TSTP Solution File: GRP682-11 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP682-11 : 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 : n001.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 01:19:41 EDT 2023
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP682-11 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 01:48:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.50
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 Axiom 1 (f01): ld(X, mult(X, X)) = X.
% 0.19/0.52 Axiom 2 (f02): rd(mult(X, X), X) = X.
% 0.19/0.52 Axiom 3 (f03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 0.19/0.52 Axiom 4 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 0.19/0.52 Axiom 5 (f07): ld(X, mult(X, ld(Y, Y))) = rd(mult(rd(X, X), Y), Y).
% 0.19/0.52 Axiom 6 (f05): ld(ld(X, Y), mult(ld(X, Y), mult(Z, W))) = mult(ld(X, mult(X, Z)), W).
% 0.19/0.52 Axiom 7 (f06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
% 0.19/0.52
% 0.19/0.52 Lemma 8: rd(X, X) = ld(X, X).
% 0.19/0.52 Proof:
% 0.19/0.52 rd(X, X)
% 0.19/0.52 = { by axiom 2 (f02) R->L }
% 0.19/0.52 rd(rd(mult(X, X), X), X)
% 0.19/0.52 = { by axiom 4 (f04) R->L }
% 0.19/0.52 rd(mult(rd(X, X), X), X)
% 0.19/0.52 = { by axiom 5 (f07) R->L }
% 0.19/0.52 ld(X, mult(X, ld(X, X)))
% 0.19/0.52 = { by axiom 3 (f03) }
% 0.19/0.52 ld(X, ld(X, mult(X, X)))
% 0.19/0.52 = { by axiom 1 (f01) }
% 0.19/0.52 ld(X, X)
% 0.19/0.52
% 0.19/0.52 Lemma 9: mult(ld(X, X), X) = X.
% 0.19/0.52 Proof:
% 0.19/0.52 mult(ld(X, X), X)
% 0.19/0.52 = { by lemma 8 R->L }
% 0.19/0.52 mult(rd(X, X), X)
% 0.19/0.52 = { by axiom 4 (f04) }
% 0.19/0.52 rd(mult(X, X), X)
% 0.19/0.52 = { by axiom 2 (f02) }
% 0.19/0.52 X
% 0.19/0.52
% 0.19/0.52 Lemma 10: mult(X, rd(mult(Y, Z), Z)) = rd(mult(mult(X, Y), Z), Z).
% 0.19/0.52 Proof:
% 0.19/0.52 mult(X, rd(mult(Y, Z), Z))
% 0.19/0.52 = { by axiom 7 (f06) R->L }
% 0.19/0.52 rd(mult(mult(X, Y), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 0.19/0.52 = { by axiom 2 (f02) }
% 0.19/0.52 rd(mult(mult(X, Y), Z), rd(mult(Z, Z), Z))
% 0.19/0.52 = { by axiom 2 (f02) }
% 0.19/0.52 rd(mult(mult(X, Y), Z), Z)
% 0.19/0.52
% 0.19/0.52 Lemma 11: rd(mult(mult(X, Y), ld(Z, Z)), ld(Z, Z)) = rd(mult(mult(X, Y), Z), Z).
% 0.19/0.52 Proof:
% 0.19/0.52 rd(mult(mult(X, Y), ld(Z, Z)), ld(Z, Z))
% 0.19/0.52 = { by lemma 8 R->L }
% 0.19/0.52 rd(mult(mult(X, Y), ld(Z, Z)), rd(Z, Z))
% 0.19/0.52 = { by lemma 8 R->L }
% 0.19/0.52 rd(mult(mult(X, Y), rd(Z, Z)), rd(Z, Z))
% 0.19/0.52 = { by axiom 7 (f06) }
% 0.19/0.52 mult(X, rd(mult(Y, Z), Z))
% 0.19/0.52 = { by lemma 10 }
% 0.19/0.52 rd(mult(mult(X, Y), Z), Z)
% 0.19/0.52
% 0.19/0.52 Lemma 12: rd(mult(X, ld(Y, Y)), ld(Y, Y)) = rd(mult(X, Y), Y).
% 0.19/0.52 Proof:
% 0.19/0.52 rd(mult(X, ld(Y, Y)), ld(Y, Y))
% 0.19/0.52 = { by lemma 9 R->L }
% 0.19/0.52 rd(mult(mult(ld(X, X), X), ld(Y, Y)), ld(Y, Y))
% 0.19/0.52 = { by lemma 11 }
% 0.19/0.52 rd(mult(mult(ld(X, X), X), Y), Y)
% 0.19/0.52 = { by lemma 9 }
% 0.19/0.52 rd(mult(X, Y), Y)
% 0.19/0.52
% 0.19/0.52 Lemma 13: mult(ld(X, mult(X, Y)), Z) = ld(X, mult(X, mult(Y, Z))).
% 0.19/0.52 Proof:
% 0.19/0.52 mult(ld(X, mult(X, Y)), Z)
% 0.19/0.52 = { by axiom 6 (f05) R->L }
% 0.19/0.52 ld(ld(X, mult(X, X)), mult(ld(X, mult(X, X)), mult(Y, Z)))
% 0.19/0.52 = { by axiom 1 (f01) }
% 0.19/0.52 ld(X, mult(ld(X, mult(X, X)), mult(Y, Z)))
% 0.19/0.52 = { by axiom 1 (f01) }
% 0.19/0.52 ld(X, mult(X, mult(Y, Z)))
% 0.19/0.52
% 0.19/0.52 Lemma 14: ld(X, mult(X, mult(X, Y))) = mult(X, Y).
% 0.19/0.52 Proof:
% 0.19/0.52 ld(X, mult(X, mult(X, Y)))
% 0.19/0.52 = { by lemma 13 R->L }
% 0.19/0.52 mult(ld(X, mult(X, X)), Y)
% 0.19/0.52 = { by axiom 1 (f01) }
% 0.19/0.52 mult(X, Y)
% 0.19/0.52
% 0.19/0.52 Lemma 15: rd(mult(mult(X, Y), Y), Y) = mult(X, Y).
% 0.19/0.52 Proof:
% 0.19/0.52 rd(mult(mult(X, Y), Y), Y)
% 0.19/0.52 = { by lemma 10 R->L }
% 0.19/0.52 mult(X, rd(mult(Y, Y), Y))
% 0.19/0.52 = { by axiom 2 (f02) }
% 0.19/0.52 mult(X, Y)
% 0.19/0.52
% 0.19/0.52 Lemma 16: mult(ld(X, X), Y) = ld(X, mult(X, Y)).
% 0.19/0.52 Proof:
% 0.19/0.52 mult(ld(X, X), Y)
% 0.19/0.52 = { by lemma 8 R->L }
% 0.19/0.52 mult(rd(X, X), Y)
% 0.19/0.52 = { by lemma 15 R->L }
% 0.19/0.52 rd(mult(mult(rd(X, X), Y), Y), Y)
% 0.19/0.52 = { by axiom 4 (f04) R->L }
% 0.19/0.52 mult(rd(mult(rd(X, X), Y), Y), Y)
% 0.19/0.52 = { by axiom 5 (f07) R->L }
% 0.19/0.52 mult(ld(X, mult(X, ld(Y, Y))), Y)
% 0.19/0.52 = { by lemma 13 }
% 0.19/0.52 ld(X, mult(X, mult(ld(Y, Y), Y)))
% 0.19/0.52 = { by lemma 9 }
% 0.19/0.52 ld(X, mult(X, Y))
% 0.19/0.52
% 0.19/0.52 Lemma 17: ld(X, rd(mult(mult(X, X), Y), Y)) = rd(mult(X, Y), Y).
% 0.19/0.52 Proof:
% 0.19/0.52 ld(X, rd(mult(mult(X, X), Y), Y))
% 0.19/0.52 = { by lemma 10 R->L }
% 0.19/0.52 ld(X, mult(X, rd(mult(X, Y), Y)))
% 0.19/0.52 = { by lemma 16 R->L }
% 0.19/0.52 mult(ld(X, X), rd(mult(X, Y), Y))
% 0.19/0.52 = { by lemma 10 }
% 0.19/0.52 rd(mult(mult(ld(X, X), X), Y), Y)
% 0.19/0.52 = { by lemma 16 }
% 0.19/0.52 rd(mult(ld(X, mult(X, X)), Y), Y)
% 0.19/0.52 = { by lemma 13 }
% 0.19/0.52 rd(ld(X, mult(X, mult(X, Y))), Y)
% 0.19/0.52 = { by lemma 14 }
% 0.19/0.52 rd(mult(X, Y), Y)
% 0.19/0.52
% 0.19/0.52 Lemma 18: ld(X, mult(X, ld(rd(Y, Z), rd(Y, Z)))) = ld(X, mult(X, ld(Z, Z))).
% 0.19/0.52 Proof:
% 0.19/0.52 ld(X, mult(X, ld(rd(Y, Z), rd(Y, Z))))
% 0.19/0.52 = { by axiom 5 (f07) }
% 0.19/0.52 rd(mult(rd(X, X), rd(Y, Z)), rd(Y, Z))
% 0.19/0.52 = { by lemma 17 R->L }
% 0.19/0.52 ld(rd(X, X), rd(mult(mult(rd(X, X), rd(X, X)), rd(Y, Z)), rd(Y, Z)))
% 0.19/0.52 = { by axiom 7 (f06) }
% 0.19/0.52 ld(rd(X, X), mult(rd(X, X), rd(mult(rd(X, X), Z), Z)))
% 0.19/0.52 = { by lemma 10 }
% 0.19/0.52 ld(rd(X, X), rd(mult(mult(rd(X, X), rd(X, X)), Z), Z))
% 0.19/0.52 = { by lemma 17 }
% 0.19/0.52 rd(mult(rd(X, X), Z), Z)
% 0.19/0.52 = { by axiom 5 (f07) R->L }
% 0.19/0.52 ld(X, mult(X, ld(Z, Z)))
% 0.19/0.52
% 0.19/0.52 Lemma 19: mult(X, ld(rd(Y, Z), rd(Y, Z))) = mult(X, ld(Z, Z)).
% 0.19/0.52 Proof:
% 0.19/0.52 mult(X, ld(rd(Y, Z), rd(Y, Z)))
% 0.19/0.52 = { by lemma 14 R->L }
% 0.19/0.52 ld(X, mult(X, mult(X, ld(rd(Y, Z), rd(Y, Z)))))
% 0.19/0.52 = { by axiom 3 (f03) R->L }
% 0.19/0.52 mult(X, ld(X, mult(X, ld(rd(Y, Z), rd(Y, Z)))))
% 0.19/0.52 = { by lemma 18 }
% 0.19/0.52 mult(X, ld(X, mult(X, ld(Z, Z))))
% 0.19/0.52 = { by axiom 3 (f03) }
% 0.19/0.52 ld(X, mult(X, mult(X, ld(Z, Z))))
% 0.19/0.52 = { by lemma 14 }
% 0.19/0.52 mult(X, ld(Z, Z))
% 0.19/0.52
% 0.19/0.52 Lemma 20: mult(rd(X, Y), ld(Y, Y)) = rd(X, Y).
% 0.19/0.52 Proof:
% 0.19/0.52 mult(rd(X, Y), ld(Y, Y))
% 0.19/0.52 = { by lemma 19 R->L }
% 0.19/0.52 mult(rd(X, Y), ld(rd(X, Y), rd(X, Y)))
% 0.19/0.52 = { by axiom 3 (f03) }
% 0.19/0.52 ld(rd(X, Y), mult(rd(X, Y), rd(X, Y)))
% 0.19/0.52 = { by axiom 1 (f01) }
% 0.19/0.52 rd(X, Y)
% 0.19/0.52
% 0.19/0.52 Lemma 21: ld(ld(X, X), ld(X, X)) = ld(X, X).
% 0.19/0.52 Proof:
% 0.19/0.52 ld(ld(X, X), ld(X, X))
% 0.19/0.52 = { by axiom 1 (f01) R->L }
% 0.19/0.52 ld(ld(X, X), ld(X, ld(X, mult(X, X))))
% 0.19/0.52 = { by axiom 3 (f03) R->L }
% 0.19/0.52 ld(ld(X, X), ld(X, mult(X, ld(X, X))))
% 0.19/0.52 = { by lemma 16 R->L }
% 0.19/0.52 ld(ld(X, X), mult(ld(X, X), ld(X, X)))
% 0.19/0.52 = { by axiom 1 (f01) }
% 0.19/0.52 ld(X, X)
% 0.19/0.52
% 0.19/0.52 Lemma 22: rd(mult(X, Y), Y) = rd(X, ld(Y, Y)).
% 0.19/0.52 Proof:
% 0.19/0.52 rd(mult(X, Y), Y)
% 0.19/0.52 = { by lemma 12 R->L }
% 0.19/0.52 rd(mult(X, ld(Y, Y)), ld(Y, Y))
% 0.19/0.52 = { by axiom 4 (f04) R->L }
% 0.19/0.52 mult(rd(X, ld(Y, Y)), ld(Y, Y))
% 0.19/0.52 = { by lemma 21 R->L }
% 0.19/0.52 mult(rd(X, ld(Y, Y)), ld(ld(Y, Y), ld(Y, Y)))
% 0.19/0.52 = { by lemma 20 }
% 0.19/0.52 rd(X, ld(Y, Y))
% 0.19/0.52
% 0.19/0.52 Lemma 23: mult(X, ld(Y, Y)) = rd(X, ld(Y, Y)).
% 0.19/0.52 Proof:
% 0.19/0.52 mult(X, ld(Y, Y))
% 0.19/0.52 = { by lemma 8 R->L }
% 0.19/0.52 mult(X, rd(Y, Y))
% 0.19/0.52 = { by lemma 9 R->L }
% 0.19/0.52 mult(X, rd(mult(ld(Y, Y), Y), Y))
% 0.19/0.52 = { by lemma 10 }
% 0.19/0.52 rd(mult(mult(X, ld(Y, Y)), Y), Y)
% 0.19/0.52 = { by lemma 11 R->L }
% 0.19/0.52 rd(mult(mult(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 0.19/0.52 = { by axiom 4 (f04) R->L }
% 0.19/0.52 mult(rd(mult(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 0.19/0.52 = { by lemma 12 }
% 0.19/0.52 mult(rd(mult(X, Y), Y), ld(Y, Y))
% 0.19/0.52 = { by lemma 20 }
% 0.19/0.52 rd(mult(X, Y), Y)
% 0.19/0.52 = { by lemma 22 }
% 0.19/0.52 rd(X, ld(Y, Y))
% 0.19/0.52
% 0.19/0.52 Lemma 24: mult(rd(X, ld(Y, Y)), Y) = mult(X, Y).
% 0.19/0.52 Proof:
% 0.19/0.52 mult(rd(X, ld(Y, Y)), Y)
% 0.19/0.52 = { by lemma 22 R->L }
% 0.19/0.52 mult(rd(mult(X, Y), Y), Y)
% 0.19/0.52 = { by axiom 4 (f04) }
% 0.19/0.52 rd(mult(mult(X, Y), Y), Y)
% 0.19/0.52 = { by lemma 15 }
% 0.19/0.52 mult(X, Y)
% 0.19/0.52
% 0.19/0.52 Lemma 25: rd(ld(X, mult(X, mult(Y, Y))), Y) = ld(X, mult(X, Y)).
% 0.19/0.52 Proof:
% 0.19/0.52 rd(ld(X, mult(X, mult(Y, Y))), Y)
% 0.19/0.52 = { by lemma 13 R->L }
% 0.19/0.52 rd(mult(ld(X, mult(X, Y)), Y), Y)
% 0.19/0.52 = { by lemma 16 R->L }
% 0.19/0.52 rd(mult(mult(ld(X, X), Y), Y), Y)
% 0.19/0.52 = { by lemma 15 }
% 0.19/0.52 mult(ld(X, X), Y)
% 0.19/0.52 = { by lemma 16 }
% 0.19/0.53 ld(X, mult(X, Y))
% 0.19/0.53
% 0.19/0.53 Lemma 26: ld(ld(X, Y), mult(ld(X, Y), Z)) = ld(X, mult(X, Z)).
% 0.19/0.53 Proof:
% 0.19/0.53 ld(ld(X, Y), mult(ld(X, Y), Z))
% 0.19/0.53 = { by lemma 25 R->L }
% 0.19/0.53 rd(ld(ld(X, Y), mult(ld(X, Y), mult(Z, Z))), Z)
% 0.19/0.53 = { by axiom 6 (f05) }
% 0.19/0.53 rd(mult(ld(X, mult(X, Z)), Z), Z)
% 0.19/0.53 = { by lemma 13 }
% 0.19/0.53 rd(ld(X, mult(X, mult(Z, Z))), Z)
% 0.19/0.53 = { by lemma 25 }
% 0.19/0.53 ld(X, mult(X, Z))
% 0.19/0.53
% 0.19/0.53 Lemma 27: ld(rd(mult(X, Y), Y), mult(rd(mult(X, Y), Y), Z)) = ld(X, mult(X, Z)).
% 0.19/0.53 Proof:
% 0.19/0.53 ld(rd(mult(X, Y), Y), mult(rd(mult(X, Y), Y), Z))
% 0.19/0.53 = { by lemma 17 R->L }
% 0.19/0.53 ld(rd(mult(X, Y), Y), mult(ld(X, rd(mult(mult(X, X), Y), Y)), Z))
% 0.19/0.53 = { by lemma 17 R->L }
% 0.19/0.53 ld(ld(X, rd(mult(mult(X, X), Y), Y)), mult(ld(X, rd(mult(mult(X, X), Y), Y)), Z))
% 0.19/0.53 = { by lemma 26 }
% 0.19/0.53 ld(X, mult(X, Z))
% 0.19/0.53
% 0.19/0.53 Lemma 28: ld(X, ld(X, mult(X, Y))) = ld(X, Y).
% 0.19/0.53 Proof:
% 0.19/0.53 ld(X, ld(X, mult(X, Y)))
% 0.19/0.53 = { by axiom 3 (f03) R->L }
% 0.19/0.53 ld(X, mult(X, ld(X, Y)))
% 0.19/0.53 = { by lemma 26 R->L }
% 0.19/0.53 ld(ld(X, Y), mult(ld(X, Y), ld(X, Y)))
% 0.19/0.53 = { by axiom 1 (f01) }
% 0.19/0.53 ld(X, Y)
% 0.19/0.53
% 0.19/0.53 Lemma 29: rd(rd(X, ld(Y, Y)), ld(Z, Z)) = rd(X, ld(Z, Z)).
% 0.19/0.53 Proof:
% 0.19/0.53 rd(rd(X, ld(Y, Y)), ld(Z, Z))
% 0.19/0.53 = { by lemma 23 R->L }
% 0.19/0.53 rd(mult(X, ld(Y, Y)), ld(Z, Z))
% 0.19/0.53 = { by lemma 22 R->L }
% 0.19/0.53 rd(mult(mult(X, ld(Y, Y)), Z), Z)
% 0.19/0.53 = { by lemma 10 R->L }
% 0.19/0.53 mult(X, rd(mult(ld(Y, Y), Z), Z))
% 0.19/0.53 = { by lemma 8 R->L }
% 0.19/0.53 mult(X, rd(mult(rd(Y, Y), Z), Z))
% 0.19/0.53 = { by axiom 5 (f07) R->L }
% 0.19/0.53 mult(X, ld(Y, mult(Y, ld(Z, Z))))
% 0.19/0.53 = { by lemma 18 R->L }
% 0.19/0.53 mult(X, ld(Y, mult(Y, ld(rd(mult(Y, Z), Z), rd(mult(Y, Z), Z)))))
% 0.19/0.53 = { by lemma 27 R->L }
% 0.19/0.53 mult(X, ld(rd(mult(Y, Z), Z), mult(rd(mult(Y, Z), Z), ld(rd(mult(Y, Z), Z), rd(mult(Y, Z), Z)))))
% 0.19/0.53 = { by axiom 3 (f03) }
% 0.19/0.53 mult(X, ld(rd(mult(Y, Z), Z), ld(rd(mult(Y, Z), Z), mult(rd(mult(Y, Z), Z), rd(mult(Y, Z), Z)))))
% 0.19/0.53 = { by lemma 28 }
% 0.19/0.53 mult(X, ld(rd(mult(Y, Z), Z), rd(mult(Y, Z), Z)))
% 0.19/0.53 = { by lemma 22 }
% 0.19/0.53 mult(X, ld(rd(mult(Y, Z), Z), rd(Y, ld(Z, Z))))
% 0.19/0.53 = { by lemma 22 }
% 0.19/0.53 mult(X, ld(rd(Y, ld(Z, Z)), rd(Y, ld(Z, Z))))
% 0.19/0.53 = { by lemma 19 }
% 0.19/0.53 mult(X, ld(ld(Z, Z), ld(Z, Z)))
% 0.19/0.53 = { by lemma 23 }
% 0.19/0.53 rd(X, ld(ld(Z, Z), ld(Z, Z)))
% 0.19/0.53 = { by lemma 21 }
% 0.19/0.53 rd(X, ld(Z, Z))
% 0.19/0.53
% 0.19/0.53 Lemma 30: mult(rd(X, ld(Y, Y)), Z) = mult(X, Z).
% 0.19/0.53 Proof:
% 0.19/0.53 mult(rd(X, ld(Y, Y)), Z)
% 0.19/0.53 = { by lemma 24 R->L }
% 0.19/0.53 mult(rd(rd(X, ld(Y, Y)), ld(Z, Z)), Z)
% 0.19/0.53 = { by lemma 29 }
% 0.19/0.53 mult(rd(X, ld(Z, Z)), Z)
% 0.19/0.53 = { by lemma 24 }
% 0.19/0.53 mult(X, Z)
% 0.19/0.53
% 0.19/0.53 Lemma 31: mult(X, ld(rd(X, ld(Y, Y)), Z)) = ld(X, mult(X, Z)).
% 0.19/0.53 Proof:
% 0.19/0.53 mult(X, ld(rd(X, ld(Y, Y)), Z))
% 0.19/0.53 = { by lemma 30 R->L }
% 0.19/0.53 mult(rd(X, ld(Y, Y)), ld(rd(X, ld(Y, Y)), Z))
% 0.19/0.53 = { by axiom 3 (f03) }
% 0.19/0.53 ld(rd(X, ld(Y, Y)), mult(rd(X, ld(Y, Y)), Z))
% 0.19/0.53 = { by lemma 22 R->L }
% 0.19/0.53 ld(rd(X, ld(Y, Y)), mult(rd(mult(X, Y), Y), Z))
% 0.19/0.53 = { by lemma 22 R->L }
% 0.19/0.53 ld(rd(mult(X, Y), Y), mult(rd(mult(X, Y), Y), Z))
% 0.19/0.53 = { by lemma 27 }
% 0.19/0.53 ld(X, mult(X, Z))
% 0.19/0.53
% 0.19/0.53 Lemma 32: ld(rd(X, Y), rd(mult(rd(X, Y), X), ld(Y, Y))) = rd(X, ld(Y, Y)).
% 0.19/0.53 Proof:
% 0.19/0.53 ld(rd(X, Y), rd(mult(rd(X, Y), X), ld(Y, Y)))
% 0.19/0.53 = { by lemma 22 R->L }
% 0.19/0.53 ld(rd(X, Y), rd(mult(mult(rd(X, Y), X), Y), Y))
% 0.19/0.53 = { by lemma 10 R->L }
% 0.19/0.53 ld(rd(X, Y), mult(rd(X, Y), rd(mult(X, Y), Y)))
% 0.19/0.53 = { by axiom 4 (f04) R->L }
% 0.19/0.53 ld(rd(X, Y), mult(rd(X, Y), mult(rd(X, Y), Y)))
% 0.19/0.53 = { by lemma 14 }
% 0.19/0.53 mult(rd(X, Y), Y)
% 0.19/0.53 = { by axiom 4 (f04) }
% 0.19/0.53 rd(mult(X, Y), Y)
% 0.19/0.53 = { by lemma 22 }
% 0.19/0.53 rd(X, ld(Y, Y))
% 0.19/0.53
% 0.19/0.53 Goal 1 (goal): ld(rd(x0, x1), mult(rd(x0, x1), x2)) = ld(x0, mult(x0, x2)).
% 0.19/0.53 Proof:
% 0.19/0.53 ld(rd(x0, x1), mult(rd(x0, x1), x2))
% 0.19/0.53 = { by lemma 26 R->L }
% 0.19/0.53 ld(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))
% 0.19/0.53 = { by lemma 32 }
% 0.19/0.53 ld(rd(x0, ld(x1, x1)), mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))
% 0.19/0.53 = { by lemma 22 R->L }
% 0.19/0.53 ld(rd(mult(x0, x1), x1), mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))
% 0.19/0.53 = { by lemma 28 R->L }
% 0.19/0.53 ld(rd(mult(x0, x1), x1), ld(rd(mult(x0, x1), x1), mult(rd(mult(x0, x1), x1), mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))))
% 0.19/0.53 = { by lemma 31 R->L }
% 0.19/0.53 ld(rd(mult(x0, x1), x1), mult(rd(mult(x0, x1), x1), ld(rd(rd(mult(x0, x1), x1), ld(X, X)), mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))))
% 0.19/0.53 = { by lemma 27 }
% 0.19/0.53 ld(x0, mult(x0, ld(rd(rd(mult(x0, x1), x1), ld(X, X)), mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))))
% 0.19/0.53 = { by lemma 22 }
% 0.19/0.53 ld(x0, mult(x0, ld(rd(rd(x0, ld(x1, x1)), ld(X, X)), mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))))
% 0.19/0.53 = { by lemma 29 }
% 0.19/0.53 ld(x0, mult(x0, ld(rd(x0, ld(X, X)), mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))))
% 0.19/0.53 = { by lemma 31 }
% 0.19/0.53 ld(x0, ld(x0, mult(x0, mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))))
% 0.19/0.53 = { by lemma 28 }
% 0.19/0.53 ld(x0, mult(ld(rd(x0, x1), rd(mult(rd(x0, x1), x0), ld(x1, x1))), x2))
% 0.19/0.53 = { by lemma 32 }
% 0.19/0.53 ld(x0, mult(rd(x0, ld(x1, x1)), x2))
% 0.19/0.53 = { by lemma 30 }
% 0.19/0.53 ld(x0, mult(x0, x2))
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53
% 0.19/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------