TSTP Solution File: GRP121-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP121-1 : TPTP v8.1.2. Released v1.2.0.
% 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 : n020.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 01:17:04 EDT 2023
% Result : Unsatisfiable 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP121-1 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 01:42:43 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Command-line arguments: --flatten
% 0.21/0.47
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47
% 0.21/0.51 % SZS output start Proof
% 0.21/0.51 Axiom 1 (single_axiom2): multiply(identity, identity) = identity.
% 0.21/0.51 Axiom 2 (single_axiom): multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, Z))), multiply(Z, multiply(Z, Z)))) = Y.
% 0.21/0.51
% 0.21/0.51 Lemma 3: multiply(multiply(identity, identity), multiply(identity, identity)) = multiply(identity, identity).
% 0.21/0.51 Proof:
% 0.21/0.51 multiply(multiply(identity, identity), multiply(identity, identity))
% 0.21/0.51 = { by axiom 1 (single_axiom2) }
% 0.21/0.51 multiply(multiply(identity, identity), identity)
% 0.21/0.51 = { by axiom 1 (single_axiom2) }
% 0.21/0.52 multiply(identity, identity)
% 0.21/0.52
% 0.21/0.52 Lemma 4: multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, multiply(identity, identity)))), multiply(identity, identity))) = Y.
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, multiply(identity, identity)))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 3 R->L }
% 0.21/0.52 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, multiply(identity, identity)))), multiply(multiply(identity, identity), multiply(identity, identity))))
% 0.21/0.52 = { by lemma 3 R->L }
% 0.21/0.52 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, multiply(identity, identity)))), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity)))))
% 0.21/0.52 = { by axiom 2 (single_axiom) }
% 0.21/0.52 Y
% 0.21/0.52
% 0.21/0.52 Lemma 5: multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), multiply(identity, identity))), multiply(identity, identity))) = Y.
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), multiply(identity, identity))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 3 R->L }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), multiply(identity, identity))), multiply(multiply(identity, identity), multiply(identity, identity))))
% 0.21/0.52 = { by lemma 3 R->L }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), multiply(identity, identity))), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity)))))
% 0.21/0.52 = { by lemma 3 R->L }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(identity, identity)))), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity)))))
% 0.21/0.52 = { by lemma 3 R->L }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity))))), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity)))))
% 0.21/0.52 = { by lemma 4 R->L }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, multiply(identity, identity)))), multiply(identity, identity)))), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity))))), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity)))))
% 0.21/0.52 = { by axiom 2 (single_axiom) }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, multiply(identity, identity)))), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity)))))
% 0.21/0.52 = { by axiom 2 (single_axiom) }
% 0.21/0.52 Y
% 0.21/0.52
% 0.21/0.52 Lemma 6: multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(X, Y))), multiply(Y, multiply(Y, Y)))) = X.
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(X, Y))), multiply(Y, multiply(Y, Y))))
% 0.21/0.52 = { by axiom 1 (single_axiom2) }
% 0.21/0.52 multiply(identity, multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(X, Y))), multiply(Y, multiply(Y, Y))))
% 0.21/0.52 = { by axiom 1 (single_axiom2) }
% 0.21/0.52 multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, Y))), multiply(Y, multiply(Y, Y))))
% 0.21/0.52 = { by axiom 2 (single_axiom) }
% 0.21/0.52 X
% 0.21/0.52
% 0.21/0.52 Lemma 7: multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(X, multiply(identity, identity)))), multiply(identity, identity))) = X.
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(X, multiply(identity, identity)))), multiply(identity, identity)))
% 0.21/0.52 = { by axiom 1 (single_axiom2) }
% 0.21/0.52 multiply(identity, multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(X, multiply(identity, identity)))), multiply(identity, identity)))
% 0.21/0.52 = { by axiom 1 (single_axiom2) }
% 0.21/0.52 multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, multiply(identity, identity)))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 4 }
% 0.21/0.52 X
% 0.21/0.52
% 0.21/0.52 Lemma 8: multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), X), multiply(identity, identity))) = multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(X, multiply(identity, identity)))).
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), X), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 4 R->L }
% 0.21/0.52 multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(X, multiply(identity, identity)))), multiply(identity, identity)))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 7 }
% 0.21/0.52 multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(X, multiply(identity, identity))))
% 0.21/0.52 = { by lemma 3 }
% 0.21/0.52 multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(X, multiply(identity, identity))))
% 0.21/0.52
% 0.21/0.52 Lemma 9: multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), X), multiply(identity, identity)), multiply(identity, identity)))) = X.
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), X), multiply(identity, identity)), multiply(identity, identity))))
% 0.21/0.52 = { by lemma 8 R->L }
% 0.21/0.52 multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), X), multiply(identity, identity))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 8 }
% 0.21/0.52 multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(X, multiply(identity, identity)))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 7 }
% 0.21/0.52 X
% 0.21/0.52
% 0.21/0.52 Lemma 10: multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z))) = multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), Z))).
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z)))
% 0.21/0.52 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.52 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))))))
% 0.21/0.52 = { by axiom 2 (single_axiom) }
% 0.21/0.52 multiply(X, multiply(multiply(X, Y), multiply(multiply(Z, multiply(Z, Z)), multiply(multiply(Z, multiply(Z, Z)), multiply(Z, multiply(Z, Z))))))
% 0.21/0.52 = { by lemma 9 R->L }
% 0.21/0.52 multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(Z, multiply(Z, Z)), multiply(multiply(Z, multiply(Z, Z)), multiply(Z, multiply(Z, Z))))), multiply(identity, identity)), multiply(identity, identity))))))
% 0.21/0.52 = { by lemma 5 R->L }
% 0.21/0.52 multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(Z, multiply(Z, Z)), multiply(multiply(Z, multiply(Z, Z)), multiply(Z, multiply(Z, Z)))))), multiply(identity, identity))), multiply(identity, identity))), multiply(identity, identity)), multiply(identity, identity))))))
% 0.21/0.52 = { by lemma 3 R->L }
% 0.21/0.52 multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(multiply(Z, multiply(Z, Z)), multiply(multiply(Z, multiply(Z, Z)), multiply(Z, multiply(Z, Z)))))), multiply(identity, identity))), multiply(identity, identity))), multiply(identity, identity)), multiply(identity, identity))))))
% 0.21/0.52 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.52 multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(multiply(identity, identity), Z))), multiply(Z, multiply(Z, Z))))), multiply(multiply(Z, multiply(Z, Z)), multiply(multiply(Z, multiply(Z, Z)), multiply(Z, multiply(Z, Z)))))), multiply(identity, identity))), multiply(identity, identity))), multiply(identity, identity)), multiply(identity, identity))))))
% 0.21/0.52 = { by lemma 6 }
% 0.21/0.52 multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(multiply(identity, identity), Z))), multiply(identity, identity))), multiply(identity, identity))), multiply(identity, identity)), multiply(identity, identity))))))
% 0.21/0.52 = { by lemma 3 }
% 0.21/0.52 multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(identity, identity), Z))), multiply(identity, identity))), multiply(identity, identity))), multiply(identity, identity)), multiply(identity, identity))))))
% 0.21/0.52 = { by lemma 5 }
% 0.21/0.52 multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), Z)), multiply(identity, identity)), multiply(identity, identity))))))
% 0.21/0.52 = { by lemma 9 }
% 0.21/0.52 multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), Z)))
% 0.21/0.52
% 0.21/0.52 Lemma 11: multiply(multiply(X, multiply(identity, identity)), multiply(Y, Z)) = multiply(multiply(X, Y), multiply(multiply(identity, identity), Z)).
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(multiply(X, multiply(identity, identity)), multiply(Y, Z))
% 0.21/0.52 = { by lemma 5 R->L }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, multiply(identity, identity)), multiply(Y, Z))), multiply(identity, identity))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 6 R->L }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, multiply(identity, identity)), multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(Y, Z), W))), multiply(W, multiply(W, W)))))), multiply(identity, identity))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 10 R->L }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(Y, Z), W))), multiply(W, multiply(W, W)))))), multiply(identity, identity))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 6 }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z))), multiply(identity, identity))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 10 }
% 0.21/0.52 multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, Y), multiply(multiply(identity, identity), Z))), multiply(identity, identity))), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 5 }
% 0.21/0.52 multiply(multiply(X, Y), multiply(multiply(identity, identity), Z))
% 0.21/0.52
% 0.21/0.52 Lemma 12: multiply(multiply(X, multiply(identity, identity)), multiply(Y, multiply(identity, identity))) = multiply(multiply(X, Y), multiply(identity, identity)).
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(multiply(X, multiply(identity, identity)), multiply(Y, multiply(identity, identity)))
% 0.21/0.52 = { by lemma 11 }
% 0.21/0.52 multiply(multiply(X, Y), multiply(multiply(identity, identity), multiply(identity, identity)))
% 0.21/0.52 = { by lemma 3 }
% 0.21/0.53 multiply(multiply(X, Y), multiply(identity, identity))
% 0.21/0.53
% 0.21/0.53 Goal 1 (prove_order3): multiply(a, identity) = a.
% 0.21/0.53 Proof:
% 0.21/0.53 multiply(a, identity)
% 0.21/0.53 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(multiply(a, identity), multiply(multiply(a, identity), multiply(a, identity))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by lemma 4 R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(a, identity), multiply(multiply(a, identity), multiply(a, identity))), multiply(identity, identity)))), multiply(identity, identity))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by lemma 5 R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(a, multiply(multiply(a, multiply(multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(a, identity), multiply(multiply(a, identity), multiply(a, identity))), multiply(identity, identity)))), multiply(identity, identity))), multiply(identity, identity))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by lemma 4 }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(a, multiply(multiply(multiply(a, identity), multiply(multiply(a, identity), multiply(a, identity))), multiply(identity, identity))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by lemma 12 R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(a, multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by lemma 12 R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(a, multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity))))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(a, multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(a, identity))), multiply(identity, multiply(identity, identity)))), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by axiom 1 (single_axiom2) R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(a, identity))), multiply(identity, multiply(identity, multiply(identity, identity))))), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by axiom 1 (single_axiom2) R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(a, identity))), multiply(identity, multiply(multiply(identity, identity), multiply(identity, identity))))), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by axiom 1 (single_axiom2) R->L }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(a, identity))), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity))))), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(a, identity))), multiply(multiply(identity, identity), multiply(identity, identity)))), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(a, identity))), multiply(identity, identity))), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.53 = { by lemma 8 }
% 0.21/0.53 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(a, identity)), multiply(identity, identity)))), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by lemma 3 }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(a, identity)), multiply(identity, identity)))), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by lemma 8 }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(a, identity), multiply(identity, identity))))), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(multiply(a, identity), multiply(identity, identity)), multiply(multiply(a, identity), multiply(identity, identity)))))), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by lemma 6 }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by lemma 8 }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity))))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by lemma 3 }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity)))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by lemma 3 }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(multiply(identity, identity), multiply(identity, identity))), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by lemma 3 }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by lemma 3 }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, a), multiply(multiply(identity, identity), multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by lemma 11 R->L }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, multiply(identity, identity)), multiply(a, multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by axiom 1 (single_axiom2) }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, identity), multiply(a, multiply(identity, identity)))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by axiom 1 (single_axiom2) }
% 0.21/0.54 multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(a, multiply(multiply(a, identity), multiply(a, identity))))), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(multiply(a, identity), multiply(a, identity)), multiply(multiply(a, identity), multiply(a, identity))))))
% 0.21/0.54 = { by axiom 2 (single_axiom) }
% 0.21/0.54 a
% 0.21/0.54 % SZS output end Proof
% 0.21/0.54
% 0.21/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------