TSTP Solution File: GRP061-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP061-1 : 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 : n031.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 2.70s 0.89s
% Output : Proof 3.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP061-1 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 00:35:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 2.70/0.89 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 2.70/0.89
% 2.70/0.89 % SZS status Unsatisfiable
% 2.70/0.90
% 3.04/1.00 % SZS output start Proof
% 3.04/1.01 Take the following subset of the input axioms:
% 3.04/1.01 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)))).
% 3.04/1.01 fof(single_axiom, axiom, ![X, Y, Z, U]: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(U, multiply(X, Z)))))))=U).
% 3.04/1.01
% 3.04/1.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.04/1.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.04/1.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.04/1.01 fresh(y, y, x1...xn) = u
% 3.04/1.01 C => fresh(s, t, x1...xn) = v
% 3.04/1.01 where fresh is a fresh function symbol and x1..xn are the free
% 3.04/1.01 variables of u and v.
% 3.04/1.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.04/1.01 input problem has no model of domain size 1).
% 3.04/1.01
% 3.04/1.01 The encoding turns the above axioms into the following unit equations and goals:
% 3.04/1.01
% 3.04/1.01 Axiom 1 (single_axiom): inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z))))))) = W.
% 3.04/1.01
% 3.04/1.01 Lemma 2: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W)))) = V.
% 3.04/1.01 Proof:
% 3.04/1.01 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W))))
% 3.04/1.01 = { by axiom 1 (single_axiom) R->L }
% 3.04/1.01 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), inverse(multiply(V, multiply(X, multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z)))))))))))
% 3.04/1.01 = { by axiom 1 (single_axiom) }
% 3.04/1.01 V
% 3.32/1.01
% 3.32/1.01 Lemma 3: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(U, W))))), V)), U)))) = Z.
% 3.32/1.01 Proof:
% 3.32/1.01 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(U, W))))), V)), U))))
% 3.32/1.01 = { by lemma 2 R->L }
% 3.32/1.01 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(U, W))))), V)), inverse(multiply(Z, multiply(X, multiply(multiply(inverse(X), multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(U, W))))), V))))))))
% 3.32/1.01 = { by axiom 1 (single_axiom) }
% 3.32/1.01 Z
% 3.32/1.01
% 3.32/1.01 Lemma 4: inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(V, U), inverse(multiply(T, multiply(X, U))))))) = T.
% 3.32/1.01 Proof:
% 3.32/1.01 inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(V, U), inverse(multiply(T, multiply(X, U)))))))
% 3.32/1.01 = { by axiom 1 (single_axiom) R->L }
% 3.32/1.01 inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W))))))), U), inverse(multiply(T, multiply(X, U)))))))
% 3.32/1.01 = { by axiom 1 (single_axiom) }
% 3.32/1.01 T
% 3.32/1.01
% 3.32/1.01 Lemma 5: multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))) = W.
% 3.32/1.01 Proof:
% 3.32/1.01 multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z))))))
% 3.32/1.01 = { by lemma 2 R->L }
% 3.32/1.01 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 3.32/1.01 = { by lemma 4 }
% 3.32/1.01 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.32/1.01 = { by lemma 3 }
% 3.32/1.01 W
% 3.32/1.01
% 3.32/1.01 Lemma 6: inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y)))))) = Z.
% 3.32/1.01 Proof:
% 3.32/1.01 inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y))))))
% 3.32/1.01 = { by lemma 5 R->L }
% 3.32/1.01 inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, multiply(inverse(X), multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(inverse(Y), multiply(inverse(X), V))))))))))))
% 3.32/1.01 = { by lemma 5 R->L }
% 3.32/1.01 inverse(multiply(inverse(X), multiply(X, multiply(multiply(inverse(X), multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(inverse(Y), multiply(inverse(X), V)))))), inverse(multiply(Z, multiply(inverse(X), multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(inverse(Y), multiply(inverse(X), V))))))))))))
% 3.32/1.01 = { by axiom 1 (single_axiom) }
% 3.32/1.01 Z
% 3.32/1.01
% 3.32/1.01 Lemma 7: multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W))) = X.
% 3.32/1.01 Proof:
% 3.32/1.01 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W)))
% 3.32/1.01 = { by lemma 6 R->L }
% 3.32/1.01 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), inverse(multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(W, Z)))))))))
% 3.32/1.01 = { by lemma 2 R->L }
% 3.32/1.01 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), inverse(multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(W, Z))))))))), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 3.32/1.01 = { by lemma 4 }
% 3.32/1.01 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.32/1.01 = { by lemma 4 R->L }
% 3.32/1.01 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(multiply(Y2, multiply(Z2, multiply(multiply(inverse(Z2), W2), inverse(multiply(inverse(X), multiply(Y2, W2)))))), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 3.32/1.01 = { by lemma 2 }
% 3.32/1.01 multiply(Y2, multiply(Z2, multiply(multiply(inverse(Z2), W2), inverse(multiply(inverse(X), multiply(Y2, W2))))))
% 3.32/1.01 = { by lemma 5 }
% 3.32/1.01 X
% 3.32/1.01
% 3.32/1.01 Lemma 8: inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X)))))) = Z.
% 3.32/1.01 Proof:
% 3.32/1.02 inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X))))))
% 3.32/1.02 = { by lemma 7 R->L }
% 3.32/1.02 inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U)))))))))
% 3.32/1.02 = { by lemma 7 R->L }
% 3.32/1.02 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U))), inverse(multiply(Z, multiply(X, multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U)))))))))
% 3.32/1.02 = { by axiom 1 (single_axiom) }
% 3.32/1.02 Z
% 3.32/1.02
% 3.32/1.02 Lemma 9: multiply(X, multiply(Y, multiply(inverse(Y), multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W)))) = X.
% 3.32/1.02 Proof:
% 3.32/1.02 multiply(X, multiply(Y, multiply(inverse(Y), multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W))))
% 3.32/1.02 = { by lemma 7 R->L }
% 3.32/1.02 multiply(X, multiply(Y, multiply(inverse(Y), multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))), W))))
% 3.32/1.02 = { by lemma 7 R->L }
% 3.32/1.02 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))), W)), multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))
% 3.32/1.02 = { by lemma 8 R->L }
% 3.32/1.02 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))), inverse(multiply(multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)), multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))))))), multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))
% 3.32/1.02 = { by lemma 7 }
% 3.32/1.02 X
% 3.32/1.02
% 3.32/1.02 Lemma 10: inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z)))) = inverse(X).
% 3.32/1.02 Proof:
% 3.32/1.02 inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z))))
% 3.32/1.02 = { by lemma 6 R->L }
% 3.32/1.02 inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y))))))))))
% 3.32/1.02 = { by lemma 8 }
% 3.32/1.02 inverse(X)
% 3.32/1.02
% 3.32/1.02 Lemma 11: multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z))) = X.
% 3.32/1.02 Proof:
% 3.32/1.02 multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z)))
% 3.32/1.02 = { by lemma 3 R->L }
% 3.32/1.02 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(multiply(multiply(X, multiply(Y, inverse(multiply(Z, Y)))), multiply(W, multiply(inverse(W), Z)))), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.32/1.02 = { by lemma 10 }
% 3.32/1.02 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(X), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 3.32/1.02 = { by lemma 3 }
% 3.32/1.02 X
% 3.32/1.02
% 3.32/1.02 Lemma 12: multiply(X, multiply(Y, inverse(multiply(multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W), Y)))) = X.
% 3.32/1.02 Proof:
% 3.32/1.02 multiply(X, multiply(Y, inverse(multiply(multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W), Y))))
% 3.32/1.02 = { by lemma 9 R->L }
% 3.32/1.02 multiply(multiply(X, multiply(Y, inverse(multiply(multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W), Y)))), multiply(V, multiply(inverse(V), multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W))))
% 3.32/1.02 = { by lemma 11 }
% 3.32/1.02 X
% 3.32/1.02
% 3.32/1.02 Lemma 13: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 3.32/1.02 Proof:
% 3.32/1.02 multiply(inverse(Y), Y)
% 3.32/1.02 = { by lemma 3 R->L }
% 3.32/1.03 inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), multiply(multiply(inverse(Z), multiply(multiply(inverse(multiply(inverse(Y), Y)), V), inverse(multiply(U, multiply(T, V))))), U)), T))))
% 3.32/1.03 = { by lemma 12 R->L }
% 3.32/1.03 inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), multiply(multiply(inverse(Z), multiply(multiply(inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), Z2), inverse(multiply(multiply(multiply(X2, multiply(inverse(X2), inverse(Y2))), Y2), multiply(inverse(Y), Z2))))))), V), inverse(multiply(U, multiply(T, V))))), U)), T))))
% 3.32/1.03 = { by axiom 1 (single_axiom) }
% 3.32/1.03 inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), multiply(multiply(inverse(Z), multiply(multiply(multiply(multiply(X2, multiply(inverse(X2), inverse(Y2))), Y2), V), inverse(multiply(U, multiply(T, V))))), U)), T))))
% 3.32/1.03 = { by axiom 1 (single_axiom) R->L }
% 3.32/1.03 inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), multiply(multiply(inverse(Z), multiply(multiply(inverse(multiply(inverse(X), multiply(X, multiply(multiply(inverse(X), S), inverse(multiply(multiply(multiply(X2, multiply(inverse(X2), inverse(Y2))), Y2), multiply(inverse(X), S))))))), V), inverse(multiply(U, multiply(T, V))))), U)), T))))
% 3.32/1.03 = { by lemma 12 }
% 3.32/1.03 inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), multiply(multiply(inverse(Z), multiply(multiply(inverse(multiply(inverse(X), X)), V), inverse(multiply(U, multiply(T, V))))), U)), T))))
% 3.32/1.03 = { by lemma 3 }
% 3.32/1.03 multiply(inverse(X), X)
% 3.32/1.03
% 3.32/1.03 Lemma 14: multiply(multiply(X, multiply(inverse(X), inverse(Y))), Y) = inverse(multiply(inverse(Z), Z)).
% 3.32/1.03 Proof:
% 3.32/1.03 multiply(multiply(X, multiply(inverse(X), inverse(Y))), Y)
% 3.32/1.03 = { by axiom 1 (single_axiom) R->L }
% 3.32/1.03 inverse(multiply(inverse(Z), multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(multiply(multiply(X, multiply(inverse(X), inverse(Y))), Y), multiply(inverse(Z), W)))))))
% 3.32/1.03 = { by lemma 12 }
% 3.32/1.03 inverse(multiply(inverse(Z), Z))
% 3.32/1.03
% 3.32/1.03 Lemma 15: multiply(X, multiply(inverse(Y), Y)) = X.
% 3.32/1.03 Proof:
% 3.32/1.03 multiply(X, multiply(inverse(Y), Y))
% 3.32/1.03 = { by lemma 13 }
% 3.32/1.03 multiply(X, multiply(inverse(multiply(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W)), multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W))), multiply(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W)), multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W))))
% 3.32/1.03 = { by lemma 14 R->L }
% 3.32/1.03 multiply(X, multiply(multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W), multiply(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W)), multiply(multiply(Z, multiply(inverse(Z), inverse(W))), W))))
% 3.32/1.03 = { by lemma 9 }
% 3.32/1.03 X
% 3.32/1.03
% 3.32/1.03 Lemma 16: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 3.32/1.03 Proof:
% 3.32/1.03 inverse(multiply(inverse(X), X))
% 3.32/1.03 = { by lemma 15 R->L }
% 3.32/1.03 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))
% 3.32/1.03 = { by lemma 13 R->L }
% 3.32/1.03 multiply(inverse(Y), Y)
% 3.32/1.03
% 3.32/1.03 Lemma 17: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 3.32/1.03 Proof:
% 3.32/1.03 multiply(inverse(X), X)
% 3.32/1.03 = { by lemma 16 R->L }
% 3.32/1.03 inverse(multiply(inverse(Z), Z))
% 3.32/1.03 = { by lemma 14 R->L }
% 3.32/1.03 multiply(multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(W), W)))), multiply(inverse(W), W))
% 3.32/1.03 = { by lemma 16 }
% 3.32/1.03 multiply(multiply(Y, multiply(inverse(Y), multiply(inverse(V), V))), multiply(inverse(W), W))
% 3.32/1.03 = { by lemma 15 }
% 3.32/1.03 multiply(Y, multiply(inverse(Y), multiply(inverse(V), V)))
% 3.32/1.03 = { by lemma 15 }
% 3.32/1.03 multiply(Y, inverse(Y))
% 3.32/1.03
% 3.32/1.03 Lemma 18: multiply(multiply(X, multiply(multiply(Y, multiply(inverse(Y), inverse(Z))), Z)), multiply(W, inverse(W))) = X.
% 3.32/1.03 Proof:
% 3.32/1.03 multiply(multiply(X, multiply(multiply(Y, multiply(inverse(Y), inverse(Z))), Z)), multiply(W, inverse(W)))
% 3.32/1.03 = { by lemma 7 R->L }
% 3.32/1.03 multiply(multiply(X, multiply(multiply(Y, multiply(inverse(Y), inverse(Z))), Z)), multiply(W, multiply(inverse(W), multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))
% 3.32/1.03 = { by lemma 7 R->L }
% 3.32/1.03 multiply(multiply(X, multiply(multiply(Y, multiply(inverse(Y), inverse(multiply(Z, multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))), Z)), multiply(W, multiply(inverse(W), multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))
% 3.32/1.03 = { by lemma 8 R->L }
% 3.32/1.03 multiply(multiply(X, multiply(multiply(Y, multiply(inverse(Y), inverse(multiply(Z, multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))), inverse(multiply(multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)), multiply(Y, multiply(inverse(Y), inverse(multiply(Z, multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))))))), multiply(W, multiply(inverse(W), multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(T, U)))), T)))))
% 3.32/1.03 = { by lemma 11 }
% 3.32/1.03 X
% 3.32/1.03
% 3.32/1.03 Lemma 19: multiply(X, multiply(Y, inverse(Y))) = X.
% 3.32/1.03 Proof:
% 3.32/1.03 multiply(X, multiply(Y, inverse(Y)))
% 3.32/1.03 = { by lemma 15 R->L }
% 3.32/1.03 multiply(multiply(X, multiply(inverse(Z), Z)), multiply(Y, inverse(Y)))
% 3.32/1.03 = { by lemma 16 R->L }
% 3.32/1.03 multiply(multiply(X, inverse(multiply(inverse(W), W))), multiply(Y, inverse(Y)))
% 3.32/1.03 = { by lemma 14 R->L }
% 3.32/1.03 multiply(multiply(X, multiply(multiply(V, multiply(inverse(V), inverse(U))), U)), multiply(Y, inverse(Y)))
% 3.32/1.03 = { by lemma 18 }
% 3.32/1.03 X
% 3.32/1.03
% 3.32/1.03 Lemma 20: inverse(multiply(X, inverse(multiply(Y, X)))) = Y.
% 3.32/1.03 Proof:
% 3.32/1.03 inverse(multiply(X, inverse(multiply(Y, X))))
% 3.32/1.03 = { by lemma 15 R->L }
% 3.32/1.03 inverse(multiply(X, multiply(inverse(multiply(Y, X)), multiply(inverse(inverse(multiply(Y, X))), inverse(multiply(Y, X))))))
% 3.32/1.03 = { by lemma 8 }
% 3.32/1.03 Y
% 3.32/1.03
% 3.32/1.03 Lemma 21: multiply(X, multiply(inverse(X), Y)) = Y.
% 3.32/1.03 Proof:
% 3.32/1.03 multiply(X, multiply(inverse(X), Y))
% 3.32/1.03 = { by lemma 20 R->L }
% 3.32/1.03 inverse(multiply(inverse(multiply(multiply(Z, multiply(W, inverse(multiply(Y, W)))), multiply(X, multiply(inverse(X), Y)))), inverse(multiply(multiply(X, multiply(inverse(X), Y)), inverse(multiply(multiply(Z, multiply(W, inverse(multiply(Y, W)))), multiply(X, multiply(inverse(X), Y))))))))
% 3.32/1.03 = { by lemma 20 }
% 3.32/1.03 inverse(multiply(inverse(multiply(multiply(Z, multiply(W, inverse(multiply(Y, W)))), multiply(X, multiply(inverse(X), Y)))), multiply(Z, multiply(W, inverse(multiply(Y, W))))))
% 3.32/1.03 = { by lemma 10 }
% 3.32/1.03 inverse(multiply(inverse(Z), multiply(Z, multiply(W, inverse(multiply(Y, W))))))
% 3.32/1.03 = { by lemma 6 }
% 3.32/1.03 Y
% 3.32/1.03
% 3.32/1.03 Lemma 22: multiply(multiply(X, inverse(X)), Y) = Y.
% 3.32/1.03 Proof:
% 3.32/1.03 multiply(multiply(X, inverse(X)), Y)
% 3.32/1.03 = { by lemma 21 R->L }
% 3.32/1.03 multiply(multiply(X, inverse(X)), multiply(Z, multiply(inverse(Z), Y)))
% 3.32/1.03 = { by lemma 17 R->L }
% 3.32/1.03 multiply(multiply(inverse(multiply(W, inverse(multiply(Y, W)))), multiply(W, inverse(multiply(Y, W)))), multiply(Z, multiply(inverse(Z), Y)))
% 3.32/1.03 = { by lemma 20 }
% 3.32/1.03 multiply(multiply(Y, multiply(W, inverse(multiply(Y, W)))), multiply(Z, multiply(inverse(Z), Y)))
% 3.32/1.03 = { by lemma 11 }
% 3.32/1.03 Y
% 3.32/1.03
% 3.32/1.03 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))).
% 3.32/1.03 Proof:
% 3.32/1.03 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 3.32/1.03 = { by lemma 17 }
% 3.32/1.03 tuple(multiply(X, inverse(X)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 3.32/1.03 = { by lemma 17 }
% 3.32/1.03 tuple(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), a2), multiply(multiply(a3, b3), c3))
% 3.32/1.03 = { by lemma 22 }
% 3.32/1.03 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 3.32/1.03 = { by lemma 8 R->L }
% 3.32/1.03 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), Z), multiply(W, multiply(inverse(W), inverse(multiply(multiply(a3, b3), multiply(inverse(multiply(a3, b3)), Z))))))), c3))
% 3.32/1.03 = { by lemma 21 }
% 3.32/1.03 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), Z), multiply(W, multiply(inverse(W), inverse(Z))))), c3))
% 3.32/1.03 = { by lemma 15 R->L }
% 3.32/1.03 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), multiply(Z, multiply(inverse(V), V))), multiply(W, multiply(inverse(W), inverse(Z))))), c3))
% 3.32/1.03 = { by lemma 19 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), multiply(multiply(Z, multiply(inverse(V), V)), multiply(U, inverse(U)))), multiply(W, multiply(inverse(W), inverse(Z))))), c3))
% 3.32/1.04 = { by lemma 15 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), multiply(multiply(Z, multiply(inverse(V), multiply(V, multiply(inverse(T), T)))), multiply(U, inverse(U)))), multiply(W, multiply(inverse(W), inverse(Z))))), c3))
% 3.32/1.04 = { by lemma 16 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), multiply(multiply(Z, multiply(inverse(V), multiply(V, inverse(multiply(inverse(S), S))))), multiply(U, inverse(U)))), multiply(W, multiply(inverse(W), inverse(Z))))), c3))
% 3.32/1.04 = { by lemma 14 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), multiply(multiply(Z, multiply(inverse(V), multiply(V, multiply(multiply(X2, multiply(inverse(X2), inverse(Y2))), Y2)))), multiply(U, inverse(U)))), multiply(W, multiply(inverse(W), inverse(Z))))), c3))
% 3.32/1.04 = { by lemma 20 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), multiply(multiply(Z, multiply(inverse(V), inverse(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(V, multiply(multiply(X2, multiply(inverse(X2), inverse(Y2))), Y2)), multiply(U, inverse(U)))))))), multiply(U, inverse(U)))), multiply(W, multiply(inverse(W), inverse(Z))))), c3))
% 3.32/1.04 = { by lemma 18 }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), multiply(multiply(Z, multiply(inverse(V), inverse(multiply(multiply(U, inverse(U)), inverse(V))))), multiply(U, inverse(U)))), multiply(W, multiply(inverse(W), inverse(Z))))), c3))
% 3.32/1.04 = { by lemma 6 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(multiply(a3, b3)), multiply(multiply(Z, multiply(inverse(V), inverse(multiply(multiply(U, inverse(U)), inverse(V))))), inverse(multiply(inverse(Z), multiply(Z, multiply(inverse(V), inverse(multiply(multiply(U, inverse(U)), inverse(V))))))))), multiply(W, multiply(inverse(W), inverse(Z))))), c3))
% 3.32/1.04 = { by lemma 11 }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(a3, b3))), c3))
% 3.32/1.04 = { by lemma 21 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(a3, multiply(Z2, multiply(inverse(Z2), b3))))), c3))
% 3.32/1.04 = { by lemma 21 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(multiply(W2, multiply(inverse(W2), a3)), multiply(Z2, multiply(inverse(Z2), b3))))), c3))
% 3.32/1.04 = { by axiom 1 (single_axiom) R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(multiply(W2, multiply(inverse(W2), inverse(multiply(b3, multiply(multiply(V2, inverse(V2)), multiply(multiply(inverse(multiply(V2, inverse(V2))), c3), inverse(multiply(a3, multiply(b3, c3))))))))), multiply(Z2, multiply(inverse(Z2), b3))))), c3))
% 3.32/1.04 = { by lemma 22 }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(multiply(W2, multiply(inverse(W2), inverse(multiply(b3, multiply(multiply(inverse(multiply(V2, inverse(V2))), c3), inverse(multiply(a3, multiply(b3, c3)))))))), multiply(Z2, multiply(inverse(Z2), b3))))), c3))
% 3.32/1.04 = { by lemma 19 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(multiply(W2, multiply(inverse(W2), inverse(multiply(b3, multiply(multiply(multiply(inverse(multiply(V2, inverse(V2))), multiply(V2, inverse(V2))), c3), inverse(multiply(a3, multiply(b3, c3)))))))), multiply(Z2, multiply(inverse(Z2), b3))))), c3))
% 3.32/1.04 = { by lemma 17 }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(multiply(W2, multiply(inverse(W2), inverse(multiply(b3, multiply(multiply(multiply(U2, inverse(U2)), c3), inverse(multiply(a3, multiply(b3, c3)))))))), multiply(Z2, multiply(inverse(Z2), b3))))), c3))
% 3.32/1.04 = { by lemma 22 }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(multiply(W2, multiply(inverse(W2), inverse(multiply(b3, multiply(c3, inverse(multiply(a3, multiply(b3, c3)))))))), multiply(Z2, multiply(inverse(Z2), b3))))), c3))
% 3.32/1.04 = { by lemma 8 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(multiply(W2, multiply(inverse(W2), inverse(multiply(b3, multiply(c3, inverse(multiply(a3, multiply(b3, c3)))))))), multiply(Z2, multiply(inverse(Z2), inverse(multiply(multiply(c3, inverse(multiply(a3, multiply(b3, c3)))), multiply(W2, multiply(inverse(W2), inverse(multiply(b3, multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))))))))))), c3))
% 3.32/1.04 = { by lemma 8 }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))), c3))
% 3.32/1.04 = { by lemma 21 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))), multiply(T2, multiply(inverse(T2), c3))))
% 3.32/1.04 = { by lemma 21 R->L }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(multiply(multiply(a3, multiply(b3, c3)), multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(multiply(c3, inverse(multiply(a3, multiply(b3, c3))))))), multiply(T2, multiply(inverse(T2), c3))))
% 3.32/1.04 = { by lemma 11 }
% 3.32/1.04 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 3.32/1.04 = { by lemma 17 R->L }
% 3.32/1.04 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 3.32/1.04 % SZS output end Proof
% 3.32/1.04
% 3.32/1.04 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------