TSTP Solution File: TOP050-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : TOP050-1 : 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 : n007.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 : Fri Sep 1 05:59:41 EDT 2023
% Result : Unsatisfiable 0.20s 0.63s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : TOP050-1 : 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 : n007.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 : Sat Aug 26 22:46:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.63 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.63
% 0.20/0.63 % SZS status Unsatisfiable
% 0.20/0.63
% 0.20/0.82 % SZS output start Proof
% 0.20/0.82 Axiom 1 (involutory_quandle): product(X, X) = X.
% 0.20/0.82 Axiom 2 (knot_32): product(a32, a21) = a1.
% 0.20/0.82 Axiom 3 (knot_03): product(a2, a25) = a3.
% 0.20/0.82 Axiom 4 (knot_05): product(a4, a11) = a5.
% 0.20/0.82 Axiom 5 (knot_08): product(a8, a5) = a9.
% 0.20/0.82 Axiom 6 (knot_10): product(a10, a7) = a11.
% 0.20/0.82 Axiom 7 (knot_12): product(a12, a19) = a13.
% 0.20/0.82 Axiom 8 (knot_13): product(a13, a7) = a14.
% 0.20/0.82 Axiom 9 (knot_14): product(a14, a17) = a15.
% 0.20/0.82 Axiom 10 (knot_16): product(a16, a19) = a17.
% 0.20/0.82 Axiom 11 (knot_18): product(a18, a15) = a19.
% 0.20/0.82 Axiom 12 (knot_20): product(a20, a29) = a21.
% 0.20/0.82 Axiom 13 (knot_22): product(a22, a31) = a23.
% 0.20/0.82 Axiom 14 (knot_24): product(a24, a3) = a25.
% 0.20/0.82 Axiom 15 (knot_26): product(a26, a1) = a27.
% 0.20/0.82 Axiom 16 (knot_27): product(a27, a21) = a28.
% 0.20/0.82 Axiom 17 (knot_28): product(a28, a3) = a29.
% 0.20/0.82 Axiom 18 (knot_30): product(a30, a23) = a31.
% 0.20/0.82 Axiom 19 (knot): product(a1, a31) = a2.
% 0.20/0.82 Axiom 20 (knot_07): product(a7, a19) = a8.
% 0.20/0.82 Axiom 21 (knot_09): product(a9, a17) = a10.
% 0.20/0.82 Axiom 22 (knot_31): product(a31, a3) = a32.
% 0.20/0.82 Axiom 23 (knot_25): product(a25, a23) = a26.
% 0.20/0.82 Axiom 24 (knot_29): product(a29, a1) = a30.
% 0.20/0.82 Axiom 25 (knot_11): product(a11, a5) = a12.
% 0.20/0.82 Axiom 26 (knot_15): product(a15, a5) = a16.
% 0.20/0.82 Axiom 27 (knot_17): product(a17, a9) = a18.
% 0.20/0.82 Axiom 28 (knot_23): product(a23, a21) = a24.
% 0.20/0.82 Axiom 29 (knot_04): product(a3, a29) = a4.
% 0.20/0.82 Axiom 30 (knot_06): product(a5, a15) = a6.
% 0.20/0.82 Axiom 31 (knot_19): product(a19, a11) = a20.
% 0.20/0.82 Axiom 32 (knot_21): product(a21, a25) = a22.
% 0.20/0.82 Axiom 33 (involutory_quandle_01): product(product(X, Y), Y) = X.
% 0.20/0.82 Axiom 34 (involutory_quandle_02): product(product(X, Y), Z) = product(product(X, Z), product(Y, Z)).
% 0.20/0.82
% 0.20/0.82 Lemma 35: product(a25, a3) = a24.
% 0.20/0.82 Proof:
% 0.20/0.82 product(a25, a3)
% 0.20/0.82 = { by axiom 14 (knot_24) R->L }
% 0.20/0.82 product(product(a24, a3), a3)
% 0.20/0.82 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.82 a24
% 0.20/0.82
% 0.20/0.82 Lemma 36: product(a27, a1) = a26.
% 0.20/0.82 Proof:
% 0.20/0.82 product(a27, a1)
% 0.20/0.82 = { by axiom 15 (knot_26) R->L }
% 0.20/0.82 product(product(a26, a1), a1)
% 0.20/0.82 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.82 a26
% 0.20/0.82
% 0.20/0.82 Lemma 37: product(a29, a3) = a28.
% 0.20/0.82 Proof:
% 0.20/0.82 product(a29, a3)
% 0.20/0.82 = { by axiom 17 (knot_28) R->L }
% 0.20/0.82 product(product(a28, a3), a3)
% 0.20/0.82 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.82 a28
% 0.20/0.82
% 0.20/0.82 Lemma 38: product(a31, a23) = a30.
% 0.20/0.82 Proof:
% 0.20/0.82 product(a31, a23)
% 0.20/0.82 = { by axiom 18 (knot_30) R->L }
% 0.20/0.82 product(product(a30, a23), a23)
% 0.20/0.82 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.82 a30
% 0.20/0.82
% 0.20/0.82 Lemma 39: product(product(X, Y), X) = product(X, product(Y, X)).
% 0.20/0.82 Proof:
% 0.20/0.82 product(product(X, Y), X)
% 0.20/0.82 = { by axiom 34 (involutory_quandle_02) }
% 0.20/0.83 product(product(X, X), product(Y, X))
% 0.20/0.83 = { by axiom 1 (involutory_quandle) }
% 0.20/0.83 product(X, product(Y, X))
% 0.20/0.83
% 0.20/0.83 Lemma 40: product(a23, a31) = a22.
% 0.20/0.83 Proof:
% 0.20/0.83 product(a23, a31)
% 0.20/0.83 = { by axiom 13 (knot_22) R->L }
% 0.20/0.83 product(product(a22, a31), a31)
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.83 a22
% 0.20/0.83
% 0.20/0.83 Lemma 41: a25 = a31.
% 0.20/0.83 Proof:
% 0.20/0.83 a25
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(a25, a22), a22)
% 0.20/0.83 = { by axiom 1 (involutory_quandle) R->L }
% 0.20/0.83 product(product(product(a25, a25), a22), a22)
% 0.20/0.83 = { by axiom 32 (knot_21) R->L }
% 0.20/0.83 product(product(product(a25, a25), product(a21, a25)), a22)
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.83 product(product(product(a25, a21), a25), a22)
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(product(product(product(a25, a23), a23), a21), a25), a22)
% 0.20/0.83 = { by axiom 23 (knot_25) }
% 0.20/0.83 product(product(product(product(a26, a23), a21), a25), a22)
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) }
% 0.20/0.83 product(product(product(product(a26, a21), product(a23, a21)), a25), a22)
% 0.20/0.83 = { by axiom 28 (knot_23) }
% 0.20/0.83 product(product(product(product(a26, a21), a24), a25), a22)
% 0.20/0.83 = { by lemma 36 R->L }
% 0.20/0.83 product(product(product(product(product(a27, a1), a21), a24), a25), a22)
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(product(product(product(product(product(a27, a21), a21), a1), a21), a24), a25), a22)
% 0.20/0.83 = { by axiom 16 (knot_27) }
% 0.20/0.83 product(product(product(product(product(product(a28, a21), a1), a21), a24), a25), a22)
% 0.20/0.83 = { by axiom 2 (knot_32) R->L }
% 0.20/0.83 product(product(product(product(product(product(a28, a21), product(a32, a21)), a21), a24), a25), a22)
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.83 product(product(product(product(product(product(a28, a32), a21), a21), a24), a25), a22)
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.83 product(product(product(product(a28, a32), a24), a25), a22)
% 0.20/0.83 = { by lemma 37 R->L }
% 0.20/0.83 product(product(product(product(product(a29, a3), a32), a24), a25), a22)
% 0.20/0.83 = { by axiom 22 (knot_31) R->L }
% 0.20/0.83 product(product(product(product(product(a29, a3), product(a31, a3)), a24), a25), a22)
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.83 product(product(product(product(product(a29, a31), a3), a24), a25), a22)
% 0.20/0.83 = { by lemma 35 R->L }
% 0.20/0.83 product(product(product(product(product(a29, a31), a3), product(a25, a3)), a25), a22)
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.83 product(product(product(product(product(a29, a31), a25), a3), a25), a22)
% 0.20/0.83 = { by axiom 3 (knot_03) R->L }
% 0.20/0.83 product(product(product(product(product(a29, a31), a25), product(a2, a25)), a25), a22)
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.83 product(product(product(product(product(a29, a31), a2), a25), a25), a22)
% 0.20/0.83 = { by axiom 19 (knot) R->L }
% 0.20/0.83 product(product(product(product(product(a29, a31), product(a1, a31)), a25), a25), a22)
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.83 product(product(product(product(product(a29, a1), a31), a25), a25), a22)
% 0.20/0.83 = { by axiom 24 (knot_29) }
% 0.20/0.83 product(product(product(product(a30, a31), a25), a25), a22)
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.83 product(product(a30, a31), a22)
% 0.20/0.83 = { by lemma 38 R->L }
% 0.20/0.83 product(product(product(a31, a23), a31), a22)
% 0.20/0.83 = { by lemma 39 }
% 0.20/0.83 product(product(a31, product(a23, a31)), a22)
% 0.20/0.83 = { by lemma 40 }
% 0.20/0.83 product(product(a31, a22), a22)
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.83 a31
% 0.20/0.83
% 0.20/0.83 Lemma 42: a24 = a32.
% 0.20/0.83 Proof:
% 0.20/0.83 a24
% 0.20/0.83 = { by lemma 35 R->L }
% 0.20/0.83 product(a25, a3)
% 0.20/0.83 = { by lemma 41 }
% 0.20/0.83 product(a31, a3)
% 0.20/0.83 = { by axiom 22 (knot_31) }
% 0.20/0.83 a32
% 0.20/0.83
% 0.20/0.83 Lemma 43: a23 = a1.
% 0.20/0.83 Proof:
% 0.20/0.83 a23
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(a23, a21), a21)
% 0.20/0.83 = { by axiom 28 (knot_23) }
% 0.20/0.83 product(a24, a21)
% 0.20/0.83 = { by lemma 42 }
% 0.20/0.83 product(a32, a21)
% 0.20/0.83 = { by axiom 2 (knot_32) }
% 0.20/0.83 a1
% 0.20/0.83
% 0.20/0.83 Lemma 44: a21 = a23.
% 0.20/0.83 Proof:
% 0.20/0.83 a21
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(a21, a25), a25)
% 0.20/0.83 = { by axiom 32 (knot_21) }
% 0.20/0.83 product(a22, a25)
% 0.20/0.83 = { by lemma 41 }
% 0.20/0.83 product(a22, a31)
% 0.20/0.83 = { by axiom 13 (knot_22) }
% 0.20/0.83 a23
% 0.20/0.83
% 0.20/0.83 Lemma 45: a1 = a32.
% 0.20/0.83 Proof:
% 0.20/0.83 a1
% 0.20/0.83 = { by lemma 43 R->L }
% 0.20/0.83 a23
% 0.20/0.83 = { by axiom 1 (involutory_quandle) R->L }
% 0.20/0.83 product(a23, a23)
% 0.20/0.83 = { by lemma 44 R->L }
% 0.20/0.83 product(a23, a21)
% 0.20/0.83 = { by axiom 28 (knot_23) }
% 0.20/0.83 a24
% 0.20/0.83 = { by lemma 42 }
% 0.20/0.83 a32
% 0.20/0.83
% 0.20/0.83 Lemma 46: a30 = a26.
% 0.20/0.83 Proof:
% 0.20/0.83 a30
% 0.20/0.83 = { by lemma 38 R->L }
% 0.20/0.83 product(a31, a23)
% 0.20/0.83 = { by lemma 41 R->L }
% 0.20/0.83 product(a25, a23)
% 0.20/0.83 = { by axiom 23 (knot_25) }
% 0.20/0.83 a26
% 0.20/0.83
% 0.20/0.83 Lemma 47: a31 = a27.
% 0.20/0.83 Proof:
% 0.20/0.83 a31
% 0.20/0.83 = { by axiom 18 (knot_30) R->L }
% 0.20/0.83 product(a30, a23)
% 0.20/0.83 = { by lemma 43 }
% 0.20/0.83 product(a30, a1)
% 0.20/0.83 = { by lemma 46 }
% 0.20/0.83 product(a26, a1)
% 0.20/0.83 = { by axiom 15 (knot_26) }
% 0.20/0.83 a27
% 0.20/0.83
% 0.20/0.83 Lemma 48: a22 = a2.
% 0.20/0.83 Proof:
% 0.20/0.83 a22
% 0.20/0.83 = { by lemma 40 R->L }
% 0.20/0.83 product(a23, a31)
% 0.20/0.83 = { by lemma 43 }
% 0.20/0.83 product(a1, a31)
% 0.20/0.83 = { by axiom 19 (knot) }
% 0.20/0.83 a2
% 0.20/0.83
% 0.20/0.83 Lemma 49: a3 = a1.
% 0.20/0.83 Proof:
% 0.20/0.83 a3
% 0.20/0.83 = { by axiom 3 (knot_03) R->L }
% 0.20/0.83 product(a2, a25)
% 0.20/0.83 = { by lemma 41 }
% 0.20/0.83 product(a2, a31)
% 0.20/0.83 = { by axiom 19 (knot) R->L }
% 0.20/0.83 product(product(a1, a31), a31)
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.83 a1
% 0.20/0.83
% 0.20/0.83 Lemma 50: a26 = a32.
% 0.20/0.83 Proof:
% 0.20/0.83 a26
% 0.20/0.83 = { by lemma 36 R->L }
% 0.20/0.83 product(a27, a1)
% 0.20/0.83 = { by lemma 49 R->L }
% 0.20/0.83 product(a27, a3)
% 0.20/0.83 = { by lemma 47 R->L }
% 0.20/0.83 product(a31, a3)
% 0.20/0.83 = { by axiom 22 (knot_31) }
% 0.20/0.83 a32
% 0.20/0.83
% 0.20/0.83 Lemma 51: a27 = a32.
% 0.20/0.83 Proof:
% 0.20/0.83 a27
% 0.20/0.83 = { by axiom 15 (knot_26) R->L }
% 0.20/0.83 product(a26, a1)
% 0.20/0.83 = { by lemma 50 }
% 0.20/0.83 product(a32, a1)
% 0.20/0.83 = { by lemma 45 }
% 0.20/0.83 product(a32, a32)
% 0.20/0.83 = { by axiom 1 (involutory_quandle) }
% 0.20/0.83 a32
% 0.20/0.83
% 0.20/0.83 Lemma 52: a2 = a32.
% 0.20/0.83 Proof:
% 0.20/0.83 a2
% 0.20/0.83 = { by axiom 1 (involutory_quandle) R->L }
% 0.20/0.83 product(a2, a2)
% 0.20/0.83 = { by lemma 48 R->L }
% 0.20/0.83 product(a2, a22)
% 0.20/0.83 = { by lemma 40 R->L }
% 0.20/0.83 product(a2, product(a23, a31))
% 0.20/0.83 = { by lemma 48 R->L }
% 0.20/0.83 product(a22, product(a23, a31))
% 0.20/0.83 = { by lemma 44 R->L }
% 0.20/0.83 product(a22, product(a21, a31))
% 0.20/0.83 = { by lemma 40 R->L }
% 0.20/0.83 product(product(a23, a31), product(a21, a31))
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.83 product(product(a23, a21), a31)
% 0.20/0.83 = { by axiom 28 (knot_23) }
% 0.20/0.83 product(a24, a31)
% 0.20/0.83 = { by lemma 42 }
% 0.20/0.83 product(a32, a31)
% 0.20/0.83 = { by lemma 47 }
% 0.20/0.83 product(a32, a27)
% 0.20/0.83 = { by lemma 51 }
% 0.20/0.83 product(a32, a32)
% 0.20/0.83 = { by axiom 1 (involutory_quandle) }
% 0.20/0.83 a32
% 0.20/0.83
% 0.20/0.83 Lemma 53: a29 = a27.
% 0.20/0.83 Proof:
% 0.20/0.83 a29
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(a29, a1), a1)
% 0.20/0.83 = { by axiom 24 (knot_29) }
% 0.20/0.83 product(a30, a1)
% 0.20/0.83 = { by lemma 46 }
% 0.20/0.83 product(a26, a1)
% 0.20/0.83 = { by axiom 15 (knot_26) }
% 0.20/0.83 a27
% 0.20/0.83
% 0.20/0.83 Lemma 54: a4 = a32.
% 0.20/0.83 Proof:
% 0.20/0.83 a4
% 0.20/0.83 = { by axiom 29 (knot_04) R->L }
% 0.20/0.83 product(a3, a29)
% 0.20/0.83 = { by lemma 49 }
% 0.20/0.83 product(a1, a29)
% 0.20/0.83 = { by lemma 45 }
% 0.20/0.83 product(a32, a29)
% 0.20/0.83 = { by lemma 53 }
% 0.20/0.83 product(a32, a27)
% 0.20/0.83 = { by lemma 51 }
% 0.20/0.83 product(a32, a32)
% 0.20/0.83 = { by axiom 1 (involutory_quandle) }
% 0.20/0.83 a32
% 0.20/0.83
% 0.20/0.83 Lemma 55: a28 = a26.
% 0.20/0.83 Proof:
% 0.20/0.83 a28
% 0.20/0.83 = { by lemma 37 R->L }
% 0.20/0.83 product(a29, a3)
% 0.20/0.83 = { by lemma 49 }
% 0.20/0.83 product(a29, a1)
% 0.20/0.83 = { by axiom 24 (knot_29) }
% 0.20/0.83 a30
% 0.20/0.83 = { by lemma 46 }
% 0.20/0.83 a26
% 0.20/0.83
% 0.20/0.83 Lemma 56: a20 = a32.
% 0.20/0.83 Proof:
% 0.20/0.83 a20
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(a20, a32), a32)
% 0.20/0.83 = { by lemma 45 R->L }
% 0.20/0.83 product(product(a20, a32), a1)
% 0.20/0.83 = { by lemma 49 R->L }
% 0.20/0.83 product(product(a20, a32), a3)
% 0.20/0.83 = { by lemma 54 R->L }
% 0.20/0.83 product(product(a20, a4), a3)
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(product(product(a20, a29), a29), a4), a3)
% 0.20/0.83 = { by axiom 12 (knot_20) }
% 0.20/0.83 product(product(product(a21, a29), a4), a3)
% 0.20/0.83 = { by axiom 29 (knot_04) R->L }
% 0.20/0.83 product(product(product(a21, a29), product(a3, a29)), a3)
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.83 product(product(product(a21, a3), a29), a3)
% 0.20/0.83 = { by axiom 17 (knot_28) R->L }
% 0.20/0.83 product(product(product(a21, a3), product(a28, a3)), a3)
% 0.20/0.83 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.83 product(product(product(a21, a28), a3), a3)
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.83 product(a21, a28)
% 0.20/0.83 = { by lemma 44 }
% 0.20/0.83 product(a23, a28)
% 0.20/0.83 = { by lemma 43 }
% 0.20/0.83 product(a1, a28)
% 0.20/0.83 = { by lemma 45 }
% 0.20/0.83 product(a32, a28)
% 0.20/0.83 = { by lemma 55 }
% 0.20/0.83 product(a32, a26)
% 0.20/0.83 = { by lemma 50 }
% 0.20/0.83 product(a32, a32)
% 0.20/0.83 = { by axiom 1 (involutory_quandle) }
% 0.20/0.83 a32
% 0.20/0.83
% 0.20/0.83 Lemma 57: a19 = a5.
% 0.20/0.83 Proof:
% 0.20/0.83 a19
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(a19, a11), a11)
% 0.20/0.83 = { by axiom 31 (knot_19) }
% 0.20/0.83 product(a20, a11)
% 0.20/0.83 = { by lemma 56 }
% 0.20/0.83 product(a32, a11)
% 0.20/0.83 = { by lemma 54 R->L }
% 0.20/0.83 product(a4, a11)
% 0.20/0.83 = { by axiom 4 (knot_05) }
% 0.20/0.83 a5
% 0.20/0.83
% 0.20/0.83 Lemma 58: a11 = a13.
% 0.20/0.83 Proof:
% 0.20/0.83 a11
% 0.20/0.83 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.83 product(product(a11, a5), a5)
% 0.20/0.83 = { by axiom 25 (knot_11) }
% 0.20/0.83 product(a12, a5)
% 0.20/0.83 = { by lemma 57 R->L }
% 0.20/0.83 product(a12, a19)
% 0.20/0.83 = { by axiom 7 (knot_12) }
% 0.20/0.83 a13
% 0.20/0.83
% 0.20/0.83 Lemma 59: product(a5, a16) = product(a6, a5).
% 0.20/0.83 Proof:
% 0.20/0.83 product(a5, a16)
% 0.20/0.83 = { by axiom 26 (knot_15) R->L }
% 0.20/0.83 product(a5, product(a15, a5))
% 0.20/0.83 = { by lemma 39 R->L }
% 0.20/0.83 product(product(a5, a15), a5)
% 0.20/0.83 = { by axiom 30 (knot_06) }
% 0.20/0.83 product(a6, a5)
% 0.20/0.83
% 0.20/0.83 Lemma 60: product(a16, a5) = a15.
% 0.20/0.83 Proof:
% 0.20/0.84 product(a16, a5)
% 0.20/0.84 = { by axiom 26 (knot_15) R->L }
% 0.20/0.84 product(product(a15, a5), a5)
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.84 a15
% 0.20/0.84
% 0.20/0.84 Lemma 61: a17 = a15.
% 0.20/0.84 Proof:
% 0.20/0.84 a17
% 0.20/0.84 = { by axiom 10 (knot_16) R->L }
% 0.20/0.84 product(a16, a19)
% 0.20/0.84 = { by lemma 57 }
% 0.20/0.84 product(a16, a5)
% 0.20/0.84 = { by lemma 60 }
% 0.20/0.84 a15
% 0.20/0.84
% 0.20/0.84 Lemma 62: product(a15, a17) = a14.
% 0.20/0.84 Proof:
% 0.20/0.84 product(a15, a17)
% 0.20/0.84 = { by axiom 9 (knot_14) R->L }
% 0.20/0.84 product(product(a14, a17), a17)
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.84 a14
% 0.20/0.84
% 0.20/0.84 Lemma 63: a15 = a14.
% 0.20/0.84 Proof:
% 0.20/0.84 a15
% 0.20/0.84 = { by axiom 1 (involutory_quandle) R->L }
% 0.20/0.84 product(a15, a15)
% 0.20/0.84 = { by lemma 61 R->L }
% 0.20/0.84 product(a15, a17)
% 0.20/0.84 = { by lemma 62 }
% 0.20/0.84 a14
% 0.20/0.84
% 0.20/0.84 Lemma 64: a9 = a7.
% 0.20/0.84 Proof:
% 0.20/0.84 a9
% 0.20/0.84 = { by axiom 5 (knot_08) R->L }
% 0.20/0.84 product(a8, a5)
% 0.20/0.84 = { by lemma 57 R->L }
% 0.20/0.84 product(a8, a19)
% 0.20/0.84 = { by axiom 20 (knot_07) R->L }
% 0.20/0.84 product(product(a7, a19), a19)
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.84 a7
% 0.20/0.84
% 0.20/0.84 Lemma 65: a18 = a6.
% 0.20/0.84 Proof:
% 0.20/0.84 a18
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.84 product(product(a18, a15), a15)
% 0.20/0.84 = { by axiom 11 (knot_18) }
% 0.20/0.84 product(a19, a15)
% 0.20/0.84 = { by lemma 57 }
% 0.20/0.84 product(a5, a15)
% 0.20/0.84 = { by axiom 30 (knot_06) }
% 0.20/0.84 a6
% 0.20/0.84
% 0.20/0.84 Lemma 66: a13 = a6.
% 0.20/0.84 Proof:
% 0.20/0.84 a13
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.84 product(product(a13, a7), a7)
% 0.20/0.84 = { by axiom 8 (knot_13) }
% 0.20/0.84 product(a14, a7)
% 0.20/0.84 = { by lemma 63 R->L }
% 0.20/0.84 product(a15, a7)
% 0.20/0.84 = { by lemma 61 R->L }
% 0.20/0.84 product(a17, a7)
% 0.20/0.84 = { by lemma 64 R->L }
% 0.20/0.84 product(a17, a9)
% 0.20/0.84 = { by axiom 27 (knot_17) }
% 0.20/0.84 a18
% 0.20/0.84 = { by lemma 65 }
% 0.20/0.84 a6
% 0.20/0.84
% 0.20/0.84 Lemma 67: product(a6, a5) = a12.
% 0.20/0.84 Proof:
% 0.20/0.84 product(a6, a5)
% 0.20/0.84 = { by lemma 66 R->L }
% 0.20/0.84 product(a13, a5)
% 0.20/0.84 = { by lemma 57 R->L }
% 0.20/0.84 product(a13, a19)
% 0.20/0.84 = { by axiom 7 (knot_12) R->L }
% 0.20/0.84 product(product(a12, a19), a19)
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.84 a12
% 0.20/0.84
% 0.20/0.84 Lemma 68: a14 = a10.
% 0.20/0.84 Proof:
% 0.20/0.84 a14
% 0.20/0.84 = { by axiom 8 (knot_13) R->L }
% 0.20/0.84 product(a13, a7)
% 0.20/0.84 = { by lemma 58 R->L }
% 0.20/0.84 product(a11, a7)
% 0.20/0.84 = { by axiom 6 (knot_10) R->L }
% 0.20/0.84 product(product(a10, a7), a7)
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.84 a10
% 0.20/0.84
% 0.20/0.84 Lemma 69: a7 = a10.
% 0.20/0.84 Proof:
% 0.20/0.84 a7
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.84 product(product(a7, a10), a10)
% 0.20/0.84 = { by lemma 68 R->L }
% 0.20/0.84 product(product(a7, a14), a10)
% 0.20/0.84 = { by lemma 63 R->L }
% 0.20/0.84 product(product(a7, a15), a10)
% 0.20/0.84 = { by lemma 64 R->L }
% 0.20/0.84 product(product(a9, a15), a10)
% 0.20/0.84 = { by lemma 61 R->L }
% 0.20/0.84 product(product(a9, a17), a10)
% 0.20/0.84 = { by axiom 21 (knot_09) }
% 0.20/0.84 product(a10, a10)
% 0.20/0.84 = { by axiom 1 (involutory_quandle) }
% 0.20/0.84 a10
% 0.20/0.84
% 0.20/0.84 Lemma 70: a10 = a6.
% 0.20/0.84 Proof:
% 0.20/0.84 a10
% 0.20/0.84 = { by axiom 1 (involutory_quandle) R->L }
% 0.20/0.84 product(a10, a10)
% 0.20/0.84 = { by lemma 69 R->L }
% 0.20/0.84 product(a10, a7)
% 0.20/0.84 = { by axiom 6 (knot_10) }
% 0.20/0.84 a11
% 0.20/0.84 = { by lemma 58 }
% 0.20/0.84 a13
% 0.20/0.84 = { by lemma 66 }
% 0.20/0.84 a6
% 0.20/0.84
% 0.20/0.84 Lemma 71: a16 = a12.
% 0.20/0.84 Proof:
% 0.20/0.84 a16
% 0.20/0.84 = { by axiom 1 (involutory_quandle) R->L }
% 0.20/0.84 product(a16, a16)
% 0.20/0.84 = { by axiom 26 (knot_15) R->L }
% 0.20/0.84 product(a16, product(a15, a5))
% 0.20/0.84 = { by lemma 61 R->L }
% 0.20/0.84 product(a16, product(a17, a5))
% 0.20/0.84 = { by axiom 26 (knot_15) R->L }
% 0.20/0.84 product(product(a15, a5), product(a17, a5))
% 0.20/0.84 = { by axiom 34 (involutory_quandle_02) R->L }
% 0.20/0.84 product(product(a15, a17), a5)
% 0.20/0.84 = { by lemma 62 }
% 0.20/0.84 product(a14, a5)
% 0.20/0.84 = { by lemma 68 }
% 0.20/0.84 product(a10, a5)
% 0.20/0.84 = { by lemma 70 }
% 0.20/0.84 product(a6, a5)
% 0.20/0.84 = { by lemma 67 }
% 0.20/0.84 a12
% 0.20/0.84
% 0.20/0.84 Lemma 72: a12 = a6.
% 0.20/0.84 Proof:
% 0.20/0.84 a12
% 0.20/0.84 = { by lemma 71 R->L }
% 0.20/0.84 a16
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.84 product(product(a16, product(a6, a5)), product(a6, a5))
% 0.20/0.84 = { by lemma 59 R->L }
% 0.20/0.84 product(product(a16, product(a5, a16)), product(a6, a5))
% 0.20/0.84 = { by lemma 39 R->L }
% 0.20/0.84 product(product(product(a16, a5), a16), product(a6, a5))
% 0.20/0.84 = { by lemma 60 }
% 0.20/0.84 product(product(a15, a16), product(a6, a5))
% 0.20/0.84 = { by lemma 71 }
% 0.20/0.84 product(product(a15, a12), product(a6, a5))
% 0.20/0.84 = { by lemma 63 }
% 0.20/0.84 product(product(a14, a12), product(a6, a5))
% 0.20/0.84 = { by lemma 68 }
% 0.20/0.84 product(product(a10, a12), product(a6, a5))
% 0.20/0.84 = { by lemma 70 }
% 0.20/0.84 product(product(a6, a12), product(a6, a5))
% 0.20/0.84 = { by lemma 67 }
% 0.20/0.84 product(product(a6, a12), a12)
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) }
% 0.20/0.84 a6
% 0.20/0.84
% 0.20/0.84 Lemma 73: a5 = a6.
% 0.20/0.84 Proof:
% 0.20/0.84 a5
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.84 product(product(a5, a16), a16)
% 0.20/0.84 = { by lemma 59 }
% 0.20/0.84 product(product(a6, a5), a16)
% 0.20/0.84 = { by lemma 67 }
% 0.20/0.84 product(a12, a16)
% 0.20/0.84 = { by lemma 72 }
% 0.20/0.84 product(a6, a16)
% 0.20/0.84 = { by lemma 71 }
% 0.20/0.84 product(a6, a12)
% 0.20/0.84 = { by lemma 72 }
% 0.20/0.84 product(a6, a6)
% 0.20/0.84 = { by axiom 1 (involutory_quandle) }
% 0.20/0.84 a6
% 0.20/0.84
% 0.20/0.84 Lemma 74: a8 = a6.
% 0.20/0.84 Proof:
% 0.20/0.84 a8
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.84 product(product(a8, a5), a5)
% 0.20/0.84 = { by axiom 5 (knot_08) }
% 0.20/0.84 product(a9, a5)
% 0.20/0.84 = { by lemma 73 }
% 0.20/0.84 product(a9, a6)
% 0.20/0.84 = { by lemma 64 }
% 0.20/0.84 product(a7, a6)
% 0.20/0.84 = { by lemma 69 }
% 0.20/0.84 product(a10, a6)
% 0.20/0.84 = { by lemma 70 }
% 0.20/0.84 product(a6, a6)
% 0.20/0.84 = { by axiom 1 (involutory_quandle) }
% 0.20/0.84 a6
% 0.20/0.84
% 0.20/0.84 Lemma 75: a32 = a6.
% 0.20/0.84 Proof:
% 0.20/0.84 a32
% 0.20/0.84 = { by lemma 54 R->L }
% 0.20/0.84 a4
% 0.20/0.84 = { by axiom 33 (involutory_quandle_01) R->L }
% 0.20/0.84 product(product(a4, a11), a11)
% 0.20/0.84 = { by axiom 4 (knot_05) }
% 0.20/0.84 product(a5, a11)
% 0.20/0.84 = { by lemma 73 }
% 0.20/0.84 product(a6, a11)
% 0.20/0.84 = { by lemma 58 }
% 0.20/0.84 product(a6, a13)
% 0.20/0.84 = { by lemma 66 }
% 0.20/0.84 product(a6, a6)
% 0.20/0.84 = { by axiom 1 (involutory_quandle) }
% 0.20/0.84 a6
% 0.20/0.84
% 0.20/0.84 Goal 1 (goal): tuple(a1, a30, a31, a2, a24, a25, a3, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a21, a22, a23, a26, a27) = tuple(a2, a31, a32, a3, a25, a26, a4, a29, a30, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a21, a22, a23, a24, a27, a28).
% 0.20/0.84 Proof:
% 0.20/0.84 tuple(a1, a30, a31, a2, a24, a25, a3, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a21, a22, a23, a26, a27)
% 0.20/0.84 = { by lemma 41 }
% 0.20/0.84 tuple(a1, a30, a31, a2, a24, a31, a3, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a21, a22, a23, a26, a27)
% 0.20/0.84 = { by lemma 49 }
% 0.20/0.84 tuple(a1, a30, a31, a2, a24, a31, a1, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a21, a22, a23, a26, a27)
% 0.20/0.84 = { by lemma 42 }
% 0.20/0.84 tuple(a1, a30, a31, a2, a32, a31, a1, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a21, a22, a23, a26, a27)
% 0.20/0.84 = { by lemma 44 }
% 0.20/0.84 tuple(a1, a30, a31, a2, a32, a31, a1, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a23, a22, a23, a26, a27)
% 0.20/0.84 = { by lemma 46 }
% 0.20/0.84 tuple(a1, a26, a31, a2, a32, a31, a1, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a23, a22, a23, a26, a27)
% 0.20/0.84 = { by lemma 43 }
% 0.20/0.84 tuple(a1, a26, a31, a2, a32, a31, a1, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a1, a22, a23, a26, a27)
% 0.20/0.84 = { by lemma 43 }
% 0.20/0.84 tuple(a1, a26, a31, a2, a32, a31, a1, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a1, a22, a1, a26, a27)
% 0.20/0.84 = { by lemma 45 }
% 0.20/0.84 tuple(a32, a26, a31, a2, a32, a31, a1, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a1, a22, a1, a26, a27)
% 0.20/0.84 = { by lemma 45 }
% 0.20/0.84 tuple(a32, a26, a31, a2, a32, a31, a32, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a1, a22, a1, a26, a27)
% 0.20/0.84 = { by lemma 45 }
% 0.20/0.84 tuple(a32, a26, a31, a2, a32, a31, a32, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a22, a1, a26, a27)
% 0.20/0.85 = { by lemma 45 }
% 0.20/0.85 tuple(a32, a26, a31, a2, a32, a31, a32, a28, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a22, a32, a26, a27)
% 0.20/0.85 = { by lemma 55 }
% 0.20/0.85 tuple(a32, a26, a31, a2, a32, a31, a32, a26, a29, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a22, a32, a26, a27)
% 0.20/0.85 = { by lemma 53 }
% 0.20/0.85 tuple(a32, a26, a31, a2, a32, a31, a32, a26, a27, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a22, a32, a26, a27)
% 0.20/0.85 = { by lemma 47 }
% 0.20/0.85 tuple(a32, a26, a27, a2, a32, a31, a32, a26, a27, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a22, a32, a26, a27)
% 0.20/0.85 = { by lemma 47 }
% 0.20/0.85 tuple(a32, a26, a27, a2, a32, a27, a32, a26, a27, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a22, a32, a26, a27)
% 0.20/0.85 = { by lemma 48 }
% 0.20/0.85 tuple(a32, a26, a27, a2, a32, a27, a32, a26, a27, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a2, a32, a26, a27)
% 0.20/0.85 = { by lemma 50 }
% 0.20/0.85 tuple(a32, a32, a27, a2, a32, a27, a32, a26, a27, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a2, a32, a26, a27)
% 0.20/0.85 = { by lemma 50 }
% 0.20/0.85 tuple(a32, a32, a27, a2, a32, a27, a32, a32, a27, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a2, a32, a26, a27)
% 0.20/0.85 = { by lemma 50 }
% 0.20/0.85 tuple(a32, a32, a27, a2, a32, a27, a32, a32, a27, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a2, a32, a32, a27)
% 0.20/0.85 = { by lemma 51 }
% 0.20/0.85 tuple(a32, a32, a32, a2, a32, a27, a32, a32, a27, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a2, a32, a32, a27)
% 0.20/0.85 = { by lemma 51 }
% 0.20/0.85 tuple(a32, a32, a32, a2, a32, a32, a32, a32, a27, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a2, a32, a32, a27)
% 0.20/0.85 = { by lemma 51 }
% 0.20/0.85 tuple(a32, a32, a32, a2, a32, a32, a32, a32, a32, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a2, a32, a32, a27)
% 0.20/0.85 = { by lemma 51 }
% 0.20/0.85 tuple(a32, a32, a32, a2, a32, a32, a32, a32, a32, a4, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a2, a32, a32, a32)
% 0.20/0.85 = { by lemma 54 }
% 0.20/0.85 tuple(a32, a32, a32, a2, a32, a32, a32, a32, a32, a32, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a20, a32, a2, a32, a32, a32)
% 0.20/0.85 = { by lemma 56 }
% 0.20/0.85 tuple(a32, a32, a32, a2, a32, a32, a32, a32, a32, a32, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a32, a32, a2, a32, a32, a32)
% 0.20/0.85 = { by lemma 52 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a32, a32, a2, a32, a32, a32)
% 0.20/0.85 = { by lemma 52 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a11, a5, a14, a15, a6, a7, a18, a19, a8, a9, a16, a17, a12, a13, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 57 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a11, a5, a14, a15, a6, a7, a18, a5, a8, a9, a16, a17, a12, a13, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 61 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a11, a5, a14, a15, a6, a7, a18, a5, a8, a9, a16, a15, a12, a13, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 65 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a11, a5, a14, a15, a6, a7, a6, a5, a8, a9, a16, a15, a12, a13, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 58 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a13, a5, a14, a15, a6, a7, a6, a5, a8, a9, a16, a15, a12, a13, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 63 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a13, a5, a14, a14, a6, a7, a6, a5, a8, a9, a16, a15, a12, a13, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 63 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a13, a5, a14, a14, a6, a7, a6, a5, a8, a9, a16, a14, a12, a13, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 64 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a13, a5, a14, a14, a6, a7, a6, a5, a8, a7, a16, a14, a12, a13, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 66 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a6, a5, a14, a14, a6, a7, a6, a5, a8, a7, a16, a14, a12, a13, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 66 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a6, a5, a14, a14, a6, a7, a6, a5, a8, a7, a16, a14, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 68 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a6, a5, a10, a14, a6, a7, a6, a5, a8, a7, a16, a14, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 68 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a6, a5, a10, a10, a6, a7, a6, a5, a8, a7, a16, a14, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 68 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a6, a5, a10, a10, a6, a7, a6, a5, a8, a7, a16, a10, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 69 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a6, a5, a10, a10, a6, a10, a6, a5, a8, a7, a16, a10, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 69 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a10, a6, a5, a10, a10, a6, a10, a6, a5, a8, a10, a16, a10, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 70 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a5, a10, a10, a6, a10, a6, a5, a8, a10, a16, a10, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 70 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a5, a6, a10, a6, a10, a6, a5, a8, a10, a16, a10, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 70 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a5, a6, a6, a6, a10, a6, a5, a8, a10, a16, a10, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 70 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a5, a6, a6, a6, a6, a6, a5, a8, a10, a16, a10, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 70 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a5, a6, a6, a6, a6, a6, a5, a8, a6, a16, a10, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 70 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a5, a6, a6, a6, a6, a6, a5, a8, a6, a16, a6, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 71 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a5, a6, a6, a6, a6, a6, a5, a8, a6, a12, a6, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 72 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a5, a6, a6, a6, a6, a6, a5, a8, a6, a6, a6, a12, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 72 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a5, a6, a6, a6, a6, a6, a5, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 73 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a5, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 73 }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a32, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a32, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a32)
% 0.20/0.85 = { by lemma 75 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.85 = { by lemma 74 }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.85 = { by lemma 74 R->L }
% 0.20/0.85 tuple(a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.85 = { by lemma 75 R->L }
% 0.20/0.85 tuple(a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.85 = { by lemma 75 R->L }
% 0.20/0.85 tuple(a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.85 = { by lemma 75 R->L }
% 0.20/0.85 tuple(a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.85 = { by lemma 75 R->L }
% 0.20/0.85 tuple(a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.85 = { by lemma 75 R->L }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.85 = { by lemma 75 R->L }
% 0.20/0.85 tuple(a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a8, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a8, a6, a32, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a8, a6, a32, a6, a6, a6, a6, a6, a6, a32, a6, a6, a6, a6, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a8, a6, a32, a6, a6, a6, a6, a6, a6, a32, a32, a6, a6, a6, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a8, a6, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a6, a6, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a8, a6, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a6, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a8, a6, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a6)
% 0.20/0.86 = { by lemma 75 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a6, a6, a6, a6, a6, a6, a6, a8, a6, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 73 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a6, a6, a6, a6, a6, a8, a6, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 73 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a6, a6, a6, a6, a6, a8, a5, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 72 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a6, a6, a6, a8, a5, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 72 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a6, a12, a6, a8, a5, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 71 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a6, a16, a6, a8, a5, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 70 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a10, a16, a6, a8, a5, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 70 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a10, a16, a10, a8, a5, a32, a6, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 70 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a10, a16, a10, a8, a5, a32, a10, a6, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 70 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a10, a16, a10, a8, a5, a32, a10, a10, a6, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 70 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a10, a16, a10, a8, a5, a32, a10, a10, a10, a6, a6, a6, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 70 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a10, a16, a10, a8, a5, a32, a10, a10, a10, a6, a6, a10, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 69 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a10, a16, a7, a8, a5, a32, a10, a10, a10, a6, a6, a10, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 69 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a10, a16, a7, a8, a5, a32, a7, a10, a10, a6, a6, a10, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 68 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a14, a16, a7, a8, a5, a32, a7, a10, a10, a6, a6, a10, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 68 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a14, a16, a7, a8, a5, a32, a7, a10, a14, a6, a6, a10, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 68 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a6, a12, a6, a14, a16, a7, a8, a5, a32, a7, a10, a14, a6, a6, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 66 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a13, a12, a6, a14, a16, a7, a8, a5, a32, a7, a10, a14, a6, a6, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 66 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a13, a12, a6, a14, a16, a7, a8, a5, a32, a7, a10, a14, a6, a13, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 64 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a13, a12, a6, a14, a16, a7, a8, a5, a32, a9, a10, a14, a6, a13, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 63 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a13, a12, a6, a15, a16, a7, a8, a5, a32, a9, a10, a14, a6, a13, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 63 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a13, a12, a6, a15, a16, a7, a8, a5, a32, a9, a10, a15, a6, a13, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 58 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a5, a32, a9, a10, a15, a6, a13, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 65 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a5, a32, a9, a10, a15, a18, a13, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 61 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a5, a32, a9, a10, a17, a18, a13, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 57 R->L }
% 0.20/0.86 tuple(a32, a32, a32, a32, a32, a32, a32, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a32, a9, a10, a17, a18, a13, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 52 R->L }
% 0.20/0.86 tuple(a2, a32, a32, a32, a32, a32, a32, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a32, a9, a10, a17, a18, a13, a14, a32, a32, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 52 R->L }
% 0.20/0.86 tuple(a2, a32, a32, a32, a32, a32, a32, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a32, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 56 R->L }
% 0.20/0.86 tuple(a2, a32, a32, a32, a32, a32, a32, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 54 R->L }
% 0.20/0.86 tuple(a2, a32, a32, a32, a32, a32, a4, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 51 R->L }
% 0.20/0.86 tuple(a2, a27, a32, a32, a32, a32, a4, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 51 R->L }
% 0.20/0.86 tuple(a2, a27, a32, a32, a27, a32, a4, a32, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 51 R->L }
% 0.20/0.86 tuple(a2, a27, a32, a32, a27, a32, a4, a27, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a32, a32)
% 0.20/0.86 = { by lemma 51 R->L }
% 0.20/0.86 tuple(a2, a27, a32, a32, a27, a32, a4, a27, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a27, a32)
% 0.20/0.86 = { by lemma 50 R->L }
% 0.20/0.86 tuple(a2, a27, a32, a32, a27, a26, a4, a27, a32, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a27, a32)
% 0.20/0.86 = { by lemma 50 R->L }
% 0.20/0.86 tuple(a2, a27, a32, a32, a27, a26, a4, a27, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a27, a32)
% 0.20/0.86 = { by lemma 50 R->L }
% 0.20/0.86 tuple(a2, a27, a32, a32, a27, a26, a4, a27, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a2, a32, a32, a27, a26)
% 0.20/0.86 = { by lemma 48 R->L }
% 0.20/0.86 tuple(a2, a27, a32, a32, a27, a26, a4, a27, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a22, a32, a32, a27, a26)
% 0.20/0.86 = { by lemma 47 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a32, a27, a26, a4, a27, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a22, a32, a32, a27, a26)
% 0.20/0.86 = { by lemma 47 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a32, a31, a26, a4, a27, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a22, a32, a32, a27, a26)
% 0.20/0.86 = { by lemma 53 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a32, a31, a26, a4, a29, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a22, a32, a32, a27, a26)
% 0.20/0.86 = { by lemma 55 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a32, a31, a26, a4, a29, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a22, a32, a32, a27, a28)
% 0.20/0.86 = { by lemma 45 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a1, a31, a26, a4, a29, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a32, a22, a32, a32, a27, a28)
% 0.20/0.86 = { by lemma 45 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a1, a31, a26, a4, a29, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a1, a22, a32, a32, a27, a28)
% 0.20/0.86 = { by lemma 45 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a1, a31, a26, a4, a29, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a1, a22, a1, a32, a27, a28)
% 0.20/0.86 = { by lemma 43 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a1, a31, a26, a4, a29, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a23, a22, a1, a32, a27, a28)
% 0.20/0.86 = { by lemma 43 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a1, a31, a26, a4, a29, a26, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a23, a22, a23, a32, a27, a28)
% 0.20/0.86 = { by lemma 46 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a1, a31, a26, a4, a29, a30, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a23, a22, a23, a32, a27, a28)
% 0.20/0.86 = { by lemma 44 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a1, a31, a26, a4, a29, a30, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a21, a22, a23, a32, a27, a28)
% 0.20/0.86 = { by lemma 42 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a1, a31, a26, a4, a29, a30, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a21, a22, a23, a24, a27, a28)
% 0.20/0.86 = { by lemma 49 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a3, a31, a26, a4, a29, a30, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a21, a22, a23, a24, a27, a28)
% 0.20/0.86 = { by lemma 41 R->L }
% 0.20/0.86 tuple(a2, a31, a32, a3, a25, a26, a4, a29, a30, a5, a11, a12, a6, a15, a16, a7, a8, a19, a20, a9, a10, a17, a18, a13, a14, a21, a22, a23, a24, a27, a28)
% 0.20/0.86 % SZS output end Proof
% 0.20/0.86
% 0.20/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------