TSTP Solution File: GRP667-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP667-3 : 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 : n029.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 25.36s 3.56s
% Output : Proof 26.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP667-3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 20:58:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 25.36/3.56 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 25.36/3.56
% 25.36/3.56 % SZS status Unsatisfiable
% 25.36/3.56
% 25.36/3.61 % SZS output start Proof
% 25.36/3.61 Axiom 1 (c05): mult(X, unit) = X.
% 25.36/3.61 Axiom 2 (c06): mult(unit, X) = X.
% 25.36/3.61 Axiom 3 (c02): ld(X, mult(X, Y)) = Y.
% 25.36/3.61 Axiom 4 (c04): rd(mult(X, Y), Y) = X.
% 25.36/3.61 Axiom 5 (c01): mult(X, ld(X, Y)) = Y.
% 25.36/3.61 Axiom 6 (c09): mult(f(X), f(X)) = X.
% 25.36/3.61 Axiom 7 (c03): mult(rd(X, Y), Y) = X.
% 25.36/3.61 Axiom 8 (c08): mult(mult(X, Y), X) = mult(X, mult(Y, X)).
% 25.36/3.61 Axiom 9 (c07): mult(mult(X, Y), mult(mult(Z, Y), Z)) = mult(mult(X, mult(mult(Y, Z), Y)), Z).
% 25.36/3.61
% 25.36/3.61 Lemma 10: ld(rd(X, Y), X) = Y.
% 25.36/3.61 Proof:
% 25.36/3.61 ld(rd(X, Y), X)
% 25.36/3.61 = { by axiom 7 (c03) R->L }
% 25.36/3.61 ld(rd(X, Y), mult(rd(X, Y), Y))
% 25.36/3.61 = { by axiom 3 (c02) }
% 25.36/3.61 Y
% 25.36/3.61
% 25.36/3.61 Lemma 11: mult(X, mult(ld(X, Y), X)) = mult(Y, X).
% 25.36/3.61 Proof:
% 25.36/3.61 mult(X, mult(ld(X, Y), X))
% 25.36/3.61 = { by axiom 8 (c08) R->L }
% 25.36/3.61 mult(mult(X, ld(X, Y)), X)
% 25.36/3.61 = { by axiom 5 (c01) }
% 25.36/3.61 mult(Y, X)
% 25.36/3.61
% 25.36/3.61 Lemma 12: mult(mult(X, mult(Y, mult(Z, Y))), Z) = mult(mult(X, Y), mult(Z, mult(Y, Z))).
% 25.36/3.61 Proof:
% 25.36/3.61 mult(mult(X, mult(Y, mult(Z, Y))), Z)
% 25.36/3.61 = { by axiom 8 (c08) R->L }
% 25.36/3.61 mult(mult(X, mult(mult(Y, Z), Y)), Z)
% 25.36/3.61 = { by axiom 9 (c07) R->L }
% 25.36/3.61 mult(mult(X, Y), mult(mult(Z, Y), Z))
% 25.36/3.61 = { by axiom 8 (c08) }
% 25.36/3.61 mult(mult(X, Y), mult(Z, mult(Y, Z)))
% 25.36/3.61
% 25.36/3.61 Lemma 13: mult(mult(X, mult(Y, X)), Y) = mult(X, mult(Y, mult(X, Y))).
% 25.36/3.61 Proof:
% 25.36/3.61 mult(mult(X, mult(Y, X)), Y)
% 25.36/3.61 = { by axiom 2 (c06) R->L }
% 25.36/3.61 mult(mult(unit, mult(X, mult(Y, X))), Y)
% 25.36/3.61 = { by lemma 12 }
% 25.36/3.61 mult(mult(unit, X), mult(Y, mult(X, Y)))
% 25.36/3.61 = { by axiom 2 (c06) }
% 25.36/3.61 mult(X, mult(Y, mult(X, Y)))
% 25.36/3.61
% 25.36/3.61 Lemma 14: mult(rd(X, Y), mult(Y, mult(Z, Y))) = rd(mult(X, mult(Z, mult(Y, Z))), Z).
% 25.36/3.61 Proof:
% 25.36/3.61 mult(rd(X, Y), mult(Y, mult(Z, Y)))
% 25.36/3.61 = { by axiom 4 (c04) R->L }
% 25.36/3.61 rd(mult(mult(rd(X, Y), mult(Y, mult(Z, Y))), Z), Z)
% 25.36/3.61 = { by lemma 12 }
% 25.36/3.61 rd(mult(mult(rd(X, Y), Y), mult(Z, mult(Y, Z))), Z)
% 25.36/3.61 = { by axiom 7 (c03) }
% 25.36/3.61 rd(mult(X, mult(Z, mult(Y, Z))), Z)
% 25.36/3.61
% 25.36/3.61 Lemma 15: rd(mult(X, mult(Y, X)), X) = mult(X, Y).
% 25.36/3.61 Proof:
% 25.36/3.61 rd(mult(X, mult(Y, X)), X)
% 25.36/3.61 = { by axiom 8 (c08) R->L }
% 25.36/3.61 rd(mult(mult(X, Y), X), X)
% 25.36/3.61 = { by axiom 4 (c04) }
% 25.36/3.61 mult(X, Y)
% 25.36/3.61
% 25.36/3.61 Lemma 16: mult(rd(unit, X), mult(X, Y)) = Y.
% 25.36/3.61 Proof:
% 25.36/3.61 mult(rd(unit, X), mult(X, Y))
% 25.36/3.61 = { by axiom 7 (c03) R->L }
% 25.36/3.61 mult(rd(unit, X), mult(X, mult(rd(Y, X), X)))
% 25.36/3.61 = { by lemma 14 }
% 25.36/3.61 rd(mult(unit, mult(rd(Y, X), mult(X, rd(Y, X)))), rd(Y, X))
% 25.36/3.61 = { by axiom 2 (c06) }
% 25.36/3.61 rd(mult(rd(Y, X), mult(X, rd(Y, X))), rd(Y, X))
% 25.36/3.61 = { by lemma 15 }
% 25.36/3.61 mult(rd(Y, X), X)
% 25.36/3.61 = { by axiom 7 (c03) }
% 25.36/3.61 Y
% 25.36/3.61
% 25.36/3.61 Lemma 17: mult(ld(X, Y), mult(Y, X)) = ld(X, mult(Y, mult(Y, X))).
% 25.36/3.61 Proof:
% 25.36/3.61 mult(ld(X, Y), mult(Y, X))
% 25.36/3.61 = { by axiom 3 (c02) R->L }
% 25.36/3.61 ld(X, mult(X, mult(ld(X, Y), mult(Y, X))))
% 25.36/3.61 = { by lemma 11 R->L }
% 25.36/3.61 ld(X, mult(X, mult(ld(X, Y), mult(X, mult(ld(X, Y), X)))))
% 25.36/3.61 = { by lemma 13 R->L }
% 25.36/3.61 ld(X, mult(X, mult(mult(ld(X, Y), mult(X, ld(X, Y))), X)))
% 25.36/3.61 = { by axiom 8 (c08) R->L }
% 25.36/3.61 ld(X, mult(mult(X, mult(ld(X, Y), mult(X, ld(X, Y)))), X))
% 25.36/3.61 = { by lemma 12 }
% 25.36/3.61 ld(X, mult(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), X))))
% 25.36/3.61 = { by axiom 5 (c01) }
% 25.36/3.61 ld(X, mult(Y, mult(X, mult(ld(X, Y), X))))
% 25.36/3.61 = { by lemma 11 }
% 25.36/3.62 ld(X, mult(Y, mult(Y, X)))
% 25.36/3.62
% 25.36/3.62 Lemma 18: mult(mult(X, Y), Y) = mult(X, mult(Y, Y)).
% 25.36/3.62 Proof:
% 25.36/3.62 mult(mult(X, Y), Y)
% 25.36/3.62 = { by axiom 1 (c05) R->L }
% 25.36/3.62 mult(mult(X, Y), mult(Y, unit))
% 25.36/3.62 = { by axiom 2 (c06) R->L }
% 25.36/3.62 mult(mult(X, Y), mult(unit, mult(Y, unit)))
% 25.36/3.62 = { by lemma 12 R->L }
% 25.36/3.62 mult(mult(X, mult(Y, mult(unit, Y))), unit)
% 25.36/3.62 = { by axiom 1 (c05) }
% 25.36/3.62 mult(X, mult(Y, mult(unit, Y)))
% 25.36/3.62 = { by axiom 2 (c06) }
% 25.36/3.62 mult(X, mult(Y, Y))
% 25.36/3.62
% 25.36/3.62 Lemma 19: mult(mult(X, Y), mult(X, Y)) = mult(X, mult(Y, mult(X, Y))).
% 25.36/3.62 Proof:
% 25.36/3.62 mult(mult(X, Y), mult(X, Y))
% 25.36/3.62 = { by lemma 16 R->L }
% 25.36/3.62 mult(rd(unit, ld(ld(rd(unit, X), unit), unit)), mult(ld(ld(rd(unit, X), unit), unit), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by axiom 5 (c01) R->L }
% 25.36/3.62 mult(rd(mult(ld(rd(unit, X), unit), ld(ld(rd(unit, X), unit), unit)), ld(ld(rd(unit, X), unit), unit)), mult(ld(ld(rd(unit, X), unit), unit), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by axiom 4 (c04) }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(ld(rd(unit, X), unit), unit), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by axiom 3 (c02) R->L }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(ld(rd(unit, X), unit), ld(rd(unit, X), mult(rd(unit, X), unit))), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by axiom 1 (c05) }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(ld(rd(unit, X), unit), ld(rd(unit, X), rd(unit, X))), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by axiom 2 (c06) R->L }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(ld(rd(unit, X), unit), ld(rd(unit, X), mult(unit, rd(unit, X)))), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by axiom 2 (c06) R->L }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(ld(rd(unit, X), unit), ld(rd(unit, X), mult(unit, mult(unit, rd(unit, X))))), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by axiom 1 (c05) R->L }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(mult(ld(rd(unit, X), unit), unit), ld(rd(unit, X), mult(unit, mult(unit, rd(unit, X))))), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by lemma 17 R->L }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(mult(ld(rd(unit, X), unit), unit), mult(ld(rd(unit, X), unit), mult(unit, rd(unit, X)))), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by lemma 11 R->L }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(mult(ld(rd(unit, X), unit), unit), mult(ld(rd(unit, X), unit), mult(rd(unit, X), mult(ld(rd(unit, X), unit), rd(unit, X))))), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by axiom 5 (c01) R->L }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(mult(ld(rd(unit, X), unit), mult(rd(unit, X), ld(rd(unit, X), unit))), mult(ld(rd(unit, X), unit), mult(rd(unit, X), mult(ld(rd(unit, X), unit), rd(unit, X))))), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by lemma 13 R->L }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(ld(mult(ld(rd(unit, X), unit), mult(rd(unit, X), ld(rd(unit, X), unit))), mult(mult(ld(rd(unit, X), unit), mult(rd(unit, X), ld(rd(unit, X), unit))), rd(unit, X))), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by axiom 3 (c02) }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(rd(unit, X), mult(mult(X, Y), mult(X, Y))))
% 25.36/3.62 = { by lemma 18 R->L }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(mult(rd(unit, X), mult(X, Y)), mult(X, Y)))
% 25.36/3.62 = { by lemma 16 }
% 25.36/3.62 mult(ld(rd(unit, X), unit), mult(Y, mult(X, Y)))
% 25.36/3.62 = { by lemma 10 }
% 25.36/3.62 mult(X, mult(Y, mult(X, Y)))
% 25.36/3.62
% 25.36/3.62 Lemma 20: mult(X, rd(X, Y)) = rd(mult(X, X), Y).
% 25.36/3.62 Proof:
% 25.36/3.62 mult(X, rd(X, Y))
% 25.36/3.62 = { by axiom 4 (c04) R->L }
% 25.36/3.62 rd(mult(mult(X, rd(X, Y)), Y), Y)
% 25.36/3.62 = { by lemma 10 R->L }
% 25.36/3.62 rd(mult(mult(X, rd(X, Y)), ld(rd(X, Y), X)), Y)
% 25.36/3.62 = { by lemma 11 R->L }
% 25.36/3.62 rd(mult(mult(rd(X, Y), mult(ld(rd(X, Y), X), rd(X, Y))), ld(rd(X, Y), X)), Y)
% 25.36/3.62 = { by lemma 13 }
% 25.36/3.62 rd(mult(rd(X, Y), mult(ld(rd(X, Y), X), mult(rd(X, Y), ld(rd(X, Y), X)))), Y)
% 25.36/3.62 = { by axiom 5 (c01) }
% 25.36/3.62 rd(mult(rd(X, Y), mult(ld(rd(X, Y), X), X)), Y)
% 25.36/3.62 = { by lemma 10 }
% 25.36/3.62 rd(mult(rd(X, Y), mult(Y, X)), Y)
% 25.36/3.62 = { by axiom 7 (c03) R->L }
% 25.36/3.62 rd(mult(rd(X, Y), mult(Y, mult(rd(X, Y), Y))), Y)
% 25.36/3.62 = { by lemma 19 R->L }
% 25.36/3.62 rd(mult(mult(rd(X, Y), Y), mult(rd(X, Y), Y)), Y)
% 25.36/3.62 = { by axiom 7 (c03) }
% 25.36/3.62 rd(mult(X, mult(rd(X, Y), Y)), Y)
% 25.36/3.62 = { by axiom 7 (c03) }
% 25.36/3.62 rd(mult(X, X), Y)
% 25.36/3.62
% 25.36/3.62 Lemma 21: rd(X, mult(X, mult(Y, X))) = rd(unit, mult(X, Y)).
% 25.36/3.62 Proof:
% 25.36/3.62 rd(X, mult(X, mult(Y, X)))
% 25.36/3.62 = { by lemma 16 R->L }
% 25.36/3.62 rd(mult(rd(unit, mult(X, Y)), mult(mult(X, Y), X)), mult(X, mult(Y, X)))
% 25.36/3.62 = { by axiom 8 (c08) }
% 25.36/3.62 rd(mult(rd(unit, mult(X, Y)), mult(X, mult(Y, X))), mult(X, mult(Y, X)))
% 25.36/3.62 = { by axiom 4 (c04) }
% 25.36/3.62 rd(unit, mult(X, Y))
% 25.36/3.62
% 25.36/3.62 Lemma 22: mult(mult(rd(X, mult(Y, mult(Z, Y))), Y), mult(Z, mult(Y, Z))) = mult(X, Z).
% 25.36/3.62 Proof:
% 25.36/3.62 mult(mult(rd(X, mult(Y, mult(Z, Y))), Y), mult(Z, mult(Y, Z)))
% 25.36/3.62 = { by lemma 12 R->L }
% 25.36/3.62 mult(mult(rd(X, mult(Y, mult(Z, Y))), mult(Y, mult(Z, Y))), Z)
% 25.36/3.62 = { by axiom 7 (c03) }
% 25.36/3.62 mult(X, Z)
% 25.36/3.62
% 25.36/3.62 Lemma 23: mult(rd(X, mult(Y, mult(Z, Y))), Y) = rd(mult(X, Z), mult(Z, mult(Y, Z))).
% 25.36/3.62 Proof:
% 25.36/3.62 mult(rd(X, mult(Y, mult(Z, Y))), Y)
% 25.36/3.62 = { by axiom 4 (c04) R->L }
% 25.36/3.62 rd(mult(mult(rd(X, mult(Y, mult(Z, Y))), Y), mult(Z, mult(Y, Z))), mult(Z, mult(Y, Z)))
% 25.36/3.62 = { by lemma 22 }
% 25.36/3.62 rd(mult(X, Z), mult(Z, mult(Y, Z)))
% 25.36/3.62
% 25.36/3.62 Lemma 24: mult(X, rd(unit, Y)) = rd(X, Y).
% 25.36/3.62 Proof:
% 25.36/3.62 mult(X, rd(unit, Y))
% 25.36/3.62 = { by axiom 7 (c03) R->L }
% 25.36/3.62 mult(X, rd(unit, mult(rd(Y, X), X)))
% 25.36/3.62 = { by lemma 21 R->L }
% 25.36/3.62 mult(X, rd(rd(Y, X), mult(rd(Y, X), mult(X, rd(Y, X)))))
% 25.36/3.62 = { by axiom 2 (c06) R->L }
% 25.36/3.62 mult(X, rd(mult(unit, rd(Y, X)), mult(rd(Y, X), mult(X, rd(Y, X)))))
% 25.36/3.62 = { by lemma 23 R->L }
% 25.36/3.62 mult(X, mult(rd(unit, mult(X, mult(rd(Y, X), X))), X))
% 25.36/3.62 = { by axiom 7 (c03) }
% 25.36/3.62 mult(X, mult(rd(unit, mult(X, Y)), X))
% 25.36/3.62 = { by lemma 21 R->L }
% 25.36/3.62 mult(X, mult(rd(X, mult(X, mult(Y, X))), X))
% 25.36/3.62 = { by axiom 8 (c08) R->L }
% 25.36/3.62 mult(mult(X, rd(X, mult(X, mult(Y, X)))), X)
% 25.36/3.62 = { by lemma 20 }
% 25.36/3.62 mult(rd(mult(X, X), mult(X, mult(Y, X))), X)
% 25.36/3.62 = { by lemma 23 }
% 25.36/3.62 rd(mult(mult(X, X), Y), mult(Y, mult(X, Y)))
% 25.36/3.62 = { by axiom 5 (c01) R->L }
% 25.36/3.62 rd(mult(mult(X, mult(Y, ld(Y, X))), Y), mult(Y, mult(X, Y)))
% 25.36/3.62 = { by axiom 5 (c01) R->L }
% 25.36/3.62 rd(mult(mult(mult(Y, ld(Y, X)), mult(Y, ld(Y, X))), Y), mult(Y, mult(X, Y)))
% 25.36/3.62 = { by lemma 19 }
% 25.36/3.62 rd(mult(mult(Y, mult(ld(Y, X), mult(Y, ld(Y, X)))), Y), mult(Y, mult(X, Y)))
% 25.36/3.62 = { by axiom 5 (c01) }
% 25.36/3.62 rd(mult(mult(Y, mult(ld(Y, X), X)), Y), mult(Y, mult(X, Y)))
% 25.36/3.62 = { by axiom 8 (c08) }
% 25.36/3.63 rd(mult(Y, mult(mult(ld(Y, X), X), Y)), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by lemma 15 R->L }
% 25.36/3.63 rd(rd(mult(Y, mult(mult(mult(ld(Y, X), X), Y), Y)), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by lemma 18 }
% 25.36/3.63 rd(rd(mult(Y, mult(mult(ld(Y, X), X), mult(Y, Y))), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by axiom 5 (c01) R->L }
% 25.36/3.63 rd(rd(mult(Y, mult(mult(ld(Y, X), mult(Y, ld(Y, X))), mult(Y, Y))), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by lemma 18 R->L }
% 25.36/3.63 rd(rd(mult(Y, mult(mult(mult(ld(Y, X), mult(Y, ld(Y, X))), Y), Y)), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by lemma 13 }
% 25.36/3.63 rd(rd(mult(Y, mult(mult(ld(Y, X), mult(Y, mult(ld(Y, X), Y))), Y)), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by lemma 11 }
% 25.36/3.63 rd(rd(mult(Y, mult(mult(ld(Y, X), mult(X, Y)), Y)), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by lemma 17 }
% 25.36/3.63 rd(rd(mult(Y, mult(ld(Y, mult(X, mult(X, Y))), Y)), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by axiom 3 (c02) R->L }
% 25.36/3.63 rd(rd(mult(Y, ld(Y, mult(Y, mult(ld(Y, mult(X, mult(X, Y))), Y)))), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by lemma 11 }
% 25.36/3.63 rd(rd(mult(Y, ld(Y, mult(mult(X, mult(X, Y)), Y))), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by axiom 5 (c01) }
% 25.36/3.63 rd(rd(mult(mult(X, mult(X, Y)), Y), Y), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by axiom 4 (c04) }
% 25.36/3.63 rd(mult(X, mult(X, Y)), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by lemma 15 R->L }
% 25.36/3.63 rd(rd(mult(X, mult(mult(X, Y), X)), X), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by axiom 8 (c08) }
% 25.36/3.63 rd(rd(mult(X, mult(X, mult(Y, X))), X), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by lemma 14 R->L }
% 25.36/3.63 rd(mult(rd(X, Y), mult(Y, mult(X, Y))), mult(Y, mult(X, Y)))
% 25.36/3.63 = { by axiom 4 (c04) }
% 25.36/3.63 rd(X, Y)
% 26.09/3.63
% 26.09/3.63 Lemma 25: rd(X, mult(Y, X)) = rd(unit, Y).
% 26.09/3.63 Proof:
% 26.09/3.63 rd(X, mult(Y, X))
% 26.09/3.63 = { by lemma 16 R->L }
% 26.09/3.63 rd(mult(rd(unit, Y), mult(Y, X)), mult(Y, X))
% 26.09/3.63 = { by axiom 4 (c04) }
% 26.09/3.63 rd(unit, Y)
% 26.09/3.63
% 26.09/3.63 Lemma 26: mult(mult(X, mult(Y, Z)), rd(Z, Y)) = mult(mult(X, Y), rd(mult(Z, Z), Y)).
% 26.09/3.63 Proof:
% 26.09/3.63 mult(mult(X, mult(Y, Z)), rd(Z, Y))
% 26.09/3.63 = { by lemma 22 R->L }
% 26.09/3.63 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))))
% 26.09/3.63 = { by axiom 7 (c03) }
% 26.09/3.63 mult(mult(rd(mult(X, mult(Y, Z)), mult(Y, Z)), Y), mult(rd(Z, Y), mult(Y, rd(Z, Y))))
% 26.09/3.63 = { by axiom 8 (c08) R->L }
% 26.09/3.63 mult(mult(rd(mult(X, mult(Y, Z)), mult(Y, Z)), Y), mult(mult(rd(Z, Y), Y), rd(Z, Y)))
% 26.09/3.63 = { by axiom 7 (c03) }
% 26.09/3.63 mult(mult(rd(mult(X, mult(Y, Z)), mult(Y, Z)), Y), mult(Z, rd(Z, Y)))
% 26.09/3.63 = { by lemma 20 }
% 26.09/3.63 mult(mult(rd(mult(X, mult(Y, Z)), mult(Y, Z)), Y), rd(mult(Z, Z), Y))
% 26.09/3.63 = { by axiom 4 (c04) }
% 26.09/3.63 mult(mult(X, Y), rd(mult(Z, Z), Y))
% 26.09/3.63
% 26.09/3.63 Goal 1 (goals): mult(a, mult(b, mult(c, b))) = mult(mult(mult(a, b), c), b).
% 26.09/3.63 Proof:
% 26.09/3.63 mult(a, mult(b, mult(c, b)))
% 26.09/3.63 = { by axiom 7 (c03) R->L }
% 26.09/3.63 mult(rd(mult(a, mult(b, mult(c, b))), b), b)
% 26.09/3.63 = { by axiom 6 (c09) R->L }
% 26.09/3.63 mult(rd(mult(a, mult(b, mult(f(mult(c, b)), f(mult(c, b))))), b), b)
% 26.09/3.63 = { by lemma 24 R->L }
% 26.09/3.63 mult(mult(mult(a, mult(b, mult(f(mult(c, b)), f(mult(c, b))))), rd(unit, b)), b)
% 26.09/3.63 = { by lemma 25 R->L }
% 26.09/3.63 mult(mult(mult(a, mult(b, mult(f(mult(c, b)), f(mult(c, b))))), rd(f(mult(c, b)), mult(b, f(mult(c, b))))), b)
% 26.09/3.63 = { by lemma 18 R->L }
% 26.09/3.63 mult(mult(mult(a, mult(mult(b, f(mult(c, b))), f(mult(c, b)))), rd(f(mult(c, b)), mult(b, f(mult(c, b))))), b)
% 26.09/3.63 = { by lemma 26 }
% 26.09/3.63 mult(mult(mult(a, mult(b, f(mult(c, b)))), rd(mult(f(mult(c, b)), f(mult(c, b))), mult(b, f(mult(c, b))))), b)
% 26.09/3.63 = { by lemma 20 R->L }
% 26.09/3.63 mult(mult(mult(a, mult(b, f(mult(c, b)))), mult(f(mult(c, b)), rd(f(mult(c, b)), mult(b, f(mult(c, b)))))), b)
% 26.09/3.63 = { by lemma 25 }
% 26.09/3.63 mult(mult(mult(a, mult(b, f(mult(c, b)))), mult(f(mult(c, b)), rd(unit, b))), b)
% 26.09/3.63 = { by lemma 24 }
% 26.09/3.63 mult(mult(mult(a, mult(b, f(mult(c, b)))), rd(f(mult(c, b)), b)), b)
% 26.09/3.63 = { by lemma 26 }
% 26.09/3.63 mult(mult(mult(a, b), rd(mult(f(mult(c, b)), f(mult(c, b))), b)), b)
% 26.09/3.63 = { by axiom 6 (c09) }
% 26.09/3.63 mult(mult(mult(a, b), rd(mult(c, b), b)), b)
% 26.09/3.63 = { by axiom 4 (c04) }
% 26.09/3.63 mult(mult(mult(a, b), c), b)
% 26.09/3.63 % SZS output end Proof
% 26.09/3.63
% 26.09/3.63 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------