/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.48 fresh(y, y, x1...xn) = u
% 0.19/0.48 C => fresh(s, t, x1...xn) = v
% 0.19/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.48 variables of u and v.
% 0.19/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.48 input problem has no model of domain size 1).
% 0.19/0.48
% 0.19/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.48
% 0.19/0.48 Axiom 1 (single_axiom): multiply(X, inverse(multiply(Y, multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, Y))), X)))) = W.
% 0.19/0.48
% 0.19/0.48 Lemma 2: multiply(X, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V))), multiply(Z, X)))) = W.
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(X, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V))), multiply(Z, X))))
% 0.19/0.48 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.48 multiply(X, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V))), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(W, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V)))))), X))))
% 0.19/0.48 = { by axiom 1 (single_axiom) }
% 0.19/0.48 W
% 0.19/0.48
% 0.19/0.48 Lemma 3: multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W))) = multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, V)))).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))
% 0.19/0.48 = { by lemma 2 R->L }
% 0.19/0.48 multiply(V, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(Z, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))))), multiply(U, inverse(U))), multiply(Z, V))))
% 0.19/0.48 = { by axiom 1 (single_axiom) }
% 0.19/0.48 multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, V))))
% 0.19/0.48
% 0.19/0.48 Lemma 4: multiply(X, inverse(multiply(multiply(Y, inverse(multiply(multiply(Z, multiply(W, inverse(W))), multiply(V, Y)))), multiply(Z, X)))) = V.
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(X, inverse(multiply(multiply(Y, inverse(multiply(multiply(Z, multiply(W, inverse(W))), multiply(V, Y)))), multiply(Z, X))))
% 0.19/0.48 = { by lemma 3 R->L }
% 0.19/0.48 multiply(X, inverse(multiply(multiply(multiply(multiply(U, inverse(U)), inverse(multiply(Z, V))), multiply(T, inverse(T))), multiply(Z, X))))
% 0.19/0.48 = { by lemma 2 }
% 0.19/0.48 V
% 0.19/0.48
% 0.19/0.48 Lemma 5: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(Y, inverse(Y))
% 0.19/0.48 = { by lemma 2 R->L }
% 0.19/0.48 multiply(Z, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(U, T))), multiply(Y, inverse(Y))))), multiply(S, inverse(S))), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(U, T))), Z))))
% 0.19/0.48 = { by lemma 3 }
% 0.19/0.48 multiply(Z, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(X2, inverse(multiply(multiply(U, multiply(Y2, inverse(Y2))), multiply(T, X2)))))), multiply(S, inverse(S))), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(U, T))), Z))))
% 0.19/0.48 = { by lemma 3 R->L }
% 0.19/0.48 multiply(Z, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(U, T))), multiply(X, inverse(X))))), multiply(S, inverse(S))), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(U, T))), Z))))
% 0.19/0.48 = { by lemma 2 }
% 0.19/0.48 multiply(X, inverse(X))
% 0.19/0.48
% 0.19/0.48 Lemma 6: multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, X)))) = inverse(W).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, X))))
% 0.19/0.48 = { by lemma 5 }
% 0.19/0.48 multiply(X, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))), multiply(Z, inverse(Z))), multiply(W, X))))
% 0.19/0.48 = { by lemma 2 }
% 0.19/0.48 inverse(W)
% 0.19/0.48
% 0.19/0.48 Lemma 7: inverse(multiply(X, inverse(multiply(Y, multiply(multiply(Z, inverse(Z)), X))))) = Y.
% 0.19/0.48 Proof:
% 0.19/0.48 inverse(multiply(X, inverse(multiply(Y, multiply(multiply(Z, inverse(Z)), X)))))
% 0.19/0.48 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.48 inverse(multiply(X, inverse(multiply(multiply(W, inverse(multiply(multiply(multiply(Z, inverse(Z)), multiply(V, inverse(V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(multiply(Z, inverse(Z)), multiply(V, inverse(V)))))), W)))), multiply(multiply(Z, inverse(Z)), X)))))
% 0.19/0.48 = { by lemma 4 }
% 0.19/0.48 inverse(multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(multiply(Z, inverse(Z)), multiply(V, inverse(V)))))))
% 0.19/0.48 = { by lemma 6 R->L }
% 0.19/0.48 multiply(T, inverse(multiply(multiply(multiply(Z, inverse(Z)), multiply(V, inverse(V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(multiply(Z, inverse(Z)), multiply(V, inverse(V)))))), T))))
% 0.19/0.48 = { by axiom 1 (single_axiom) }
% 0.19/0.48 Y
% 0.19/0.48
% 0.19/0.48 Lemma 8: multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))) = inverse(inverse(multiply(Z, inverse(Z)))).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))
% 0.19/0.48 = { by lemma 7 R->L }
% 0.19/0.48 inverse(multiply(W, inverse(multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), multiply(multiply(Z, inverse(Z)), W)))))
% 0.19/0.48 = { by lemma 6 }
% 0.19/0.48 inverse(inverse(multiply(Z, inverse(Z))))
% 0.19/0.48
% 0.19/0.48 Lemma 9: multiply(inverse(X), inverse(multiply(Y, multiply(Z, inverse(Z))))) = multiply(W, inverse(multiply(Y, multiply(X, W)))).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(inverse(X), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 0.19/0.48 = { by lemma 5 }
% 0.19/0.48 multiply(inverse(X), inverse(multiply(Y, multiply(X, inverse(X)))))
% 0.19/0.48 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.48 multiply(inverse(X), inverse(multiply(multiply(V, inverse(multiply(multiply(X, multiply(U, inverse(U))), multiply(multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(X, multiply(U, inverse(U)))))), V)))), multiply(X, inverse(X)))))
% 0.19/0.48 = { by lemma 4 }
% 0.19/0.48 multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(X, multiply(U, inverse(U))))))
% 0.19/0.48 = { by lemma 4 R->L }
% 0.19/0.48 multiply(W, inverse(multiply(multiply(S, inverse(multiply(multiply(X, multiply(U, inverse(U))), multiply(multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(X, multiply(U, inverse(U)))))), S)))), multiply(X, W))))
% 0.19/0.48 = { by axiom 1 (single_axiom) }
% 0.19/0.48 multiply(W, inverse(multiply(Y, multiply(X, W))))
% 0.19/0.48
% 0.19/0.48 Lemma 10: multiply(X, inverse(multiply(multiply(Y, inverse(Y)), multiply(Z, X)))) = multiply(inverse(Z), inverse(inverse(inverse(multiply(W, inverse(W)))))).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(X, inverse(multiply(multiply(Y, inverse(Y)), multiply(Z, X))))
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 multiply(inverse(Z), inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))))
% 0.19/0.48 = { by lemma 8 }
% 0.19/0.48 multiply(inverse(Z), inverse(inverse(inverse(multiply(W, inverse(W))))))
% 0.19/0.48
% 0.19/0.48 Lemma 11: multiply(multiply(inverse(X), inverse(inverse(inverse(multiply(Y, inverse(Y)))))), multiply(Z, inverse(Z))) = inverse(multiply(X, multiply(W, inverse(W)))).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(multiply(inverse(X), inverse(inverse(inverse(multiply(Y, inverse(Y)))))), multiply(Z, inverse(Z)))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 multiply(multiply(multiply(W, inverse(W)), inverse(multiply(multiply(V, inverse(V)), multiply(X, multiply(W, inverse(W)))))), multiply(Z, inverse(Z)))
% 0.19/0.48 = { by lemma 3 }
% 0.19/0.48 multiply(U, inverse(multiply(multiply(multiply(V, inverse(V)), multiply(T, inverse(T))), multiply(multiply(X, multiply(W, inverse(W))), U))))
% 0.19/0.48 = { by lemma 6 }
% 0.19/0.48 inverse(multiply(X, multiply(W, inverse(W))))
% 0.19/0.48
% 0.19/0.48 Lemma 12: multiply(multiply(inverse(multiply(X, inverse(X))), inverse(inverse(inverse(multiply(Y, inverse(Y)))))), multiply(Z, inverse(Z))) = multiply(W, inverse(W)).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(multiply(inverse(multiply(X, inverse(X))), inverse(inverse(inverse(multiply(Y, inverse(Y)))))), multiply(Z, inverse(Z)))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 multiply(multiply(V, inverse(multiply(multiply(Z, inverse(Z)), multiply(multiply(X, inverse(X)), V)))), multiply(Z, inverse(Z)))
% 0.19/0.48 = { by lemma 7 R->L }
% 0.19/0.48 multiply(multiply(V, inverse(multiply(multiply(Z, inverse(Z)), multiply(multiply(X, inverse(X)), V)))), inverse(multiply(V, inverse(multiply(multiply(Z, inverse(Z)), multiply(multiply(X, inverse(X)), V))))))
% 0.19/0.48 = { by lemma 5 R->L }
% 0.19/0.48 multiply(W, inverse(W))
% 0.19/0.48
% 0.19/0.48 Lemma 13: inverse(inverse(inverse(multiply(X, inverse(X))))) = multiply(Y, inverse(Y)).
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(inverse(inverse(multiply(X, inverse(X)))))
% 0.19/0.49 = { by lemma 8 R->L }
% 0.19/0.49 inverse(multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W))))
% 0.19/0.49 = { by lemma 11 R->L }
% 0.19/0.49 multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(inverse(multiply(V, inverse(V)))))), multiply(U, inverse(U)))
% 0.19/0.49 = { by lemma 12 }
% 0.19/0.49 multiply(Y, inverse(Y))
% 0.19/0.49
% 0.19/0.49 Lemma 14: multiply(X, inverse(multiply(inverse(Y), multiply(multiply(Z, inverse(Z)), X)))) = Y.
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, inverse(multiply(inverse(Y), multiply(multiply(Z, inverse(Z)), X))))
% 0.19/0.49 = { by lemma 5 }
% 0.19/0.49 multiply(X, inverse(multiply(inverse(Y), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), X))))
% 0.19/0.49 = { by axiom 1 (single_axiom) }
% 0.19/0.49 Y
% 0.19/0.49
% 0.19/0.49 Lemma 15: multiply(X, inverse(multiply(inverse(inverse(multiply(Y, inverse(Y)))), multiply(Z, X)))) = inverse(Z).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, inverse(multiply(inverse(inverse(multiply(Y, inverse(Y)))), multiply(Z, X))))
% 0.19/0.49 = { by lemma 8 R->L }
% 0.19/0.49 multiply(X, inverse(multiply(multiply(multiply(W, inverse(W)), multiply(V, inverse(V))), multiply(Z, X))))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 inverse(Z)
% 0.19/0.49
% 0.19/0.49 Lemma 16: multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y))) = inverse(multiply(Z, inverse(Z))).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))
% 0.19/0.49 = { by lemma 14 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))), multiply(multiply(Z, inverse(Z)), W))))
% 0.19/0.49 = { by lemma 11 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(multiply(multiply(inverse(inverse(multiply(X, inverse(X)))), inverse(inverse(inverse(multiply(X, inverse(X)))))), multiply(V, inverse(V))), multiply(multiply(Z, inverse(Z)), W))))
% 0.19/0.49 = { by lemma 8 }
% 0.19/0.49 multiply(W, inverse(multiply(inverse(inverse(multiply(U, inverse(U)))), multiply(multiply(Z, inverse(Z)), W))))
% 0.19/0.49 = { by lemma 15 }
% 0.19/0.49 inverse(multiply(Z, inverse(Z)))
% 0.19/0.49
% 0.19/0.49 Lemma 17: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(multiply(X, inverse(X)))
% 0.19/0.49 = { by lemma 16 R->L }
% 0.19/0.49 multiply(inverse(multiply(Z, inverse(Z))), multiply(W, inverse(W)))
% 0.19/0.49 = { by lemma 16 R->L }
% 0.19/0.49 multiply(multiply(inverse(multiply(V, inverse(V))), multiply(U, inverse(U))), multiply(W, inverse(W)))
% 0.19/0.49 = { by lemma 13 R->L }
% 0.19/0.49 multiply(multiply(inverse(multiply(V, inverse(V))), inverse(inverse(inverse(multiply(T, inverse(T)))))), multiply(W, inverse(W)))
% 0.19/0.49 = { by lemma 12 }
% 0.19/0.49 multiply(Y, inverse(Y))
% 0.19/0.49
% 0.19/0.49 Lemma 18: multiply(inverse(X), multiply(Y, inverse(Y))) = inverse(X).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(X), multiply(Y, inverse(Y)))
% 0.19/0.49 = { by lemma 13 R->L }
% 0.19/0.49 multiply(inverse(X), inverse(inverse(inverse(multiply(Z, inverse(Z))))))
% 0.19/0.49 = { by lemma 10 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(multiply(V, inverse(V)), multiply(X, W))))
% 0.19/0.49 = { by lemma 17 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(inverse(multiply(U, inverse(U))), multiply(X, W))))
% 0.19/0.49 = { by lemma 17 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(inverse(inverse(multiply(T, inverse(T)))), multiply(X, W))))
% 0.19/0.49 = { by lemma 15 }
% 0.19/0.49 inverse(X)
% 0.19/0.49
% 0.19/0.49 Lemma 19: multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z))) = inverse(inverse(multiply(Y, inverse(inverse(multiply(W, inverse(W))))))).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z)))
% 0.19/0.49 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.49 multiply(multiply(multiply(X, inverse(X)), multiply(V, inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(Y, inverse(inverse(multiply(W, inverse(W))))))), V))))), multiply(Z, inverse(Z)))
% 0.19/0.49 = { by lemma 15 }
% 0.19/0.49 multiply(multiply(multiply(X, inverse(X)), inverse(multiply(multiply(U, inverse(U)), inverse(multiply(Y, inverse(inverse(multiply(W, inverse(W))))))))), multiply(Z, inverse(Z)))
% 0.19/0.49 = { by lemma 3 }
% 0.19/0.49 multiply(T, inverse(multiply(multiply(multiply(U, inverse(U)), multiply(S, inverse(S))), multiply(inverse(multiply(Y, inverse(inverse(multiply(W, inverse(W)))))), T))))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 inverse(inverse(multiply(Y, inverse(inverse(multiply(W, inverse(W)))))))
% 0.19/0.49
% 0.19/0.49 Lemma 20: inverse(inverse(inverse(inverse(X)))) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(inverse(inverse(inverse(X))))
% 0.19/0.49 = { by lemma 18 R->L }
% 0.19/0.49 inverse(inverse(multiply(inverse(inverse(X)), multiply(Y, inverse(Y)))))
% 0.19/0.49 = { by lemma 17 R->L }
% 0.19/0.49 inverse(inverse(multiply(inverse(inverse(X)), inverse(multiply(Z, inverse(Z))))))
% 0.19/0.49 = { by lemma 17 R->L }
% 0.19/0.49 inverse(inverse(multiply(inverse(inverse(X)), inverse(inverse(multiply(W, inverse(W)))))))
% 0.19/0.49 = { by lemma 19 R->L }
% 0.19/0.49 multiply(multiply(multiply(V, inverse(V)), inverse(inverse(X))), multiply(U, inverse(U)))
% 0.19/0.49 = { by lemma 18 R->L }
% 0.19/0.49 multiply(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(X), multiply(T, inverse(T))))), multiply(U, inverse(U)))
% 0.19/0.49 = { by lemma 3 }
% 0.19/0.49 multiply(S, inverse(multiply(multiply(inverse(X), multiply(X2, inverse(X2))), multiply(multiply(T, inverse(T)), S))))
% 0.19/0.49 = { by lemma 18 }
% 0.19/0.49 multiply(S, inverse(multiply(inverse(X), multiply(multiply(T, inverse(T)), S))))
% 0.19/0.49 = { by lemma 14 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 21: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, multiply(Y, inverse(Y)))
% 0.19/0.49 = { by lemma 7 R->L }
% 0.19/0.49 multiply(inverse(multiply(Z, inverse(multiply(X, multiply(multiply(W, inverse(W)), Z))))), multiply(Y, inverse(Y)))
% 0.19/0.49 = { by lemma 18 }
% 0.19/0.49 inverse(multiply(Z, inverse(multiply(X, multiply(multiply(W, inverse(W)), Z)))))
% 0.19/0.49 = { by lemma 7 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 22: multiply(multiply(X, inverse(X)), Y) = inverse(inverse(Y)).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(multiply(X, inverse(X)), Y)
% 0.19/0.49 = { by lemma 21 R->L }
% 0.19/0.49 multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z)))
% 0.19/0.49 = { by lemma 19 }
% 0.19/0.49 inverse(inverse(multiply(Y, inverse(inverse(multiply(W, inverse(W)))))))
% 0.19/0.49 = { by lemma 17 }
% 0.19/0.49 inverse(inverse(multiply(Y, inverse(multiply(V, inverse(V))))))
% 0.19/0.49 = { by lemma 17 }
% 0.19/0.49 inverse(inverse(multiply(Y, multiply(U, inverse(U)))))
% 0.19/0.49 = { by lemma 21 }
% 0.19/0.49 inverse(inverse(Y))
% 0.19/0.49
% 0.19/0.49 Lemma 23: multiply(X, inverse(multiply(Y, multiply(Z, X)))) = multiply(inverse(Z), inverse(Y)).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, inverse(multiply(Y, multiply(Z, X))))
% 0.19/0.49 = { by lemma 9 R->L }
% 0.19/0.49 multiply(inverse(Z), inverse(multiply(Y, multiply(W, inverse(W)))))
% 0.19/0.49 = { by lemma 21 }
% 0.19/0.49 multiply(inverse(Z), inverse(Y))
% 0.19/0.49
% 0.19/0.49 Lemma 24: multiply(multiply(X, Y), inverse(Y)) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(multiply(X, Y), inverse(Y))
% 0.19/0.49 = { by lemma 20 R->L }
% 0.19/0.49 multiply(inverse(inverse(inverse(inverse(multiply(X, Y))))), inverse(Y))
% 0.19/0.49 = { by lemma 22 R->L }
% 0.19/0.49 multiply(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(X, Y)))), inverse(Y))
% 0.19/0.49 = { by lemma 23 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(Y, multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(X, Y))), W))))
% 0.19/0.49 = { by axiom 1 (single_axiom) }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 25: multiply(X, inverse(inverse(Y))) = multiply(X, Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, inverse(inverse(Y)))
% 0.19/0.49 = { by lemma 20 R->L }
% 0.19/0.49 multiply(inverse(inverse(inverse(inverse(X)))), inverse(inverse(Y)))
% 0.19/0.49 = { by lemma 22 R->L }
% 0.19/0.49 multiply(inverse(multiply(multiply(Z, inverse(Z)), inverse(X))), inverse(inverse(Y)))
% 0.19/0.49 = { by lemma 23 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(inverse(Y), multiply(multiply(multiply(Z, inverse(Z)), inverse(X)), W))))
% 0.19/0.49 = { by lemma 24 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(inverse(Y), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(multiply(X, Y), inverse(Y)))), W))))
% 0.19/0.49 = { by axiom 1 (single_axiom) }
% 0.19/0.49 multiply(X, Y)
% 0.19/0.49
% 0.19/0.49 Lemma 26: inverse(inverse(X)) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(inverse(X))
% 0.19/0.49 = { by lemma 2 R->L }
% 0.19/0.49 multiply(Y, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, inverse(inverse(X))))), multiply(V, inverse(V))), multiply(W, Y))))
% 0.19/0.49 = { by lemma 25 }
% 0.19/0.49 multiply(Y, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, X))), multiply(V, inverse(V))), multiply(W, Y))))
% 0.19/0.49 = { by lemma 2 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 27: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(X), X)
% 0.19/0.49 = { by lemma 25 R->L }
% 0.19/0.49 multiply(inverse(X), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 5 R->L }
% 0.19/0.49 multiply(Y, inverse(Y))
% 0.19/0.49
% 0.19/0.49 Lemma 28: multiply(inverse(multiply(X, Y)), X) = inverse(Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(multiply(X, Y)), X)
% 0.19/0.49 = { by lemma 25 R->L }
% 0.19/0.49 multiply(inverse(multiply(X, Y)), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 25 R->L }
% 0.19/0.49 multiply(inverse(multiply(X, Y)), inverse(inverse(inverse(inverse(X)))))
% 0.19/0.49 = { by lemma 22 R->L }
% 0.19/0.49 multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(Z, inverse(Z)), inverse(X))))
% 0.19/0.49 = { by lemma 23 R->L }
% 0.19/0.49 multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(multiply(Z, inverse(Z)), inverse(X)), multiply(multiply(X, Y), inverse(multiply(X, Y))))))
% 0.19/0.49 = { by lemma 23 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(X)), multiply(multiply(X, Y), inverse(multiply(X, Y)))), multiply(multiply(X, Y), W))))
% 0.19/0.49 = { by lemma 24 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(multiply(X, Y), inverse(Y)))), multiply(multiply(X, Y), inverse(multiply(X, Y)))), multiply(multiply(X, Y), W))))
% 0.19/0.49 = { by lemma 2 }
% 0.19/0.49 inverse(Y)
% 0.19/0.49
% 0.19/0.49 Lemma 29: multiply(inverse(X), inverse(Y)) = inverse(multiply(Y, X)).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(X), inverse(Y))
% 0.19/0.49 = { by lemma 26 R->L }
% 0.19/0.49 multiply(inverse(inverse(inverse(X))), inverse(Y))
% 0.19/0.49 = { by lemma 22 R->L }
% 0.19/0.49 multiply(inverse(multiply(multiply(Z, inverse(Z)), X)), inverse(Y))
% 0.19/0.49 = { by lemma 25 R->L }
% 0.19/0.49 multiply(inverse(multiply(multiply(Z, inverse(Z)), inverse(inverse(X)))), inverse(Y))
% 0.19/0.49 = { by lemma 23 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(Y, multiply(multiply(multiply(Z, inverse(Z)), inverse(inverse(X))), W))))
% 0.19/0.49 = { by lemma 28 R->L }
% 0.19/0.49 multiply(W, inverse(multiply(Y, multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(multiply(Y, X)), Y))), W))))
% 0.19/0.49 = { by axiom 1 (single_axiom) }
% 0.19/0.49 inverse(multiply(Y, X))
% 0.19/0.50
% 0.19/0.50 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1)).
% 0.19/0.50 Proof:
% 0.19/0.50 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.19/0.50 = { by lemma 27 }
% 0.19/0.50 tuple(multiply(multiply(X, inverse(X)), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.19/0.50 = { by lemma 22 }
% 0.19/0.50 tuple(inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.19/0.50 = { by lemma 26 }
% 0.19/0.50 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.19/0.50 = { by lemma 27 }
% 0.19/0.50 tuple(a2, multiply(multiply(a3, b3), c3), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 14 R->L }
% 0.19/0.50 tuple(a2, multiply(Z, inverse(multiply(inverse(multiply(multiply(a3, b3), c3)), multiply(multiply(W, inverse(W)), Z)))), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 29 R->L }
% 0.19/0.50 tuple(a2, multiply(Z, inverse(multiply(multiply(inverse(c3), inverse(multiply(a3, b3))), multiply(multiply(W, inverse(W)), Z)))), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 29 R->L }
% 0.19/0.50 tuple(a2, multiply(Z, inverse(multiply(multiply(inverse(c3), multiply(inverse(b3), inverse(a3))), multiply(multiply(W, inverse(W)), Z)))), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 23 R->L }
% 0.19/0.50 tuple(a2, multiply(Z, inverse(multiply(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(a3, multiply(b3, inverse(b3)))))), multiply(multiply(W, inverse(W)), Z)))), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 23 R->L }
% 0.19/0.50 tuple(a2, multiply(Z, inverse(multiply(multiply(inverse(c3), multiply(c3, inverse(multiply(multiply(a3, multiply(b3, inverse(b3))), multiply(b3, c3))))), multiply(multiply(W, inverse(W)), Z)))), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 24 R->L }
% 0.19/0.50 tuple(a2, multiply(Z, inverse(multiply(multiply(inverse(multiply(multiply(c3, inverse(multiply(multiply(a3, multiply(b3, inverse(b3))), multiply(b3, c3)))), inverse(inverse(multiply(multiply(a3, multiply(b3, inverse(b3))), multiply(b3, c3)))))), multiply(c3, inverse(multiply(multiply(a3, multiply(b3, inverse(b3))), multiply(b3, c3))))), multiply(multiply(W, inverse(W)), Z)))), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 28 }
% 0.19/0.50 tuple(a2, multiply(Z, inverse(multiply(inverse(inverse(inverse(multiply(multiply(a3, multiply(b3, inverse(b3))), multiply(b3, c3))))), multiply(multiply(W, inverse(W)), Z)))), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 26 }
% 0.19/0.50 tuple(a2, multiply(Z, inverse(multiply(inverse(multiply(multiply(a3, multiply(b3, inverse(b3))), multiply(b3, c3))), multiply(multiply(W, inverse(W)), Z)))), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 21 }
% 0.19/0.50 tuple(a2, multiply(Z, inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), multiply(multiply(W, inverse(W)), Z)))), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 14 }
% 0.19/0.50 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(Y, inverse(Y)))
% 0.19/0.50 = { by lemma 27 R->L }
% 0.19/0.50 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50
% 0.19/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------