TSTP Solution File: GRP654-12 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP654-12 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:19:27 EDT 2023
% Result : Unsatisfiable 3.69s 0.89s
% Output : Proof 4.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP654-12 : TPTP v8.1.2. Released v8.1.0.
% 0.14/0.13 % 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 : n011.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 02:30:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.69/0.89 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.69/0.89
% 3.69/0.89 % SZS status Unsatisfiable
% 3.69/0.89
% 4.21/0.93 % SZS output start Proof
% 4.21/0.93 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 4.21/0.93 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 4.21/0.93 Axiom 3 (f04): rd(mult(X, Y), Y) = X.
% 4.21/0.93 Axiom 4 (f02): ld(X, mult(X, Y)) = Y.
% 4.21/0.93 Axiom 5 (f05): mult(X, mult(Y, mult(X, Z))) = mult(mult(mult(X, Y), X), Z).
% 4.21/0.93
% 4.21/0.93 Lemma 6: mult(X, mult(ld(X, Y), mult(X, Z))) = mult(mult(Y, X), Z).
% 4.21/0.93 Proof:
% 4.21/0.93 mult(X, mult(ld(X, Y), mult(X, Z)))
% 4.21/0.93 = { by axiom 5 (f05) }
% 4.21/0.93 mult(mult(mult(X, ld(X, Y)), X), Z)
% 4.21/0.93 = { by axiom 1 (f01) }
% 4.21/0.93 mult(mult(Y, X), Z)
% 4.21/0.93
% 4.21/0.93 Lemma 7: ld(X, mult(mult(Y, X), Z)) = mult(ld(X, Y), mult(X, Z)).
% 4.21/0.93 Proof:
% 4.21/0.93 ld(X, mult(mult(Y, X), Z))
% 4.21/0.93 = { by lemma 6 R->L }
% 4.21/0.93 ld(X, mult(X, mult(ld(X, Y), mult(X, Z))))
% 4.21/0.93 = { by axiom 4 (f02) }
% 4.21/0.93 mult(ld(X, Y), mult(X, Z))
% 4.21/0.93
% 4.21/0.93 Lemma 8: rd(mult(X, mult(Y, mult(X, Z))), Z) = mult(mult(X, Y), X).
% 4.21/0.93 Proof:
% 4.21/0.93 rd(mult(X, mult(Y, mult(X, Z))), Z)
% 4.21/0.93 = { by axiom 5 (f05) }
% 4.21/0.93 rd(mult(mult(mult(X, Y), X), Z), Z)
% 4.21/0.93 = { by axiom 3 (f04) }
% 4.21/0.93 mult(mult(X, Y), X)
% 4.21/0.93
% 4.21/0.93 Lemma 9: rd(rd(mult(X, Y), Z), X) = mult(X, rd(Y, mult(X, Z))).
% 4.21/0.93 Proof:
% 4.21/0.93 rd(rd(mult(X, Y), Z), X)
% 4.21/0.93 = { by axiom 2 (f03) R->L }
% 4.21/0.93 rd(rd(mult(X, mult(rd(Y, mult(X, Z)), mult(X, Z))), Z), X)
% 4.21/0.93 = { by lemma 8 }
% 4.21/0.93 rd(mult(mult(X, rd(Y, mult(X, Z))), X), X)
% 4.21/0.93 = { by axiom 3 (f04) }
% 4.21/0.93 mult(X, rd(Y, mult(X, Z)))
% 4.21/0.93
% 4.21/0.93 Lemma 10: mult(X, rd(Y, mult(X, Y))) = rd(X, X).
% 4.21/0.93 Proof:
% 4.21/0.93 mult(X, rd(Y, mult(X, Y)))
% 4.21/0.93 = { by lemma 9 R->L }
% 4.21/0.93 rd(rd(mult(X, Y), Y), X)
% 4.21/0.93 = { by axiom 3 (f04) }
% 4.21/0.93 rd(X, X)
% 4.21/0.93
% 4.21/0.93 Lemma 11: rd(Z, mult(Y, Z)) = rd(X, mult(Y, X)).
% 4.21/0.93 Proof:
% 4.21/0.93 rd(Z, mult(Y, Z))
% 4.21/0.93 = { by axiom 4 (f02) R->L }
% 4.21/0.93 ld(Y, mult(Y, rd(Z, mult(Y, Z))))
% 4.21/0.93 = { by lemma 10 }
% 4.21/0.93 ld(Y, rd(Y, Y))
% 4.21/0.93 = { by lemma 10 R->L }
% 4.21/0.93 ld(Y, mult(Y, rd(X, mult(Y, X))))
% 4.21/0.93 = { by axiom 4 (f02) }
% 4.21/0.93 rd(X, mult(Y, X))
% 4.21/0.93
% 4.21/0.93 Lemma 12: mult(mult(X, rd(X, Y)), Y) = mult(rd(X, Y), mult(Y, X)).
% 4.21/0.93 Proof:
% 4.21/0.93 mult(mult(X, rd(X, Y)), Y)
% 4.21/0.93 = { by axiom 2 (f03) R->L }
% 4.21/0.93 mult(mult(mult(rd(X, Y), Y), rd(X, Y)), Y)
% 4.21/0.93 = { by axiom 5 (f05) R->L }
% 4.21/0.93 mult(rd(X, Y), mult(Y, mult(rd(X, Y), Y)))
% 4.21/0.93 = { by axiom 2 (f03) }
% 4.21/0.93 mult(rd(X, Y), mult(Y, X))
% 4.21/0.93
% 4.21/0.93 Lemma 13: mult(ld(X, X), mult(X, X)) = mult(rd(X, X), mult(X, X)).
% 4.21/0.93 Proof:
% 4.21/0.94 mult(ld(X, X), mult(X, X))
% 4.21/0.94 = { by lemma 7 R->L }
% 4.21/0.94 ld(X, mult(mult(X, X), X))
% 4.21/0.94 = { by axiom 2 (f03) R->L }
% 4.21/0.94 mult(rd(ld(X, mult(mult(X, X), X)), mult(mult(X, X), X)), mult(mult(X, X), X))
% 4.21/0.94 = { by axiom 1 (f01) R->L }
% 4.21/0.94 mult(rd(ld(X, mult(mult(X, X), X)), mult(X, ld(X, mult(mult(X, X), X)))), mult(mult(X, X), X))
% 4.21/0.94 = { by lemma 11 R->L }
% 4.21/0.94 mult(rd(X, mult(X, X)), mult(mult(X, X), X))
% 4.21/0.94 = { by lemma 12 R->L }
% 4.21/0.94 mult(mult(X, rd(X, mult(X, X))), mult(X, X))
% 4.21/0.94 = { by lemma 10 }
% 4.21/0.94 mult(rd(X, X), mult(X, X))
% 4.21/0.94
% 4.21/0.94 Lemma 14: ld(X, X) = rd(X, X).
% 4.21/0.94 Proof:
% 4.21/0.94 ld(X, X)
% 4.21/0.94 = { by axiom 3 (f04) R->L }
% 4.21/0.94 rd(mult(ld(X, X), mult(X, X)), mult(X, X))
% 4.21/0.94 = { by lemma 13 }
% 4.21/0.94 rd(mult(rd(X, X), mult(X, X)), mult(X, X))
% 4.21/0.94 = { by axiom 3 (f04) }
% 4.21/0.94 rd(X, X)
% 4.21/0.94
% 4.21/0.94 Lemma 15: ld(rd(X, Y), X) = Y.
% 4.21/0.94 Proof:
% 4.21/0.94 ld(rd(X, Y), X)
% 4.21/0.94 = { by axiom 2 (f03) R->L }
% 4.21/0.94 ld(rd(X, Y), mult(rd(X, Y), Y))
% 4.21/0.94 = { by axiom 4 (f02) }
% 4.21/0.94 Y
% 4.21/0.94
% 4.21/0.94 Lemma 16: ld(rd(X, Y), Z) = mult(rd(Y, X), Z).
% 4.21/0.94 Proof:
% 4.21/0.94 ld(rd(X, Y), Z)
% 4.21/0.94 = { by axiom 2 (f03) R->L }
% 4.21/0.94 ld(rd(X, mult(rd(Y, X), X)), Z)
% 4.21/0.94 = { by lemma 11 R->L }
% 4.21/0.94 ld(rd(Z, mult(rd(Y, X), Z)), Z)
% 4.21/0.94 = { by lemma 15 }
% 4.21/0.94 mult(rd(Y, X), Z)
% 4.21/0.94
% 4.21/0.94 Lemma 17: mult(X, rd(X, X)) = X.
% 4.21/0.94 Proof:
% 4.21/0.94 mult(X, rd(X, X))
% 4.21/0.94 = { by lemma 14 R->L }
% 4.21/0.94 mult(X, ld(X, X))
% 4.21/0.94 = { by axiom 1 (f01) }
% 4.21/0.94 X
% 4.21/0.94
% 4.21/0.94 Lemma 18: mult(mult(X, Y), ld(Y, Z)) = mult(Y, mult(ld(Y, X), Z)).
% 4.21/0.94 Proof:
% 4.21/0.94 mult(mult(X, Y), ld(Y, Z))
% 4.21/0.94 = { by lemma 6 R->L }
% 4.21/0.94 mult(Y, mult(ld(Y, X), mult(Y, ld(Y, Z))))
% 4.21/0.94 = { by axiom 1 (f01) }
% 4.21/0.94 mult(Y, mult(ld(Y, X), Z))
% 4.21/0.94
% 4.21/0.94 Lemma 19: mult(rd(X, X), mult(X, X)) = mult(X, X).
% 4.21/0.94 Proof:
% 4.21/0.94 mult(rd(X, X), mult(X, X))
% 4.21/0.94 = { by lemma 12 R->L }
% 4.21/0.94 mult(mult(X, rd(X, X)), X)
% 4.21/0.94 = { by lemma 8 R->L }
% 4.21/0.94 rd(mult(X, mult(rd(X, X), mult(X, X))), X)
% 4.21/0.94 = { by lemma 13 R->L }
% 4.21/0.94 rd(mult(X, mult(ld(X, X), mult(X, X))), X)
% 4.21/0.94 = { by lemma 8 }
% 4.21/0.94 mult(mult(X, ld(X, X)), X)
% 4.21/0.94 = { by axiom 1 (f01) }
% 4.21/0.94 mult(X, X)
% 4.21/0.94
% 4.21/0.94 Lemma 20: mult(rd(X, X), rd(X, X)) = rd(X, X).
% 4.21/0.94 Proof:
% 4.21/0.94 mult(rd(X, X), rd(X, X))
% 4.21/0.94 = { by axiom 4 (f02) R->L }
% 4.21/0.94 ld(X, mult(X, mult(rd(X, X), rd(X, X))))
% 4.21/0.94 = { by axiom 2 (f03) R->L }
% 4.21/0.94 ld(X, mult(X, mult(rd(X, X), rd(X, mult(rd(X, X), X)))))
% 4.21/0.94 = { by lemma 10 }
% 4.21/0.94 ld(X, mult(X, rd(rd(X, X), rd(X, X))))
% 4.21/0.94 = { by lemma 17 R->L }
% 4.21/0.94 ld(X, mult(mult(X, rd(X, X)), rd(rd(X, X), rd(X, X))))
% 4.21/0.94 = { by lemma 14 R->L }
% 4.21/0.94 ld(X, mult(mult(X, rd(X, X)), ld(rd(X, X), rd(X, X))))
% 4.21/0.94 = { by lemma 18 }
% 4.21/0.94 ld(X, mult(rd(X, X), mult(ld(rd(X, X), X), rd(X, X))))
% 4.21/0.94 = { by lemma 15 }
% 4.21/0.94 ld(X, mult(rd(X, X), mult(X, rd(X, X))))
% 4.21/0.94 = { by lemma 17 }
% 4.21/0.94 ld(X, mult(rd(X, X), X))
% 4.21/0.94 = { by axiom 2 (f03) }
% 4.21/0.94 ld(X, X)
% 4.21/0.94 = { by lemma 14 }
% 4.21/0.94 rd(X, X)
% 4.21/0.94
% 4.21/0.94 Lemma 21: rd(mult(rd(X, Y), mult(Z, X)), Y) = mult(mult(rd(X, Y), Z), rd(X, Y)).
% 4.21/0.94 Proof:
% 4.21/0.94 rd(mult(rd(X, Y), mult(Z, X)), Y)
% 4.21/0.94 = { by axiom 2 (f03) R->L }
% 4.21/0.94 rd(mult(rd(X, Y), mult(Z, mult(rd(X, Y), Y))), Y)
% 4.21/0.94 = { by lemma 8 }
% 4.21/0.94 mult(mult(rd(X, Y), Z), rd(X, Y))
% 4.21/0.94
% 4.21/0.94 Lemma 22: mult(rd(X, Y), mult(rd(Y, X), Z)) = Z.
% 4.21/0.94 Proof:
% 4.21/0.94 mult(rd(X, Y), mult(rd(Y, X), Z))
% 4.21/0.94 = { by axiom 4 (f02) R->L }
% 4.21/0.94 mult(rd(X, Y), mult(ld(rd(X, Y), mult(rd(X, Y), rd(Y, X))), Z))
% 4.21/0.94 = { by lemma 18 R->L }
% 4.21/0.94 mult(mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y)), ld(rd(X, Y), Z))
% 4.21/0.94 = { by lemma 21 R->L }
% 4.21/0.94 mult(rd(mult(rd(X, Y), mult(rd(Y, X), X)), Y), ld(rd(X, Y), Z))
% 4.21/0.94 = { by axiom 2 (f03) }
% 4.21/0.94 mult(rd(mult(rd(X, Y), Y), Y), ld(rd(X, Y), Z))
% 4.21/0.94 = { by axiom 3 (f04) }
% 4.21/0.94 mult(rd(X, Y), ld(rd(X, Y), Z))
% 4.21/0.94 = { by axiom 1 (f01) }
% 4.21/0.94 Z
% 4.21/0.94
% 4.21/0.94 Lemma 23: mult(rd(Z, W), rd(mult(rd(W, Z), X), mult(rd(Z, W), Y))) = rd(rd(X, Y), rd(Z, W)).
% 4.21/0.94 Proof:
% 4.21/0.94 mult(rd(Z, W), rd(mult(rd(W, Z), X), mult(rd(Z, W), Y)))
% 4.21/0.94 = { by lemma 9 R->L }
% 4.21/0.94 rd(rd(mult(rd(Z, W), mult(rd(W, Z), X)), Y), rd(Z, W))
% 4.21/0.94 = { by lemma 22 }
% 4.21/0.94 rd(rd(X, Y), rd(Z, W))
% 4.21/0.94
% 4.21/0.94 Lemma 24: mult(mult(rd(X, X), Y), Y) = mult(rd(X, X), mult(Y, Y)).
% 4.21/0.94 Proof:
% 4.21/0.94 mult(mult(rd(X, X), Y), Y)
% 4.21/0.94 = { by lemma 22 R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(rd(X, X), Y)))
% 4.21/0.94 = { by lemma 17 R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(rd(X, X), Y), mult(rd(X, X), Y)))))
% 4.21/0.94 = { by lemma 16 R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(ld(rd(X, X), Y), rd(mult(rd(X, X), Y), mult(rd(X, X), Y)))))
% 4.21/0.94 = { by lemma 22 R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(ld(rd(X, X), Y), mult(rd(X, X), mult(rd(X, X), rd(mult(rd(X, X), Y), mult(rd(X, X), Y)))))))
% 4.21/0.94 = { by lemma 6 }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(mult(Y, rd(X, X)), mult(rd(X, X), rd(mult(rd(X, X), Y), mult(rd(X, X), Y)))))
% 4.21/0.94 = { by lemma 23 }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(mult(Y, rd(X, X)), rd(rd(Y, Y), rd(X, X))))
% 4.21/0.94 = { by axiom 3 (f04) R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(mult(Y, rd(X, X)), rd(rd(mult(rd(Y, Y), mult(Y, Y)), mult(Y, Y)), rd(X, X))))
% 4.21/0.94 = { by lemma 19 }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(mult(Y, rd(X, X)), rd(rd(mult(Y, Y), mult(Y, Y)), rd(X, X))))
% 4.21/0.94 = { by lemma 22 R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(mult(mult(rd(X, X), mult(rd(X, X), Y)), rd(X, X)), rd(rd(mult(Y, Y), mult(Y, Y)), rd(X, X))))
% 4.21/0.94 = { by axiom 5 (f05) R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), mult(rd(X, X), rd(rd(mult(Y, Y), mult(Y, Y)), rd(X, X))))))
% 4.21/0.94 = { by axiom 3 (f04) R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(mult(rd(X, X), rd(rd(mult(Y, Y), mult(Y, Y)), rd(X, X))), X), X))))
% 4.21/0.94 = { by lemma 16 R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(ld(rd(X, X), rd(rd(mult(Y, Y), mult(Y, Y)), rd(X, X))), X), X))))
% 4.21/0.94 = { by lemma 22 R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(rd(X, X), mult(rd(X, X), mult(ld(rd(X, X), rd(rd(mult(Y, Y), mult(Y, Y)), rd(X, X))), X))), X))))
% 4.21/0.94 = { by axiom 2 (f03) R->L }
% 4.21/0.94 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(rd(X, X), mult(rd(X, X), mult(ld(rd(X, X), rd(rd(mult(Y, Y), mult(Y, Y)), rd(X, X))), mult(rd(X, X), X)))), X))))
% 4.21/0.95 = { by lemma 6 }
% 4.21/0.95 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(rd(X, X), mult(mult(rd(rd(mult(Y, Y), mult(Y, Y)), rd(X, X)), rd(X, X)), X)), X))))
% 4.21/0.95 = { by lemma 21 }
% 4.21/0.95 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), mult(mult(rd(X, X), mult(rd(rd(mult(Y, Y), mult(Y, Y)), rd(X, X)), rd(X, X))), rd(X, X)))))
% 4.21/0.95 = { by axiom 2 (f03) }
% 4.21/0.95 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), mult(mult(rd(X, X), rd(mult(Y, Y), mult(Y, Y))), rd(X, X)))))
% 4.21/0.95 = { by lemma 8 R->L }
% 4.21/0.95 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(rd(X, X), mult(rd(mult(Y, Y), mult(Y, Y)), mult(rd(X, X), ld(rd(X, X), mult(Y, Y))))), ld(rd(X, X), mult(Y, Y))))))
% 4.21/0.95 = { by axiom 1 (f01) }
% 4.21/0.95 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(rd(X, X), mult(rd(mult(Y, Y), mult(Y, Y)), mult(Y, Y))), ld(rd(X, X), mult(Y, Y))))))
% 4.21/0.95 = { by axiom 2 (f03) }
% 4.21/0.95 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(rd(X, X), mult(Y, Y)), ld(rd(X, X), mult(Y, Y))))))
% 4.21/0.95 = { by lemma 16 }
% 4.21/0.95 mult(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(rd(X, X), Y), rd(mult(rd(X, X), mult(Y, Y)), mult(rd(X, X), mult(Y, Y))))))
% 4.21/0.95 = { by axiom 5 (f05) }
% 4.21/0.95 mult(mult(mult(mult(rd(X, X), Y), rd(X, X)), mult(rd(X, X), Y)), rd(mult(rd(X, X), mult(Y, Y)), mult(rd(X, X), mult(Y, Y))))
% 4.21/0.95 = { by axiom 5 (f05) R->L }
% 4.21/0.95 mult(mult(rd(X, X), mult(Y, mult(rd(X, X), mult(rd(X, X), Y)))), rd(mult(rd(X, X), mult(Y, Y)), mult(rd(X, X), mult(Y, Y))))
% 4.21/0.95 = { by lemma 22 }
% 4.21/0.95 mult(mult(rd(X, X), mult(Y, Y)), rd(mult(rd(X, X), mult(Y, Y)), mult(rd(X, X), mult(Y, Y))))
% 4.21/0.95 = { by lemma 17 }
% 4.21/0.95 mult(rd(X, X), mult(Y, Y))
% 4.21/0.95
% 4.21/0.95 Lemma 25: mult(mult(rd(X, Y), Z), mult(rd(Y, X), W)) = mult(rd(X, Y), mult(mult(Z, rd(Y, X)), W)).
% 4.21/0.95 Proof:
% 4.21/0.95 mult(mult(rd(X, Y), Z), mult(rd(Y, X), W))
% 4.21/0.95 = { by lemma 16 R->L }
% 4.21/0.95 mult(ld(rd(Y, X), Z), mult(rd(Y, X), W))
% 4.21/0.95 = { by lemma 22 R->L }
% 4.21/0.95 mult(rd(X, Y), mult(rd(Y, X), mult(ld(rd(Y, X), Z), mult(rd(Y, X), W))))
% 4.21/0.95 = { by lemma 6 }
% 4.21/0.95 mult(rd(X, Y), mult(mult(Z, rd(Y, X)), W))
% 4.21/0.95
% 4.21/0.95 Lemma 26: mult(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), Y) = Y.
% 4.21/0.95 Proof:
% 4.21/0.95 mult(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), Y)
% 4.21/0.95 = { by axiom 4 (f02) R->L }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(mult(rd(X, X), Y), mult(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), Y)))
% 4.21/0.95 = { by lemma 16 R->L }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(mult(rd(X, X), Y), ld(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), Y)))
% 4.21/0.95 = { by lemma 17 R->L }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(mult(mult(rd(X, X), Y), rd(mult(rd(X, X), Y), mult(rd(X, X), Y))), ld(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), Y)))
% 4.21/0.95 = { by lemma 18 }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), mult(ld(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), mult(rd(X, X), Y)), Y)))
% 4.21/0.95 = { by lemma 15 }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), mult(mult(rd(X, X), Y), Y)))
% 4.21/0.95 = { by lemma 24 }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), mult(rd(X, X), mult(Y, Y))))
% 4.21/0.95 = { by lemma 22 R->L }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(rd(X, X), mult(rd(X, X), mult(rd(mult(rd(X, X), Y), mult(rd(X, X), Y)), mult(rd(X, X), mult(Y, Y))))))
% 4.21/0.95 = { by axiom 5 (f05) }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(rd(X, X), mult(mult(mult(rd(X, X), rd(mult(rd(X, X), Y), mult(rd(X, X), Y))), rd(X, X)), mult(Y, Y))))
% 4.21/0.95 = { by lemma 25 R->L }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(mult(rd(X, X), mult(rd(X, X), rd(mult(rd(X, X), Y), mult(rd(X, X), Y)))), mult(rd(X, X), mult(Y, Y))))
% 4.21/0.95 = { by lemma 16 R->L }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(ld(rd(X, X), mult(rd(X, X), rd(mult(rd(X, X), Y), mult(rd(X, X), Y)))), mult(rd(X, X), mult(Y, Y))))
% 4.21/0.95 = { by lemma 23 }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(ld(rd(X, X), rd(rd(Y, Y), rd(X, X))), mult(rd(X, X), mult(Y, Y))))
% 4.21/0.95 = { by lemma 7 R->L }
% 4.21/0.95 ld(mult(rd(X, X), Y), ld(rd(X, X), mult(mult(rd(rd(Y, Y), rd(X, X)), rd(X, X)), mult(Y, Y))))
% 4.21/0.95 = { by axiom 2 (f03) }
% 4.21/0.95 ld(mult(rd(X, X), Y), ld(rd(X, X), mult(rd(Y, Y), mult(Y, Y))))
% 4.21/0.95 = { by lemma 16 }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(rd(X, X), mult(rd(Y, Y), mult(Y, Y))))
% 4.21/0.95 = { by lemma 19 }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(rd(X, X), mult(Y, Y)))
% 4.21/0.95 = { by lemma 24 R->L }
% 4.21/0.95 ld(mult(rd(X, X), Y), mult(mult(rd(X, X), Y), Y))
% 4.21/0.95 = { by axiom 4 (f02) }
% 4.21/0.95 Y
% 4.21/0.95
% 4.21/0.95 Goal 1 (goal): mult(rd(x1, x1), x0) = x0.
% 4.21/0.95 Proof:
% 4.21/0.95 mult(rd(x1, x1), x0)
% 4.21/0.95 = { by lemma 22 R->L }
% 4.21/0.95 mult(rd(x1, x1), mult(rd(x1, x1), mult(rd(x1, x1), x0)))
% 4.21/0.95 = { by axiom 4 (f02) R->L }
% 4.21/0.95 mult(rd(x1, x1), mult(ld(rd(x0, x0), mult(rd(x0, x0), rd(x1, x1))), mult(rd(x1, x1), x0)))
% 4.21/0.95 = { by axiom 3 (f04) R->L }
% 4.21/0.95 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(mult(rd(x0, x0), rd(x1, x1)), ld(mult(rd(x0, x0), rd(x1, x1)), mult(rd(x0, x0), rd(x1, x1)))), ld(mult(rd(x0, x0), rd(x1, x1)), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.95 = { by axiom 1 (f01) }
% 4.21/0.95 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), ld(mult(rd(x0, x0), rd(x1, x1)), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.95 = { by lemma 14 }
% 4.21/0.95 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(rd(x0, x0), rd(x1, x1)), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.95 = { by lemma 20 R->L }
% 4.21/0.95 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(rd(x0, x0), mult(rd(x1, x1), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.95 = { by lemma 16 R->L }
% 4.21/0.95 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(rd(x0, x0), ld(rd(x1, x1), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by axiom 2 (f03) R->L }
% 4.21/0.96 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(mult(rd(rd(x0, x0), rd(x1, x1)), rd(x1, x1)), ld(rd(x1, x1), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by lemma 18 }
% 4.21/0.96 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(rd(x1, x1), mult(ld(rd(x1, x1), rd(rd(x0, x0), rd(x1, x1))), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by lemma 23 R->L }
% 4.21/0.96 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(rd(x1, x1), mult(ld(rd(x1, x1), mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)))), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by lemma 16 }
% 4.21/0.96 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(rd(x1, x1), mult(mult(rd(x1, x1), mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)))), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by lemma 22 }
% 4.21/0.96 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(rd(x1, x1), mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by axiom 3 (f04) R->L }
% 4.21/0.96 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(rd(x1, x1), mult(rd(mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), x0), x0), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by lemma 26 }
% 4.21/0.96 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(mult(rd(x1, x1), mult(rd(x0, x0), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1))))), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by axiom 3 (f04) }
% 4.21/0.96 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(mult(rd(x0, x0), rd(x1, x1)), rd(x1, x1))), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by axiom 3 (f04) }
% 4.21/0.96 mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(x0, x0)), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by lemma 16 }
% 4.21/0.96 mult(rd(x1, x1), mult(mult(rd(x0, x0), rd(x0, x0)), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by lemma 20 }
% 4.21/0.96 mult(rd(x1, x1), mult(rd(x0, x0), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by axiom 2 (f03) R->L }
% 4.21/0.96 mult(rd(x1, x1), mult(mult(rd(rd(x0, x0), rd(x1, x1)), rd(x1, x1)), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by lemma 25 R->L }
% 4.21/0.96 mult(mult(rd(x1, x1), rd(rd(x0, x0), rd(x1, x1))), mult(rd(x1, x1), mult(rd(x1, x1), x0)))
% 4.21/0.96 = { by lemma 22 }
% 4.21/0.96 mult(mult(rd(x1, x1), rd(rd(x0, x0), rd(x1, x1))), x0)
% 4.21/0.96 = { by lemma 23 R->L }
% 4.56/0.96 mult(mult(rd(x1, x1), mult(rd(x1, x1), rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)))), x0)
% 4.56/0.96 = { by lemma 22 }
% 4.56/0.96 mult(rd(mult(rd(x1, x1), x0), mult(rd(x1, x1), x0)), x0)
% 4.56/0.96 = { by lemma 26 }
% 4.56/0.96 x0
% 4.56/0.96 % SZS output end Proof
% 4.56/0.96
% 4.56/0.96 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------