TSTP Solution File: GRP705-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP705-1 : 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 : n015.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 01:19:49 EDT 2023
% Result : Unsatisfiable 4.39s 1.00s
% Output : Proof 5.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP705-1 : 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
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 02:15:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.39/1.00 Command-line arguments: --flatten
% 4.39/1.00
% 4.39/1.00 % SZS status Unsatisfiable
% 4.39/1.00
% 5.11/1.04 % SZS output start Proof
% 5.11/1.04 Axiom 1 (c05): mult(X, unit) = X.
% 5.11/1.04 Axiom 2 (c06): mult(unit, X) = X.
% 5.11/1.04 Axiom 3 (c02): ld(X, mult(X, Y)) = Y.
% 5.11/1.04 Axiom 4 (c04): rd(mult(X, Y), Y) = X.
% 5.11/1.04 Axiom 5 (c01): mult(X, ld(X, Y)) = Y.
% 5.11/1.04 Axiom 6 (c03): mult(rd(X, Y), Y) = X.
% 5.11/1.04 Axiom 7 (c08): mult(op_a, mult(op_a, mult(op_a, op_a))) = unit.
% 5.11/1.04 Axiom 8 (c07): mult(X, mult(Y, mult(Y, Z))) = mult(mult(mult(X, Y), Y), Z).
% 5.11/1.04 Axiom 9 (c09): mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))) = unit.
% 5.11/1.04
% 5.11/1.04 Lemma 10: mult(mult(X, X), Y) = mult(X, mult(X, Y)).
% 5.11/1.04 Proof:
% 5.11/1.04 mult(mult(X, X), Y)
% 5.11/1.04 = { by axiom 2 (c06) R->L }
% 5.11/1.04 mult(mult(mult(unit, X), X), Y)
% 5.11/1.04 = { by axiom 8 (c07) R->L }
% 5.11/1.04 mult(unit, mult(X, mult(X, Y)))
% 5.11/1.04 = { by axiom 2 (c06) }
% 5.11/1.04 mult(X, mult(X, Y))
% 5.11/1.04
% 5.11/1.04 Lemma 11: mult(mult(X, Y), Y) = mult(X, mult(Y, Y)).
% 5.11/1.04 Proof:
% 5.11/1.04 mult(mult(X, Y), Y)
% 5.11/1.04 = { by axiom 1 (c05) R->L }
% 5.11/1.04 mult(mult(mult(X, Y), Y), unit)
% 5.11/1.04 = { by axiom 8 (c07) R->L }
% 5.11/1.04 mult(X, mult(Y, mult(Y, unit)))
% 5.11/1.04 = { by axiom 1 (c05) }
% 5.11/1.04 mult(X, mult(Y, Y))
% 5.11/1.04
% 5.11/1.04 Lemma 12: mult(mult(X, X), mult(X, Y)) = mult(X, mult(mult(X, X), Y)).
% 5.11/1.04 Proof:
% 5.11/1.04 mult(mult(X, X), mult(X, Y))
% 5.11/1.04 = { by lemma 10 }
% 5.11/1.04 mult(X, mult(X, mult(X, Y)))
% 5.11/1.04 = { by lemma 10 R->L }
% 5.11/1.04 mult(X, mult(mult(X, X), Y))
% 5.11/1.04
% 5.11/1.04 Lemma 13: mult(rd(X, Y), mult(Y, Y)) = mult(X, Y).
% 5.11/1.04 Proof:
% 5.11/1.05 mult(rd(X, Y), mult(Y, Y))
% 5.11/1.05 = { by lemma 11 R->L }
% 5.11/1.05 mult(mult(rd(X, Y), Y), Y)
% 5.11/1.05 = { by axiom 6 (c03) }
% 5.11/1.05 mult(X, Y)
% 5.11/1.05
% 5.11/1.05 Lemma 14: mult(mult(X, mult(Y, Y)), Y) = mult(mult(X, Y), mult(Y, Y)).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(X, mult(Y, Y)), Y)
% 5.11/1.05 = { by lemma 11 R->L }
% 5.11/1.05 mult(mult(mult(X, Y), Y), Y)
% 5.11/1.05 = { by lemma 11 }
% 5.11/1.05 mult(mult(X, Y), mult(Y, Y))
% 5.11/1.05
% 5.11/1.05 Lemma 15: mult(mult(X, mult(X, X)), X) = mult(X, mult(X, mult(X, X))).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(X, mult(X, X)), X)
% 5.11/1.05 = { by lemma 14 }
% 5.11/1.05 mult(mult(X, X), mult(X, X))
% 5.11/1.05 = { by lemma 10 }
% 5.11/1.05 mult(X, mult(X, mult(X, X)))
% 5.11/1.05
% 5.11/1.05 Lemma 16: mult(mult(X, mult(X, X)), Y) = mult(mult(X, X), mult(X, Y)).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(X, mult(X, X)), Y)
% 5.11/1.05 = { by lemma 11 R->L }
% 5.11/1.05 mult(mult(mult(X, X), X), Y)
% 5.11/1.05 = { by axiom 8 (c07) R->L }
% 5.11/1.05 mult(X, mult(X, mult(X, Y)))
% 5.11/1.05 = { by lemma 10 R->L }
% 5.11/1.05 mult(mult(X, X), mult(X, Y))
% 5.11/1.05
% 5.11/1.05 Lemma 17: rd(mult(X, mult(X, Y)), Y) = mult(X, X).
% 5.11/1.05 Proof:
% 5.11/1.05 rd(mult(X, mult(X, Y)), Y)
% 5.11/1.05 = { by lemma 10 R->L }
% 5.11/1.05 rd(mult(mult(X, X), Y), Y)
% 5.11/1.05 = { by axiom 4 (c04) }
% 5.11/1.05 mult(X, X)
% 5.11/1.05
% 5.11/1.05 Lemma 18: rd(mult(X, mult(Y, Y)), Y) = mult(X, Y).
% 5.11/1.05 Proof:
% 5.11/1.05 rd(mult(X, mult(Y, Y)), Y)
% 5.11/1.05 = { by lemma 11 R->L }
% 5.11/1.05 rd(mult(mult(X, Y), Y), Y)
% 5.11/1.05 = { by axiom 4 (c04) }
% 5.11/1.05 mult(X, Y)
% 5.11/1.05
% 5.11/1.05 Lemma 19: mult(X, mult(op_a, mult(op_a, mult(op_a, op_a)))) = X.
% 5.11/1.05 Proof:
% 5.11/1.05 mult(X, mult(op_a, mult(op_a, mult(op_a, op_a))))
% 5.11/1.05 = { by axiom 7 (c08) }
% 5.11/1.05 mult(X, unit)
% 5.11/1.05 = { by axiom 1 (c05) }
% 5.11/1.05 X
% 5.11/1.05
% 5.11/1.05 Lemma 20: rd(mult(X, mult(X, mult(Y, mult(Y, mult(Y, Y))))), mult(Y, Y)) = mult(mult(X, X), mult(Y, Y)).
% 5.11/1.05 Proof:
% 5.11/1.05 rd(mult(X, mult(X, mult(Y, mult(Y, mult(Y, Y))))), mult(Y, Y))
% 5.11/1.05 = { by lemma 10 R->L }
% 5.11/1.05 rd(mult(mult(X, X), mult(Y, mult(Y, mult(Y, Y)))), mult(Y, Y))
% 5.11/1.05 = { by lemma 15 R->L }
% 5.11/1.05 rd(mult(mult(X, X), mult(mult(Y, mult(Y, Y)), Y)), mult(Y, Y))
% 5.11/1.05 = { by lemma 14 }
% 5.11/1.05 rd(mult(mult(X, X), mult(mult(Y, Y), mult(Y, Y))), mult(Y, Y))
% 5.11/1.05 = { by lemma 18 }
% 5.11/1.05 mult(mult(X, X), mult(Y, Y))
% 5.11/1.05
% 5.11/1.05 Lemma 21: rd(mult(X, mult(X, mult(X, mult(X, mult(X, X))))), mult(X, X)) = mult(X, mult(X, mult(X, X))).
% 5.11/1.05 Proof:
% 5.11/1.05 rd(mult(X, mult(X, mult(X, mult(X, mult(X, X))))), mult(X, X))
% 5.11/1.05 = { by lemma 20 }
% 5.11/1.05 mult(mult(X, X), mult(X, X))
% 5.11/1.05 = { by lemma 14 R->L }
% 5.11/1.05 mult(mult(X, mult(X, X)), X)
% 5.11/1.05 = { by lemma 15 }
% 5.11/1.05 mult(X, mult(X, mult(X, X)))
% 5.11/1.05
% 5.11/1.05 Lemma 22: mult(mult(X, mult(X, mult(X, X))), Y) = mult(X, mult(X, mult(X, mult(X, Y)))).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(X, mult(X, mult(X, X))), Y)
% 5.11/1.05 = { by lemma 21 R->L }
% 5.11/1.05 mult(rd(mult(X, mult(X, mult(X, mult(X, mult(X, X))))), mult(X, X)), Y)
% 5.11/1.05 = { by lemma 20 }
% 5.11/1.05 mult(mult(mult(X, X), mult(X, X)), Y)
% 5.11/1.05 = { by lemma 17 R->L }
% 5.11/1.05 mult(rd(mult(mult(X, X), mult(mult(X, X), Y)), Y), Y)
% 5.11/1.05 = { by lemma 10 }
% 5.11/1.05 mult(rd(mult(mult(X, X), mult(X, mult(X, Y))), Y), Y)
% 5.11/1.05 = { by lemma 10 }
% 5.11/1.05 mult(rd(mult(X, mult(X, mult(X, mult(X, Y)))), Y), Y)
% 5.11/1.05 = { by axiom 6 (c03) }
% 5.11/1.05 mult(X, mult(X, mult(X, mult(X, Y))))
% 5.11/1.05
% 5.11/1.05 Lemma 23: mult(mult(X, mult(X, mult(X, X))), Y) = mult(mult(X, X), mult(mult(X, X), Y)).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(X, mult(X, mult(X, X))), Y)
% 5.11/1.05 = { by lemma 15 R->L }
% 5.11/1.05 mult(mult(mult(X, mult(X, X)), X), Y)
% 5.11/1.05 = { by lemma 14 }
% 5.11/1.05 mult(mult(mult(X, X), mult(X, X)), Y)
% 5.11/1.05 = { by lemma 10 }
% 5.11/1.05 mult(mult(X, X), mult(mult(X, X), Y))
% 5.11/1.05
% 5.11/1.05 Lemma 24: mult(mult(X, mult(X, mult(X, X))), Y) = mult(mult(X, mult(X, X)), mult(X, Y)).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(X, mult(X, mult(X, X))), Y)
% 5.11/1.05 = { by lemma 23 }
% 5.11/1.05 mult(mult(X, X), mult(mult(X, X), Y))
% 5.11/1.05 = { by lemma 10 }
% 5.11/1.05 mult(mult(X, X), mult(X, mult(X, Y)))
% 5.11/1.05 = { by lemma 16 R->L }
% 5.11/1.05 mult(mult(X, mult(X, X)), mult(X, Y))
% 5.11/1.05
% 5.11/1.05 Lemma 25: mult(mult(op_a, mult(op_a, mult(op_a, op_a))), X) = X.
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(op_a, mult(op_a, mult(op_a, op_a))), X)
% 5.11/1.05 = { by axiom 7 (c08) }
% 5.11/1.05 mult(unit, X)
% 5.11/1.05 = { by axiom 2 (c06) }
% 5.11/1.05 X
% 5.11/1.05
% 5.11/1.05 Lemma 26: ld(mult(X, mult(X, X)), mult(mult(X, X), Y)) = ld(X, Y).
% 5.11/1.05 Proof:
% 5.11/1.05 ld(mult(X, mult(X, X)), mult(mult(X, X), Y))
% 5.11/1.05 = { by axiom 5 (c01) R->L }
% 5.11/1.05 ld(mult(X, mult(X, X)), mult(mult(X, X), mult(X, ld(X, Y))))
% 5.11/1.05 = { by lemma 16 R->L }
% 5.11/1.05 ld(mult(X, mult(X, X)), mult(mult(X, mult(X, X)), ld(X, Y)))
% 5.11/1.05 = { by axiom 3 (c02) }
% 5.11/1.05 ld(X, Y)
% 5.11/1.05
% 5.11/1.05 Lemma 27: mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))) = mult(op_a, mult(op_a, mult(op_a, op_a))).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))))
% 5.11/1.05 = { by axiom 9 (c09) }
% 5.11/1.05 unit
% 5.11/1.05 = { by axiom 7 (c08) R->L }
% 5.11/1.05 mult(op_a, mult(op_a, mult(op_a, op_a)))
% 5.11/1.05
% 5.11/1.05 Lemma 28: mult(mult(X, mult(X, mult(X, mult(X, X)))), Y) = mult(mult(X, mult(X, X)), mult(mult(X, X), Y)).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(X, mult(X, mult(X, mult(X, X)))), Y)
% 5.11/1.05 = { by lemma 22 R->L }
% 5.11/1.05 mult(mult(mult(X, mult(X, mult(X, X))), X), Y)
% 5.11/1.05 = { by lemma 15 R->L }
% 5.11/1.05 mult(mult(mult(mult(X, mult(X, X)), X), X), Y)
% 5.11/1.05 = { by axiom 8 (c07) R->L }
% 5.11/1.05 mult(mult(X, mult(X, X)), mult(X, mult(X, Y)))
% 5.11/1.05 = { by lemma 10 R->L }
% 5.11/1.05 mult(mult(X, mult(X, X)), mult(mult(X, X), Y))
% 5.11/1.05
% 5.11/1.05 Lemma 29: ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), X) = mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X).
% 5.11/1.05 Proof:
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), X)
% 5.11/1.05 = { by lemma 25 R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_a, mult(op_a, mult(op_a, op_a))), X))
% 5.11/1.05 = { by lemma 27 R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), X))
% 5.11/1.05 = { by lemma 22 R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, mult(op_b, mult(op_b, op_b))))), X))
% 5.11/1.05 = { by lemma 11 R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, mult(op_b, mult(op_b, op_b)))), X))
% 5.11/1.05 = { by axiom 8 (c07) R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X))))
% 5.11/1.05 = { by lemma 24 }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, mult(mult(op_b, mult(op_b, op_b)), mult(op_b, mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X)))))
% 5.11/1.05 = { by lemma 16 }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, mult(mult(op_b, op_b), mult(op_b, mult(op_b, mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X))))))
% 5.11/1.05 = { by lemma 12 R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, op_b), mult(op_b, mult(op_b, mult(op_b, mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X))))))
% 5.11/1.05 = { by lemma 16 R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, mult(op_b, op_b)), mult(op_b, mult(op_b, mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X)))))
% 5.11/1.05 = { by lemma 24 R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X))))
% 5.11/1.05 = { by lemma 23 }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, op_b), mult(mult(op_b, op_b), mult(op_b, mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X)))))
% 5.11/1.05 = { by lemma 12 }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, op_b), mult(op_b, mult(mult(op_b, op_b), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X)))))
% 5.11/1.05 = { by lemma 16 R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, mult(op_b, op_b)), mult(mult(op_b, op_b), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X))))
% 5.11/1.05 = { by lemma 28 R->L }
% 5.11/1.05 ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X)))
% 5.11/1.05 = { by axiom 3 (c02) }
% 5.11/1.05 mult(mult(op_b, mult(op_b, mult(op_b, op_b))), X)
% 5.11/1.05
% 5.11/1.05 Lemma 30: mult(mult(X, mult(Y, mult(Y, mult(Y, Y)))), Y) = mult(mult(X, Y), mult(Y, mult(Y, mult(Y, Y)))).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(X, mult(Y, mult(Y, mult(Y, Y)))), Y)
% 5.11/1.05 = { by lemma 13 R->L }
% 5.11/1.05 mult(rd(mult(X, mult(Y, mult(Y, mult(Y, Y)))), Y), mult(Y, Y))
% 5.11/1.05 = { by lemma 21 R->L }
% 5.11/1.05 mult(rd(mult(X, rd(mult(Y, mult(Y, mult(Y, mult(Y, mult(Y, Y))))), mult(Y, Y))), Y), mult(Y, Y))
% 5.11/1.05 = { by lemma 20 }
% 5.11/1.05 mult(rd(mult(X, mult(mult(Y, Y), mult(Y, Y))), Y), mult(Y, Y))
% 5.11/1.05 = { by lemma 11 R->L }
% 5.11/1.05 mult(rd(mult(mult(X, mult(Y, Y)), mult(Y, Y)), Y), mult(Y, Y))
% 5.11/1.05 = { by lemma 18 }
% 5.11/1.05 mult(mult(mult(X, mult(Y, Y)), Y), mult(Y, Y))
% 5.11/1.05 = { by lemma 13 R->L }
% 5.11/1.05 mult(mult(rd(mult(X, mult(Y, Y)), Y), mult(Y, Y)), mult(Y, Y))
% 5.11/1.05 = { by lemma 18 }
% 5.11/1.05 mult(mult(mult(X, Y), mult(Y, Y)), mult(Y, Y))
% 5.11/1.05 = { by lemma 11 }
% 5.11/1.05 mult(mult(X, Y), mult(mult(Y, Y), mult(Y, Y)))
% 5.11/1.05 = { by lemma 20 R->L }
% 5.11/1.05 mult(mult(X, Y), rd(mult(Y, mult(Y, mult(Y, mult(Y, mult(Y, Y))))), mult(Y, Y)))
% 5.11/1.05 = { by lemma 21 }
% 5.11/1.05 mult(mult(X, Y), mult(Y, mult(Y, mult(Y, Y))))
% 5.11/1.05
% 5.11/1.05 Lemma 31: mult(mult(mult(X, mult(X, mult(X, mult(X, Y)))), Y), Z) = mult(mult(X, mult(X, mult(X, X))), mult(mult(Y, Y), Z)).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(mult(X, mult(X, mult(X, mult(X, Y)))), Y), Z)
% 5.11/1.05 = { by lemma 22 R->L }
% 5.11/1.05 mult(mult(mult(mult(X, mult(X, mult(X, X))), Y), Y), Z)
% 5.11/1.05 = { by axiom 8 (c07) R->L }
% 5.11/1.05 mult(mult(X, mult(X, mult(X, X))), mult(Y, mult(Y, Z)))
% 5.11/1.05 = { by lemma 10 R->L }
% 5.11/1.05 mult(mult(X, mult(X, mult(X, X))), mult(mult(Y, Y), Z))
% 5.11/1.05
% 5.11/1.05 Lemma 32: mult(mult(X, op_b), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))) = X.
% 5.11/1.05 Proof:
% 5.11/1.05 mult(mult(X, op_b), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))))
% 5.11/1.05 = { by lemma 22 R->L }
% 5.11/1.05 mult(mult(X, op_b), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, mult(op_b, mult(op_b, op_b)))))
% 5.11/1.05 = { by lemma 11 R->L }
% 5.11/1.05 mult(mult(mult(X, op_b), mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, mult(op_b, mult(op_b, op_b))))
% 5.11/1.05 = { by lemma 30 R->L }
% 5.11/1.05 mult(mult(mult(X, mult(op_b, mult(op_b, mult(op_b, op_b)))), op_b), mult(op_b, mult(op_b, mult(op_b, op_b))))
% 5.11/1.05 = { by lemma 30 R->L }
% 5.11/1.05 mult(mult(mult(X, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, mult(op_b, mult(op_b, op_b)))), op_b)
% 5.11/1.05 = { by axiom 8 (c07) R->L }
% 5.11/1.05 mult(X, mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), op_b)))
% 5.11/1.05 = { by lemma 29 R->L }
% 5.11/1.05 mult(X, ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), op_b)))
% 5.11/1.05 = { by lemma 22 }
% 5.11/1.05 mult(X, ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))
% 5.11/1.05 = { by axiom 1 (c05) R->L }
% 5.11/1.05 mult(X, ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), unit)))
% 5.11/1.05 = { by axiom 3 (c02) }
% 5.11/1.05 mult(X, unit)
% 5.11/1.05 = { by axiom 7 (c08) R->L }
% 5.11/1.05 mult(X, mult(op_a, mult(op_a, mult(op_a, op_a))))
% 5.11/1.05 = { by lemma 19 }
% 5.11/1.05 X
% 5.11/1.05
% 5.11/1.05 Goal 1 (goals): mult(op_a, mult(op_b, a)) = mult(mult(op_a, op_b), a).
% 5.11/1.05 Proof:
% 5.11/1.05 mult(op_a, mult(op_b, a))
% 5.11/1.05 = { by axiom 4 (c04) R->L }
% 5.11/1.05 mult(rd(mult(op_a, op_b), op_b), mult(op_b, a))
% 5.11/1.06 = { by lemma 32 R->L }
% 5.11/1.06 mult(mult(mult(rd(mult(op_a, op_b), op_b), op_b), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, a))
% 5.11/1.06 = { by axiom 6 (c03) }
% 5.11/1.06 mult(mult(mult(op_a, op_b), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, a))
% 5.11/1.06 = { by axiom 3 (c02) R->L }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(rd(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))))), mult(op_b, a))
% 5.11/1.06 = { by axiom 6 (c03) }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 19 R->L }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_a, mult(op_a, mult(op_a, op_a)))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 27 R->L }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 10 R->L }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(mult(op_b, op_b), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 31 R->L }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), op_b), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by axiom 3 (c02) R->L }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), op_b), ld(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 25 R->L }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), op_b), ld(op_b, mult(mult(op_a, mult(op_a, mult(op_a, op_a))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 27 R->L }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), op_b), ld(op_b, mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 11 }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), op_b), ld(op_b, mult(op_b, mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by axiom 3 (c02) }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(rd(mult(mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), op_b), mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))))), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 18 }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(mult(mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), op_b), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 31 }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(mult(op_b, op_b), mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b))))))))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 32 }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(mult(mult(op_b, mult(op_b, mult(op_b, op_b))), op_b), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 22 }
% 5.11/1.06 mult(mult(mult(op_a, op_b), ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 29 }
% 5.11/1.06 mult(mult(mult(op_a, op_b), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, mult(op_b, mult(op_b, op_b))))), mult(op_b, a))
% 5.11/1.06 = { by lemma 11 R->L }
% 5.11/1.06 mult(mult(mult(mult(op_a, op_b), mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a))
% 5.11/1.06 = { by axiom 8 (c07) R->L }
% 5.11/1.06 mult(mult(op_a, op_b), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, a))))
% 5.11/1.06 = { by lemma 10 R->L }
% 5.11/1.06 mult(mult(op_a, op_b), mult(mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a)))
% 5.11/1.06 = { by lemma 17 R->L }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(mult(op_b, mult(op_b, mult(op_b, op_b))), mult(op_b, a))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by lemma 29 R->L }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(mult(mult(op_b, mult(op_b, mult(op_b, op_b))), ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by lemma 23 }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(mult(mult(op_b, op_b), mult(mult(op_b, op_b), ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a)))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by lemma 10 }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(mult(op_b, mult(op_b, mult(mult(op_b, op_b), ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a))))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by axiom 3 (c02) R->L }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(ld(op_b, mult(op_b, mult(op_b, mult(op_b, mult(mult(op_b, op_b), ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a))))))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by lemma 10 R->L }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(ld(op_b, mult(mult(op_b, op_b), mult(op_b, mult(mult(op_b, op_b), ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a)))))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by lemma 16 R->L }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(ld(op_b, mult(mult(op_b, mult(op_b, op_b)), mult(mult(op_b, op_b), ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a))))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by lemma 28 R->L }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(ld(op_b, mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a)))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by lemma 26 R->L }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(ld(mult(op_b, mult(op_b, op_b)), mult(mult(op_b, op_b), mult(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), ld(mult(op_b, mult(op_b, mult(op_b, mult(op_b, op_b)))), mult(op_b, a))))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by axiom 5 (c01) }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(ld(mult(op_b, mult(op_b, op_b)), mult(mult(op_b, op_b), mult(op_b, a))), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by lemma 26 }
% 5.11/1.06 mult(mult(op_a, op_b), mult(rd(ld(op_b, mult(op_b, a)), mult(op_b, a)), mult(op_b, a)))
% 5.11/1.06 = { by axiom 6 (c03) }
% 5.11/1.06 mult(mult(op_a, op_b), ld(op_b, mult(op_b, a)))
% 5.11/1.06 = { by axiom 3 (c02) }
% 5.11/1.06 mult(mult(op_a, op_b), a)
% 5.11/1.06 % SZS output end Proof
% 5.11/1.06
% 5.11/1.06 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------