TSTP Solution File: GRP002-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP002-3 : 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 : n006.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 01:16:30 EDT 2023
% Result : Unsatisfiable 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP002-3 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 23:48:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.45 Command-line arguments: --ground-connectedness --complete-subsets
% 0.19/0.45
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.19/0.49 Axiom 2 (left_inverse): multiply(inverse(X), X) = identity.
% 0.19/0.49 Axiom 3 (x_cubed_is_identity): multiply(X, multiply(X, X)) = identity.
% 0.19/0.49 Axiom 4 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.19/0.49 Axiom 5 (commutator): commutator(X, Y) = multiply(X, multiply(Y, multiply(inverse(X), inverse(Y)))).
% 0.19/0.49
% 0.19/0.49 Lemma 6: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(X), multiply(X, Y))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(multiply(inverse(X), X), Y)
% 0.19/0.49 = { by axiom 2 (left_inverse) }
% 0.19/0.49 multiply(identity, Y)
% 0.19/0.49 = { by axiom 1 (left_identity) }
% 0.19/0.49 Y
% 0.19/0.49
% 0.19/0.49 Lemma 7: multiply(inverse(X), identity) = multiply(X, X).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(X), identity)
% 0.19/0.49 = { by axiom 3 (x_cubed_is_identity) R->L }
% 0.19/0.49 multiply(inverse(X), multiply(X, multiply(X, X)))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 multiply(X, X)
% 0.19/0.49
% 0.19/0.49 Lemma 8: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(inverse(X)), Y)
% 0.19/0.49 = { by lemma 6 R->L }
% 0.19/0.49 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 multiply(X, Y)
% 0.19/0.49
% 0.19/0.49 Lemma 9: multiply(X, identity) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, identity)
% 0.19/0.49 = { by lemma 8 R->L }
% 0.19/0.49 multiply(inverse(inverse(X)), identity)
% 0.19/0.49 = { by axiom 2 (left_inverse) R->L }
% 0.19/0.49 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 10: multiply(X, X) = inverse(X).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, X)
% 0.19/0.49 = { by lemma 7 R->L }
% 0.19/0.49 multiply(inverse(X), identity)
% 0.19/0.49 = { by lemma 9 }
% 0.19/0.49 inverse(X)
% 0.19/0.49
% 0.19/0.49 Lemma 11: inverse(inverse(X)) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(inverse(X))
% 0.19/0.49 = { by lemma 9 R->L }
% 0.19/0.49 multiply(inverse(inverse(X)), identity)
% 0.19/0.49 = { by lemma 8 }
% 0.19/0.49 multiply(X, identity)
% 0.19/0.49 = { by lemma 9 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 12: multiply(X, multiply(X, multiply(X, Y))) = Y.
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, multiply(X, multiply(X, Y)))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(X, multiply(multiply(X, X), Y))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(multiply(X, multiply(X, X)), Y)
% 0.19/0.49 = { by axiom 3 (x_cubed_is_identity) }
% 0.19/0.49 multiply(identity, Y)
% 0.19/0.49 = { by axiom 1 (left_identity) }
% 0.19/0.49 Y
% 0.19/0.49
% 0.19/0.49 Lemma 13: multiply(inverse(multiply(X, Y)), multiply(X, multiply(Y, Z))) = Z.
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(multiply(X, Y)), multiply(X, multiply(Y, Z)))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(inverse(multiply(X, Y)), multiply(multiply(X, Y), Z))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 Z
% 0.19/0.49
% 0.19/0.49 Lemma 14: multiply(X, multiply(X, Y)) = multiply(inverse(X), Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, multiply(X, Y))
% 0.19/0.49 = { by lemma 6 R->L }
% 0.19/0.49 multiply(inverse(X), multiply(X, multiply(X, multiply(X, Y))))
% 0.19/0.49 = { by lemma 12 }
% 0.19/0.49 multiply(inverse(X), Y)
% 0.19/0.49
% 0.19/0.49 Lemma 15: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(inverse(Y), Z).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.19/0.49 = { by lemma 12 R->L }
% 0.19/0.49 multiply(inverse(multiply(X, Y)), multiply(X, multiply(Y, multiply(Y, multiply(Y, Z)))))
% 0.19/0.49 = { by lemma 13 }
% 0.19/0.49 multiply(Y, multiply(Y, Z))
% 0.19/0.49 = { by lemma 14 }
% 0.19/0.49 multiply(inverse(Y), Z)
% 0.19/0.49
% 0.19/0.49 Lemma 16: multiply(inverse(X), multiply(inverse(Y), Z)) = multiply(inverse(multiply(Y, X)), Z).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(X), multiply(inverse(Y), Z))
% 0.19/0.49 = { by lemma 6 R->L }
% 0.19/0.49 multiply(inverse(multiply(inverse(Y), multiply(Y, X))), multiply(inverse(Y), Z))
% 0.19/0.49 = { by lemma 15 }
% 0.19/0.49 multiply(inverse(multiply(Y, X)), Z)
% 0.19/0.49
% 0.19/0.49 Lemma 17: multiply(X, multiply(Y, inverse(multiply(X, Y)))) = identity.
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, multiply(Y, inverse(multiply(X, Y))))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(multiply(X, Y), inverse(multiply(X, Y)))
% 0.19/0.49 = { by lemma 8 R->L }
% 0.19/0.49 multiply(inverse(inverse(multiply(X, Y))), inverse(multiply(X, Y)))
% 0.19/0.49 = { by axiom 2 (left_inverse) }
% 0.19/0.49 identity
% 0.19/0.49
% 0.19/0.49 Lemma 18: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, inverse(multiply(Y, X)))
% 0.19/0.49 = { by lemma 6 R->L }
% 0.19/0.49 multiply(inverse(Y), multiply(Y, multiply(X, inverse(multiply(Y, X)))))
% 0.19/0.49 = { by lemma 17 }
% 0.19/0.49 multiply(inverse(Y), identity)
% 0.19/0.49 = { by lemma 9 }
% 0.19/0.49 inverse(Y)
% 0.19/0.49
% 0.19/0.49 Lemma 19: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, multiply(inverse(X), Y))
% 0.19/0.49 = { by lemma 8 R->L }
% 0.19/0.49 multiply(inverse(inverse(X)), multiply(inverse(X), Y))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 Y
% 0.19/0.49
% 0.19/0.49 Lemma 20: 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 18 R->L }
% 0.19/0.49 multiply(inverse(X), multiply(X, inverse(multiply(Y, X))))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 inverse(multiply(Y, X))
% 0.19/0.49
% 0.19/0.49 Lemma 21: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(multiply(inverse(X), Y))
% 0.19/0.49 = { by lemma 20 R->L }
% 0.19/0.49 multiply(inverse(Y), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 11 }
% 0.19/0.49 multiply(inverse(Y), X)
% 0.19/0.49
% 0.19/0.49 Lemma 22: multiply(inverse(multiply(X, Y)), commutator(X, Y)) = inverse(multiply(Y, X)).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(multiply(X, Y)), commutator(X, Y))
% 0.19/0.49 = { by axiom 5 (commutator) }
% 0.19/0.49 multiply(inverse(multiply(X, Y)), multiply(X, multiply(Y, multiply(inverse(X), inverse(Y)))))
% 0.19/0.49 = { by lemma 13 }
% 0.19/0.49 multiply(inverse(X), inverse(Y))
% 0.19/0.49 = { by lemma 20 }
% 0.19/0.49 inverse(multiply(Y, X))
% 0.19/0.49
% 0.19/0.49 Lemma 23: inverse(multiply(X, multiply(inverse(Y), multiply(X, multiply(Y, X))))) = commutator(Y, X).
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(multiply(X, multiply(inverse(Y), multiply(X, multiply(Y, X)))))
% 0.19/0.49 = { by lemma 14 R->L }
% 0.19/0.49 inverse(multiply(X, multiply(Y, multiply(Y, multiply(X, multiply(Y, X))))))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 inverse(multiply(X, multiply(Y, multiply(multiply(Y, X), multiply(Y, X)))))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 inverse(multiply(multiply(X, Y), multiply(multiply(Y, X), multiply(Y, X))))
% 0.19/0.49 = { by lemma 20 R->L }
% 0.19/0.49 multiply(inverse(multiply(multiply(Y, X), multiply(Y, X))), inverse(multiply(X, Y)))
% 0.19/0.49 = { by lemma 16 R->L }
% 0.19/0.49 multiply(inverse(multiply(Y, X)), multiply(inverse(multiply(Y, X)), inverse(multiply(X, Y))))
% 0.19/0.49 = { by lemma 22 R->L }
% 0.19/0.49 multiply(inverse(multiply(Y, X)), multiply(inverse(multiply(Y, X)), multiply(inverse(multiply(Y, X)), commutator(Y, X))))
% 0.19/0.49 = { by lemma 12 }
% 0.19/0.49 commutator(Y, X)
% 0.19/0.49
% 0.19/0.49 Lemma 24: commutator(inverse(X), Y) = commutator(X, inverse(Y)).
% 0.19/0.49 Proof:
% 0.19/0.49 commutator(inverse(X), Y)
% 0.19/0.49 = { by lemma 6 R->L }
% 0.19/0.49 multiply(inverse(X), multiply(X, commutator(inverse(X), Y)))
% 0.19/0.49 = { by lemma 8 R->L }
% 0.19/0.49 multiply(inverse(X), multiply(inverse(inverse(X)), commutator(inverse(X), Y)))
% 0.19/0.49 = { by axiom 5 (commutator) }
% 0.19/0.49 multiply(inverse(X), multiply(inverse(inverse(X)), multiply(inverse(X), multiply(Y, multiply(inverse(inverse(X)), inverse(Y))))))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 multiply(inverse(X), multiply(Y, multiply(inverse(inverse(X)), inverse(Y))))
% 0.19/0.49 = { by lemma 8 }
% 0.19/0.49 multiply(inverse(X), multiply(Y, multiply(X, inverse(Y))))
% 0.19/0.49 = { by lemma 10 R->L }
% 0.19/0.49 multiply(inverse(X), multiply(Y, multiply(X, multiply(Y, Y))))
% 0.19/0.49 = { by lemma 8 R->L }
% 0.19/0.49 multiply(inverse(X), multiply(Y, multiply(inverse(inverse(X)), multiply(Y, Y))))
% 0.19/0.49 = { by lemma 10 R->L }
% 0.19/0.49 multiply(inverse(X), multiply(Y, multiply(inverse(multiply(X, X)), multiply(Y, Y))))
% 0.19/0.49 = { by lemma 16 R->L }
% 0.19/0.49 multiply(inverse(X), multiply(Y, multiply(inverse(X), multiply(inverse(X), multiply(Y, Y)))))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(inverse(X), multiply(Y, multiply(inverse(X), multiply(multiply(inverse(X), Y), Y))))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(multiply(inverse(X), Y), multiply(inverse(X), multiply(multiply(inverse(X), Y), Y)))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(multiply(multiply(inverse(X), Y), inverse(X)), multiply(multiply(inverse(X), Y), Y))
% 0.19/0.49 = { by lemma 18 R->L }
% 0.19/0.49 multiply(multiply(multiply(inverse(X), Y), multiply(inverse(multiply(inverse(X), Y)), inverse(multiply(X, inverse(multiply(inverse(X), Y)))))), multiply(multiply(inverse(X), Y), Y))
% 0.19/0.49 = { by lemma 19 }
% 0.19/0.49 multiply(inverse(multiply(X, inverse(multiply(inverse(X), Y)))), multiply(multiply(inverse(X), Y), Y))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(X), Y)))), multiply(inverse(X), Y)), Y)
% 0.19/0.49 = { by lemma 21 R->L }
% 0.19/0.49 multiply(inverse(multiply(inverse(multiply(inverse(X), Y)), multiply(X, inverse(multiply(inverse(X), Y))))), Y)
% 0.19/0.49 = { by lemma 21 R->L }
% 0.19/0.49 inverse(multiply(inverse(Y), multiply(inverse(multiply(inverse(X), Y)), multiply(X, inverse(multiply(inverse(X), Y))))))
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 inverse(multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(X), multiply(inverse(multiply(inverse(X), Y)), multiply(X, inverse(multiply(inverse(X), Y)))))))
% 0.19/0.49 = { by lemma 23 }
% 0.19/0.49 commutator(X, inverse(multiply(inverse(X), Y)))
% 0.19/0.49 = { by lemma 21 }
% 0.19/0.49 commutator(X, multiply(inverse(Y), X))
% 0.19/0.49 = { by lemma 11 R->L }
% 0.19/0.49 commutator(X, inverse(inverse(multiply(inverse(Y), X))))
% 0.19/0.49 = { by axiom 5 (commutator) }
% 0.19/0.49 multiply(X, multiply(inverse(inverse(multiply(inverse(Y), X))), multiply(inverse(X), inverse(inverse(inverse(multiply(inverse(Y), X)))))))
% 0.19/0.49 = { by axiom 4 (associativity) R->L }
% 0.19/0.49 multiply(X, multiply(multiply(inverse(inverse(multiply(inverse(Y), X))), inverse(X)), inverse(inverse(inverse(multiply(inverse(Y), X))))))
% 0.19/0.49 = { by lemma 18 R->L }
% 0.19/0.49 multiply(X, multiply(multiply(inverse(inverse(multiply(inverse(Y), X))), inverse(X)), multiply(inverse(X), inverse(multiply(inverse(inverse(multiply(inverse(Y), X))), inverse(X))))))
% 0.19/0.49 = { by axiom 5 (commutator) R->L }
% 0.19/0.49 commutator(X, multiply(inverse(inverse(multiply(inverse(Y), X))), inverse(X)))
% 0.19/0.49 = { by lemma 20 }
% 0.19/0.49 commutator(X, inverse(multiply(X, inverse(multiply(inverse(Y), X)))))
% 0.19/0.49 = { by lemma 18 }
% 0.19/0.49 commutator(X, inverse(inverse(inverse(Y))))
% 0.19/0.49 = { by lemma 11 }
% 0.19/0.50 commutator(X, inverse(Y))
% 0.19/0.50
% 0.19/0.50 Lemma 25: multiply(X, multiply(Y, inverse(multiply(Y, X)))) = commutator(X, Y).
% 0.19/0.50 Proof:
% 0.19/0.50 multiply(X, multiply(Y, inverse(multiply(Y, X))))
% 0.19/0.50 = { by axiom 4 (associativity) R->L }
% 0.19/0.50 multiply(multiply(X, Y), inverse(multiply(Y, X)))
% 0.19/0.50 = { by lemma 8 R->L }
% 0.19/0.50 multiply(inverse(inverse(multiply(X, Y))), inverse(multiply(Y, X)))
% 0.19/0.50 = { by lemma 22 R->L }
% 0.19/0.50 multiply(inverse(inverse(multiply(X, Y))), multiply(inverse(multiply(X, Y)), commutator(X, Y)))
% 0.19/0.50 = { by lemma 6 }
% 0.19/0.50 commutator(X, Y)
% 0.19/0.50
% 0.19/0.50 Lemma 26: commutator(multiply(X, Y), inverse(X)) = commutator(X, Y).
% 0.19/0.50 Proof:
% 0.19/0.50 commutator(multiply(X, Y), inverse(X))
% 0.19/0.50 = { by lemma 25 R->L }
% 0.19/0.50 multiply(multiply(X, Y), multiply(inverse(X), inverse(multiply(inverse(X), multiply(X, Y)))))
% 0.19/0.50 = { by lemma 6 }
% 0.19/0.50 multiply(multiply(X, Y), multiply(inverse(X), inverse(Y)))
% 0.19/0.50 = { by axiom 4 (associativity) }
% 0.19/0.50 multiply(X, multiply(Y, multiply(inverse(X), inverse(Y))))
% 0.19/0.50 = { by axiom 5 (commutator) R->L }
% 0.19/0.50 commutator(X, Y)
% 0.19/0.50
% 0.19/0.50 Lemma 27: commutator(inverse(X), multiply(X, Y)) = commutator(Y, X).
% 0.19/0.50 Proof:
% 0.19/0.50 commutator(inverse(X), multiply(X, Y))
% 0.19/0.50 = { by lemma 26 R->L }
% 0.19/0.50 commutator(multiply(inverse(X), multiply(X, Y)), inverse(inverse(X)))
% 0.19/0.50 = { by lemma 6 }
% 0.19/0.50 commutator(Y, inverse(inverse(X)))
% 0.19/0.50 = { by lemma 11 }
% 0.19/0.50 commutator(Y, X)
% 0.19/0.50
% 0.19/0.50 Goal 1 (prove_commutator): commutator(commutator(a, b), b) = identity.
% 0.19/0.50 Proof:
% 0.19/0.50 commutator(commutator(a, b), b)
% 0.19/0.50 = { by lemma 25 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, inverse(multiply(b, commutator(a, b)))))
% 0.19/0.50 = { by lemma 19 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, inverse(multiply(b, multiply(a, multiply(inverse(a), commutator(a, b)))))))
% 0.19/0.50 = { by axiom 4 (associativity) R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, inverse(multiply(multiply(b, a), multiply(inverse(a), commutator(a, b))))))
% 0.19/0.50 = { by lemma 20 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(inverse(multiply(inverse(a), commutator(a, b))), inverse(multiply(b, a)))))
% 0.19/0.50 = { by lemma 25 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(inverse(multiply(inverse(a), multiply(a, multiply(b, inverse(multiply(b, a)))))), inverse(multiply(b, a)))))
% 0.19/0.50 = { by lemma 6 }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(inverse(multiply(b, inverse(multiply(b, a)))), inverse(multiply(b, a)))))
% 0.19/0.50 = { by lemma 6 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(inverse(multiply(b, inverse(multiply(b, a)))), multiply(inverse(b), multiply(b, inverse(multiply(b, a)))))))
% 0.19/0.50 = { by lemma 14 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), multiply(multiply(b, inverse(multiply(b, a))), multiply(inverse(b), multiply(b, inverse(multiply(b, a))))))))
% 0.19/0.50 = { by lemma 8 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), multiply(inverse(inverse(multiply(b, inverse(multiply(b, a))))), multiply(inverse(b), multiply(b, inverse(multiply(b, a))))))))
% 0.19/0.50 = { by axiom 4 (associativity) R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), multiply(multiply(inverse(inverse(multiply(b, inverse(multiply(b, a))))), inverse(b)), multiply(b, inverse(multiply(b, a)))))))
% 0.19/0.50 = { by lemma 21 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), multiply(inverse(multiply(inverse(inverse(b)), inverse(multiply(b, inverse(multiply(b, a)))))), multiply(b, inverse(multiply(b, a)))))))
% 0.19/0.50 = { by lemma 21 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), inverse(multiply(inverse(multiply(b, inverse(multiply(b, a)))), multiply(inverse(inverse(b)), inverse(multiply(b, inverse(multiply(b, a))))))))))
% 0.19/0.50 = { by lemma 21 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), inverse(multiply(inverse(multiply(b, inverse(multiply(b, a)))), inverse(multiply(inverse(inverse(multiply(b, inverse(multiply(b, a))))), inverse(b))))))))
% 0.19/0.50 = { by lemma 9 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), inverse(multiply(inverse(multiply(b, inverse(multiply(b, a)))), multiply(inverse(multiply(inverse(inverse(multiply(b, inverse(multiply(b, a))))), inverse(b))), identity))))))
% 0.19/0.50 = { by lemma 7 }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), inverse(multiply(inverse(multiply(b, inverse(multiply(b, a)))), multiply(multiply(inverse(inverse(multiply(b, inverse(multiply(b, a))))), inverse(b)), multiply(inverse(inverse(multiply(b, inverse(multiply(b, a))))), inverse(b))))))))
% 0.19/0.50 = { by axiom 4 (associativity) }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), inverse(multiply(inverse(multiply(b, inverse(multiply(b, a)))), multiply(inverse(inverse(multiply(b, inverse(multiply(b, a))))), multiply(inverse(b), multiply(inverse(inverse(multiply(b, inverse(multiply(b, a))))), inverse(b)))))))))
% 0.19/0.50 = { by lemma 19 }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), inverse(multiply(inverse(b), multiply(inverse(inverse(multiply(b, inverse(multiply(b, a))))), inverse(b)))))))
% 0.19/0.50 = { by lemma 14 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), inverse(multiply(inverse(b), multiply(inverse(multiply(b, inverse(multiply(b, a)))), multiply(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b))))))))
% 0.19/0.50 = { by axiom 4 (associativity) R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), inverse(multiply(multiply(inverse(b), inverse(multiply(b, inverse(multiply(b, a))))), multiply(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b)))))))
% 0.19/0.50 = { by lemma 20 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), multiply(inverse(multiply(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b))), inverse(multiply(inverse(b), inverse(multiply(b, inverse(multiply(b, a))))))))))
% 0.19/0.50 = { by lemma 22 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), multiply(inverse(multiply(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b))), multiply(inverse(multiply(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b))), commutator(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b)))))))
% 0.19/0.50 = { by lemma 14 }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), multiply(inverse(inverse(multiply(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b)))), commutator(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b))))))
% 0.19/0.50 = { by lemma 8 }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), multiply(multiply(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b)), commutator(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b))))))
% 0.19/0.50 = { by axiom 4 (associativity) }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(multiply(b, inverse(multiply(b, a))), multiply(inverse(multiply(b, inverse(multiply(b, a)))), multiply(inverse(b), commutator(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b)))))))
% 0.19/0.50 = { by lemma 19 }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(inverse(b), commutator(inverse(multiply(b, inverse(multiply(b, a)))), inverse(b)))))
% 0.19/0.50 = { by lemma 24 }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(inverse(b), commutator(multiply(b, inverse(multiply(b, a))), inverse(inverse(b))))))
% 0.19/0.50 = { by lemma 6 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(inverse(b), commutator(multiply(inverse(inverse(b)), multiply(inverse(b), multiply(b, inverse(multiply(b, a))))), inverse(inverse(b))))))
% 0.19/0.50 = { by lemma 23 R->L }
% 0.19/0.50 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(inverse(inverse(b)), multiply(inverse(multiply(inverse(inverse(b)), multiply(inverse(b), multiply(b, inverse(multiply(b, a)))))), multiply(inverse(inverse(b)), multiply(multiply(inverse(inverse(b)), multiply(inverse(b), multiply(b, inverse(multiply(b, a))))), inverse(inverse(b))))))))))
% 0.19/0.51 = { by lemma 15 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(inverse(inverse(b)), multiply(inverse(multiply(inverse(b), multiply(b, inverse(multiply(b, a))))), multiply(multiply(inverse(inverse(b)), multiply(inverse(b), multiply(b, inverse(multiply(b, a))))), inverse(inverse(b)))))))))
% 0.19/0.51 = { by axiom 4 (associativity) }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(inverse(inverse(b)), multiply(inverse(multiply(inverse(b), multiply(b, inverse(multiply(b, a))))), multiply(inverse(inverse(b)), multiply(multiply(inverse(b), multiply(b, inverse(multiply(b, a)))), inverse(inverse(b))))))))))
% 0.19/0.51 = { by lemma 23 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), commutator(multiply(inverse(b), multiply(b, inverse(multiply(b, a)))), inverse(inverse(b))))))
% 0.19/0.51 = { by lemma 26 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), commutator(inverse(b), multiply(b, inverse(multiply(b, a)))))))
% 0.19/0.51 = { by lemma 27 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), commutator(inverse(multiply(b, a)), b))))
% 0.19/0.51 = { by lemma 24 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), commutator(multiply(b, a), inverse(b)))))
% 0.19/0.51 = { by lemma 26 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), commutator(b, a))))
% 0.19/0.51 = { by lemma 27 R->L }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), commutator(inverse(a), multiply(a, b)))))
% 0.19/0.51 = { by lemma 23 R->L }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(multiply(a, b), multiply(inverse(inverse(a)), multiply(multiply(a, b), multiply(inverse(a), multiply(a, b)))))))))
% 0.19/0.51 = { by lemma 6 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(multiply(a, b), multiply(inverse(inverse(a)), multiply(multiply(a, b), b)))))))
% 0.19/0.51 = { by axiom 4 (associativity) }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(a, multiply(b, multiply(inverse(inverse(a)), multiply(multiply(a, b), b))))))))
% 0.19/0.51 = { by lemma 8 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(a, multiply(b, multiply(a, multiply(multiply(a, b), b))))))))
% 0.19/0.51 = { by axiom 4 (associativity) }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, b)))))))))
% 0.19/0.51 = { by lemma 14 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(a, multiply(b, multiply(inverse(a), multiply(b, b))))))))
% 0.19/0.51 = { by lemma 10 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(multiply(a, multiply(b, multiply(inverse(a), inverse(b))))))))
% 0.19/0.51 = { by axiom 5 (commutator) R->L }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, multiply(inverse(b), inverse(commutator(a, b)))))
% 0.19/0.51 = { by lemma 20 }
% 0.19/0.51 multiply(commutator(a, b), multiply(b, inverse(multiply(commutator(a, b), b))))
% 0.19/0.51 = { by lemma 17 }
% 0.19/0.51 identity
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51
% 0.19/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------