TSTP Solution File: GRP119-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP119-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:17:03 EDT 2023
% Result : Unsatisfiable 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP119-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon Aug 28 23:47:58 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.20/0.52 Command-line arguments: --no-flatten-goal
% 0.20/0.52
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52
% 0.20/0.55 % SZS output start Proof
% 0.20/0.55 Axiom 1 (single_axiom2): multiply(identity, identity) = identity.
% 0.20/0.55 Axiom 2 (single_axiom): multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, Z))), multiply(Z, multiply(Z, Z)))) = Y.
% 0.20/0.55
% 0.20/0.55 Lemma 3: multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, identity))), identity)) = Y.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, identity))), identity))
% 0.20/0.55 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.55 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, identity))), multiply(identity, identity)))
% 0.20/0.55 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.55 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, identity))), multiply(identity, multiply(identity, identity))))
% 0.20/0.55 = { by axiom 2 (single_axiom) }
% 0.20/0.55 Y
% 0.20/0.55
% 0.20/0.55 Lemma 4: multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, identity))), identity)) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, identity))), identity))
% 0.20/0.55 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.55 multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, identity))), identity))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 5: multiply(identity, multiply(multiply(identity, X), identity)) = multiply(identity, multiply(identity, multiply(X, identity))).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(identity, multiply(multiply(identity, X), identity))
% 0.20/0.55 = { by lemma 3 R->L }
% 0.20/0.55 multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, identity))), identity))), identity))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 multiply(identity, multiply(multiply(identity, identity), multiply(X, identity)))
% 0.20/0.55 = { by axiom 1 (single_axiom2) }
% 0.20/0.55 multiply(identity, multiply(identity, multiply(X, identity)))
% 0.20/0.55
% 0.20/0.55 Lemma 6: multiply(identity, multiply(identity, multiply(identity, multiply(multiply(X, identity), identity)))) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(X, identity), identity))))
% 0.20/0.55 = { by lemma 5 R->L }
% 0.20/0.55 multiply(identity, multiply(identity, multiply(multiply(identity, multiply(X, identity)), identity)))
% 0.20/0.55 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.55 multiply(identity, multiply(identity, multiply(multiply(multiply(identity, identity), multiply(X, identity)), identity)))
% 0.20/0.55 = { by lemma 5 R->L }
% 0.20/0.55 multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, identity))), identity))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 7: multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, identity))) = multiply(X, multiply(multiply(X, Y), identity)).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, identity)))
% 0.20/0.55 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.55 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, identity))), identity))), multiply(identity, multiply(identity, identity))))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 multiply(X, multiply(multiply(X, Y), multiply(identity, multiply(identity, identity))))
% 0.20/0.55 = { by axiom 1 (single_axiom2) }
% 0.20/0.55 multiply(X, multiply(multiply(X, Y), multiply(identity, identity)))
% 0.20/0.55 = { by axiom 1 (single_axiom2) }
% 0.20/0.55 multiply(X, multiply(multiply(X, Y), identity))
% 0.20/0.55
% 0.20/0.55 Lemma 8: multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), identity)), identity)) = Y.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), identity)), identity))
% 0.20/0.55 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.55 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), identity)), multiply(identity, identity)))
% 0.20/0.55 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.55 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), identity)), multiply(identity, multiply(identity, identity))))
% 0.20/0.55 = { by lemma 7 R->L }
% 0.20/0.55 multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, identity))), multiply(identity, multiply(identity, identity))))
% 0.20/0.55 = { by axiom 2 (single_axiom) }
% 0.20/0.55 Y
% 0.20/0.55
% 0.20/0.55 Lemma 9: multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, Y))), multiply(Y, multiply(Y, Y)))) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, Y))), multiply(Y, multiply(Y, Y))))
% 0.20/0.55 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.55 multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, Y))), multiply(Y, multiply(Y, Y))))
% 0.20/0.55 = { by axiom 2 (single_axiom) }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 10: multiply(identity, multiply(identity, multiply(multiply(multiply(identity, X), identity), identity))) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(identity, multiply(identity, multiply(multiply(multiply(identity, X), identity), identity)))
% 0.20/0.55 = { by lemma 5 R->L }
% 0.20/0.55 multiply(identity, multiply(multiply(identity, multiply(multiply(identity, X), identity)), identity))
% 0.20/0.55 = { by lemma 5 }
% 0.20/0.55 multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, identity))), identity))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 11: multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X)))) = multiply(identity, X).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X))))
% 0.20/0.55 = { by lemma 10 R->L }
% 0.20/0.55 multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X))))), identity), identity)))
% 0.20/0.55 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.55 multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X))))), identity), identity)))
% 0.20/0.55 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.55 multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(identity, X))), multiply(X, multiply(X, X))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X))))), identity), identity)))
% 0.20/0.56 = { by lemma 8 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(identity, X))), multiply(X, multiply(X, X))))), multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X)))))), identity)), identity)), identity), identity)))
% 0.20/0.56 = { by lemma 9 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(identity, X))), identity)), identity)), identity), identity)))
% 0.20/0.56 = { by axiom 1 (single_axiom2) }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(identity, X))), identity)), identity)), identity), identity)))
% 0.20/0.56 = { by lemma 5 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(multiply(identity, identity), multiply(identity, X))), identity), identity))), identity), identity)))
% 0.20/0.56 = { by lemma 10 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(identity, identity), multiply(identity, X)), identity), identity)))
% 0.20/0.56 = { by axiom 1 (single_axiom2) }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(identity, X)), identity), identity)))
% 0.20/0.56 = { by lemma 10 }
% 0.20/0.56 multiply(identity, X)
% 0.20/0.56
% 0.20/0.56 Lemma 12: multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z))) = multiply(X, multiply(multiply(X, Y), multiply(identity, Z))).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z)))
% 0.20/0.56 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.56 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z))), multiply(Z, multiply(Z, Z))))), multiply(multiply(Z, multiply(Z, Z)), multiply(multiply(Z, multiply(Z, Z)), multiply(Z, multiply(Z, Z))))))
% 0.20/0.56 = { by axiom 2 (single_axiom) }
% 0.20/0.56 multiply(X, multiply(multiply(X, Y), multiply(multiply(Z, multiply(Z, Z)), multiply(multiply(Z, multiply(Z, Z)), multiply(Z, multiply(Z, Z))))))
% 0.20/0.56 = { by lemma 11 }
% 0.20/0.56 multiply(X, multiply(multiply(X, Y), multiply(identity, Z)))
% 0.20/0.56
% 0.20/0.56 Lemma 13: multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), Y)) = multiply(X, multiply(multiply(X, identity), Y)).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), Y))
% 0.20/0.56 = { by lemma 9 R->L }
% 0.20/0.56 multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(identity, multiply(multiply(identity, multiply(identity, multiply(Y, Z))), multiply(Z, multiply(Z, Z))))))
% 0.20/0.56 = { by lemma 12 }
% 0.20/0.56 multiply(X, multiply(multiply(X, identity), multiply(identity, multiply(multiply(identity, multiply(identity, multiply(Y, Z))), multiply(Z, multiply(Z, Z))))))
% 0.20/0.56 = { by lemma 9 }
% 0.20/0.56 multiply(X, multiply(multiply(X, identity), Y))
% 0.20/0.56
% 0.20/0.56 Lemma 14: multiply(multiply(X, identity), multiply(Y, identity)) = multiply(multiply(X, Y), identity).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(X, identity), multiply(Y, identity))
% 0.20/0.56 = { by lemma 8 R->L }
% 0.20/0.56 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, identity), multiply(Y, identity))), identity)), identity))
% 0.20/0.56 = { by lemma 13 R->L }
% 0.20/0.56 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, identity))), identity)), identity))
% 0.20/0.56 = { by lemma 7 }
% 0.20/0.56 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, Y), identity)), identity)), identity))
% 0.20/0.56 = { by lemma 8 }
% 0.20/0.56 multiply(multiply(X, Y), identity)
% 0.20/0.56
% 0.20/0.56 Lemma 15: multiply(X, multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity)))) = identity.
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(X, multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity))))
% 0.20/0.56 = { by lemma 10 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(X, multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity))))), identity), identity)))
% 0.20/0.56 = { by lemma 6 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(multiply(identity, multiply(identity, multiply(identity, multiply(multiply(X, identity), identity)))), multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity))))), identity), identity)))
% 0.20/0.56 = { by lemma 9 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(multiply(identity, identity), identity)))
% 0.20/0.56 = { by lemma 5 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(identity, identity))))
% 0.20/0.56 = { by axiom 1 (single_axiom2) }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, identity)))
% 0.20/0.56 = { by axiom 1 (single_axiom2) }
% 0.20/0.56 multiply(identity, multiply(identity, identity))
% 0.20/0.56 = { by axiom 1 (single_axiom2) }
% 0.20/0.56 multiply(identity, identity)
% 0.20/0.56 = { by axiom 1 (single_axiom2) }
% 0.20/0.56 identity
% 0.20/0.56
% 0.20/0.56 Lemma 16: multiply(X, multiply(multiply(multiply(X, multiply(X, X)), identity), identity)) = identity.
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(X, multiply(multiply(multiply(X, multiply(X, X)), identity), identity))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(X, multiply(multiply(multiply(X, identity), multiply(multiply(X, X), identity)), identity))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(X, multiply(multiply(multiply(X, identity), multiply(multiply(X, identity), multiply(X, identity))), identity))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(X, multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), multiply(X, identity)), identity)))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(X, multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity))))
% 0.20/0.56 = { by lemma 15 }
% 0.20/0.56 identity
% 0.20/0.56
% 0.20/0.56 Lemma 17: multiply(multiply(identity, X), identity) = multiply(identity, multiply(X, identity)).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(identity, X), identity)
% 0.20/0.56 = { by lemma 4 R->L }
% 0.20/0.56 multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(multiply(identity, X), identity), identity))), identity))
% 0.20/0.56 = { by lemma 10 }
% 0.20/0.56 multiply(identity, multiply(X, identity))
% 0.20/0.56
% 0.20/0.56 Lemma 18: multiply(multiply(X, identity), multiply(Y, Z)) = multiply(multiply(X, Y), multiply(identity, Z)).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(X, identity), multiply(Y, Z))
% 0.20/0.56 = { by lemma 8 R->L }
% 0.20/0.56 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, identity), multiply(Y, Z))), identity)), identity))
% 0.20/0.56 = { by lemma 13 R->L }
% 0.20/0.56 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z))), identity)), identity))
% 0.20/0.56 = { by lemma 12 }
% 0.20/0.56 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, Y), multiply(identity, Z))), identity)), identity))
% 0.20/0.56 = { by lemma 8 }
% 0.20/0.56 multiply(multiply(X, Y), multiply(identity, Z))
% 0.20/0.56
% 0.20/0.56 Lemma 19: multiply(multiply(X, X), identity) = multiply(X, X).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(X, X), identity)
% 0.20/0.56 = { by lemma 6 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, X), identity), identity), identity))))
% 0.20/0.56 = { by lemma 16 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, X), multiply(multiply(X, multiply(X, X)), multiply(multiply(multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X)))), identity), identity))), identity), identity))))
% 0.20/0.56 = { by lemma 11 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, X), multiply(multiply(X, multiply(X, X)), multiply(multiply(multiply(identity, X), identity), identity))), identity), identity))))
% 0.20/0.56 = { by lemma 17 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, X), multiply(multiply(X, multiply(X, X)), multiply(multiply(identity, multiply(X, identity)), identity))), identity), identity))))
% 0.20/0.56 = { by lemma 17 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, X), multiply(multiply(X, multiply(X, X)), multiply(identity, multiply(multiply(X, identity), identity)))), identity), identity))))
% 0.20/0.56 = { by lemma 18 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, X), multiply(multiply(X, identity), multiply(multiply(X, X), multiply(multiply(X, identity), identity)))), identity), identity))))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, X), identity), multiply(multiply(multiply(X, identity), multiply(multiply(X, X), multiply(multiply(X, identity), identity))), identity)), identity))))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, identity), multiply(X, identity)), multiply(multiply(multiply(X, identity), multiply(multiply(X, X), multiply(multiply(X, identity), identity))), identity)), identity))))
% 0.20/0.56 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, identity), multiply(X, identity)), multiply(multiply(multiply(X, identity), multiply(multiply(X, X), multiply(multiply(X, multiply(identity, identity)), identity))), identity)), identity))))
% 0.20/0.56 = { by lemma 15 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, identity), multiply(X, identity)), multiply(multiply(multiply(X, identity), multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity)))), identity)), identity))), identity)), identity))))
% 0.20/0.56 = { by lemma 8 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, identity), multiply(X, identity)), multiply(multiply(multiply(X, identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity)))), identity)), identity))))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, identity), multiply(X, identity)), multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity))), identity))), identity))))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, identity), multiply(X, identity)), identity), multiply(multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity))), identity)), identity)))))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity)), multiply(multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity))), identity)), identity)))))
% 0.20/0.56 = { by lemma 8 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity)))))
% 0.20/0.56 = { by lemma 18 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(X, identity), multiply(X, identity)), multiply(identity, identity)))))
% 0.20/0.56 = { by lemma 14 }
% 0.20/0.56 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(X, X), identity), multiply(identity, identity)))))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(multiply(X, X), identity), identity))))
% 0.20/0.57 = { by lemma 6 }
% 0.20/0.57 multiply(X, X)
% 0.20/0.57
% 0.20/0.57 Goal 1 (prove_order4): multiply(a, multiply(a, multiply(a, a))) = identity.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(a, multiply(a, multiply(a, a)))
% 0.20/0.57 = { by lemma 19 R->L }
% 0.20/0.57 multiply(a, multiply(a, multiply(multiply(a, a), identity)))
% 0.20/0.57 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.57 multiply(a, multiply(a, multiply(multiply(a, a), multiply(identity, identity))))
% 0.20/0.57 = { by lemma 16 R->L }
% 0.20/0.57 multiply(a, multiply(a, multiply(multiply(a, a), multiply(multiply(a, multiply(multiply(multiply(a, multiply(a, a)), identity), identity)), identity))))
% 0.20/0.57 = { by lemma 3 R->L }
% 0.20/0.57 multiply(a, multiply(a, multiply(multiply(a, a), multiply(multiply(a, multiply(multiply(a, multiply(multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(a, multiply(a, a)), identity), identity))), identity)), identity)), identity))))
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 multiply(a, multiply(a, multiply(multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(a, multiply(a, a)), identity), identity))), identity)))
% 0.20/0.57 = { by lemma 3 }
% 0.20/0.57 multiply(a, multiply(multiply(a, multiply(a, a)), identity))
% 0.20/0.57 = { by lemma 19 R->L }
% 0.20/0.57 multiply(a, multiply(multiply(a, multiply(multiply(a, a), identity)), identity))
% 0.20/0.57 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.57 multiply(a, multiply(multiply(a, multiply(multiply(a, a), identity)), multiply(identity, identity)))
% 0.20/0.57 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.57 multiply(a, multiply(multiply(a, multiply(multiply(a, a), identity)), multiply(identity, multiply(identity, identity))))
% 0.20/0.57 = { by axiom 1 (single_axiom2) R->L }
% 0.20/0.57 multiply(a, multiply(multiply(a, multiply(multiply(a, a), multiply(identity, identity))), multiply(identity, multiply(identity, identity))))
% 0.20/0.57 = { by axiom 2 (single_axiom) }
% 0.20/0.57 identity
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------