TSTP Solution File: GRP667-2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP667-2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n021.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 01:19:36 EDT 2023
% Result : Unsatisfiable 40.73s 5.63s
% Output : Proof 41.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP667-2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 20:06:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 40.73/5.63 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 40.73/5.63
% 40.73/5.63 % SZS status Unsatisfiable
% 40.73/5.63
% 41.88/5.73 % SZS output start Proof
% 41.88/5.73 Axiom 1 (c05): mult(X, unit) = X.
% 41.88/5.73 Axiom 2 (c06): mult(unit, X) = X.
% 41.88/5.73 Axiom 3 (c02): ld(X, mult(X, Y)) = Y.
% 41.88/5.73 Axiom 4 (c04): rd(mult(X, Y), Y) = X.
% 41.88/5.73 Axiom 5 (c01): mult(X, ld(X, Y)) = Y.
% 41.88/5.73 Axiom 6 (c09): mult(f(X), f(X)) = X.
% 41.88/5.73 Axiom 7 (c03): mult(rd(X, Y), Y) = X.
% 41.88/5.73 Axiom 8 (c08): mult(mult(X, Y), X) = mult(X, mult(Y, X)).
% 41.88/5.73 Axiom 9 (c07): mult(mult(X, Y), mult(mult(Z, Y), Z)) = mult(mult(X, mult(mult(Y, Z), Y)), Z).
% 41.88/5.73
% 41.88/5.73 Lemma 10: ld(X, X) = unit.
% 41.88/5.73 Proof:
% 41.88/5.73 ld(X, X)
% 41.88/5.73 = { by axiom 1 (c05) R->L }
% 41.88/5.73 ld(X, mult(X, unit))
% 41.88/5.73 = { by axiom 3 (c02) }
% 41.88/5.73 unit
% 41.88/5.73
% 41.88/5.73 Lemma 11: mult(X, mult(ld(X, Y), X)) = mult(Y, X).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(X, mult(ld(X, Y), X))
% 41.88/5.73 = { by axiom 8 (c08) R->L }
% 41.88/5.73 mult(mult(X, ld(X, Y)), X)
% 41.88/5.73 = { by axiom 5 (c01) }
% 41.88/5.73 mult(Y, X)
% 41.88/5.73
% 41.88/5.73 Lemma 12: mult(mult(X, mult(Y, mult(Z, Y))), Z) = mult(mult(X, Y), mult(Z, mult(Y, Z))).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(mult(X, mult(Y, mult(Z, Y))), Z)
% 41.88/5.73 = { by axiom 8 (c08) R->L }
% 41.88/5.73 mult(mult(X, mult(mult(Y, Z), Y)), Z)
% 41.88/5.73 = { by axiom 9 (c07) R->L }
% 41.88/5.73 mult(mult(X, Y), mult(mult(Z, Y), Z))
% 41.88/5.73 = { by axiom 8 (c08) }
% 41.88/5.73 mult(mult(X, Y), mult(Z, mult(Y, Z)))
% 41.88/5.73
% 41.88/5.73 Lemma 13: mult(mult(X, mult(Y, X)), Y) = mult(X, mult(Y, mult(X, Y))).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(mult(X, mult(Y, X)), Y)
% 41.88/5.73 = { by axiom 2 (c06) R->L }
% 41.88/5.73 mult(mult(unit, mult(X, mult(Y, X))), Y)
% 41.88/5.73 = { by lemma 12 }
% 41.88/5.73 mult(mult(unit, X), mult(Y, mult(X, Y)))
% 41.88/5.73 = { by axiom 2 (c06) }
% 41.88/5.73 mult(X, mult(Y, mult(X, Y)))
% 41.88/5.73
% 41.88/5.73 Lemma 14: mult(mult(X, Y), mult(X, mult(Y, X))) = mult(X, mult(Y, mult(X, mult(Y, X)))).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(mult(X, Y), mult(X, mult(Y, X)))
% 41.88/5.73 = { by lemma 12 R->L }
% 41.88/5.73 mult(mult(X, mult(Y, mult(X, Y))), X)
% 41.88/5.73 = { by axiom 8 (c08) }
% 41.88/5.73 mult(X, mult(mult(Y, mult(X, Y)), X))
% 41.88/5.73 = { by lemma 13 }
% 41.88/5.73 mult(X, mult(Y, mult(X, mult(Y, X))))
% 41.88/5.73
% 41.88/5.73 Lemma 15: mult(ld(X, Y), mult(Y, X)) = ld(X, mult(Y, mult(Y, X))).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(ld(X, Y), mult(Y, X))
% 41.88/5.73 = { by axiom 3 (c02) R->L }
% 41.88/5.73 ld(X, mult(X, mult(ld(X, Y), mult(Y, X))))
% 41.88/5.73 = { by lemma 11 R->L }
% 41.88/5.73 ld(X, mult(X, mult(ld(X, Y), mult(X, mult(ld(X, Y), X)))))
% 41.88/5.73 = { by lemma 14 R->L }
% 41.88/5.73 ld(X, mult(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), X))))
% 41.88/5.73 = { by axiom 5 (c01) }
% 41.88/5.73 ld(X, mult(Y, mult(X, mult(ld(X, Y), X))))
% 41.88/5.73 = { by lemma 11 }
% 41.88/5.73 ld(X, mult(Y, mult(Y, X)))
% 41.88/5.73
% 41.88/5.73 Lemma 16: ld(ld(X, unit), unit) = X.
% 41.88/5.73 Proof:
% 41.88/5.73 ld(ld(X, unit), unit)
% 41.88/5.73 = { by lemma 10 R->L }
% 41.88/5.73 ld(ld(X, unit), ld(X, X))
% 41.88/5.73 = { by axiom 2 (c06) R->L }
% 41.88/5.73 ld(ld(X, unit), ld(X, mult(unit, X)))
% 41.88/5.73 = { by axiom 2 (c06) R->L }
% 41.88/5.73 ld(ld(X, unit), ld(X, mult(unit, mult(unit, X))))
% 41.88/5.73 = { by axiom 1 (c05) R->L }
% 41.88/5.73 ld(mult(ld(X, unit), unit), ld(X, mult(unit, mult(unit, X))))
% 41.88/5.73 = { by lemma 15 R->L }
% 41.88/5.73 ld(mult(ld(X, unit), unit), mult(ld(X, unit), mult(unit, X)))
% 41.88/5.73 = { by lemma 11 R->L }
% 41.88/5.73 ld(mult(ld(X, unit), unit), mult(ld(X, unit), mult(X, mult(ld(X, unit), X))))
% 41.88/5.73 = { by axiom 5 (c01) R->L }
% 41.88/5.73 ld(mult(ld(X, unit), mult(X, ld(X, unit))), mult(ld(X, unit), mult(X, mult(ld(X, unit), X))))
% 41.88/5.73 = { by lemma 13 R->L }
% 41.88/5.73 ld(mult(ld(X, unit), mult(X, ld(X, unit))), mult(mult(ld(X, unit), mult(X, ld(X, unit))), X))
% 41.88/5.73 = { by axiom 3 (c02) }
% 41.88/5.73 X
% 41.88/5.73
% 41.88/5.73 Lemma 17: ld(rd(X, Y), X) = Y.
% 41.88/5.73 Proof:
% 41.88/5.73 ld(rd(X, Y), X)
% 41.88/5.73 = { by axiom 7 (c03) R->L }
% 41.88/5.73 ld(rd(X, Y), mult(rd(X, Y), Y))
% 41.88/5.73 = { by axiom 3 (c02) }
% 41.88/5.73 Y
% 41.88/5.73
% 41.88/5.73 Lemma 18: rd(X, ld(Y, X)) = Y.
% 41.88/5.73 Proof:
% 41.88/5.73 rd(X, ld(Y, X))
% 41.88/5.73 = { by axiom 5 (c01) R->L }
% 41.88/5.73 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 41.88/5.73 = { by axiom 4 (c04) }
% 41.88/5.73 Y
% 41.88/5.73
% 41.88/5.73 Lemma 19: rd(mult(mult(X, Y), mult(Z, mult(Y, Z))), Z) = mult(X, mult(Y, mult(Z, Y))).
% 41.88/5.73 Proof:
% 41.88/5.73 rd(mult(mult(X, Y), mult(Z, mult(Y, Z))), Z)
% 41.88/5.73 = { by lemma 12 R->L }
% 41.88/5.73 rd(mult(mult(X, mult(Y, mult(Z, Y))), Z), Z)
% 41.88/5.73 = { by axiom 4 (c04) }
% 41.88/5.73 mult(X, mult(Y, mult(Z, Y)))
% 41.88/5.73
% 41.88/5.73 Lemma 20: rd(mult(X, mult(Y, X)), X) = mult(X, Y).
% 41.88/5.73 Proof:
% 41.88/5.73 rd(mult(X, mult(Y, X)), X)
% 41.88/5.73 = { by axiom 8 (c08) R->L }
% 41.88/5.73 rd(mult(mult(X, Y), X), X)
% 41.88/5.73 = { by axiom 4 (c04) }
% 41.88/5.73 mult(X, Y)
% 41.88/5.73
% 41.88/5.73 Lemma 21: mult(rd(unit, X), mult(X, Y)) = Y.
% 41.88/5.73 Proof:
% 41.88/5.73 mult(rd(unit, X), mult(X, Y))
% 41.88/5.73 = { by axiom 7 (c03) R->L }
% 41.88/5.73 mult(rd(unit, X), mult(X, mult(rd(Y, X), X)))
% 41.88/5.73 = { by lemma 19 R->L }
% 41.88/5.73 rd(mult(mult(rd(unit, X), X), mult(rd(Y, X), mult(X, rd(Y, X)))), rd(Y, X))
% 41.88/5.73 = { by axiom 7 (c03) }
% 41.88/5.73 rd(mult(unit, mult(rd(Y, X), mult(X, rd(Y, X)))), rd(Y, X))
% 41.88/5.73 = { by axiom 2 (c06) }
% 41.88/5.73 rd(mult(rd(Y, X), mult(X, rd(Y, X))), rd(Y, X))
% 41.88/5.73 = { by lemma 20 }
% 41.88/5.73 mult(rd(Y, X), X)
% 41.88/5.73 = { by axiom 7 (c03) }
% 41.88/5.73 Y
% 41.88/5.73
% 41.88/5.73 Lemma 22: mult(X, mult(ld(X, unit), Y)) = Y.
% 41.88/5.73 Proof:
% 41.88/5.73 mult(X, mult(ld(X, unit), Y))
% 41.88/5.73 = { by lemma 18 R->L }
% 41.88/5.73 mult(rd(unit, ld(X, unit)), mult(ld(X, unit), Y))
% 41.88/5.73 = { by lemma 21 }
% 41.88/5.73 Y
% 41.88/5.73
% 41.88/5.73 Lemma 23: mult(ld(X, unit), mult(X, Y)) = Y.
% 41.88/5.73 Proof:
% 41.88/5.73 mult(ld(X, unit), mult(X, Y))
% 41.88/5.73 = { by lemma 16 R->L }
% 41.88/5.73 mult(ld(X, unit), mult(ld(ld(X, unit), unit), Y))
% 41.88/5.73 = { by lemma 22 }
% 41.88/5.73 Y
% 41.88/5.73
% 41.88/5.73 Lemma 24: mult(mult(X, Y), Y) = mult(X, mult(Y, Y)).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(mult(X, Y), Y)
% 41.88/5.73 = { by axiom 1 (c05) R->L }
% 41.88/5.73 mult(mult(X, Y), mult(Y, unit))
% 41.88/5.73 = { by axiom 2 (c06) R->L }
% 41.88/5.73 mult(mult(X, Y), mult(unit, mult(Y, unit)))
% 41.88/5.73 = { by lemma 12 R->L }
% 41.88/5.73 mult(mult(X, mult(Y, mult(unit, Y))), unit)
% 41.88/5.73 = { by axiom 1 (c05) }
% 41.88/5.73 mult(X, mult(Y, mult(unit, Y)))
% 41.88/5.73 = { by axiom 2 (c06) }
% 41.88/5.73 mult(X, mult(Y, Y))
% 41.88/5.73
% 41.88/5.73 Lemma 25: mult(mult(X, Y), mult(X, Y)) = mult(X, mult(Y, mult(X, Y))).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(mult(X, Y), mult(X, Y))
% 41.88/5.73 = { by lemma 23 R->L }
% 41.88/5.73 mult(ld(rd(unit, X), unit), mult(rd(unit, X), mult(mult(X, Y), mult(X, Y))))
% 41.88/5.73 = { by lemma 24 R->L }
% 41.88/5.73 mult(ld(rd(unit, X), unit), mult(mult(rd(unit, X), mult(X, Y)), mult(X, Y)))
% 41.88/5.73 = { by lemma 21 }
% 41.88/5.73 mult(ld(rd(unit, X), unit), mult(Y, mult(X, Y)))
% 41.88/5.73 = { by lemma 17 }
% 41.88/5.73 mult(X, mult(Y, mult(X, Y)))
% 41.88/5.73
% 41.88/5.73 Lemma 26: mult(rd(X, Y), mult(Y, X)) = mult(X, X).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(rd(X, Y), mult(Y, X))
% 41.88/5.73 = { by axiom 7 (c03) R->L }
% 41.88/5.73 mult(rd(X, Y), mult(Y, mult(rd(X, Y), Y)))
% 41.88/5.73 = { by lemma 25 R->L }
% 41.88/5.73 mult(mult(rd(X, Y), Y), mult(rd(X, Y), Y))
% 41.88/5.73 = { by axiom 7 (c03) }
% 41.88/5.73 mult(X, mult(rd(X, Y), Y))
% 41.88/5.73 = { by axiom 7 (c03) }
% 41.88/5.73 mult(X, X)
% 41.88/5.73
% 41.88/5.73 Lemma 27: mult(X, rd(X, Y)) = rd(mult(X, X), Y).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(X, rd(X, Y))
% 41.88/5.73 = { by axiom 4 (c04) R->L }
% 41.88/5.73 rd(mult(mult(X, rd(X, Y)), Y), Y)
% 41.88/5.73 = { by lemma 17 R->L }
% 41.88/5.73 rd(mult(mult(X, rd(X, Y)), ld(rd(X, Y), X)), Y)
% 41.88/5.73 = { by lemma 11 R->L }
% 41.88/5.73 rd(mult(mult(rd(X, Y), mult(ld(rd(X, Y), X), rd(X, Y))), ld(rd(X, Y), X)), Y)
% 41.88/5.73 = { by lemma 13 }
% 41.88/5.73 rd(mult(rd(X, Y), mult(ld(rd(X, Y), X), mult(rd(X, Y), ld(rd(X, Y), X)))), Y)
% 41.88/5.73 = { by axiom 5 (c01) }
% 41.88/5.73 rd(mult(rd(X, Y), mult(ld(rd(X, Y), X), X)), Y)
% 41.88/5.73 = { by lemma 17 }
% 41.88/5.73 rd(mult(rd(X, Y), mult(Y, X)), Y)
% 41.88/5.73 = { by lemma 26 }
% 41.88/5.73 rd(mult(X, X), Y)
% 41.88/5.73
% 41.88/5.73 Lemma 28: mult(X, rd(Y, X)) = rd(mult(X, Y), X).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(X, rd(Y, X))
% 41.88/5.73 = { by lemma 20 R->L }
% 41.88/5.73 rd(mult(X, mult(rd(Y, X), X)), X)
% 41.88/5.73 = { by axiom 7 (c03) }
% 41.88/5.73 rd(mult(X, Y), X)
% 41.88/5.73
% 41.88/5.73 Lemma 29: mult(X, rd(unit, Y)) = rd(X, Y).
% 41.88/5.73 Proof:
% 41.88/5.73 mult(X, rd(unit, Y))
% 41.88/5.73 = { by axiom 5 (c01) R->L }
% 41.88/5.73 mult(mult(Y, ld(Y, X)), rd(unit, Y))
% 41.88/5.73 = { by lemma 20 R->L }
% 41.88/5.73 rd(mult(mult(Y, ld(Y, X)), mult(rd(unit, Y), mult(Y, ld(Y, X)))), mult(Y, ld(Y, X)))
% 41.88/5.73 = { by lemma 21 }
% 41.88/5.73 rd(mult(mult(Y, ld(Y, X)), ld(Y, X)), mult(Y, ld(Y, X)))
% 41.88/5.73 = { by lemma 24 }
% 41.88/5.73 rd(mult(Y, mult(ld(Y, X), ld(Y, X))), mult(Y, ld(Y, X)))
% 41.88/5.74 = { by lemma 26 R->L }
% 41.88/5.74 rd(mult(Y, mult(rd(ld(Y, X), Y), mult(Y, ld(Y, X)))), mult(Y, ld(Y, X)))
% 41.88/5.74 = { by axiom 7 (c03) R->L }
% 41.88/5.74 rd(mult(Y, mult(rd(ld(Y, X), Y), mult(Y, mult(rd(ld(Y, X), Y), Y)))), mult(Y, ld(Y, X)))
% 41.88/5.74 = { by lemma 14 R->L }
% 41.88/5.74 rd(mult(mult(Y, rd(ld(Y, X), Y)), mult(Y, mult(rd(ld(Y, X), Y), Y))), mult(Y, ld(Y, X)))
% 41.88/5.74 = { by axiom 7 (c03) }
% 41.88/5.74 rd(mult(mult(Y, rd(ld(Y, X), Y)), mult(Y, ld(Y, X))), mult(Y, ld(Y, X)))
% 41.88/5.74 = { by lemma 28 }
% 41.88/5.74 rd(mult(rd(mult(Y, ld(Y, X)), Y), mult(Y, ld(Y, X))), mult(Y, ld(Y, X)))
% 41.88/5.74 = { by axiom 4 (c04) }
% 41.88/5.74 rd(mult(Y, ld(Y, X)), Y)
% 41.88/5.74 = { by axiom 5 (c01) }
% 41.88/5.74 rd(X, Y)
% 41.88/5.74
% 41.88/5.74 Lemma 30: mult(ld(X, Y), X) = ld(X, mult(Y, X)).
% 41.88/5.74 Proof:
% 41.88/5.74 mult(ld(X, Y), X)
% 41.88/5.74 = { by axiom 3 (c02) R->L }
% 41.88/5.74 ld(X, mult(X, mult(ld(X, Y), X)))
% 41.88/5.74 = { by lemma 11 }
% 41.88/5.74 ld(X, mult(Y, X))
% 41.88/5.74
% 41.88/5.74 Lemma 31: mult(ld(X, unit), Y) = ld(X, Y).
% 41.88/5.74 Proof:
% 41.88/5.74 mult(ld(X, unit), Y)
% 41.88/5.74 = { by axiom 3 (c02) R->L }
% 41.88/5.74 ld(X, mult(X, mult(ld(X, unit), Y)))
% 41.88/5.74 = { by lemma 22 }
% 41.88/5.74 ld(X, Y)
% 41.88/5.74
% 41.88/5.74 Lemma 32: mult(ld(X, Y), Y) = ld(X, mult(Y, Y)).
% 41.88/5.74 Proof:
% 41.88/5.74 mult(ld(X, Y), Y)
% 41.88/5.74 = { by lemma 31 R->L }
% 41.88/5.74 mult(mult(ld(X, unit), Y), Y)
% 41.88/5.74 = { by lemma 24 }
% 41.88/5.74 mult(ld(X, unit), mult(Y, Y))
% 41.88/5.74 = { by lemma 31 }
% 41.88/5.74 ld(X, mult(Y, Y))
% 41.88/5.74
% 41.88/5.74 Lemma 33: rd(X, mult(Y, X)) = rd(unit, Y).
% 41.88/5.74 Proof:
% 41.88/5.74 rd(X, mult(Y, X))
% 41.88/5.74 = { by lemma 21 R->L }
% 41.88/5.74 rd(mult(rd(unit, Y), mult(Y, X)), mult(Y, X))
% 41.88/5.74 = { by axiom 4 (c04) }
% 41.88/5.74 rd(unit, Y)
% 41.88/5.74
% 41.88/5.74 Lemma 34: mult(mult(rd(X, mult(Y, mult(Z, Y))), Y), mult(Z, mult(Y, Z))) = mult(X, Z).
% 41.88/5.74 Proof:
% 41.88/5.74 mult(mult(rd(X, mult(Y, mult(Z, Y))), Y), mult(Z, mult(Y, Z)))
% 41.88/5.74 = { by lemma 12 R->L }
% 41.88/5.74 mult(mult(rd(X, mult(Y, mult(Z, Y))), mult(Y, mult(Z, Y))), Z)
% 41.88/5.74 = { by axiom 7 (c03) }
% 41.88/5.74 mult(X, Z)
% 41.88/5.74
% 41.88/5.74 Lemma 35: rd(X, rd(unit, Y)) = mult(X, Y).
% 41.88/5.74 Proof:
% 41.88/5.74 rd(X, rd(unit, Y))
% 41.88/5.74 = { by axiom 7 (c03) R->L }
% 41.88/5.74 mult(rd(rd(X, rd(unit, Y)), Y), Y)
% 41.88/5.74 = { by axiom 1 (c05) R->L }
% 41.88/5.74 mult(rd(rd(X, rd(unit, Y)), Y), mult(Y, unit))
% 41.88/5.74 = { by axiom 2 (c06) R->L }
% 41.88/5.74 mult(rd(rd(X, rd(mult(unit, unit), Y)), Y), mult(Y, unit))
% 41.88/5.74 = { by lemma 29 R->L }
% 41.88/5.74 mult(mult(rd(X, rd(mult(unit, unit), Y)), rd(unit, Y)), mult(Y, unit))
% 41.88/5.74 = { by axiom 7 (c03) R->L }
% 41.88/5.74 mult(mult(rd(X, rd(mult(unit, unit), Y)), rd(unit, Y)), mult(Y, mult(rd(unit, Y), Y)))
% 41.88/5.74 = { by lemma 27 R->L }
% 41.88/5.74 mult(mult(rd(X, mult(unit, rd(unit, Y))), rd(unit, Y)), mult(Y, mult(rd(unit, Y), Y)))
% 41.88/5.74 = { by axiom 7 (c03) R->L }
% 41.88/5.74 mult(mult(rd(X, mult(mult(rd(unit, Y), Y), rd(unit, Y))), rd(unit, Y)), mult(Y, mult(rd(unit, Y), Y)))
% 41.88/5.74 = { by axiom 8 (c08) }
% 41.88/5.74 mult(mult(rd(X, mult(rd(unit, Y), mult(Y, rd(unit, Y)))), rd(unit, Y)), mult(Y, mult(rd(unit, Y), Y)))
% 41.88/5.74 = { by lemma 34 }
% 41.88/5.74 mult(X, Y)
% 41.88/5.74
% 41.88/5.74 Lemma 36: mult(X, mult(rd(unit, X), Y)) = Y.
% 41.88/5.74 Proof:
% 41.88/5.74 mult(X, mult(rd(unit, X), Y))
% 41.88/5.74 = { by lemma 17 R->L }
% 41.88/5.74 mult(ld(rd(unit, X), unit), mult(rd(unit, X), Y))
% 41.88/5.74 = { by lemma 23 }
% 41.88/5.74 Y
% 41.88/5.74
% 41.88/5.74 Lemma 37: mult(mult(X, Y), rd(unit, Y)) = X.
% 41.88/5.74 Proof:
% 41.88/5.74 mult(mult(X, Y), rd(unit, Y))
% 41.88/5.74 = { by axiom 7 (c03) R->L }
% 41.88/5.74 mult(mult(X, Y), rd(unit, mult(rd(Y, X), X)))
% 41.88/5.74 = { by axiom 7 (c03) R->L }
% 41.88/5.74 mult(mult(X, mult(rd(Y, X), X)), rd(unit, mult(rd(Y, X), X)))
% 41.88/5.74 = { by axiom 4 (c04) R->L }
% 41.88/5.74 mult(mult(X, mult(rd(Y, X), X)), rd(mult(rd(unit, mult(rd(Y, X), X)), mult(rd(Y, X), mult(X, rd(Y, X)))), mult(rd(Y, X), mult(X, rd(Y, X)))))
% 41.88/5.74 = { by axiom 8 (c08) R->L }
% 41.88/5.74 mult(mult(X, mult(rd(Y, X), X)), rd(mult(rd(unit, mult(rd(Y, X), X)), mult(mult(rd(Y, X), X), rd(Y, X))), mult(rd(Y, X), mult(X, rd(Y, X)))))
% 41.88/5.74 = { by lemma 21 }
% 41.88/5.74 mult(mult(X, mult(rd(Y, X), X)), rd(rd(Y, X), mult(rd(Y, X), mult(X, rd(Y, X)))))
% 41.88/5.74 = { by axiom 2 (c06) R->L }
% 41.88/5.74 mult(mult(X, mult(rd(Y, X), X)), rd(mult(unit, rd(Y, X)), mult(rd(Y, X), mult(X, rd(Y, X)))))
% 41.88/5.74 = { by lemma 34 R->L }
% 41.88/5.74 mult(mult(X, mult(rd(Y, X), X)), rd(mult(mult(rd(unit, mult(X, mult(rd(Y, X), X))), X), mult(rd(Y, X), mult(X, rd(Y, X)))), mult(rd(Y, X), mult(X, rd(Y, X)))))
% 41.88/5.74 = { by axiom 4 (c04) }
% 41.88/5.74 mult(mult(X, mult(rd(Y, X), X)), mult(rd(unit, mult(X, mult(rd(Y, X), X))), X))
% 41.88/5.74 = { by lemma 36 }
% 41.88/5.74 X
% 41.88/5.74
% 41.88/5.74 Lemma 38: mult(mult(X, ld(Y, unit)), Y) = X.
% 41.88/5.74 Proof:
% 41.88/5.74 mult(mult(X, ld(Y, unit)), Y)
% 41.88/5.74 = { by lemma 18 R->L }
% 41.88/5.74 mult(mult(X, ld(Y, unit)), rd(unit, ld(Y, unit)))
% 41.88/5.74 = { by lemma 37 }
% 41.88/5.74 X
% 41.88/5.74
% 41.88/5.74 Lemma 39: mult(mult(X, Y), ld(Y, unit)) = X.
% 41.88/5.74 Proof:
% 41.88/5.74 mult(mult(X, Y), ld(Y, unit))
% 41.88/5.74 = { by lemma 16 R->L }
% 41.88/5.74 mult(mult(X, ld(ld(Y, unit), unit)), ld(Y, unit))
% 41.88/5.74 = { by lemma 38 }
% 41.88/5.74 X
% 41.88/5.74
% 41.88/5.74 Lemma 40: ld(mult(X, Y), mult(X, mult(Y, X))) = X.
% 41.88/5.74 Proof:
% 41.88/5.74 ld(mult(X, Y), mult(X, mult(Y, X)))
% 41.88/5.74 = { by axiom 8 (c08) R->L }
% 41.88/5.74 ld(mult(X, Y), mult(mult(X, Y), X))
% 41.88/5.74 = { by axiom 3 (c02) }
% 41.88/5.74 X
% 41.88/5.74
% 41.88/5.74 Lemma 41: mult(mult(X, mult(Y, Z)), rd(Z, Y)) = mult(mult(X, Y), rd(mult(Z, Z), Y)).
% 41.88/5.74 Proof:
% 41.88/5.74 mult(mult(X, mult(Y, Z)), rd(Z, Y))
% 41.88/5.74 = { by lemma 34 R->L }
% 41.88/5.74 mult(mult(rd(mult(X, mult(Y, Z)), mult(Y, mult(rd(Z, Y), Y))), Y), mult(rd(Z, Y), mult(Y, rd(Z, Y))))
% 41.88/5.74 = { by axiom 7 (c03) }
% 41.88/5.74 mult(mult(rd(mult(X, mult(Y, Z)), mult(Y, Z)), Y), mult(rd(Z, Y), mult(Y, rd(Z, Y))))
% 41.88/5.74 = { by axiom 8 (c08) R->L }
% 41.88/5.74 mult(mult(rd(mult(X, mult(Y, Z)), mult(Y, Z)), Y), mult(mult(rd(Z, Y), Y), rd(Z, Y)))
% 41.88/5.74 = { by axiom 7 (c03) }
% 41.88/5.74 mult(mult(rd(mult(X, mult(Y, Z)), mult(Y, Z)), Y), mult(Z, rd(Z, Y)))
% 41.88/5.74 = { by lemma 27 }
% 41.88/5.74 mult(mult(rd(mult(X, mult(Y, Z)), mult(Y, Z)), Y), rd(mult(Z, Z), Y))
% 41.88/5.74 = { by axiom 4 (c04) }
% 41.88/5.74 mult(mult(X, Y), rd(mult(Z, Z), Y))
% 41.88/5.74
% 41.88/5.74 Lemma 42: rd(mult(X, mult(Y, mult(Z, Y))), Y) = mult(mult(X, Y), Z).
% 41.88/5.74 Proof:
% 41.88/5.74 rd(mult(X, mult(Y, mult(Z, Y))), Y)
% 41.88/5.74 = { by axiom 6 (c09) R->L }
% 41.88/5.74 rd(mult(X, mult(Y, mult(f(mult(Z, Y)), f(mult(Z, Y))))), Y)
% 41.88/5.74 = { by lemma 29 R->L }
% 41.88/5.74 mult(mult(X, mult(Y, mult(f(mult(Z, Y)), f(mult(Z, Y))))), rd(unit, Y))
% 41.88/5.74 = { by lemma 33 R->L }
% 41.88/5.74 mult(mult(X, mult(Y, mult(f(mult(Z, Y)), f(mult(Z, Y))))), rd(f(mult(Z, Y)), mult(Y, f(mult(Z, Y)))))
% 41.88/5.74 = { by lemma 24 R->L }
% 41.88/5.74 mult(mult(X, mult(mult(Y, f(mult(Z, Y))), f(mult(Z, Y)))), rd(f(mult(Z, Y)), mult(Y, f(mult(Z, Y)))))
% 41.88/5.74 = { by lemma 41 }
% 41.88/5.74 mult(mult(X, mult(Y, f(mult(Z, Y)))), rd(mult(f(mult(Z, Y)), f(mult(Z, Y))), mult(Y, f(mult(Z, Y)))))
% 41.88/5.74 = { by lemma 27 R->L }
% 41.88/5.74 mult(mult(X, mult(Y, f(mult(Z, Y)))), mult(f(mult(Z, Y)), rd(f(mult(Z, Y)), mult(Y, f(mult(Z, Y))))))
% 41.88/5.74 = { by lemma 33 }
% 41.88/5.74 mult(mult(X, mult(Y, f(mult(Z, Y)))), mult(f(mult(Z, Y)), rd(unit, Y)))
% 41.88/5.74 = { by lemma 29 }
% 41.88/5.74 mult(mult(X, mult(Y, f(mult(Z, Y)))), rd(f(mult(Z, Y)), Y))
% 41.88/5.74 = { by lemma 41 }
% 41.88/5.74 mult(mult(X, Y), rd(mult(f(mult(Z, Y)), f(mult(Z, Y))), Y))
% 41.88/5.74 = { by axiom 6 (c09) }
% 41.88/5.74 mult(mult(X, Y), rd(mult(Z, Y), Y))
% 41.88/5.74 = { by axiom 4 (c04) }
% 41.88/5.74 mult(mult(X, Y), Z)
% 41.88/5.74
% 41.88/5.74 Lemma 43: mult(mult(X, Y), mult(Z, ld(mult(Y, Z), unit))) = X.
% 41.88/5.74 Proof:
% 41.88/5.74 mult(mult(X, Y), mult(Z, ld(mult(Y, Z), unit)))
% 41.88/5.74 = { by lemma 42 R->L }
% 41.88/5.74 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(Y, Z), unit)), Y))), Y)
% 41.88/5.74 = { by lemma 40 R->L }
% 41.88/5.74 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z))), mult(mult(Y, Z), mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))), unit)), Y))), Y)
% 41.88/5.74 = { by axiom 5 (c01) R->L }
% 41.88/5.74 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(ld(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), ld(mult(Y, Z), mult(Y, Z))))), mult(mult(Y, Z), mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))), unit)), Y))), Y)
% 41.88/5.74 = { by lemma 25 R->L }
% 41.88/5.74 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(mult(Y, Z), ld(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), ld(mult(Y, Z), mult(Y, Z)))), mult(mult(Y, Z), mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))), unit)), Y))), Y)
% 41.88/5.74 = { by axiom 5 (c01) }
% 41.88/5.74 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(mult(Y, Z), ld(mult(Y, Z), mult(Y, Z)))), mult(mult(Y, Z), mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))), unit)), Y))), Y)
% 41.88/5.74 = { by axiom 5 (c01) }
% 41.88/5.74 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))), unit)), Y))), Y)
% 41.88/5.74 = { by lemma 20 R->L }
% 41.88/5.74 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), rd(mult(mult(Y, Z), mult(mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)), mult(Y, Z))), mult(Y, Z))), unit)), Y))), Y)
% 41.88/5.75 = { by lemma 24 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), rd(mult(mult(Y, Z), mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z)))), mult(Y, Z))), unit)), Y))), Y)
% 41.88/5.75 = { by axiom 5 (c01) R->L }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), rd(mult(mult(Y, Z), mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), ld(mult(Y, Z), mult(Y, Z)))), mult(mult(Y, Z), mult(Y, Z)))), mult(Y, Z))), unit)), Y))), Y)
% 41.88/5.75 = { by lemma 24 R->L }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), rd(mult(mult(Y, Z), mult(mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), ld(mult(Y, Z), mult(Y, Z)))), mult(Y, Z)), mult(Y, Z))), mult(Y, Z))), unit)), Y))), Y)
% 41.88/5.75 = { by lemma 13 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), rd(mult(mult(Y, Z), mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), mult(ld(mult(Y, Z), mult(Y, Z)), mult(Y, Z)))), mult(Y, Z))), mult(Y, Z))), unit)), Y))), Y)
% 41.88/5.75 = { by lemma 11 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), rd(mult(mult(Y, Z), mult(mult(ld(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z))), mult(Y, Z))), unit)), Y))), Y)
% 41.88/5.75 = { by lemma 15 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), rd(mult(mult(Y, Z), mult(ld(mult(Y, Z), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), mult(Y, Z))), mult(Y, Z))), unit)), Y))), Y)
% 41.88/5.75 = { by lemma 30 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), rd(mult(mult(Y, Z), ld(mult(Y, Z), mult(mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)))), mult(Y, Z))), unit)), Y))), Y)
% 41.88/5.75 = { by axiom 5 (c01) }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), rd(mult(mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), mult(Y, Z))), unit)), Y))), Y)
% 41.88/5.75 = { by axiom 4 (c04) }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), unit)), Y))), Y)
% 41.88/5.75 = { by lemma 10 R->L }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), ld(mult(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))))), Y))), Y)
% 41.88/5.75 = { by lemma 32 R->L }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(ld(mult(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))), Y))), Y)
% 41.88/5.75 = { by lemma 30 R->L }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))), Y))), Y)
% 41.88/5.75 = { by axiom 5 (c01) R->L }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(mult(mult(Y, Z), mult(Y, Z)), ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)))))), Y))), Y)
% 41.88/5.75 = { by lemma 40 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z))), Y))), Y)
% 41.88/5.75 = { by axiom 3 (c02) R->L }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(mult(Y, Z), mult(Y, Z)), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))))), mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(mult(Y, Z), mult(Y, Z)), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))))), ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z))))), Y))), Y)
% 41.88/5.75 = { by lemma 12 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(mult(Y, Z), mult(Y, Z)), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))))), mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(Y, Z))), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(mult(mult(Y, Z), mult(Y, Z)), ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z))))))), Y))), Y)
% 41.88/5.75 = { by axiom 5 (c01) }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(mult(Y, Z), mult(Y, Z)), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))))), mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(Y, Z))), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z))))), Y))), Y)
% 41.88/5.75 = { by lemma 30 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(mult(Y, Z), mult(Y, Z)), ld(mult(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))))), mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(Y, Z))), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z))))), Y))), Y)
% 41.88/5.75 = { by axiom 5 (c01) }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(Y, Z))), mult(ld(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z)), mult(Y, Z))))), Y))), Y)
% 41.88/5.75 = { by lemma 32 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(Y, Z))), ld(mult(mult(Y, Z), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z)))))), Y))), Y)
% 41.88/5.75 = { by lemma 10 }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(Y, Z))), unit))), Y))), Y)
% 41.88/5.75 = { by axiom 1 (c05) }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(Y, Z))))), Y))), Y)
% 41.88/5.75 = { by axiom 7 (c03) }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), Z)), Y))), Y)
% 41.88/5.75 = { by lemma 37 R->L }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), rd(unit, mult(Y, Z))), mult(mult(Y, Z), mult(mult(Y, Z), mult(Y, Z)))), Z)), Y))), Y)
% 41.88/5.75 = { by axiom 8 (c08) R->L }
% 41.88/5.75 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), rd(unit, mult(Y, Z))), mult(mult(mult(Y, Z), mult(Y, Z)), mult(Y, Z))), Z)), Y))), Y)
% 41.88/5.76 = { by axiom 2 (c06) R->L }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), rd(unit, mult(Y, Z))), mult(mult(mult(Y, Z), mult(Y, Z)), mult(unit, mult(Y, Z)))), Z)), Y))), Y)
% 41.88/5.76 = { by axiom 7 (c03) R->L }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), rd(unit, mult(Y, Z))), mult(mult(mult(Y, Z), mult(Y, Z)), mult(mult(rd(unit, mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))), Z)), Y))), Y)
% 41.88/5.76 = { by lemma 24 }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), rd(unit, mult(Y, Z))), mult(mult(mult(Y, Z), mult(Y, Z)), mult(rd(unit, mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))))), Z)), Y))), Y)
% 41.88/5.76 = { by lemma 12 R->L }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), mult(rd(unit, mult(Y, Z)), mult(mult(mult(Y, Z), mult(Y, Z)), rd(unit, mult(Y, Z))))), mult(mult(Y, Z), mult(Y, Z))), Z)), Y))), Y)
% 41.88/5.76 = { by lemma 37 }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), mult(rd(unit, mult(Y, Z)), mult(Y, Z))), mult(mult(Y, Z), mult(Y, Z))), Z)), Y))), Y)
% 41.88/5.76 = { by axiom 7 (c03) }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), unit), mult(mult(Y, Z), mult(Y, Z))), Z)), Y))), Y)
% 41.88/5.76 = { by axiom 1 (c05) }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), mult(mult(Y, Z), mult(Y, Z))), Z)), Y))), Y)
% 41.88/5.76 = { by lemma 24 R->L }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), mult(Y, Z)), mult(Y, Z)), Z)), Y))), Y)
% 41.88/5.76 = { by lemma 24 }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(mult(rd(Z, mult(mult(Y, Z), mult(Y, Z))), mult(mult(Y, Z), mult(Y, Z))), mult(Y, Z)), Z)), Y))), Y)
% 41.88/5.76 = { by axiom 7 (c03) }
% 41.88/5.76 rd(mult(X, mult(Y, mult(mult(Z, ld(mult(Z, mult(Y, Z)), Z)), Y))), Y)
% 41.88/5.76 = { by axiom 3 (c02) R->L }
% 41.88/5.76 rd(mult(X, ld(Z, mult(Z, mult(Y, mult(mult(Z, ld(mult(Z, mult(Y, Z)), Z)), Y))))), Y)
% 41.88/5.76 = { by axiom 4 (c04) R->L }
% 41.88/5.76 rd(mult(X, ld(rd(mult(Z, ld(mult(mult(Z, Y), Z), unit)), ld(mult(mult(Z, Y), Z), unit)), mult(Z, mult(Y, mult(mult(Z, ld(mult(Z, mult(Y, Z)), Z)), Y))))), Y)
% 41.88/5.76 = { by lemma 22 R->L }
% 41.88/5.76 rd(mult(X, ld(rd(mult(mult(mult(Z, Y), Z), mult(ld(mult(mult(Z, Y), Z), unit), mult(Z, ld(mult(mult(Z, Y), Z), unit)))), ld(mult(mult(Z, Y), Z), unit)), mult(Z, mult(Y, mult(mult(Z, ld(mult(Z, mult(Y, Z)), Z)), Y))))), Y)
% 41.88/5.76 = { by lemma 19 }
% 41.88/5.76 rd(mult(X, ld(mult(mult(Z, Y), mult(Z, mult(ld(mult(mult(Z, Y), Z), unit), Z))), mult(Z, mult(Y, mult(mult(Z, ld(mult(Z, mult(Y, Z)), Z)), Y))))), Y)
% 41.88/5.76 = { by axiom 8 (c08) }
% 41.88/5.76 rd(mult(X, ld(mult(mult(Z, Y), mult(Z, mult(ld(mult(Z, mult(Y, Z)), unit), Z))), mult(Z, mult(Y, mult(mult(Z, ld(mult(Z, mult(Y, Z)), Z)), Y))))), Y)
% 41.88/5.76 = { by lemma 31 }
% 41.88/5.76 rd(mult(X, ld(mult(mult(Z, Y), mult(Z, ld(mult(Z, mult(Y, Z)), Z))), mult(Z, mult(Y, mult(mult(Z, ld(mult(Z, mult(Y, Z)), Z)), Y))))), Y)
% 41.88/5.76 = { by lemma 42 R->L }
% 41.88/5.76 rd(mult(X, ld(rd(mult(Z, mult(Y, mult(mult(Z, ld(mult(Z, mult(Y, Z)), Z)), Y))), Y), mult(Z, mult(Y, mult(mult(Z, ld(mult(Z, mult(Y, Z)), Z)), Y))))), Y)
% 41.88/5.76 = { by lemma 17 }
% 41.88/5.76 rd(mult(X, Y), Y)
% 41.88/5.76 = { by axiom 4 (c04) }
% 41.88/5.76 X
% 41.88/5.76
% 41.88/5.76 Goal 1 (goals): mult(a, mult(b, mult(a, c))) = mult(mult(mult(a, b), a), c).
% 41.88/5.76 Proof:
% 41.88/5.76 mult(a, mult(b, mult(a, c)))
% 41.88/5.76 = { by lemma 20 R->L }
% 41.88/5.76 rd(mult(a, mult(mult(b, mult(a, c)), a)), a)
% 41.88/5.76 = { by lemma 39 R->L }
% 41.88/5.76 rd(mult(a, mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), a)
% 41.88/5.76 = { by lemma 39 R->L }
% 41.88/5.76 rd(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), a)
% 41.88/5.76 = { by lemma 43 R->L }
% 41.88/5.76 rd(mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))), a)
% 41.88/5.76 = { by lemma 23 R->L }
% 41.88/5.76 rd(mult(mult(ld(mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))), unit), mult(mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))), mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)))), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))), a)
% 41.88/5.76 = { by axiom 8 (c08) }
% 41.88/5.76 rd(mult(mult(ld(mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))), unit), mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit)), mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b))))), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))), a)
% 41.88/5.76 = { by lemma 12 }
% 41.88/5.76 rd(mult(mult(ld(mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))), unit), mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b))), mult(mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit)), mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))))), a)
% 41.88/5.76 = { by lemma 31 }
% 41.88/5.76 rd(mult(ld(mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))), mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b))), mult(mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit)), mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))))), a)
% 41.88/5.76 = { by lemma 43 }
% 41.88/5.76 rd(mult(ld(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b))), mult(mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit)), mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))))), a)
% 41.88/5.76 = { by axiom 3 (c02) }
% 41.88/5.76 rd(mult(mult(a, b), mult(mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit)), mult(mult(mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))), mult(a, b)), mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit))))), a)
% 41.88/5.76 = { by lemma 43 }
% 41.88/5.76 rd(mult(mult(a, b), mult(mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit)), mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit)))))), a)
% 41.88/5.76 = { by axiom 7 (c03) R->L }
% 41.88/5.76 rd(mult(mult(a, b), mult(rd(mult(mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit)), mult(mult(mult(a, b), ld(b, unit)), mult(mult(b, mult(a, c)), mult(mult(a, b), ld(b, unit))))), mult(mult(a, b), ld(b, unit))), mult(mult(a, b), ld(b, unit)))), a)
% 41.88/5.76 = { by lemma 42 }
% 41.88/5.76 rd(mult(mult(a, b), mult(mult(mult(mult(ld(b, unit), ld(mult(mult(a, b), ld(b, unit)), unit)), mult(mult(a, b), ld(b, unit))), mult(b, mult(a, c))), mult(mult(a, b), ld(b, unit)))), a)
% 41.88/5.76 = { by lemma 38 }
% 41.88/5.76 rd(mult(mult(a, b), mult(mult(ld(b, unit), mult(b, mult(a, c))), mult(mult(a, b), ld(b, unit)))), a)
% 41.88/5.76 = { by lemma 31 }
% 41.88/5.76 rd(mult(mult(a, b), mult(ld(b, mult(b, mult(a, c))), mult(mult(a, b), ld(b, unit)))), a)
% 41.88/5.76 = { by lemma 39 }
% 41.88/5.76 rd(mult(mult(a, b), mult(ld(b, mult(b, mult(a, c))), a)), a)
% 41.88/5.76 = { by axiom 3 (c02) }
% 41.88/5.76 rd(mult(mult(a, b), mult(mult(a, c), a)), a)
% 41.88/5.76 = { by lemma 36 R->L }
% 41.88/5.76 rd(mult(mult(a, b), mult(a, mult(rd(unit, a), mult(mult(a, c), a)))), a)
% 41.88/5.76 = { by lemma 35 R->L }
% 41.88/5.76 rd(mult(mult(a, b), mult(a, mult(rd(unit, a), rd(mult(a, c), rd(unit, a))))), a)
% 41.88/5.76 = { by lemma 28 }
% 41.88/5.76 rd(mult(mult(a, b), mult(a, rd(mult(rd(unit, a), mult(a, c)), rd(unit, a)))), a)
% 41.88/5.76 = { by lemma 35 }
% 41.88/5.76 rd(mult(mult(a, b), mult(a, mult(mult(rd(unit, a), mult(a, c)), a))), a)
% 41.88/5.76 = { by lemma 42 }
% 41.88/5.76 mult(mult(mult(a, b), a), mult(rd(unit, a), mult(a, c)))
% 41.88/5.76 = { by axiom 8 (c08) }
% 41.88/5.76 mult(mult(a, mult(b, a)), mult(rd(unit, a), mult(a, c)))
% 41.88/5.76 = { by lemma 21 }
% 41.88/5.76 mult(mult(a, mult(b, a)), c)
% 41.88/5.76 = { by axiom 8 (c08) R->L }
% 41.88/5.76 mult(mult(mult(a, b), a), c)
% 41.88/5.76 % SZS output end Proof
% 41.88/5.76
% 41.88/5.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------