%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP667+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:11:39 AM UTC 2026
% Result : Theorem 134.11s 17.43s
% Output : Proof 119.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP667+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:33:55 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 134.11/17.43 Command-line arguments: --no-flatten-goal
% 134.11/17.43
% 134.11/17.43 % SZS status Theorem
% 134.11/17.43
% 119.25/17.55 % SZS output start Proof
% 119.25/17.55 Axiom 1 (f05): mult(X, unit) = X.
% 119.25/17.55 Axiom 2 (f06): mult(unit, X) = X.
% 119.25/17.55 Axiom 3 (f09): mult(f(X), f(X)) = X.
% 119.25/17.55 Axiom 4 (f02): ld(X, mult(X, Y)) = Y.
% 119.25/17.55 Axiom 5 (f04): rd(mult(X, Y), Y) = X.
% 119.25/17.55 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 119.25/17.55 Axiom 7 (f01): mult(X, ld(X, Y)) = Y.
% 119.25/17.55 Axiom 8 (f03): mult(rd(X, Y), Y) = X.
% 119.25/17.55 Axiom 9 (f08): mult(mult(X, Y), X) = mult(X, mult(Y, X)).
% 119.25/17.55 Axiom 10 (f07): mult(mult(X, Y), mult(mult(Z, Y), Z)) = mult(mult(X, mult(mult(Y, Z), Y)), Z).
% 119.25/17.55 Axiom 11 (f10): ifeq(mult(X, mult(Y, mult(Z, Y))), mult(mult(mult(X, Y), Z), Y), mult(Y, mult(X, mult(Y, Z))), mult(mult(mult(Y, X), Y), Z)) = mult(mult(mult(Y, X), Y), Z).
% 119.25/17.55
% 119.25/17.55 Lemma 12: ld(X, X) = unit.
% 119.25/17.55 Proof:
% 119.25/17.55 ld(X, X)
% 119.25/17.55 = { by axiom 1 (f05) R->L }
% 119.25/17.55 ld(X, mult(X, unit))
% 119.25/17.55 = { by axiom 4 (f02) }
% 119.25/17.55 unit
% 119.25/17.55
% 119.25/17.55 Lemma 13: mult(f(X), X) = mult(X, f(X)).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(f(X), X)
% 119.25/17.55 = { by axiom 3 (f09) R->L }
% 119.25/17.55 mult(f(X), mult(f(X), f(X)))
% 119.25/17.55 = { by axiom 9 (f08) R->L }
% 119.25/17.55 mult(mult(f(X), f(X)), f(X))
% 119.25/17.55 = { by axiom 3 (f09) }
% 119.25/17.55 mult(X, f(X))
% 119.25/17.55
% 119.25/17.55 Lemma 14: mult(X, rd(Y, X)) = rd(mult(X, Y), X).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(X, rd(Y, X))
% 119.25/17.55 = { by axiom 5 (f04) R->L }
% 119.25/17.55 rd(mult(mult(X, rd(Y, X)), X), X)
% 119.25/17.55 = { by axiom 9 (f08) }
% 119.25/17.55 rd(mult(X, mult(rd(Y, X), X)), X)
% 119.25/17.55 = { by axiom 8 (f03) }
% 119.25/17.55 rd(mult(X, Y), X)
% 119.25/17.55
% 119.25/17.55 Lemma 15: ld(X, rd(mult(X, Y), X)) = rd(Y, X).
% 119.25/17.55 Proof:
% 119.25/17.55 ld(X, rd(mult(X, Y), X))
% 119.25/17.55 = { by lemma 14 R->L }
% 119.25/17.55 ld(X, mult(X, rd(Y, X)))
% 119.25/17.55 = { by axiom 4 (f02) }
% 119.25/17.55 rd(Y, X)
% 119.25/17.55
% 119.25/17.55 Lemma 16: rd(mult(X, f(X)), X) = f(X).
% 119.25/17.55 Proof:
% 119.25/17.55 rd(mult(X, f(X)), X)
% 119.25/17.55 = { by lemma 13 R->L }
% 119.25/17.55 rd(mult(f(X), X), X)
% 119.25/17.55 = { by axiom 5 (f04) }
% 119.25/17.55 f(X)
% 119.25/17.55
% 119.25/17.55 Lemma 17: rd(f(X), X) = ld(X, f(X)).
% 119.25/17.55 Proof:
% 119.25/17.55 rd(f(X), X)
% 119.25/17.55 = { by lemma 15 R->L }
% 119.25/17.55 ld(X, rd(mult(X, f(X)), X))
% 119.25/17.55 = { by lemma 16 }
% 119.25/17.55 ld(X, f(X))
% 119.25/17.55
% 119.25/17.55 Lemma 18: ld(rd(X, Y), X) = Y.
% 119.25/17.55 Proof:
% 119.25/17.55 ld(rd(X, Y), X)
% 119.25/17.55 = { by axiom 8 (f03) R->L }
% 119.25/17.55 ld(rd(X, Y), mult(rd(X, Y), Y))
% 119.25/17.55 = { by axiom 4 (f02) }
% 119.25/17.55 Y
% 119.25/17.55
% 119.25/17.55 Lemma 19: ifeq(mult(X, mult(Y, mult(Z, Y))), mult(mult(mult(X, Y), Z), Y), mult(Y, mult(X, mult(Y, Z))), mult(mult(Y, mult(X, Y)), Z)) = mult(mult(Y, mult(X, Y)), Z).
% 119.25/17.55 Proof:
% 119.25/17.55 ifeq(mult(X, mult(Y, mult(Z, Y))), mult(mult(mult(X, Y), Z), Y), mult(Y, mult(X, mult(Y, Z))), mult(mult(Y, mult(X, Y)), Z))
% 119.25/17.55 = { by axiom 9 (f08) R->L }
% 119.25/17.55 ifeq(mult(X, mult(Y, mult(Z, Y))), mult(mult(mult(X, Y), Z), Y), mult(Y, mult(X, mult(Y, Z))), mult(mult(mult(Y, X), Y), Z))
% 119.25/17.55 = { by axiom 11 (f10) }
% 119.25/17.55 mult(mult(mult(Y, X), Y), Z)
% 119.25/17.55 = { by axiom 9 (f08) }
% 119.25/17.55 mult(mult(Y, mult(X, Y)), Z)
% 119.25/17.55
% 119.25/17.55 Lemma 20: mult(mult(X, X), Y) = mult(X, mult(X, Y)).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(mult(X, X), Y)
% 119.25/17.55 = { by axiom 2 (f06) R->L }
% 119.25/17.55 mult(mult(X, mult(unit, X)), Y)
% 119.25/17.55 = { by lemma 19 R->L }
% 119.25/17.55 ifeq(mult(unit, mult(X, mult(Y, X))), mult(mult(mult(unit, X), Y), X), mult(X, mult(unit, mult(X, Y))), mult(mult(X, mult(unit, X)), Y))
% 119.25/17.55 = { by axiom 2 (f06) }
% 119.25/17.55 ifeq(mult(X, mult(Y, X)), mult(mult(mult(unit, X), Y), X), mult(X, mult(unit, mult(X, Y))), mult(mult(X, mult(unit, X)), Y))
% 119.25/17.55 = { by axiom 2 (f06) }
% 119.25/17.55 ifeq(mult(X, mult(Y, X)), mult(mult(X, Y), X), mult(X, mult(unit, mult(X, Y))), mult(mult(X, mult(unit, X)), Y))
% 119.25/17.55 = { by axiom 2 (f06) }
% 119.25/17.55 ifeq(mult(X, mult(Y, X)), mult(mult(X, Y), X), mult(X, mult(unit, mult(X, Y))), mult(mult(X, X), Y))
% 119.25/17.55 = { by axiom 9 (f08) }
% 119.25/17.55 ifeq(mult(X, mult(Y, X)), mult(X, mult(Y, X)), mult(X, mult(unit, mult(X, Y))), mult(mult(X, X), Y))
% 119.25/17.55 = { by axiom 6 (ifeq_axiom) }
% 119.25/17.55 mult(X, mult(unit, mult(X, Y)))
% 119.25/17.55 = { by axiom 2 (f06) }
% 119.25/17.55 mult(X, mult(X, Y))
% 119.25/17.55
% 119.25/17.55 Lemma 21: mult(f(X), mult(f(X), Y)) = mult(X, Y).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(f(X), mult(f(X), Y))
% 119.25/17.55 = { by lemma 20 R->L }
% 119.25/17.55 mult(mult(f(X), f(X)), Y)
% 119.25/17.55 = { by axiom 3 (f09) }
% 119.25/17.55 mult(X, Y)
% 119.25/17.55
% 119.25/17.55 Lemma 22: ld(f(X), mult(X, Y)) = mult(f(X), Y).
% 119.25/17.55 Proof:
% 119.25/17.55 ld(f(X), mult(X, Y))
% 119.25/17.55 = { by lemma 21 R->L }
% 119.25/17.55 ld(f(X), mult(f(X), mult(f(X), Y)))
% 119.25/17.55 = { by axiom 4 (f02) }
% 119.25/17.55 mult(f(X), Y)
% 119.25/17.55
% 119.25/17.55 Lemma 23: mult(f(X), ld(X, Y)) = ld(f(X), Y).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(f(X), ld(X, Y))
% 119.25/17.55 = { by lemma 22 R->L }
% 119.25/17.55 ld(f(X), mult(X, ld(X, Y)))
% 119.25/17.55 = { by axiom 7 (f01) }
% 119.25/17.55 ld(f(X), Y)
% 119.25/17.55
% 119.25/17.55 Lemma 24: rd(mult(X, mult(X, Y)), Y) = mult(X, X).
% 119.25/17.55 Proof:
% 119.25/17.55 rd(mult(X, mult(X, Y)), Y)
% 119.25/17.55 = { by lemma 20 R->L }
% 119.25/17.55 rd(mult(mult(X, X), Y), Y)
% 119.25/17.55 = { by axiom 5 (f04) }
% 119.25/17.55 mult(X, X)
% 119.25/17.55
% 119.25/17.55 Lemma 25: rd(mult(X, Y), ld(X, Y)) = mult(X, X).
% 119.25/17.55 Proof:
% 119.25/17.55 rd(mult(X, Y), ld(X, Y))
% 119.25/17.55 = { by axiom 7 (f01) R->L }
% 119.25/17.55 rd(mult(X, mult(X, ld(X, Y))), ld(X, Y))
% 119.25/17.55 = { by lemma 24 }
% 119.25/17.55 mult(X, X)
% 119.25/17.55
% 119.25/17.55 Lemma 26: mult(mult(X, mult(Y, mult(Z, Y))), Z) = mult(mult(X, Y), mult(Z, mult(Y, Z))).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(mult(X, mult(Y, mult(Z, Y))), Z)
% 119.25/17.55 = { by axiom 9 (f08) R->L }
% 119.25/17.55 mult(mult(X, mult(mult(Y, Z), Y)), Z)
% 119.25/17.55 = { by axiom 10 (f07) R->L }
% 119.25/17.55 mult(mult(X, Y), mult(mult(Z, Y), Z))
% 119.25/17.55 = { by axiom 9 (f08) }
% 119.25/17.55 mult(mult(X, Y), mult(Z, mult(Y, Z)))
% 119.25/17.55
% 119.25/17.55 Lemma 27: mult(mult(X, Y), Y) = mult(X, mult(Y, Y)).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(mult(X, Y), Y)
% 119.25/17.55 = { by axiom 1 (f05) R->L }
% 119.25/17.55 mult(mult(X, Y), mult(Y, unit))
% 119.25/17.55 = { by axiom 2 (f06) R->L }
% 119.25/17.55 mult(mult(X, Y), mult(unit, mult(Y, unit)))
% 119.25/17.55 = { by lemma 26 R->L }
% 119.25/17.55 mult(mult(X, mult(Y, mult(unit, Y))), unit)
% 119.25/17.55 = { by axiom 1 (f05) }
% 119.25/17.55 mult(X, mult(Y, mult(unit, Y)))
% 119.25/17.55 = { by axiom 2 (f06) }
% 119.25/17.55 mult(X, mult(Y, Y))
% 119.25/17.55
% 119.25/17.55 Lemma 28: rd(mult(X, mult(Y, Y)), Y) = mult(X, Y).
% 119.25/17.55 Proof:
% 119.25/17.55 rd(mult(X, mult(Y, Y)), Y)
% 119.25/17.55 = { by lemma 27 R->L }
% 119.25/17.55 rd(mult(mult(X, Y), Y), Y)
% 119.25/17.55 = { by axiom 5 (f04) }
% 119.25/17.55 mult(X, Y)
% 119.25/17.55
% 119.25/17.55 Lemma 29: ld(X, mult(f(X), Y)) = ld(f(X), Y).
% 119.25/17.55 Proof:
% 119.25/17.55 ld(X, mult(f(X), Y))
% 119.25/17.55 = { by axiom 7 (f01) R->L }
% 119.25/17.55 ld(X, mult(f(X), mult(f(X), ld(f(X), Y))))
% 119.25/17.55 = { by lemma 21 }
% 119.25/17.55 ld(X, mult(X, ld(f(X), Y)))
% 119.25/17.55 = { by axiom 4 (f02) }
% 119.25/17.55 ld(f(X), Y)
% 119.25/17.55
% 119.25/17.55 Lemma 30: mult(mult(X, mult(Y, X)), Y) = mult(X, mult(Y, mult(X, Y))).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(mult(X, mult(Y, X)), Y)
% 119.25/17.55 = { by axiom 2 (f06) R->L }
% 119.25/17.55 mult(mult(unit, mult(X, mult(Y, X))), Y)
% 119.25/17.55 = { by lemma 26 }
% 119.25/17.55 mult(mult(unit, X), mult(Y, mult(X, Y)))
% 119.25/17.55 = { by axiom 2 (f06) }
% 119.25/17.55 mult(X, mult(Y, mult(X, Y)))
% 119.25/17.55
% 119.25/17.55 Lemma 31: mult(X, mult(ld(X, Y), X)) = mult(Y, X).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(X, mult(ld(X, Y), X))
% 119.25/17.55 = { by axiom 9 (f08) R->L }
% 119.25/17.55 mult(mult(X, ld(X, Y)), X)
% 119.25/17.55 = { by axiom 7 (f01) }
% 119.25/17.55 mult(Y, X)
% 119.25/17.55
% 119.25/17.55 Lemma 32: mult(mult(X, Y), mult(X, mult(Y, X))) = mult(X, mult(Y, mult(X, mult(Y, X)))).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(mult(X, Y), mult(X, mult(Y, X)))
% 119.25/17.55 = { by lemma 26 R->L }
% 119.25/17.55 mult(mult(X, mult(Y, mult(X, Y))), X)
% 119.25/17.55 = { by axiom 9 (f08) }
% 119.25/17.55 mult(X, mult(mult(Y, mult(X, Y)), X))
% 119.25/17.55 = { by lemma 30 }
% 119.25/17.55 mult(X, mult(Y, mult(X, mult(Y, X))))
% 119.25/17.55
% 119.25/17.55 Lemma 33: mult(ld(X, Y), Y) = ld(X, mult(Y, Y)).
% 119.25/17.55 Proof:
% 119.25/17.55 mult(ld(X, Y), Y)
% 119.25/17.55 = { by axiom 5 (f04) R->L }
% 119.25/17.55 rd(mult(mult(ld(X, Y), Y), X), X)
% 119.25/17.55 = { by axiom 7 (f01) R->L }
% 119.25/17.55 rd(mult(mult(ld(X, Y), mult(X, ld(X, Y))), X), X)
% 119.25/17.55 = { by lemma 30 }
% 119.25/17.55 rd(mult(ld(X, Y), mult(X, mult(ld(X, Y), X))), X)
% 119.25/17.56 = { by lemma 31 }
% 119.25/17.56 rd(mult(ld(X, Y), mult(Y, X)), X)
% 119.25/17.56 = { by axiom 4 (f02) R->L }
% 119.25/17.56 rd(ld(X, mult(X, mult(ld(X, Y), mult(Y, X)))), X)
% 119.25/17.56 = { by lemma 31 R->L }
% 119.25/17.56 rd(ld(X, mult(X, mult(ld(X, Y), mult(X, mult(ld(X, Y), X))))), X)
% 119.25/17.56 = { by lemma 32 R->L }
% 119.25/17.56 rd(ld(X, mult(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), X)))), X)
% 119.25/17.56 = { by axiom 7 (f01) }
% 119.25/17.56 rd(ld(X, mult(Y, mult(X, mult(ld(X, Y), X)))), X)
% 119.25/17.56 = { by lemma 31 }
% 119.25/17.56 rd(ld(X, mult(Y, mult(Y, X))), X)
% 119.25/17.56 = { by lemma 15 R->L }
% 119.25/17.56 ld(X, rd(mult(X, ld(X, mult(Y, mult(Y, X)))), X))
% 119.25/17.56 = { by axiom 7 (f01) }
% 119.25/17.56 ld(X, rd(mult(Y, mult(Y, X)), X))
% 119.25/17.56 = { by lemma 24 }
% 119.25/17.56 ld(X, mult(Y, Y))
% 119.25/17.56
% 119.25/17.56 Lemma 34: rd(X, ld(Y, f(Y))) = mult(X, f(Y)).
% 119.25/17.56 Proof:
% 119.25/17.56 rd(X, ld(Y, f(Y)))
% 119.25/17.56 = { by axiom 8 (f03) R->L }
% 119.25/17.56 rd(mult(rd(X, Y), Y), ld(Y, f(Y)))
% 119.25/17.56 = { by axiom 1 (f05) R->L }
% 119.25/17.56 rd(mult(mult(rd(X, Y), Y), unit), ld(Y, f(Y)))
% 119.25/17.56 = { by lemma 12 R->L }
% 119.25/17.56 rd(mult(mult(rd(X, Y), Y), ld(f(Y), f(Y))), ld(Y, f(Y)))
% 119.25/17.56 = { by lemma 29 R->L }
% 119.25/17.56 rd(mult(mult(rd(X, Y), Y), ld(Y, mult(f(Y), f(Y)))), ld(Y, f(Y)))
% 119.25/17.56 = { by lemma 33 R->L }
% 119.25/17.56 rd(mult(mult(rd(X, Y), Y), mult(ld(Y, f(Y)), f(Y))), ld(Y, f(Y)))
% 119.25/17.56 = { by axiom 7 (f01) R->L }
% 119.25/17.56 rd(mult(mult(rd(X, Y), Y), mult(ld(Y, f(Y)), mult(Y, ld(Y, f(Y))))), ld(Y, f(Y)))
% 119.25/17.56 = { by lemma 26 R->L }
% 119.25/17.56 rd(mult(mult(rd(X, Y), mult(Y, mult(ld(Y, f(Y)), Y))), ld(Y, f(Y))), ld(Y, f(Y)))
% 119.25/17.56 = { by lemma 31 }
% 119.25/17.56 rd(mult(mult(rd(X, Y), mult(f(Y), Y)), ld(Y, f(Y))), ld(Y, f(Y)))
% 119.25/17.56 = { by lemma 13 }
% 119.25/17.56 rd(mult(mult(rd(X, Y), mult(Y, f(Y))), ld(Y, f(Y))), ld(Y, f(Y)))
% 119.25/17.56 = { by axiom 5 (f04) }
% 119.25/17.56 mult(rd(X, Y), mult(Y, f(Y)))
% 119.25/17.56 = { by lemma 21 R->L }
% 119.25/17.56 mult(rd(X, Y), mult(f(Y), mult(f(Y), f(Y))))
% 119.25/17.56 = { by axiom 4 (f02) R->L }
% 119.25/17.56 ld(f(Y), mult(f(Y), mult(rd(X, Y), mult(f(Y), mult(f(Y), f(Y))))))
% 119.25/17.56 = { by axiom 6 (ifeq_axiom) R->L }
% 119.25/17.56 ld(f(Y), ifeq(mult(rd(X, Y), mult(f(Y), mult(f(Y), mult(f(Y), f(Y))))), mult(rd(X, Y), mult(f(Y), mult(f(Y), mult(f(Y), f(Y))))), mult(f(Y), mult(rd(X, Y), mult(f(Y), mult(f(Y), f(Y))))), mult(mult(f(Y), mult(rd(X, Y), f(Y))), mult(f(Y), f(Y)))))
% 119.25/17.56 = { by lemma 20 R->L }
% 119.25/17.56 ld(f(Y), ifeq(mult(rd(X, Y), mult(f(Y), mult(f(Y), mult(f(Y), f(Y))))), mult(rd(X, Y), mult(mult(f(Y), f(Y)), mult(f(Y), f(Y)))), mult(f(Y), mult(rd(X, Y), mult(f(Y), mult(f(Y), f(Y))))), mult(mult(f(Y), mult(rd(X, Y), f(Y))), mult(f(Y), f(Y)))))
% 119.25/17.56 = { by lemma 27 R->L }
% 119.25/17.56 ld(f(Y), ifeq(mult(rd(X, Y), mult(f(Y), mult(f(Y), mult(f(Y), f(Y))))), mult(mult(rd(X, Y), mult(f(Y), f(Y))), mult(f(Y), f(Y))), mult(f(Y), mult(rd(X, Y), mult(f(Y), mult(f(Y), f(Y))))), mult(mult(f(Y), mult(rd(X, Y), f(Y))), mult(f(Y), f(Y)))))
% 119.25/17.56 = { by lemma 27 R->L }
% 119.25/17.56 ld(f(Y), ifeq(mult(rd(X, Y), mult(f(Y), mult(f(Y), mult(f(Y), f(Y))))), mult(mult(mult(rd(X, Y), f(Y)), f(Y)), mult(f(Y), f(Y))), mult(f(Y), mult(rd(X, Y), mult(f(Y), mult(f(Y), f(Y))))), mult(mult(f(Y), mult(rd(X, Y), f(Y))), mult(f(Y), f(Y)))))
% 119.25/17.56 = { by lemma 20 R->L }
% 119.25/17.56 ld(f(Y), ifeq(mult(rd(X, Y), mult(f(Y), mult(mult(f(Y), f(Y)), f(Y)))), mult(mult(mult(rd(X, Y), f(Y)), f(Y)), mult(f(Y), f(Y))), mult(f(Y), mult(rd(X, Y), mult(f(Y), mult(f(Y), f(Y))))), mult(mult(f(Y), mult(rd(X, Y), f(Y))), mult(f(Y), f(Y)))))
% 119.25/17.56 = { by lemma 27 R->L }
% 119.25/17.56 ld(f(Y), ifeq(mult(rd(X, Y), mult(f(Y), mult(mult(f(Y), f(Y)), f(Y)))), mult(mult(mult(mult(rd(X, Y), f(Y)), f(Y)), f(Y)), f(Y)), mult(f(Y), mult(rd(X, Y), mult(f(Y), mult(f(Y), f(Y))))), mult(mult(f(Y), mult(rd(X, Y), f(Y))), mult(f(Y), f(Y)))))
% 119.25/17.56 = { by lemma 27 }
% 119.25/17.56 ld(f(Y), ifeq(mult(rd(X, Y), mult(f(Y), mult(mult(f(Y), f(Y)), f(Y)))), mult(mult(mult(rd(X, Y), f(Y)), mult(f(Y), f(Y))), f(Y)), mult(f(Y), mult(rd(X, Y), mult(f(Y), mult(f(Y), f(Y))))), mult(mult(f(Y), mult(rd(X, Y), f(Y))), mult(f(Y), f(Y)))))
% 119.25/17.56 = { by lemma 19 }
% 119.25/17.56 ld(f(Y), mult(mult(f(Y), mult(rd(X, Y), f(Y))), mult(f(Y), f(Y))))
% 119.25/17.56 = { by lemma 27 R->L }
% 119.25/17.56 ld(f(Y), mult(mult(mult(f(Y), mult(rd(X, Y), f(Y))), f(Y)), f(Y)))
% 119.25/17.56 = { by axiom 9 (f08) }
% 119.25/17.56 ld(f(Y), mult(mult(f(Y), mult(mult(rd(X, Y), f(Y)), f(Y))), f(Y)))
% 119.25/17.56 = { by axiom 9 (f08) }
% 119.25/17.56 ld(f(Y), mult(f(Y), mult(mult(mult(rd(X, Y), f(Y)), f(Y)), f(Y))))
% 119.25/17.56 = { by lemma 27 }
% 119.25/17.56 ld(f(Y), mult(f(Y), mult(mult(rd(X, Y), f(Y)), mult(f(Y), f(Y)))))
% 119.25/17.56 = { by axiom 4 (f02) }
% 119.25/17.56 mult(mult(rd(X, Y), f(Y)), mult(f(Y), f(Y)))
% 119.25/17.56 = { by lemma 28 R->L }
% 119.25/17.56 mult(rd(mult(rd(X, Y), mult(f(Y), f(Y))), f(Y)), mult(f(Y), f(Y)))
% 119.25/17.56 = { by axiom 3 (f09) }
% 119.25/17.56 mult(rd(mult(rd(X, Y), Y), f(Y)), mult(f(Y), f(Y)))
% 119.25/17.56 = { by axiom 8 (f03) }
% 119.25/17.56 mult(rd(X, f(Y)), mult(f(Y), f(Y)))
% 119.25/17.56 = { by lemma 27 R->L }
% 119.25/17.56 mult(mult(rd(X, f(Y)), f(Y)), f(Y))
% 119.25/17.56 = { by axiom 8 (f03) }
% 119.25/17.56 mult(X, f(Y))
% 119.25/17.56
% 119.25/17.56 Lemma 35: rd(X, ld(Y, unit)) = mult(X, Y).
% 119.25/17.56 Proof:
% 119.25/17.56 rd(X, ld(Y, unit))
% 119.25/17.56 = { by lemma 18 R->L }
% 119.25/17.56 rd(X, ld(ld(rd(f(Y), Y), f(Y)), unit))
% 119.25/17.56 = { by lemma 17 }
% 119.25/17.56 rd(X, ld(ld(ld(Y, f(Y)), f(Y)), unit))
% 119.25/17.56 = { by axiom 5 (f04) R->L }
% 119.25/17.56 rd(X, ld(ld(ld(Y, f(Y)), f(Y)), rd(mult(unit, ld(ld(Y, f(Y)), f(Y))), ld(ld(Y, f(Y)), f(Y)))))
% 119.25/17.56 = { by axiom 2 (f06) }
% 119.25/17.56 rd(X, ld(ld(ld(Y, f(Y)), f(Y)), rd(ld(ld(Y, f(Y)), f(Y)), ld(ld(Y, f(Y)), f(Y)))))
% 119.25/17.56 = { by axiom 1 (f05) R->L }
% 119.25/17.56 rd(X, ld(ld(ld(Y, f(Y)), f(Y)), rd(mult(ld(ld(Y, f(Y)), f(Y)), unit), ld(ld(Y, f(Y)), f(Y)))))
% 119.25/17.56 = { by lemma 15 }
% 119.25/17.56 rd(X, rd(unit, ld(ld(Y, f(Y)), f(Y))))
% 119.25/17.56 = { by lemma 12 R->L }
% 119.25/17.56 rd(X, rd(ld(f(Y), f(Y)), ld(ld(Y, f(Y)), f(Y))))
% 119.25/17.56 = { by lemma 23 R->L }
% 119.25/17.56 rd(X, rd(mult(f(Y), ld(Y, f(Y))), ld(ld(Y, f(Y)), f(Y))))
% 119.25/17.56 = { by lemma 17 R->L }
% 119.25/17.56 rd(X, rd(mult(f(Y), rd(f(Y), Y)), ld(ld(Y, f(Y)), f(Y))))
% 119.25/17.56 = { by axiom 8 (f03) R->L }
% 119.25/17.56 rd(X, rd(mult(mult(rd(f(Y), Y), Y), rd(f(Y), Y)), ld(ld(Y, f(Y)), f(Y))))
% 119.25/17.56 = { by axiom 9 (f08) }
% 119.25/17.56 rd(X, rd(mult(rd(f(Y), Y), mult(Y, rd(f(Y), Y))), ld(ld(Y, f(Y)), f(Y))))
% 119.25/17.56 = { by lemma 14 }
% 119.25/17.56 rd(X, rd(mult(rd(f(Y), Y), rd(mult(Y, f(Y)), Y)), ld(ld(Y, f(Y)), f(Y))))
% 119.25/17.56 = { by lemma 17 }
% 119.25/17.56 rd(X, rd(mult(ld(Y, f(Y)), rd(mult(Y, f(Y)), Y)), ld(ld(Y, f(Y)), f(Y))))
% 119.25/17.56 = { by lemma 16 }
% 119.25/17.56 rd(X, rd(mult(ld(Y, f(Y)), f(Y)), ld(ld(Y, f(Y)), f(Y))))
% 119.25/17.56 = { by lemma 25 }
% 119.25/17.56 rd(X, mult(ld(Y, f(Y)), ld(Y, f(Y))))
% 119.25/17.56 = { by axiom 5 (f04) R->L }
% 119.25/17.56 rd(mult(rd(X, mult(ld(Y, f(Y)), ld(Y, f(Y)))), ld(Y, f(Y))), ld(Y, f(Y)))
% 119.25/17.56 = { by lemma 28 R->L }
% 119.25/17.56 rd(rd(mult(rd(X, mult(ld(Y, f(Y)), ld(Y, f(Y)))), mult(ld(Y, f(Y)), ld(Y, f(Y)))), ld(Y, f(Y))), ld(Y, f(Y)))
% 119.25/17.56 = { by axiom 8 (f03) }
% 119.25/17.56 rd(rd(X, ld(Y, f(Y))), ld(Y, f(Y)))
% 119.25/17.56 = { by lemma 34 }
% 119.25/17.56 mult(rd(X, ld(Y, f(Y))), f(Y))
% 119.25/17.56 = { by lemma 34 }
% 119.25/17.56 mult(mult(X, f(Y)), f(Y))
% 119.25/17.56 = { by lemma 27 }
% 119.25/17.56 mult(X, mult(f(Y), f(Y)))
% 119.25/17.56 = { by axiom 3 (f09) }
% 119.25/17.56 mult(X, Y)
% 119.25/17.56
% 119.25/17.56 Lemma 36: ld(mult(X, Y), X) = ld(Y, unit).
% 119.25/17.56 Proof:
% 119.25/17.56 ld(mult(X, Y), X)
% 119.25/17.56 = { by lemma 35 R->L }
% 119.25/17.56 ld(rd(X, ld(Y, unit)), X)
% 119.25/17.56 = { by lemma 18 }
% 119.25/17.56 ld(Y, unit)
% 119.25/17.56
% 119.25/17.56 Lemma 37: mult(X, ld(Y, Z)) = rd(X, ld(Z, Y)).
% 119.25/17.56 Proof:
% 119.25/17.56 mult(X, ld(Y, Z))
% 119.25/17.56 = { by lemma 35 R->L }
% 119.25/17.56 rd(X, ld(ld(Y, Z), unit))
% 119.25/17.56 = { by lemma 36 R->L }
% 119.25/17.56 rd(X, ld(mult(Y, ld(Y, Z)), Y))
% 119.25/17.56 = { by axiom 7 (f01) }
% 119.25/17.56 rd(X, ld(Z, Y))
% 119.25/17.56
% 119.25/17.56 Lemma 38: ld(rd(X, Y), mult(X, X)) = mult(Y, X).
% 119.25/17.56 Proof:
% 119.25/17.56 ld(rd(X, Y), mult(X, X))
% 119.25/17.56 = { by lemma 33 R->L }
% 119.25/17.56 mult(ld(rd(X, Y), X), X)
% 119.25/17.56 = { by lemma 18 }
% 119.25/17.56 mult(Y, X)
% 119.25/17.56
% 119.25/17.56 Lemma 39: mult(rd(X, Y), X) = mult(X, ld(Y, X)).
% 119.25/17.56 Proof:
% 119.25/17.56 mult(rd(X, Y), X)
% 119.25/17.56 = { by axiom 7 (f01) R->L }
% 119.25/17.56 mult(rd(X, Y), mult(Y, ld(Y, X)))
% 119.25/17.56 = { by axiom 7 (f01) R->L }
% 119.25/17.56 mult(rd(mult(Y, ld(Y, X)), Y), mult(Y, ld(Y, X)))
% 119.25/17.56 = { by lemma 14 R->L }
% 119.25/17.56 mult(mult(Y, rd(ld(Y, X), Y)), mult(Y, ld(Y, X)))
% 119.25/17.56 = { by axiom 8 (f03) R->L }
% 119.25/17.56 mult(mult(Y, rd(ld(Y, X), Y)), mult(Y, mult(rd(ld(Y, X), Y), Y)))
% 119.25/17.56 = { by lemma 32 }
% 119.25/17.56 mult(Y, mult(rd(ld(Y, X), Y), mult(Y, mult(rd(ld(Y, X), Y), Y))))
% 119.25/17.56 = { by axiom 8 (f03) }
% 119.25/17.56 mult(Y, mult(rd(ld(Y, X), Y), mult(Y, ld(Y, X))))
% 119.25/17.56 = { by lemma 38 R->L }
% 119.25/17.56 mult(Y, mult(rd(ld(Y, X), Y), ld(rd(ld(Y, X), Y), mult(ld(Y, X), ld(Y, X)))))
% 119.25/17.56 = { by axiom 7 (f01) }
% 119.25/17.56 mult(Y, mult(ld(Y, X), ld(Y, X)))
% 119.25/17.56 = { by lemma 27 R->L }
% 119.25/17.56 mult(mult(Y, ld(Y, X)), ld(Y, X))
% 119.25/17.56 = { by axiom 7 (f01) }
% 119.25/17.56 mult(X, ld(Y, X))
% 119.25/17.56
% 119.25/17.56 Lemma 40: rd(X, ld(Y, X)) = Y.
% 119.25/17.56 Proof:
% 119.25/17.56 rd(X, ld(Y, X))
% 119.25/17.56 = { by axiom 7 (f01) R->L }
% 119.25/17.56 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 119.25/17.56 = { by axiom 5 (f04) }
% 119.25/17.56 Y
% 119.25/17.56
% 119.25/17.56 Lemma 41: rd(ld(X, mult(Y, Y)), Y) = ld(X, Y).
% 119.25/17.56 Proof:
% 119.25/17.56 rd(ld(X, mult(Y, Y)), Y)
% 119.25/17.56 = { by lemma 33 R->L }
% 119.25/17.56 rd(mult(ld(X, Y), Y), Y)
% 119.25/17.56 = { by axiom 5 (f04) }
% 119.25/17.57 ld(X, Y)
% 119.25/17.57
% 119.25/17.57 Lemma 42: rd(mult(X, X), ld(Y, X)) = mult(X, Y).
% 119.25/17.57 Proof:
% 119.25/17.57 rd(mult(X, X), ld(Y, X))
% 119.25/17.57 = { by axiom 7 (f01) R->L }
% 119.25/17.57 rd(mult(Y, ld(Y, mult(X, X))), ld(Y, X))
% 119.25/17.57 = { by lemma 33 R->L }
% 119.25/17.57 rd(mult(Y, mult(ld(Y, X), X)), ld(Y, X))
% 119.25/17.57 = { by axiom 7 (f01) R->L }
% 119.25/17.57 rd(mult(Y, mult(ld(Y, X), mult(Y, ld(Y, X)))), ld(Y, X))
% 119.25/17.57 = { by lemma 30 R->L }
% 119.25/17.57 rd(mult(mult(Y, mult(ld(Y, X), Y)), ld(Y, X)), ld(Y, X))
% 119.25/17.57 = { by lemma 31 }
% 119.25/17.57 rd(mult(mult(X, Y), ld(Y, X)), ld(Y, X))
% 119.25/17.57 = { by axiom 5 (f04) }
% 119.25/17.57 mult(X, Y)
% 119.25/17.57
% 119.25/17.57 Lemma 43: ld(f(X), rd(X, Y)) = rd(f(X), Y).
% 119.25/17.57 Proof:
% 119.25/17.57 ld(f(X), rd(X, Y))
% 119.25/17.57 = { by lemma 40 R->L }
% 119.25/17.57 ld(f(X), rd(f(X), ld(rd(X, Y), f(X))))
% 119.25/17.57 = { by lemma 41 R->L }
% 119.25/17.57 ld(f(X), rd(f(X), rd(ld(rd(X, Y), mult(f(X), f(X))), f(X))))
% 119.25/17.57 = { by axiom 3 (f09) }
% 119.25/17.57 ld(f(X), rd(f(X), rd(ld(rd(X, Y), X), f(X))))
% 119.25/17.57 = { by lemma 18 }
% 119.25/17.57 ld(f(X), rd(f(X), rd(Y, f(X))))
% 119.25/17.57 = { by lemma 18 R->L }
% 119.25/17.57 ld(f(X), rd(f(X), rd(ld(rd(mult(f(X), f(X)), Y), mult(f(X), f(X))), f(X))))
% 119.25/17.57 = { by lemma 41 }
% 119.25/17.57 ld(f(X), rd(f(X), ld(rd(mult(f(X), f(X)), Y), f(X))))
% 119.25/17.57 = { by lemma 40 }
% 119.25/17.57 ld(f(X), rd(mult(f(X), f(X)), Y))
% 119.25/17.57 = { by lemma 18 R->L }
% 119.25/17.57 ld(f(X), rd(mult(f(X), f(X)), ld(rd(f(X), Y), f(X))))
% 119.25/17.57 = { by lemma 42 }
% 119.25/17.57 ld(f(X), mult(f(X), rd(f(X), Y)))
% 119.25/17.57 = { by axiom 4 (f02) }
% 119.25/17.57 rd(f(X), Y)
% 119.25/17.57
% 119.25/17.57 Lemma 44: ld(f(X), ld(f(X), Y)) = ld(X, Y).
% 119.25/17.57 Proof:
% 119.25/17.57 ld(f(X), ld(f(X), Y))
% 119.25/17.57 = { by lemma 23 R->L }
% 119.25/17.57 ld(f(X), mult(f(X), ld(X, Y)))
% 119.25/17.57 = { by axiom 4 (f02) }
% 119.25/17.57 ld(X, Y)
% 119.25/17.57
% 119.25/17.57 Lemma 45: rd(mult(X, mult(Y, Z)), ld(Y, Z)) = rd(mult(X, Z), ld(Y, ld(Y, Z))).
% 119.25/17.57 Proof:
% 119.25/17.57 rd(mult(X, mult(Y, Z)), ld(Y, Z))
% 119.25/17.57 = { by lemma 37 R->L }
% 119.25/17.57 mult(mult(X, mult(Y, Z)), ld(Z, Y))
% 119.25/17.57 = { by lemma 31 R->L }
% 119.25/17.57 mult(mult(X, mult(Z, mult(ld(Z, Y), Z))), ld(Z, Y))
% 119.25/17.57 = { by lemma 26 }
% 119.25/17.57 mult(mult(X, Z), mult(ld(Z, Y), mult(Z, ld(Z, Y))))
% 119.25/17.57 = { by axiom 7 (f01) }
% 119.25/17.57 mult(mult(X, Z), mult(ld(Z, Y), Y))
% 119.25/17.57 = { by lemma 33 }
% 119.25/17.57 mult(mult(X, Z), ld(Z, mult(Y, Y)))
% 119.25/17.57 = { by lemma 37 }
% 119.25/17.57 rd(mult(X, Z), ld(mult(Y, Y), Z))
% 119.25/17.57 = { by lemma 25 R->L }
% 119.25/17.57 rd(mult(X, Z), ld(rd(mult(Y, ld(Y, Z)), ld(Y, ld(Y, Z))), Z))
% 119.25/17.57 = { by axiom 7 (f01) }
% 119.25/17.57 rd(mult(X, Z), ld(rd(Z, ld(Y, ld(Y, Z))), Z))
% 119.25/17.57 = { by lemma 18 }
% 119.25/17.57 rd(mult(X, Z), ld(Y, ld(Y, Z)))
% 119.25/17.57
% 119.25/17.57 Goal 1 (goals): mult(a, mult(b, mult(a, c))) = mult(mult(mult(a, b), a), c).
% 119.25/17.57 Proof:
% 119.25/17.57 mult(a, mult(b, mult(a, c)))
% 119.25/17.57 = { by axiom 7 (f01) R->L }
% 119.25/17.57 mult(a, mult(b, mult(a, mult(a, ld(a, c)))))
% 119.25/17.57 = { by axiom 6 (ifeq_axiom) R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by axiom 9 (f08) R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(b, mult(a, mult(mult(a, ld(a, c)), a))), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by axiom 9 (f08) R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(b, mult(mult(a, mult(a, ld(a, c))), a)), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by axiom 8 (f03) R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(rd(mult(b, mult(mult(a, mult(a, ld(a, c))), a)), a), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by axiom 4 (f02) R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(rd(mult(b, mult(mult(a, mult(a, ld(a, c))), a)), ld(f(mult(a, mult(a, ld(a, c)))), mult(f(mult(a, mult(a, ld(a, c)))), a))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 21 R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(rd(mult(b, mult(f(mult(a, mult(a, ld(a, c)))), mult(f(mult(a, mult(a, ld(a, c)))), a))), ld(f(mult(a, mult(a, ld(a, c)))), mult(f(mult(a, mult(a, ld(a, c)))), a))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 45 }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(rd(mult(b, mult(f(mult(a, mult(a, ld(a, c)))), a)), ld(f(mult(a, mult(a, ld(a, c)))), ld(f(mult(a, mult(a, ld(a, c)))), mult(f(mult(a, mult(a, ld(a, c)))), a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 44 }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(rd(mult(b, mult(f(mult(a, mult(a, ld(a, c)))), a)), ld(mult(a, mult(a, ld(a, c))), mult(f(mult(a, mult(a, ld(a, c)))), a))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 29 }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(rd(mult(b, mult(f(mult(a, mult(a, ld(a, c)))), a)), ld(f(mult(a, mult(a, ld(a, c)))), a)), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 45 }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(rd(mult(b, a), ld(f(mult(a, mult(a, ld(a, c)))), ld(f(mult(a, mult(a, ld(a, c)))), a))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 44 }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(rd(mult(b, a), ld(mult(a, mult(a, ld(a, c))), a)), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 18 R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(rd(f(f(mult(b, a))), rd(mult(b, a), ld(mult(a, mult(a, ld(a, c))), a))), f(f(mult(b, a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 43 R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(ld(f(f(mult(b, a))), rd(f(mult(b, a)), rd(mult(b, a), ld(mult(a, mult(a, ld(a, c))), a)))), f(f(mult(b, a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 43 R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(ld(f(f(mult(b, a))), ld(f(mult(b, a)), rd(mult(b, a), rd(mult(b, a), ld(mult(a, mult(a, ld(a, c))), a))))), f(f(mult(b, a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by axiom 5 (f04) R->L }
% 119.25/17.57 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(ld(f(f(mult(b, a))), ld(f(mult(b, a)), rd(mult(rd(mult(b, a), rd(mult(b, a), ld(mult(a, mult(a, ld(a, c))), a))), mult(b, a)), mult(b, a)))), f(f(mult(b, a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.57 = { by lemma 39 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(ld(f(f(mult(b, a))), ld(f(mult(b, a)), rd(mult(mult(b, a), ld(rd(mult(b, a), ld(mult(a, mult(a, ld(a, c))), a)), mult(b, a))), mult(b, a)))), f(f(mult(b, a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 18 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(ld(f(f(mult(b, a))), ld(f(mult(b, a)), rd(mult(mult(b, a), ld(mult(a, mult(a, ld(a, c))), a)), mult(b, a)))), f(f(mult(b, a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 14 R->L }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(ld(f(f(mult(b, a))), ld(f(mult(b, a)), mult(mult(b, a), rd(ld(mult(a, mult(a, ld(a, c))), a), mult(b, a))))), f(f(mult(b, a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 22 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(ld(f(f(mult(b, a))), mult(f(mult(b, a)), rd(ld(mult(a, mult(a, ld(a, c))), a), mult(b, a)))), f(f(mult(b, a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 22 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(mult(f(f(mult(b, a))), rd(ld(mult(a, mult(a, ld(a, c))), a), mult(b, a))), f(f(mult(b, a)))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 36 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(ld(rd(ld(mult(a, mult(a, ld(a, c))), a), mult(b, a)), unit), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 38 R->L }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(rd(a, ld(rd(ld(mult(a, mult(a, ld(a, c))), a), mult(b, a)), unit)), mult(a, a)), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 35 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(mult(a, rd(ld(mult(a, mult(a, ld(a, c))), a), mult(b, a))), mult(a, a)), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 42 R->L }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(rd(mult(a, a), ld(rd(ld(mult(a, mult(a, ld(a, c))), a), mult(b, a)), a)), mult(a, a)), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 18 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(rd(ld(mult(a, mult(a, ld(a, c))), a), mult(b, a)), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 36 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(rd(ld(mult(a, ld(a, c)), unit), mult(b, a)), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 36 R->L }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(rd(ld(mult(mult(mult(b, a), mult(b, a)), mult(a, ld(a, c))), mult(mult(b, a), mult(b, a))), mult(b, a)), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 41 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(ld(mult(mult(mult(b, a), mult(b, a)), mult(a, ld(a, c))), mult(b, a)), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 20 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(ld(mult(mult(b, a), mult(mult(b, a), mult(a, ld(a, c)))), mult(b, a)), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 36 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(ld(mult(mult(b, a), mult(a, ld(a, c))), unit), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 36 R->L }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(ld(mult(a, mult(mult(b, a), mult(a, ld(a, c)))), a), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by axiom 4 (f02) R->L }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(a, mult(a, ld(ld(mult(a, mult(mult(b, a), mult(a, ld(a, c)))), a), a))), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 39 R->L }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(a, mult(rd(a, ld(mult(a, mult(mult(b, a), mult(a, ld(a, c)))), a)), a)), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 40 }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(a, mult(mult(a, mult(mult(b, a), mult(a, ld(a, c)))), a)), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by axiom 9 (f08) }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), ld(a, mult(a, mult(mult(mult(b, a), mult(a, ld(a, c))), a))), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by axiom 4 (f02) }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(a, mult(ld(a, c), a)))), mult(mult(mult(b, a), mult(a, ld(a, c))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by axiom 9 (f08) R->L }
% 119.25/17.58 ifeq(mult(b, mult(a, mult(mult(a, ld(a, c)), a))), mult(mult(mult(b, a), mult(a, ld(a, c))), a), mult(a, mult(b, mult(a, mult(a, ld(a, c))))), mult(mult(a, mult(b, a)), mult(a, ld(a, c))))
% 119.25/17.58 = { by lemma 19 }
% 119.25/17.58 mult(mult(a, mult(b, a)), mult(a, ld(a, c)))
% 119.25/17.58 = { by axiom 7 (f01) }
% 119.25/17.58 mult(mult(a, mult(b, a)), c)
% 119.25/17.58 = { by axiom 9 (f08) R->L }
% 119.25/17.58 mult(mult(mult(a, b), a), c)
% 119.25/17.58 % SZS output end Proof
% 119.25/17.58
% 119.25/17.58 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------