TSTP Solution File: TOP053-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : TOP053-1 : 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 : n031.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 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : TOP053-1 : TPTP v8.1.2. Released v8.1.0.
% 0.13/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n031.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 00:23:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.44 Command-line arguments: --no-flatten-goal
% 0.21/0.44
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 Axiom 1 (involutory_quandle): product(X, X) = X.
% 0.21/0.48 Axiom 2 (knot_14): product(a15, a8) = a4.
% 0.21/0.48 Axiom 3 (knot): product(a1, a2) = a3.
% 0.21/0.48 Axiom 4 (knot_04): product(a5, a6) = a7.
% 0.21/0.48 Axiom 5 (knot_07): product(a9, a1) = a10.
% 0.21/0.48 Axiom 6 (knot_10): product(a13, a8) = a6.
% 0.21/0.48 Axiom 7 (knot_13): product(a14, a3) = a15.
% 0.21/0.48 Axiom 8 (knot_15): product(a4, a7) = a11.
% 0.21/0.48 Axiom 9 (knot_11): product(a6, a7) = a2.
% 0.21/0.48 Axiom 10 (knot_08): product(a10, a11) = a12.
% 0.21/0.48 Axiom 11 (knot_16): product(a11, a10) = a1.
% 0.21/0.48 Axiom 12 (knot_09): product(a12, a3) = a13.
% 0.21/0.48 Axiom 13 (knot_12): product(a2, a12) = a14.
% 0.21/0.48 Axiom 14 (knot_05): product(a7, a3) = a8.
% 0.21/0.48 Axiom 15 (knot_06): product(a8, a2) = a9.
% 0.21/0.48 Axiom 16 (knot_03): product(a3, a4) = a5.
% 0.21/0.48 Axiom 17 (involutory_quandle_01): product(product(X, Y), Y) = X.
% 0.21/0.48 Axiom 18 (involutory_quandle_02): product(product(X, Y), Z) = product(product(X, Z), product(Y, Z)).
% 0.21/0.48
% 0.21/0.48 Lemma 19: product(a9, a2) = a8.
% 0.21/0.48 Proof:
% 0.21/0.48 product(a9, a2)
% 0.21/0.48 = { by axiom 15 (knot_06) R->L }
% 0.21/0.48 product(product(a8, a2), a2)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 a8
% 0.21/0.48
% 0.21/0.48 Lemma 20: product(product(a1, X), a2) = product(a3, product(X, a2)).
% 0.21/0.48 Proof:
% 0.21/0.48 product(product(a1, X), a2)
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) }
% 0.21/0.48 product(product(a1, a2), product(X, a2))
% 0.21/0.48 = { by axiom 3 (knot) }
% 0.21/0.48 product(a3, product(X, a2))
% 0.21/0.48
% 0.21/0.48 Lemma 21: product(a10, a1) = a9.
% 0.21/0.48 Proof:
% 0.21/0.48 product(a10, a1)
% 0.21/0.48 = { by axiom 5 (knot_07) R->L }
% 0.21/0.48 product(product(a9, a1), a1)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 a9
% 0.21/0.48
% 0.21/0.48 Lemma 22: product(product(X, Y), X) = product(X, product(Y, X)).
% 0.21/0.48 Proof:
% 0.21/0.48 product(product(X, Y), X)
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) }
% 0.21/0.48 product(product(X, X), product(Y, X))
% 0.21/0.48 = { by axiom 1 (involutory_quandle) }
% 0.21/0.48 product(X, product(Y, X))
% 0.21/0.48
% 0.21/0.48 Lemma 23: product(product(X, a2), a3) = product(product(X, a1), a2).
% 0.21/0.48 Proof:
% 0.21/0.48 product(product(X, a2), a3)
% 0.21/0.48 = { by axiom 3 (knot) R->L }
% 0.21/0.48 product(product(X, a2), product(a1, a2))
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) R->L }
% 0.21/0.48 product(product(X, a1), a2)
% 0.21/0.48
% 0.21/0.48 Lemma 24: product(a5, a4) = a3.
% 0.21/0.48 Proof:
% 0.21/0.48 product(a5, a4)
% 0.21/0.48 = { by axiom 16 (knot_03) R->L }
% 0.21/0.48 product(product(a3, a4), a4)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 a3
% 0.21/0.48
% 0.21/0.48 Lemma 25: product(a8, a3) = a7.
% 0.21/0.48 Proof:
% 0.21/0.48 product(a8, a3)
% 0.21/0.48 = { by axiom 14 (knot_05) R->L }
% 0.21/0.48 product(product(a7, a3), a3)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 a7
% 0.21/0.48
% 0.21/0.48 Lemma 26: product(a5, a7) = a10.
% 0.21/0.48 Proof:
% 0.21/0.48 product(a5, a7)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) R->L }
% 0.21/0.48 product(product(product(a5, a6), a6), a7)
% 0.21/0.48 = { by axiom 4 (knot_04) }
% 0.21/0.48 product(product(a7, a6), a7)
% 0.21/0.48 = { by lemma 22 }
% 0.21/0.48 product(a7, product(a6, a7))
% 0.21/0.48 = { by axiom 9 (knot_11) }
% 0.21/0.48 product(a7, a2)
% 0.21/0.48 = { by lemma 25 R->L }
% 0.21/0.48 product(product(a8, a3), a2)
% 0.21/0.48 = { by lemma 19 R->L }
% 0.21/0.48 product(product(product(a9, a2), a3), a2)
% 0.21/0.48 = { by lemma 23 }
% 0.21/0.48 product(product(product(a9, a1), a2), a2)
% 0.21/0.48 = { by axiom 5 (knot_07) }
% 0.21/0.48 product(product(a10, a2), a2)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 a10
% 0.21/0.48
% 0.21/0.48 Lemma 27: product(a3, a7) = a12.
% 0.21/0.48 Proof:
% 0.21/0.48 product(a3, a7)
% 0.21/0.48 = { by lemma 24 R->L }
% 0.21/0.48 product(product(a5, a4), a7)
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) }
% 0.21/0.48 product(product(a5, a7), product(a4, a7))
% 0.21/0.48 = { by axiom 8 (knot_15) }
% 0.21/0.48 product(product(a5, a7), a11)
% 0.21/0.48 = { by lemma 26 }
% 0.21/0.48 product(a10, a11)
% 0.21/0.48 = { by axiom 10 (knot_08) }
% 0.21/0.48 a12
% 0.21/0.48
% 0.21/0.48 Lemma 28: product(a11, a2) = a14.
% 0.21/0.48 Proof:
% 0.21/0.48 product(a11, a2)
% 0.21/0.48 = { by axiom 9 (knot_11) R->L }
% 0.21/0.48 product(a11, product(a6, a7))
% 0.21/0.48 = { by axiom 8 (knot_15) R->L }
% 0.21/0.48 product(product(a4, a7), product(a6, a7))
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) R->L }
% 0.21/0.48 product(product(a4, a6), a7)
% 0.21/0.48 = { by axiom 6 (knot_10) R->L }
% 0.21/0.48 product(product(a4, product(a13, a8)), a7)
% 0.21/0.48 = { by axiom 2 (knot_14) R->L }
% 0.21/0.48 product(product(product(a15, a8), product(a13, a8)), a7)
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) R->L }
% 0.21/0.48 product(product(product(a15, a13), a8), a7)
% 0.21/0.48 = { by axiom 12 (knot_09) R->L }
% 0.21/0.48 product(product(product(a15, product(a12, a3)), a8), a7)
% 0.21/0.48 = { by axiom 7 (knot_13) R->L }
% 0.21/0.48 product(product(product(product(a14, a3), product(a12, a3)), a8), a7)
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) R->L }
% 0.21/0.48 product(product(product(product(a14, a12), a3), a8), a7)
% 0.21/0.48 = { by axiom 13 (knot_12) R->L }
% 0.21/0.48 product(product(product(product(product(a2, a12), a12), a3), a8), a7)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 product(product(product(a2, a3), a8), a7)
% 0.21/0.48 = { by axiom 14 (knot_05) R->L }
% 0.21/0.48 product(product(product(a2, a3), product(a7, a3)), a7)
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) R->L }
% 0.21/0.48 product(product(product(a2, a7), a3), a7)
% 0.21/0.48 = { by axiom 9 (knot_11) R->L }
% 0.21/0.48 product(product(product(product(a6, a7), a7), a3), a7)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 product(product(a6, a3), a7)
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) }
% 0.21/0.48 product(product(a6, a7), product(a3, a7))
% 0.21/0.48 = { by axiom 9 (knot_11) }
% 0.21/0.48 product(a2, product(a3, a7))
% 0.21/0.48 = { by lemma 27 }
% 0.21/0.48 product(a2, a12)
% 0.21/0.48 = { by axiom 13 (knot_12) }
% 0.21/0.48 a14
% 0.21/0.48
% 0.21/0.48 Lemma 29: a3 = a4.
% 0.21/0.48 Proof:
% 0.21/0.48 a3
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) R->L }
% 0.21/0.48 product(product(a3, a8), a8)
% 0.21/0.48 = { by lemma 19 R->L }
% 0.21/0.48 product(product(a3, product(a9, a2)), a8)
% 0.21/0.48 = { by lemma 20 R->L }
% 0.21/0.48 product(product(product(a1, a9), a2), a8)
% 0.21/0.48 = { by lemma 21 R->L }
% 0.21/0.48 product(product(product(a1, product(a10, a1)), a2), a8)
% 0.21/0.48 = { by lemma 22 R->L }
% 0.21/0.48 product(product(product(product(a1, a10), a1), a2), a8)
% 0.21/0.48 = { by axiom 11 (knot_16) R->L }
% 0.21/0.48 product(product(product(product(product(a11, a10), a10), a1), a2), a8)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 product(product(product(a11, a1), a2), a8)
% 0.21/0.48 = { by lemma 23 R->L }
% 0.21/0.48 product(product(product(a11, a2), a3), a8)
% 0.21/0.48 = { by lemma 28 }
% 0.21/0.48 product(product(a14, a3), a8)
% 0.21/0.48 = { by axiom 7 (knot_13) }
% 0.21/0.48 product(a15, a8)
% 0.21/0.48 = { by axiom 2 (knot_14) }
% 0.21/0.48 a4
% 0.21/0.48
% 0.21/0.48 Lemma 30: a4 = a5.
% 0.21/0.48 Proof:
% 0.21/0.48 a4
% 0.21/0.48 = { by axiom 1 (involutory_quandle) R->L }
% 0.21/0.48 product(a4, a4)
% 0.21/0.48 = { by lemma 29 R->L }
% 0.21/0.48 product(a3, a4)
% 0.21/0.48 = { by axiom 16 (knot_03) }
% 0.21/0.48 a5
% 0.21/0.48
% 0.21/0.48 Lemma 31: a11 = a10.
% 0.21/0.48 Proof:
% 0.21/0.48 a11
% 0.21/0.48 = { by axiom 8 (knot_15) R->L }
% 0.21/0.48 product(a4, a7)
% 0.21/0.48 = { by lemma 30 }
% 0.21/0.48 product(a5, a7)
% 0.21/0.48 = { by lemma 26 }
% 0.21/0.48 a10
% 0.21/0.48
% 0.21/0.48 Lemma 32: a10 = a1.
% 0.21/0.48 Proof:
% 0.21/0.48 a10
% 0.21/0.48 = { by axiom 1 (involutory_quandle) R->L }
% 0.21/0.48 product(a10, a10)
% 0.21/0.48 = { by lemma 31 R->L }
% 0.21/0.48 product(a11, a10)
% 0.21/0.48 = { by axiom 11 (knot_16) }
% 0.21/0.48 a1
% 0.21/0.48
% 0.21/0.48 Lemma 33: a12 = a11.
% 0.21/0.48 Proof:
% 0.21/0.48 a12
% 0.21/0.48 = { by lemma 27 R->L }
% 0.21/0.48 product(a3, a7)
% 0.21/0.48 = { by lemma 29 }
% 0.21/0.48 product(a4, a7)
% 0.21/0.48 = { by axiom 8 (knot_15) }
% 0.21/0.48 a11
% 0.21/0.48
% 0.21/0.48 Lemma 34: a9 = a1.
% 0.21/0.48 Proof:
% 0.21/0.48 a9
% 0.21/0.48 = { by lemma 21 R->L }
% 0.21/0.48 product(a10, a1)
% 0.21/0.48 = { by axiom 11 (knot_16) R->L }
% 0.21/0.48 product(a10, product(a11, a10))
% 0.21/0.48 = { by lemma 22 R->L }
% 0.21/0.48 product(product(a10, a11), a10)
% 0.21/0.48 = { by axiom 10 (knot_08) }
% 0.21/0.48 product(a12, a10)
% 0.21/0.48 = { by lemma 33 }
% 0.21/0.48 product(a11, a10)
% 0.21/0.48 = { by axiom 11 (knot_16) }
% 0.21/0.48 a1
% 0.21/0.48
% 0.21/0.48 Lemma 35: product(a8, X) = product(a5, X).
% 0.21/0.48 Proof:
% 0.21/0.48 product(a8, X)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) R->L }
% 0.21/0.48 product(product(product(a8, X), a2), a2)
% 0.21/0.48 = { by axiom 18 (involutory_quandle_02) }
% 0.21/0.48 product(product(product(a8, a2), product(X, a2)), a2)
% 0.21/0.48 = { by axiom 15 (knot_06) }
% 0.21/0.48 product(product(a9, product(X, a2)), a2)
% 0.21/0.48 = { by lemma 34 }
% 0.21/0.48 product(product(a1, product(X, a2)), a2)
% 0.21/0.48 = { by lemma 20 }
% 0.21/0.48 product(a3, product(product(X, a2), a2))
% 0.21/0.48 = { by lemma 29 }
% 0.21/0.48 product(a4, product(product(X, a2), a2))
% 0.21/0.48 = { by lemma 30 }
% 0.21/0.48 product(a5, product(product(X, a2), a2))
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 product(a5, X)
% 0.21/0.48
% 0.21/0.48 Lemma 36: a7 = a5.
% 0.21/0.48 Proof:
% 0.21/0.48 a7
% 0.21/0.48 = { by lemma 25 R->L }
% 0.21/0.48 product(a8, a3)
% 0.21/0.48 = { by lemma 35 }
% 0.21/0.48 product(a5, a3)
% 0.21/0.48 = { by lemma 29 }
% 0.21/0.48 product(a5, a4)
% 0.21/0.48 = { by lemma 24 }
% 0.21/0.48 a3
% 0.21/0.48 = { by lemma 29 }
% 0.21/0.48 a4
% 0.21/0.48 = { by lemma 30 }
% 0.21/0.48 a5
% 0.21/0.48
% 0.21/0.48 Lemma 37: a8 = a5.
% 0.21/0.48 Proof:
% 0.21/0.48 a8
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) R->L }
% 0.21/0.48 product(product(a8, X), X)
% 0.21/0.48 = { by lemma 35 }
% 0.21/0.48 product(product(a5, X), X)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 a5
% 0.21/0.48
% 0.21/0.48 Lemma 38: a5 = a15.
% 0.21/0.48 Proof:
% 0.21/0.48 a5
% 0.21/0.48 = { by axiom 1 (involutory_quandle) R->L }
% 0.21/0.48 product(a5, a5)
% 0.21/0.48 = { by lemma 30 R->L }
% 0.21/0.48 product(a4, a5)
% 0.21/0.48 = { by lemma 37 R->L }
% 0.21/0.48 product(a4, a8)
% 0.21/0.48 = { by axiom 2 (knot_14) R->L }
% 0.21/0.48 product(product(a15, a8), a8)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 a15
% 0.21/0.48
% 0.21/0.48 Lemma 39: a1 = a15.
% 0.21/0.48 Proof:
% 0.21/0.48 a1
% 0.21/0.48 = { by lemma 32 R->L }
% 0.21/0.48 a10
% 0.21/0.48 = { by lemma 31 R->L }
% 0.21/0.48 a11
% 0.21/0.48 = { by axiom 8 (knot_15) R->L }
% 0.21/0.48 product(a4, a7)
% 0.21/0.48 = { by lemma 36 }
% 0.21/0.48 product(a4, a5)
% 0.21/0.48 = { by lemma 30 }
% 0.21/0.48 product(a5, a5)
% 0.21/0.48 = { by axiom 1 (involutory_quandle) }
% 0.21/0.48 a5
% 0.21/0.48 = { by lemma 38 }
% 0.21/0.48 a15
% 0.21/0.48
% 0.21/0.48 Lemma 40: a2 = a13.
% 0.21/0.48 Proof:
% 0.21/0.48 a2
% 0.21/0.48 = { by axiom 9 (knot_11) R->L }
% 0.21/0.48 product(a6, a7)
% 0.21/0.48 = { by lemma 36 }
% 0.21/0.48 product(a6, a5)
% 0.21/0.48 = { by lemma 37 R->L }
% 0.21/0.48 product(a6, a8)
% 0.21/0.48 = { by axiom 6 (knot_10) R->L }
% 0.21/0.48 product(product(a13, a8), a8)
% 0.21/0.48 = { by axiom 17 (involutory_quandle_01) }
% 0.21/0.48 a13
% 0.21/0.48
% 0.21/0.48 Lemma 41: a14 = a5.
% 0.21/0.48 Proof:
% 0.21/0.48 a14
% 0.21/0.48 = { by lemma 28 R->L }
% 0.21/0.48 product(a11, a2)
% 0.21/0.48 = { by lemma 31 }
% 0.21/0.48 product(a10, a2)
% 0.21/0.48 = { by lemma 32 }
% 0.21/0.48 product(a1, a2)
% 0.21/0.48 = { by axiom 3 (knot) }
% 0.21/0.48 a3
% 0.21/0.48 = { by lemma 29 }
% 0.21/0.48 a4
% 0.21/0.48 = { by lemma 30 }
% 0.21/0.48 a5
% 0.21/0.48
% 0.21/0.48 Lemma 42: a6 = a15.
% 0.21/0.48 Proof:
% 0.21/0.48 a6
% 0.21/0.48 = { by axiom 6 (knot_10) R->L }
% 0.21/0.48 product(a13, a8)
% 0.21/0.48 = { by lemma 37 }
% 0.21/0.48 product(a13, a5)
% 0.21/0.48 = { by lemma 38 }
% 0.21/0.48 product(a13, a15)
% 0.21/0.48 = { by lemma 39 R->L }
% 0.21/0.48 product(a13, a1)
% 0.21/0.48 = { by lemma 32 R->L }
% 0.21/0.48 product(a13, a10)
% 0.21/0.48 = { by lemma 31 R->L }
% 0.21/0.48 product(a13, a11)
% 0.21/0.48 = { by lemma 33 R->L }
% 0.21/0.48 product(a13, a12)
% 0.21/0.48 = { by lemma 40 R->L }
% 0.21/0.48 product(a2, a12)
% 0.21/0.48 = { by axiom 13 (knot_12) }
% 0.21/0.48 a14
% 0.21/0.48 = { by lemma 41 }
% 0.21/0.48 a5
% 0.21/0.48 = { by lemma 38 }
% 0.21/0.48 a15
% 0.21/0.48
% 0.21/0.48 Lemma 43: a13 = a15.
% 0.21/0.48 Proof:
% 0.21/0.48 a13
% 0.21/0.48 = { by lemma 40 R->L }
% 0.21/0.48 a2
% 0.21/0.48 = { by axiom 9 (knot_11) R->L }
% 0.21/0.48 product(a6, a7)
% 0.21/0.48 = { by lemma 42 }
% 0.21/0.48 product(a15, a7)
% 0.21/0.48 = { by lemma 36 }
% 0.21/0.48 product(a15, a5)
% 0.21/0.48 = { by lemma 38 }
% 0.21/0.48 product(a15, a15)
% 0.21/0.48 = { by axiom 1 (involutory_quandle) }
% 0.21/0.49 a15
% 0.21/0.49
% 0.21/0.49 Goal 1 (goal): tuple(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14) = tuple(a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15).
% 0.21/0.49 Proof:
% 0.21/0.49 tuple(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14)
% 0.21/0.49 = { by lemma 29 }
% 0.21/0.49 tuple(a1, a2, a4, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14)
% 0.21/0.49 = { by lemma 30 }
% 0.21/0.49 tuple(a1, a2, a5, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14)
% 0.21/0.49 = { by lemma 30 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14)
% 0.21/0.49 = { by lemma 33 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a8, a9, a10, a11, a11, a13, a14)
% 0.21/0.49 = { by lemma 31 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a8, a9, a10, a10, a11, a13, a14)
% 0.21/0.49 = { by lemma 31 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a8, a9, a10, a10, a10, a13, a14)
% 0.21/0.49 = { by lemma 34 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a8, a1, a10, a10, a10, a13, a14)
% 0.21/0.49 = { by lemma 32 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a8, a1, a1, a10, a10, a13, a14)
% 0.21/0.49 = { by lemma 32 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a8, a1, a1, a1, a10, a13, a14)
% 0.21/0.49 = { by lemma 32 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a8, a1, a1, a1, a1, a13, a14)
% 0.21/0.49 = { by lemma 41 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a8, a1, a1, a1, a1, a13, a5)
% 0.21/0.49 = { by lemma 37 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a7, a5, a1, a1, a1, a1, a13, a5)
% 0.21/0.49 = { by lemma 36 }
% 0.21/0.49 tuple(a1, a2, a5, a5, a5, a6, a5, a5, a1, a1, a1, a1, a13, a5)
% 0.21/0.49 = { by lemma 38 }
% 0.21/0.49 tuple(a1, a2, a15, a5, a5, a6, a5, a5, a1, a1, a1, a1, a13, a5)
% 0.21/0.49 = { by lemma 38 }
% 0.21/0.49 tuple(a1, a2, a15, a15, a5, a6, a5, a5, a1, a1, a1, a1, a13, a5)
% 0.21/0.49 = { by lemma 38 }
% 0.21/0.49 tuple(a1, a2, a15, a15, a15, a6, a5, a5, a1, a1, a1, a1, a13, a5)
% 0.21/0.49 = { by lemma 38 }
% 0.21/0.49 tuple(a1, a2, a15, a15, a15, a6, a15, a5, a1, a1, a1, a1, a13, a5)
% 0.21/0.49 = { by lemma 38 }
% 0.21/0.49 tuple(a1, a2, a15, a15, a15, a6, a15, a15, a1, a1, a1, a1, a13, a5)
% 0.21/0.49 = { by lemma 38 }
% 0.21/0.49 tuple(a1, a2, a15, a15, a15, a6, a15, a15, a1, a1, a1, a1, a13, a15)
% 0.21/0.49 = { by lemma 39 }
% 0.21/0.49 tuple(a15, a2, a15, a15, a15, a6, a15, a15, a1, a1, a1, a1, a13, a15)
% 0.21/0.49 = { by lemma 39 }
% 0.21/0.49 tuple(a15, a2, a15, a15, a15, a6, a15, a15, a15, a1, a1, a1, a13, a15)
% 0.21/0.49 = { by lemma 39 }
% 0.21/0.49 tuple(a15, a2, a15, a15, a15, a6, a15, a15, a15, a15, a1, a1, a13, a15)
% 0.21/0.49 = { by lemma 39 }
% 0.21/0.49 tuple(a15, a2, a15, a15, a15, a6, a15, a15, a15, a15, a15, a1, a13, a15)
% 0.21/0.49 = { by lemma 39 }
% 0.21/0.49 tuple(a15, a2, a15, a15, a15, a6, a15, a15, a15, a15, a15, a15, a13, a15)
% 0.21/0.49 = { by lemma 40 }
% 0.21/0.49 tuple(a15, a13, a15, a15, a15, a6, a15, a15, a15, a15, a15, a15, a13, a15)
% 0.21/0.49 = { by lemma 42 }
% 0.21/0.49 tuple(a15, a13, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a13, a15)
% 0.21/0.49 = { by lemma 43 }
% 0.21/0.49 tuple(a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a13, a15)
% 0.21/0.49 = { by lemma 43 }
% 0.21/0.49 tuple(a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15)
% 0.21/0.49 = { by lemma 43 R->L }
% 0.21/0.49 tuple(a13, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15)
% 0.21/0.49 = { by lemma 43 R->L }
% 0.21/0.49 tuple(a13, a15, a15, a15, a15, a15, a15, a15, a15, a15, a15, a13, a15, a15)
% 0.21/0.49 = { by lemma 42 R->L }
% 0.21/0.49 tuple(a13, a15, a15, a15, a6, a15, a15, a15, a15, a15, a15, a13, a15, a15)
% 0.21/0.49 = { by lemma 40 R->L }
% 0.21/0.49 tuple(a2, a15, a15, a15, a6, a15, a15, a15, a15, a15, a15, a13, a15, a15)
% 0.21/0.49 = { by lemma 39 R->L }
% 0.21/0.49 tuple(a2, a15, a15, a15, a6, a15, a15, a1, a15, a15, a15, a13, a15, a15)
% 0.21/0.49 = { by lemma 39 R->L }
% 0.21/0.49 tuple(a2, a15, a15, a15, a6, a15, a15, a1, a1, a15, a15, a13, a15, a15)
% 0.21/0.49 = { by lemma 39 R->L }
% 0.21/0.49 tuple(a2, a15, a15, a15, a6, a15, a15, a1, a1, a1, a15, a13, a15, a15)
% 0.21/0.49 = { by lemma 39 R->L }
% 0.21/0.49 tuple(a2, a15, a15, a15, a6, a15, a15, a1, a1, a1, a1, a13, a15, a15)
% 0.21/0.49 = { by lemma 38 R->L }
% 0.21/0.49 tuple(a2, a5, a15, a15, a6, a15, a15, a1, a1, a1, a1, a13, a15, a15)
% 0.21/0.49 = { by lemma 38 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a15, a6, a15, a15, a1, a1, a1, a1, a13, a15, a15)
% 0.21/0.49 = { by lemma 38 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a15, a15, a1, a1, a1, a1, a13, a15, a15)
% 0.21/0.49 = { by lemma 38 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a5, a15, a1, a1, a1, a1, a13, a15, a15)
% 0.21/0.49 = { by lemma 38 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a5, a5, a1, a1, a1, a1, a13, a15, a15)
% 0.21/0.49 = { by lemma 38 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a5, a5, a1, a1, a1, a1, a13, a5, a15)
% 0.21/0.49 = { by lemma 36 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a5, a1, a1, a1, a1, a13, a5, a15)
% 0.21/0.49 = { by lemma 37 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a8, a1, a1, a1, a1, a13, a5, a15)
% 0.21/0.49 = { by lemma 41 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a8, a1, a1, a1, a1, a13, a14, a15)
% 0.21/0.49 = { by lemma 32 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a8, a1, a10, a1, a1, a13, a14, a15)
% 0.21/0.49 = { by lemma 32 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a8, a1, a10, a10, a1, a13, a14, a15)
% 0.21/0.49 = { by lemma 32 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a8, a1, a10, a10, a10, a13, a14, a15)
% 0.21/0.49 = { by lemma 34 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a8, a9, a10, a10, a10, a13, a14, a15)
% 0.21/0.49 = { by lemma 31 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a8, a9, a10, a11, a10, a13, a14, a15)
% 0.21/0.49 = { by lemma 31 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a8, a9, a10, a11, a11, a13, a14, a15)
% 0.21/0.49 = { by lemma 33 R->L }
% 0.21/0.49 tuple(a2, a5, a5, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15)
% 0.21/0.49 = { by lemma 30 R->L }
% 0.21/0.49 tuple(a2, a4, a5, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15)
% 0.21/0.49 = { by lemma 30 R->L }
% 0.21/0.49 tuple(a2, a4, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15)
% 0.21/0.49 = { by lemma 29 R->L }
% 0.21/0.49 tuple(a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15)
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49
% 0.21/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------