TSTP Solution File: GRP655-11 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP655-11 : TPTP v8.1.2. Released v8.1.0.
% 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 : n018.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 01:19:28 EDT 2023
% Result : Unsatisfiable 2.66s 0.72s
% Output : Proof 3.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP655-11 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n018.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 01:57:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.66/0.72 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.66/0.72
% 2.66/0.72 % SZS status Unsatisfiable
% 2.66/0.72
% 2.66/0.77 % SZS output start Proof
% 2.66/0.77 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 2.66/0.77 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 2.66/0.77 Axiom 3 (f04): rd(mult(X, Y), Y) = X.
% 2.66/0.77 Axiom 4 (f02): ld(X, mult(X, Y)) = Y.
% 2.66/0.77 Axiom 5 (f05): mult(X, mult(Y, mult(Z, Y))) = mult(mult(mult(X, Y), Z), Y).
% 2.66/0.77
% 2.66/0.77 Lemma 6: mult(rd(X, Y), mult(Y, mult(Z, Y))) = mult(mult(X, Z), Y).
% 2.66/0.77 Proof:
% 2.66/0.77 mult(rd(X, Y), mult(Y, mult(Z, Y)))
% 2.66/0.77 = { by axiom 5 (f05) }
% 2.66/0.77 mult(mult(mult(rd(X, Y), Y), Z), Y)
% 2.66/0.77 = { by axiom 2 (f03) }
% 2.66/0.78 mult(mult(X, Z), Y)
% 2.66/0.78
% 2.66/0.78 Lemma 7: ld(rd(X, Y), mult(Z, Y)) = mult(Y, mult(ld(X, Z), Y)).
% 2.66/0.78 Proof:
% 2.66/0.78 ld(rd(X, Y), mult(Z, Y))
% 2.66/0.78 = { by axiom 1 (f01) R->L }
% 2.66/0.78 ld(rd(X, Y), mult(mult(X, ld(X, Z)), Y))
% 2.66/0.78 = { by lemma 6 R->L }
% 2.66/0.78 ld(rd(X, Y), mult(rd(X, Y), mult(Y, mult(ld(X, Z), Y))))
% 2.66/0.78 = { by axiom 4 (f02) }
% 2.66/0.78 mult(Y, mult(ld(X, Z), Y))
% 2.66/0.78
% 2.66/0.78 Lemma 8: mult(ld(X, rd(X, Y)), Y) = ld(Y, Y).
% 2.66/0.78 Proof:
% 2.66/0.78 mult(ld(X, rd(X, Y)), Y)
% 2.66/0.78 = { by axiom 4 (f02) R->L }
% 2.66/0.78 ld(Y, mult(Y, mult(ld(X, rd(X, Y)), Y)))
% 2.66/0.78 = { by lemma 7 R->L }
% 2.66/0.78 ld(Y, ld(rd(X, Y), mult(rd(X, Y), Y)))
% 2.66/0.78 = { by axiom 4 (f02) }
% 2.66/0.78 ld(Y, Y)
% 2.66/0.78
% 2.66/0.78 Lemma 9: ld(X, rd(X, Y)) = rd(ld(Y, Y), Y).
% 2.66/0.78 Proof:
% 2.66/0.78 ld(X, rd(X, Y))
% 2.66/0.78 = { by axiom 3 (f04) R->L }
% 2.66/0.78 rd(mult(ld(X, rd(X, Y)), Y), Y)
% 2.66/0.78 = { by lemma 8 }
% 2.66/0.78 rd(ld(Y, Y), Y)
% 2.66/0.78
% 2.66/0.78 Lemma 10: ld(mult(Y, X), Y) = rd(ld(X, X), X).
% 2.66/0.78 Proof:
% 2.66/0.78 ld(mult(Y, X), Y)
% 2.66/0.78 = { by axiom 3 (f04) R->L }
% 2.66/0.78 ld(mult(Y, X), rd(mult(Y, X), X))
% 2.66/0.78 = { by lemma 9 }
% 2.66/0.78 rd(ld(X, X), X)
% 2.66/0.78
% 2.66/0.78 Lemma 11: mult(X, ld(Y, rd(Y, Z))) = rd(X, Z).
% 2.66/0.78 Proof:
% 2.66/0.78 mult(X, ld(Y, rd(Y, Z)))
% 2.66/0.78 = { by axiom 3 (f04) R->L }
% 2.66/0.78 mult(X, rd(mult(ld(Y, rd(Y, Z)), Z), Z))
% 2.66/0.78 = { by lemma 8 }
% 2.66/0.78 mult(X, rd(ld(Z, Z), Z))
% 2.66/0.78 = { by lemma 8 R->L }
% 2.66/0.78 mult(X, rd(mult(ld(X, rd(X, Z)), Z), Z))
% 2.66/0.78 = { by axiom 3 (f04) }
% 2.66/0.78 mult(X, ld(X, rd(X, Z)))
% 2.66/0.78 = { by axiom 1 (f01) }
% 3.24/0.78 rd(X, Z)
% 3.24/0.78
% 3.24/0.78 Lemma 12: rd(X, ld(Y, X)) = Y.
% 3.24/0.78 Proof:
% 3.24/0.78 rd(X, ld(Y, X))
% 3.24/0.78 = { by axiom 1 (f01) R->L }
% 3.24/0.78 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 3.24/0.78 = { by axiom 3 (f04) }
% 3.24/0.78 Y
% 3.24/0.78
% 3.24/0.78 Lemma 13: rd(X, ld(Y, Z)) = mult(X, ld(Z, Y)).
% 3.24/0.78 Proof:
% 3.24/0.78 rd(X, ld(Y, Z))
% 3.24/0.78 = { by lemma 11 R->L }
% 3.24/0.78 mult(X, ld(Z, rd(Z, ld(Y, Z))))
% 3.24/0.78 = { by lemma 12 }
% 3.24/0.78 mult(X, ld(Z, Y))
% 3.24/0.78
% 3.24/0.78 Lemma 14: rd(X, rd(ld(Y, Y), Y)) = mult(X, Y).
% 3.24/0.78 Proof:
% 3.24/0.78 rd(X, rd(ld(Y, Y), Y))
% 3.24/0.78 = { by lemma 10 R->L }
% 3.24/0.78 rd(X, ld(mult(Z, Y), Z))
% 3.24/0.78 = { by lemma 13 }
% 3.24/0.78 mult(X, ld(Z, mult(Z, Y)))
% 3.24/0.78 = { by axiom 4 (f02) }
% 3.24/0.78 mult(X, Y)
% 3.24/0.78
% 3.24/0.78 Lemma 15: rd(mult(X, mult(Y, Z)), Y) = mult(mult(X, Y), rd(Z, Y)).
% 3.24/0.78 Proof:
% 3.24/0.78 rd(mult(X, mult(Y, Z)), Y)
% 3.24/0.78 = { by axiom 2 (f03) R->L }
% 3.24/0.78 rd(mult(X, mult(Y, mult(rd(Z, Y), Y))), Y)
% 3.24/0.78 = { by axiom 5 (f05) }
% 3.24/0.78 rd(mult(mult(mult(X, Y), rd(Z, Y)), Y), Y)
% 3.24/0.78 = { by axiom 3 (f04) }
% 3.24/0.78 mult(mult(X, Y), rd(Z, Y))
% 3.24/0.78
% 3.24/0.78 Lemma 16: mult(mult(X, rd(Y, Z)), rd(Z, rd(Y, Z))) = rd(mult(X, Y), rd(Y, Z)).
% 3.24/0.78 Proof:
% 3.24/0.78 mult(mult(X, rd(Y, Z)), rd(Z, rd(Y, Z)))
% 3.24/0.78 = { by lemma 15 R->L }
% 3.24/0.78 rd(mult(X, mult(rd(Y, Z), Z)), rd(Y, Z))
% 3.24/0.78 = { by axiom 2 (f03) }
% 3.24/0.78 rd(mult(X, Y), rd(Y, Z))
% 3.24/0.78
% 3.24/0.78 Lemma 17: mult(X, ld(Y, Y)) = mult(X, rd(Y, Y)).
% 3.24/0.78 Proof:
% 3.24/0.78 mult(X, ld(Y, Y))
% 3.24/0.78 = { by axiom 3 (f04) R->L }
% 3.24/0.78 rd(mult(mult(X, ld(Y, Y)), Y), Y)
% 3.24/0.78 = { by lemma 14 R->L }
% 3.24/0.78 rd(rd(mult(X, ld(Y, Y)), rd(ld(Y, Y), Y)), Y)
% 3.24/0.78 = { by lemma 16 R->L }
% 3.24/0.78 rd(mult(mult(X, rd(ld(Y, Y), Y)), rd(Y, rd(ld(Y, Y), Y))), Y)
% 3.24/0.78 = { by lemma 9 R->L }
% 3.24/0.78 rd(mult(mult(X, ld(Z, rd(Z, Y))), rd(Y, rd(ld(Y, Y), Y))), Y)
% 3.24/0.78 = { by lemma 11 }
% 3.24/0.78 rd(mult(rd(X, Y), rd(Y, rd(ld(Y, Y), Y))), Y)
% 3.24/0.78 = { by lemma 14 }
% 3.24/0.78 rd(mult(rd(X, Y), mult(Y, Y)), Y)
% 3.24/0.78 = { by axiom 1 (f01) R->L }
% 3.24/0.78 rd(mult(rd(X, Y), mult(Y, ld(Y, mult(Y, Y)))), Y)
% 3.24/0.78 = { by lemma 15 }
% 3.24/0.78 mult(mult(rd(X, Y), Y), rd(ld(Y, mult(Y, Y)), Y))
% 3.24/0.78 = { by axiom 2 (f03) }
% 3.24/0.78 mult(X, rd(ld(Y, mult(Y, Y)), Y))
% 3.24/0.78 = { by axiom 4 (f02) }
% 3.24/0.78 mult(X, rd(Y, Y))
% 3.24/0.78
% 3.24/0.78 Lemma 18: ld(X, X) = rd(X, X).
% 3.24/0.78 Proof:
% 3.24/0.78 ld(X, X)
% 3.24/0.78 = { by axiom 4 (f02) R->L }
% 3.24/0.78 ld(Y, mult(Y, ld(X, X)))
% 3.24/0.78 = { by lemma 17 }
% 3.24/0.78 ld(Y, mult(Y, rd(X, X)))
% 3.24/0.78 = { by axiom 4 (f02) }
% 3.24/0.78 rd(X, X)
% 3.24/0.78
% 3.24/0.78 Lemma 19: ld(mult(X, Y), X) = ld(Z, rd(Z, Y)).
% 3.24/0.78 Proof:
% 3.24/0.78 ld(mult(X, Y), X)
% 3.24/0.78 = { by lemma 10 }
% 3.24/0.78 rd(ld(Y, Y), Y)
% 3.24/0.78 = { by lemma 9 R->L }
% 3.24/0.78 ld(Z, rd(Z, Y))
% 3.24/0.78
% 3.24/0.78 Lemma 20: mult(X, rd(X, X)) = X.
% 3.24/0.78 Proof:
% 3.24/0.78 mult(X, rd(X, X))
% 3.24/0.78 = { by lemma 17 R->L }
% 3.24/0.78 mult(X, ld(X, X))
% 3.24/0.78 = { by axiom 1 (f01) }
% 3.24/0.78 X
% 3.24/0.78
% 3.24/0.78 Lemma 21: rd(X, ld(mult(Y, Z), Y)) = mult(X, Z).
% 3.24/0.78 Proof:
% 3.24/0.78 rd(X, ld(mult(Y, Z), Y))
% 3.24/0.78 = { by axiom 2 (f03) R->L }
% 3.24/0.78 mult(rd(rd(X, ld(mult(Y, Z), Y)), Z), Z)
% 3.24/0.78 = { by axiom 1 (f01) R->L }
% 3.24/0.78 mult(rd(rd(X, ld(mult(Y, Z), Y)), Z), mult(Z, ld(Z, Z)))
% 3.24/0.78 = { by axiom 4 (f02) R->L }
% 3.24/0.78 mult(rd(rd(X, ld(mult(Y, Z), Y)), Z), mult(Z, ld(Z, ld(Y, mult(Y, Z)))))
% 3.24/0.78 = { by axiom 1 (f01) R->L }
% 3.24/0.78 mult(rd(rd(X, ld(mult(Y, Z), Y)), Z), mult(Z, ld(Z, ld(Y, mult(mult(mult(Y, Z), ld(mult(Y, Z), Y)), Z)))))
% 3.24/0.78 = { by axiom 5 (f05) R->L }
% 3.24/0.78 mult(rd(rd(X, ld(mult(Y, Z), Y)), Z), mult(Z, ld(Z, ld(Y, mult(Y, mult(Z, mult(ld(mult(Y, Z), Y), Z)))))))
% 3.24/0.78 = { by axiom 4 (f02) }
% 3.24/0.78 mult(rd(rd(X, ld(mult(Y, Z), Y)), Z), mult(Z, ld(Z, mult(Z, mult(ld(mult(Y, Z), Y), Z)))))
% 3.24/0.78 = { by axiom 4 (f02) }
% 3.24/0.78 mult(rd(rd(X, ld(mult(Y, Z), Y)), Z), mult(Z, mult(ld(mult(Y, Z), Y), Z)))
% 3.24/0.78 = { by lemma 6 }
% 3.24/0.78 mult(mult(rd(X, ld(mult(Y, Z), Y)), ld(mult(Y, Z), Y)), Z)
% 3.24/0.78 = { by axiom 2 (f03) }
% 3.24/0.78 mult(X, Z)
% 3.24/0.78
% 3.24/0.78 Lemma 22: ld(mult(X, rd(Y, Y)), X) = rd(Y, Y).
% 3.24/0.78 Proof:
% 3.24/0.78 ld(mult(X, rd(Y, Y)), X)
% 3.24/0.78 = { by axiom 4 (f02) R->L }
% 3.24/0.78 ld(rd(Y, ld(mult(X, rd(Y, Y)), X)), mult(rd(Y, ld(mult(X, rd(Y, Y)), X)), ld(mult(X, rd(Y, Y)), X)))
% 3.24/0.78 = { by axiom 2 (f03) }
% 3.24/0.78 ld(rd(Y, ld(mult(X, rd(Y, Y)), X)), Y)
% 3.24/0.78 = { by lemma 21 }
% 3.24/0.78 ld(mult(Y, rd(Y, Y)), Y)
% 3.24/0.78 = { by lemma 20 }
% 3.24/0.78 ld(Y, Y)
% 3.24/0.78 = { by lemma 18 }
% 3.24/0.78 rd(Y, Y)
% 3.24/0.78
% 3.24/0.78 Lemma 23: rd(X, rd(Y, Y)) = mult(X, rd(Y, Y)).
% 3.24/0.78 Proof:
% 3.24/0.78 rd(X, rd(Y, Y))
% 3.24/0.78 = { by lemma 22 R->L }
% 3.24/0.78 rd(X, ld(mult(Z, rd(Y, Y)), Z))
% 3.24/0.78 = { by lemma 21 }
% 3.24/0.79 mult(X, rd(Y, Y))
% 3.24/0.79
% 3.24/0.79 Lemma 24: mult(rd(X, X), rd(X, X)) = rd(X, X).
% 3.24/0.79 Proof:
% 3.24/0.79 mult(rd(X, X), rd(X, X))
% 3.24/0.79 = { by axiom 2 (f03) R->L }
% 3.24/0.79 mult(mult(rd(rd(X, X), X), X), rd(X, X))
% 3.24/0.79 = { by lemma 23 R->L }
% 3.24/0.79 rd(mult(rd(rd(X, X), X), X), rd(X, X))
% 3.24/0.79 = { by lemma 16 R->L }
% 3.24/0.79 mult(mult(rd(rd(X, X), X), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 18 R->L }
% 3.24/0.79 mult(mult(rd(ld(X, X), X), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 23 R->L }
% 3.24/0.79 mult(rd(rd(ld(X, X), X), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 9 R->L }
% 3.24/0.79 mult(rd(ld(Y, rd(Y, X)), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 19 R->L }
% 3.24/0.79 mult(rd(ld(mult(Z, X), Z), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by axiom 1 (f01) R->L }
% 3.24/0.79 mult(rd(ld(mult(Z, X), mult(mult(Z, X), ld(mult(Z, X), Z))), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by axiom 1 (f01) R->L }
% 3.24/0.79 mult(rd(ld(mult(Z, X), mult(mult(mult(mult(Z, X), ld(mult(Z, X), Z)), X), ld(mult(Z, X), Z))), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by axiom 5 (f05) R->L }
% 3.24/0.79 mult(rd(ld(mult(Z, X), mult(mult(Z, X), mult(ld(mult(Z, X), Z), mult(X, ld(mult(Z, X), Z))))), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by axiom 4 (f02) }
% 3.24/0.79 mult(rd(mult(ld(mult(Z, X), Z), mult(X, ld(mult(Z, X), Z))), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 19 }
% 3.24/0.79 mult(rd(mult(ld(mult(Z, X), Z), mult(X, ld(W, rd(W, X)))), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 19 }
% 3.24/0.79 mult(rd(mult(ld(V, rd(V, X)), mult(X, ld(W, rd(W, X)))), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 11 }
% 3.24/0.79 mult(rd(mult(ld(V, rd(V, X)), rd(X, X)), rd(X, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by axiom 3 (f04) }
% 3.24/0.79 mult(ld(V, rd(V, X)), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 9 }
% 3.24/0.79 mult(rd(ld(X, X), X), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 18 }
% 3.24/0.79 mult(rd(rd(X, X), X), rd(X, rd(X, X)))
% 3.24/0.79 = { by lemma 18 R->L }
% 3.24/0.79 mult(rd(rd(X, X), X), rd(X, ld(X, X)))
% 3.24/0.79 = { by lemma 12 }
% 3.24/0.79 mult(rd(rd(X, X), X), X)
% 3.24/0.79 = { by axiom 2 (f03) }
% 3.24/0.79 rd(X, X)
% 3.24/0.79
% 3.24/0.79 Lemma 25: ld(mult(Y, rd(X, X)), mult(Z, rd(X, X))) = mult(rd(X, X), mult(ld(Y, Z), rd(X, X))).
% 3.24/0.79 Proof:
% 3.24/0.79 ld(mult(Y, rd(X, X)), mult(Z, rd(X, X)))
% 3.24/0.79 = { by lemma 23 R->L }
% 3.24/0.79 ld(rd(Y, rd(X, X)), mult(Z, rd(X, X)))
% 3.24/0.79 = { by lemma 7 }
% 3.24/0.79 mult(rd(X, X), mult(ld(Y, Z), rd(X, X)))
% 3.24/0.79
% 3.24/0.79 Lemma 26: ld(rd(ld(X, X), X), rd(ld(X, X), X)) = rd(X, X).
% 3.24/0.79 Proof:
% 3.24/0.79 ld(rd(ld(X, X), X), rd(ld(X, X), X))
% 3.24/0.79 = { by lemma 8 R->L }
% 3.24/0.79 mult(ld(Y, rd(Y, rd(ld(X, X), X))), rd(ld(X, X), X))
% 3.24/0.79 = { by lemma 14 }
% 3.24/0.79 mult(ld(Y, mult(Y, X)), rd(ld(X, X), X))
% 3.24/0.79 = { by lemma 9 R->L }
% 3.24/0.79 mult(ld(Y, mult(Y, X)), ld(Z, rd(Z, X)))
% 3.24/0.79 = { by lemma 11 }
% 3.24/0.79 rd(ld(Y, mult(Y, X)), X)
% 3.24/0.79 = { by axiom 4 (f02) }
% 3.24/0.79 rd(X, X)
% 3.24/0.79
% 3.24/0.79 Goal 1 (goal): mult(x0, rd(x1, x1)) = x0.
% 3.24/0.79 Proof:
% 3.24/0.79 mult(x0, rd(x1, x1))
% 3.24/0.79 = { by lemma 20 R->L }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(mult(x0, rd(x1, x1)), mult(x0, rd(x1, x1))))
% 3.24/0.79 = { by lemma 12 R->L }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), ld(rd(mult(x0, rd(x1, x1)), mult(x0, rd(x1, x1))), rd(x1, x1))))
% 3.24/0.79 = { by axiom 4 (f02) R->L }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), ld(X, mult(X, ld(rd(mult(x0, rd(x1, x1)), mult(x0, rd(x1, x1))), rd(x1, x1))))))
% 3.24/0.79 = { by lemma 18 R->L }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), ld(X, mult(X, ld(ld(mult(x0, rd(x1, x1)), mult(x0, rd(x1, x1))), rd(x1, x1))))))
% 3.24/0.79 = { by lemma 13 R->L }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), ld(X, rd(X, ld(rd(x1, x1), ld(mult(x0, rd(x1, x1)), mult(x0, rd(x1, x1))))))))
% 3.24/0.79 = { by lemma 25 }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), ld(X, rd(X, ld(rd(x1, x1), mult(rd(x1, x1), mult(ld(x0, x0), rd(x1, x1))))))))
% 3.24/0.79 = { by axiom 4 (f02) }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), ld(X, rd(X, mult(ld(x0, x0), rd(x1, x1))))))
% 3.24/0.79 = { by lemma 18 }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), ld(X, rd(X, mult(rd(x0, x0), rd(x1, x1))))))
% 3.24/0.79 = { by lemma 9 }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(ld(mult(rd(x0, x0), rd(x1, x1)), mult(rd(x0, x0), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1)))))
% 3.24/0.79 = { by lemma 25 }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(mult(rd(x1, x1), mult(ld(rd(x0, x0), rd(x0, x0)), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1)))))
% 3.24/0.79 = { by lemma 26 R->L }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(mult(rd(x1, x1), mult(ld(rd(x0, x0), ld(rd(ld(x0, x0), x0), rd(ld(x0, x0), x0))), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1)))))
% 3.24/0.79 = { by lemma 26 R->L }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(mult(rd(x1, x1), mult(ld(ld(rd(ld(x0, x0), x0), rd(ld(x0, x0), x0)), ld(rd(ld(x0, x0), x0), rd(ld(x0, x0), x0))), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1)))))
% 3.24/0.79 = { by lemma 8 R->L }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(mult(rd(x1, x1), mult(mult(ld(rd(ld(x0, x0), x0), rd(rd(ld(x0, x0), x0), ld(rd(ld(x0, x0), x0), rd(ld(x0, x0), x0)))), ld(rd(ld(x0, x0), x0), rd(ld(x0, x0), x0))), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1)))))
% 3.24/0.79 = { by lemma 12 }
% 3.24/0.79 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(mult(rd(x1, x1), mult(mult(ld(rd(ld(x0, x0), x0), rd(ld(x0, x0), x0)), ld(rd(ld(x0, x0), x0), rd(ld(x0, x0), x0))), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1)))))
% 3.24/0.79 = { by lemma 26 }
% 3.24/0.80 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(mult(rd(x1, x1), mult(mult(rd(x0, x0), ld(rd(ld(x0, x0), x0), rd(ld(x0, x0), x0))), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1)))))
% 3.24/0.80 = { by lemma 26 }
% 3.24/0.80 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(mult(rd(x1, x1), mult(mult(rd(x0, x0), rd(x0, x0)), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1)))))
% 3.24/0.80 = { by lemma 24 }
% 3.24/0.80 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(mult(rd(x1, x1), mult(rd(x0, x0), rd(x1, x1))), mult(rd(x0, x0), rd(x1, x1)))))
% 3.24/0.80 = { by axiom 3 (f04) }
% 3.24/0.80 mult(mult(x0, rd(x1, x1)), rd(rd(x1, x1), rd(x1, x1)))
% 3.24/0.80 = { by lemma 23 }
% 3.24/0.80 mult(mult(x0, rd(x1, x1)), mult(rd(x1, x1), rd(x1, x1)))
% 3.24/0.80 = { by lemma 24 }
% 3.24/0.80 mult(mult(x0, rd(x1, x1)), rd(x1, x1))
% 3.24/0.80 = { by lemma 22 R->L }
% 3.24/0.80 mult(mult(x0, rd(x1, x1)), ld(mult(x0, rd(x1, x1)), x0))
% 3.24/0.80 = { by axiom 1 (f01) }
% 3.24/0.80 x0
% 3.24/0.80 % SZS output end Proof
% 3.24/0.80
% 3.24/0.80 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------