TSTP Solution File: GRP707-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP707-1 : 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 : n010.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 01:19:50 EDT 2023
% Result : Unsatisfiable 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP707-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.36 % Computer : n010.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Tue Aug 29 01:09:34 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.22/0.53 Command-line arguments: --flatten
% 0.22/0.53
% 0.22/0.53 % SZS status Unsatisfiable
% 0.22/0.53
% 0.22/0.56 % SZS output start Proof
% 0.22/0.56 Axiom 1 (c05): mult(X, unit) = X.
% 0.22/0.56 Axiom 2 (c06): mult(unit, X) = X.
% 0.22/0.56 Axiom 3 (c02): ld(X, mult(X, Y)) = Y.
% 0.22/0.56 Axiom 4 (c04): rd(mult(X, Y), Y) = X.
% 0.22/0.56 Axiom 5 (c01): mult(X, ld(X, Y)) = Y.
% 0.22/0.56 Axiom 6 (c03): mult(rd(X, Y), Y) = X.
% 0.22/0.56 Axiom 7 (c09): mult(mult(X, X), Y) = mult(Y, mult(X, X)).
% 0.22/0.56 Axiom 8 (c08): mult(X, mult(X, mult(X, X))) = unit.
% 0.22/0.56 Axiom 9 (c07): mult(X, mult(Y, mult(Y, Z))) = mult(mult(mult(X, Y), Y), Z).
% 0.22/0.56
% 0.22/0.56 Lemma 10: ld(X, X) = unit.
% 0.22/0.56 Proof:
% 0.22/0.56 ld(X, X)
% 0.22/0.56 = { by axiom 1 (c05) R->L }
% 0.22/0.56 ld(X, mult(X, unit))
% 0.22/0.56 = { by axiom 3 (c02) }
% 0.22/0.56 unit
% 0.22/0.56
% 0.22/0.56 Lemma 11: mult(Y, mult(X, X)) = mult(X, mult(X, Y)).
% 0.22/0.56 Proof:
% 0.22/0.56 mult(Y, mult(X, X))
% 0.22/0.56 = { by axiom 7 (c09) R->L }
% 0.22/0.56 mult(mult(X, X), Y)
% 0.22/0.56 = { by axiom 2 (c06) R->L }
% 0.22/0.56 mult(mult(mult(unit, X), X), Y)
% 0.22/0.56 = { by axiom 9 (c07) R->L }
% 0.22/0.56 mult(unit, mult(X, mult(X, Y)))
% 0.22/0.56 = { by axiom 2 (c06) }
% 0.22/0.56 mult(X, mult(X, Y))
% 0.22/0.56
% 0.22/0.56 Lemma 12: ld(mult(X, X), mult(X, mult(X, Y))) = Y.
% 0.22/0.56 Proof:
% 0.22/0.56 ld(mult(X, X), mult(X, mult(X, Y)))
% 0.22/0.56 = { by lemma 11 R->L }
% 0.22/0.56 ld(mult(X, X), mult(Y, mult(X, X)))
% 0.22/0.56 = { by axiom 7 (c09) R->L }
% 0.22/0.56 ld(mult(X, X), mult(mult(X, X), Y))
% 0.22/0.56 = { by axiom 3 (c02) }
% 0.22/0.56 Y
% 0.22/0.56
% 0.22/0.56 Lemma 13: ld(mult(X, X), mult(X, Y)) = ld(X, Y).
% 0.22/0.56 Proof:
% 0.22/0.56 ld(mult(X, X), mult(X, Y))
% 0.22/0.56 = { by axiom 5 (c01) R->L }
% 0.22/0.56 ld(mult(X, X), mult(X, mult(X, ld(X, Y))))
% 0.22/0.56 = { by lemma 12 }
% 0.22/0.56 ld(X, Y)
% 0.22/0.56
% 0.22/0.56 Lemma 14: ld(mult(X, X), Y) = ld(X, ld(X, Y)).
% 0.22/0.56 Proof:
% 0.22/0.56 ld(mult(X, X), Y)
% 0.22/0.56 = { by axiom 5 (c01) R->L }
% 0.22/0.56 ld(mult(X, X), mult(X, ld(X, Y)))
% 0.22/0.56 = { by lemma 13 }
% 0.22/0.56 ld(X, ld(X, Y))
% 0.22/0.56
% 0.22/0.56 Lemma 15: mult(X, mult(X, X)) = ld(X, unit).
% 0.22/0.56 Proof:
% 0.22/0.56 mult(X, mult(X, X))
% 0.22/0.56 = { by axiom 3 (c02) R->L }
% 0.22/0.56 ld(X, mult(X, mult(X, mult(X, X))))
% 0.22/0.56 = { by axiom 8 (c08) }
% 0.22/0.56 ld(X, unit)
% 0.22/0.56
% 0.22/0.56 Lemma 16: ld(mult(X, X), unit) = mult(X, X).
% 0.22/0.56 Proof:
% 0.22/0.56 ld(mult(X, X), unit)
% 0.22/0.56 = { by lemma 15 R->L }
% 0.22/0.56 mult(mult(X, X), mult(mult(X, X), mult(X, X)))
% 0.22/0.56 = { by lemma 11 }
% 0.22/0.56 mult(mult(X, X), mult(X, mult(X, mult(X, X))))
% 0.22/0.56 = { by axiom 8 (c08) }
% 0.22/0.56 mult(mult(X, X), unit)
% 0.22/0.56 = { by axiom 1 (c05) }
% 0.22/0.56 mult(X, X)
% 0.22/0.56
% 0.22/0.56 Lemma 17: mult(mult(X, X), Y) = mult(X, mult(X, Y)).
% 0.22/0.56 Proof:
% 0.22/0.56 mult(mult(X, X), Y)
% 0.22/0.56 = { by axiom 7 (c09) }
% 0.22/0.56 mult(Y, mult(X, X))
% 0.22/0.56 = { by lemma 11 }
% 0.22/0.56 mult(X, mult(X, Y))
% 0.22/0.56
% 0.22/0.56 Lemma 18: mult(X, mult(X, Y)) = ld(mult(X, X), Y).
% 0.22/0.56 Proof:
% 0.22/0.56 mult(X, mult(X, Y))
% 0.22/0.56 = { by lemma 12 R->L }
% 0.22/0.56 ld(mult(X, X), mult(X, mult(X, mult(X, mult(X, Y)))))
% 0.22/0.56 = { by lemma 17 R->L }
% 0.22/0.56 ld(mult(X, X), mult(X, mult(X, mult(mult(X, X), Y))))
% 0.22/0.56 = { by lemma 17 R->L }
% 0.22/0.56 ld(mult(X, X), mult(mult(X, X), mult(mult(X, X), Y)))
% 0.22/0.56 = { by lemma 17 R->L }
% 0.22/0.56 ld(mult(X, X), mult(mult(mult(X, X), mult(X, X)), Y))
% 0.22/0.56 = { by axiom 7 (c09) }
% 0.22/0.56 ld(mult(X, X), mult(Y, mult(mult(X, X), mult(X, X))))
% 0.22/0.56 = { by lemma 11 }
% 0.22/0.56 ld(mult(X, X), mult(Y, mult(X, mult(X, mult(X, X)))))
% 0.22/0.56 = { by axiom 8 (c08) }
% 0.22/0.56 ld(mult(X, X), mult(Y, unit))
% 0.22/0.56 = { by axiom 1 (c05) }
% 0.22/0.56 ld(mult(X, X), Y)
% 0.22/0.56
% 0.22/0.56 Lemma 19: mult(mult(mult(X, Y), Y), Z) = mult(X, ld(Y, ld(Y, Z))).
% 0.22/0.56 Proof:
% 0.22/0.56 mult(mult(mult(X, Y), Y), Z)
% 0.22/0.56 = { by axiom 9 (c07) R->L }
% 0.22/0.56 mult(X, mult(Y, mult(Y, Z)))
% 0.22/0.56 = { by lemma 18 }
% 0.22/0.56 mult(X, ld(mult(Y, Y), Z))
% 0.22/0.56 = { by lemma 14 }
% 0.22/0.57 mult(X, ld(Y, ld(Y, Z)))
% 0.22/0.57
% 0.22/0.57 Lemma 20: mult(mult(X, Y), Y) = mult(X, mult(Y, Y)).
% 0.22/0.57 Proof:
% 0.22/0.57 mult(mult(X, Y), Y)
% 0.22/0.57 = { by axiom 1 (c05) R->L }
% 0.22/0.57 mult(mult(mult(X, Y), Y), unit)
% 0.22/0.57 = { by axiom 9 (c07) R->L }
% 0.22/0.57 mult(X, mult(Y, mult(Y, unit)))
% 0.22/0.57 = { by axiom 1 (c05) }
% 0.22/0.57 mult(X, mult(Y, Y))
% 0.22/0.57
% 0.22/0.57 Lemma 21: mult(X, mult(Y, Y)) = ld(mult(Y, Y), X).
% 0.22/0.57 Proof:
% 0.22/0.57 mult(X, mult(Y, Y))
% 0.22/0.57 = { by lemma 11 }
% 0.22/0.57 mult(Y, mult(Y, X))
% 0.22/0.57 = { by lemma 18 }
% 0.22/0.57 ld(mult(Y, Y), X)
% 0.22/0.57
% 0.22/0.57 Lemma 22: mult(mult(Y, X), X) = mult(X, mult(X, Y)).
% 0.22/0.57 Proof:
% 0.22/0.57 mult(mult(Y, X), X)
% 0.22/0.57 = { by lemma 20 }
% 0.22/0.57 mult(Y, mult(X, X))
% 0.22/0.57 = { by lemma 11 }
% 0.22/0.57 mult(X, mult(X, Y))
% 0.22/0.57
% 0.22/0.57 Lemma 23: rd(ld(mult(X, X), Y), X) = mult(Y, X).
% 0.22/0.57 Proof:
% 0.22/0.57 rd(ld(mult(X, X), Y), X)
% 0.22/0.57 = { by lemma 21 R->L }
% 0.22/0.57 rd(mult(Y, mult(X, X)), X)
% 0.22/0.57 = { by lemma 20 R->L }
% 0.22/0.57 rd(mult(mult(Y, X), X), X)
% 0.22/0.57 = { by axiom 4 (c04) }
% 0.22/0.57 mult(Y, X)
% 0.22/0.57
% 0.22/0.57 Lemma 24: ld(X, ld(X, mult(Y, X))) = rd(Y, X).
% 0.22/0.57 Proof:
% 0.22/0.57 ld(X, ld(X, mult(Y, X)))
% 0.22/0.57 = { by lemma 14 R->L }
% 0.22/0.57 ld(mult(X, X), mult(Y, X))
% 0.22/0.57 = { by lemma 21 R->L }
% 0.22/0.57 mult(mult(Y, X), mult(X, X))
% 0.22/0.57 = { by lemma 20 R->L }
% 0.22/0.57 mult(mult(mult(Y, X), X), X)
% 0.22/0.57 = { by lemma 22 }
% 0.22/0.57 mult(mult(X, mult(X, Y)), X)
% 0.22/0.57 = { by lemma 23 R->L }
% 0.22/0.57 rd(ld(mult(X, X), mult(X, mult(X, Y))), X)
% 0.22/0.57 = { by lemma 13 }
% 0.22/0.57 rd(ld(X, mult(X, Y)), X)
% 0.22/0.57 = { by axiom 3 (c02) }
% 0.22/0.57 rd(Y, X)
% 0.22/0.57
% 0.22/0.57 Lemma 25: mult(X, ld(Y, unit)) = rd(X, Y).
% 0.22/0.57 Proof:
% 0.22/0.57 mult(X, ld(Y, unit))
% 0.22/0.57 = { by lemma 10 R->L }
% 0.22/0.57 mult(X, ld(Y, ld(Y, Y)))
% 0.22/0.57 = { by lemma 19 R->L }
% 0.22/0.57 mult(mult(mult(X, Y), Y), Y)
% 0.22/0.57 = { by lemma 20 }
% 0.22/0.57 mult(mult(X, Y), mult(Y, Y))
% 0.22/0.57 = { by lemma 21 }
% 0.22/0.57 ld(mult(Y, Y), mult(X, Y))
% 0.22/0.57 = { by lemma 14 }
% 0.22/0.57 ld(Y, ld(Y, mult(X, Y)))
% 0.22/0.57 = { by lemma 24 }
% 0.22/0.57 rd(X, Y)
% 0.22/0.57
% 0.22/0.57 Lemma 26: mult(ld(X, Y), X) = rd(mult(X, Y), X).
% 0.22/0.57 Proof:
% 0.22/0.57 mult(ld(X, Y), X)
% 0.22/0.57 = { by lemma 23 R->L }
% 0.22/0.57 rd(ld(mult(X, X), ld(X, Y)), X)
% 0.22/0.57 = { by lemma 21 R->L }
% 0.22/0.57 rd(mult(ld(X, Y), mult(X, X)), X)
% 0.22/0.57 = { by lemma 11 }
% 0.22/0.57 rd(mult(X, mult(X, ld(X, Y))), X)
% 0.22/0.57 = { by axiom 5 (c01) }
% 0.22/0.57 rd(mult(X, Y), X)
% 0.22/0.57
% 0.22/0.57 Lemma 27: mult(ld(X, unit), Y) = ld(X, Y).
% 0.22/0.57 Proof:
% 0.22/0.57 mult(ld(X, unit), Y)
% 0.22/0.57 = { by lemma 15 R->L }
% 0.22/0.57 mult(mult(X, mult(X, X)), Y)
% 0.22/0.57 = { by axiom 7 (c09) R->L }
% 0.22/0.57 mult(mult(mult(X, X), X), Y)
% 0.22/0.57 = { by axiom 9 (c07) R->L }
% 0.22/0.57 mult(X, mult(X, mult(X, Y)))
% 0.22/0.57 = { by lemma 18 }
% 0.22/0.57 ld(mult(X, X), mult(X, Y))
% 0.22/0.57 = { by lemma 13 }
% 0.22/0.57 ld(X, Y)
% 0.22/0.57
% 0.22/0.57 Lemma 28: rd(ld(X, Y), Y) = ld(X, unit).
% 0.22/0.57 Proof:
% 0.22/0.57 rd(ld(X, Y), Y)
% 0.22/0.57 = { by lemma 27 R->L }
% 0.22/0.57 rd(mult(ld(X, unit), Y), Y)
% 0.22/0.57 = { by axiom 4 (c04) }
% 0.22/0.57 ld(X, unit)
% 0.22/0.57
% 0.22/0.57 Lemma 29: ld(mult(X, X), rd(Y, X)) = mult(Y, X).
% 0.22/0.57 Proof:
% 0.22/0.57 ld(mult(X, X), rd(Y, X))
% 0.22/0.57 = { by lemma 21 R->L }
% 0.22/0.57 mult(rd(Y, X), mult(X, X))
% 0.22/0.57 = { by lemma 20 R->L }
% 0.22/0.57 mult(mult(rd(Y, X), X), X)
% 0.22/0.57 = { by axiom 6 (c03) }
% 0.22/0.57 mult(Y, X)
% 0.22/0.57
% 0.22/0.57 Lemma 30: mult(X, ld(mult(Y, X), unit)) = ld(Y, unit).
% 0.22/0.57 Proof:
% 0.22/0.57 mult(X, ld(mult(Y, X), unit))
% 0.22/0.57 = { by lemma 10 R->L }
% 0.22/0.57 mult(X, ld(mult(Y, X), ld(mult(Y, X), mult(Y, X))))
% 0.22/0.57 = { by lemma 19 R->L }
% 0.22/0.57 mult(mult(mult(X, mult(Y, X)), mult(Y, X)), mult(Y, X))
% 0.22/0.57 = { by lemma 20 }
% 0.22/0.57 mult(mult(X, mult(Y, X)), mult(mult(Y, X), mult(Y, X)))
% 0.22/0.57 = { by lemma 21 }
% 0.22/0.57 ld(mult(mult(Y, X), mult(Y, X)), mult(X, mult(Y, X)))
% 0.22/0.57 = { by lemma 14 }
% 0.22/0.57 ld(mult(Y, X), ld(mult(Y, X), mult(X, mult(Y, X))))
% 0.22/0.57 = { by lemma 24 }
% 0.22/0.57 rd(X, mult(Y, X))
% 0.22/0.57 = { by axiom 3 (c02) R->L }
% 0.22/0.57 rd(ld(Y, mult(Y, X)), mult(Y, X))
% 0.22/0.57 = { by lemma 28 }
% 0.22/0.57 ld(Y, unit)
% 0.22/0.57
% 0.22/0.57 Goal 1 (goals): mult(mult(a, b), a) = mult(a, mult(b, a)).
% 0.22/0.57 Proof:
% 0.22/0.57 mult(mult(a, b), a)
% 0.22/0.57 = { by axiom 4 (c04) R->L }
% 0.22/0.57 rd(mult(mult(mult(a, b), a), b), b)
% 0.22/0.57 = { by axiom 3 (c02) R->L }
% 0.22/0.57 rd(mult(mult(mult(a, b), ld(b, mult(b, a))), b), b)
% 0.22/0.57 = { by axiom 3 (c02) R->L }
% 0.22/0.57 rd(mult(mult(mult(a, b), ld(b, ld(b, mult(b, mult(b, a))))), b), b)
% 0.22/0.57 = { by lemma 22 R->L }
% 0.22/0.57 rd(mult(mult(mult(a, b), ld(b, ld(b, mult(mult(a, b), b)))), b), b)
% 0.22/0.57 = { by lemma 14 R->L }
% 0.22/0.57 rd(mult(mult(mult(a, b), ld(mult(b, b), mult(mult(a, b), b))), b), b)
% 0.22/0.57 = { by lemma 21 R->L }
% 0.22/0.57 rd(mult(mult(mult(a, b), mult(mult(mult(a, b), b), mult(b, b))), b), b)
% 0.22/0.57 = { by lemma 20 R->L }
% 0.22/0.57 rd(mult(mult(mult(a, b), mult(mult(mult(mult(a, b), b), b), b)), b), b)
% 0.22/0.57 = { by axiom 9 (c07) R->L }
% 0.22/0.57 rd(mult(mult(mult(a, b), mult(mult(a, b), mult(b, mult(b, b)))), b), b)
% 0.22/0.57 = { by lemma 15 }
% 0.22/0.57 rd(mult(mult(mult(a, b), mult(mult(a, b), ld(b, unit))), b), b)
% 0.22/0.57 = { by lemma 11 R->L }
% 0.22/0.57 rd(mult(mult(ld(b, unit), mult(mult(a, b), mult(a, b))), b), b)
% 0.22/0.57 = { by lemma 27 }
% 0.22/0.57 rd(mult(ld(b, mult(mult(a, b), mult(a, b))), b), b)
% 0.22/0.57 = { by lemma 26 }
% 0.22/0.57 rd(rd(mult(b, mult(mult(a, b), mult(a, b))), b), b)
% 0.22/0.57 = { by lemma 21 }
% 0.22/0.57 rd(rd(ld(mult(mult(a, b), mult(a, b)), b), b), b)
% 0.22/0.57 = { by lemma 28 }
% 0.22/0.57 rd(ld(mult(mult(a, b), mult(a, b)), unit), b)
% 0.22/0.57 = { by lemma 16 }
% 0.22/0.57 rd(mult(mult(a, b), mult(a, b)), b)
% 0.22/0.57 = { by lemma 29 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(b, b), rd(a, b))), b)
% 0.22/0.57 = { by lemma 21 R->L }
% 0.22/0.57 rd(mult(mult(a, b), mult(rd(a, b), mult(b, b))), b)
% 0.22/0.57 = { by axiom 4 (c04) R->L }
% 0.22/0.57 rd(mult(mult(a, b), mult(rd(a, b), rd(mult(mult(b, b), ld(mult(b, b), rd(a, b))), ld(mult(b, b), rd(a, b))))), b)
% 0.22/0.57 = { by axiom 5 (c01) }
% 0.22/0.57 rd(mult(mult(a, b), mult(rd(a, b), rd(rd(a, b), ld(mult(b, b), rd(a, b))))), b)
% 0.22/0.57 = { by lemma 29 }
% 0.22/0.57 rd(mult(mult(a, b), mult(rd(a, b), rd(rd(a, b), mult(a, b)))), b)
% 0.22/0.57 = { by lemma 25 R->L }
% 0.22/0.57 rd(mult(mult(a, b), mult(rd(a, b), mult(rd(a, b), ld(mult(a, b), unit)))), b)
% 0.22/0.57 = { by lemma 11 R->L }
% 0.22/0.57 rd(mult(mult(a, b), mult(ld(mult(a, b), unit), mult(rd(a, b), rd(a, b)))), b)
% 0.22/0.57 = { by lemma 27 }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), mult(rd(a, b), rd(a, b)))), b)
% 0.22/0.57 = { by axiom 3 (c02) R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(mult(b, a), mult(rd(a, b), rd(a, b)))))), b)
% 0.22/0.57 = { by axiom 7 (c09) R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(mult(rd(a, b), rd(a, b)), mult(b, a))))), b)
% 0.22/0.57 = { by lemma 17 }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(rd(a, b), mult(rd(a, b), mult(b, a)))))), b)
% 0.22/0.57 = { by lemma 25 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(rd(a, b), mult(mult(a, ld(b, unit)), mult(b, a)))))), b)
% 0.22/0.57 = { by lemma 30 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(rd(a, b), mult(mult(a, mult(a, ld(mult(b, a), unit))), mult(b, a)))))), b)
% 0.22/0.57 = { by lemma 11 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(rd(a, b), mult(mult(ld(mult(b, a), unit), mult(a, a)), mult(b, a)))))), b)
% 0.22/0.57 = { by lemma 27 }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(rd(a, b), mult(ld(mult(b, a), mult(a, a)), mult(b, a)))))), b)
% 0.22/0.57 = { by lemma 26 }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(rd(a, b), rd(mult(mult(b, a), mult(a, a)), mult(b, a)))))), b)
% 0.22/0.57 = { by axiom 7 (c09) R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(rd(a, b), rd(mult(mult(a, a), mult(b, a)), mult(b, a)))))), b)
% 0.22/0.57 = { by axiom 4 (c04) }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(rd(a, b), mult(a, a))))), b)
% 0.22/0.57 = { by lemma 21 }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), ld(mult(a, a), rd(a, b))))), b)
% 0.22/0.57 = { by lemma 14 }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), ld(a, ld(a, rd(a, b)))))), b)
% 0.22/0.57 = { by lemma 25 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), ld(a, ld(a, mult(a, ld(b, unit))))))), b)
% 0.22/0.57 = { by axiom 3 (c02) }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), ld(a, ld(b, unit))))), b)
% 0.22/0.57 = { by lemma 30 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), ld(a, mult(a, ld(mult(b, a), unit)))))), b)
% 0.22/0.57 = { by axiom 3 (c02) }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), ld(mult(b, a), unit)))), b)
% 0.22/0.57 = { by lemma 15 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(b, a), mult(mult(b, a), mult(mult(b, a), mult(b, a)))))), b)
% 0.22/0.57 = { by axiom 3 (c02) }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), mult(mult(b, a), mult(b, a)))), b)
% 0.22/0.57 = { by lemma 16 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), ld(mult(mult(b, a), mult(b, a)), unit))), b)
% 0.22/0.57 = { by lemma 28 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), rd(ld(mult(mult(b, a), mult(b, a)), b), b))), b)
% 0.22/0.57 = { by lemma 21 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), rd(mult(b, mult(mult(b, a), mult(b, a))), b))), b)
% 0.22/0.57 = { by lemma 26 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), mult(ld(b, mult(mult(b, a), mult(b, a))), b))), b)
% 0.22/0.57 = { by lemma 27 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), mult(mult(ld(b, unit), mult(mult(b, a), mult(b, a))), b))), b)
% 0.22/0.57 = { by lemma 20 R->L }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), mult(mult(mult(ld(b, unit), mult(b, a)), mult(b, a)), b))), b)
% 0.22/0.57 = { by lemma 27 }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), mult(mult(ld(b, mult(b, a)), mult(b, a)), b))), b)
% 0.22/0.57 = { by axiom 3 (c02) }
% 0.22/0.57 rd(mult(mult(a, b), ld(mult(a, b), mult(mult(a, mult(b, a)), b))), b)
% 0.22/0.57 = { by axiom 5 (c01) }
% 0.22/0.57 rd(mult(mult(a, mult(b, a)), b), b)
% 0.22/0.57 = { by axiom 4 (c04) }
% 0.22/0.57 mult(a, mult(b, a))
% 0.22/0.57 % SZS output end Proof
% 0.22/0.57
% 0.22/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------