TSTP Solution File: TOP049-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : TOP049-1 : 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 : n022.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 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : TOP049-1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n022.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 : Sat Aug 26 23:19:40 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.41 Command-line arguments: --no-flatten-goal
% 0.21/0.41
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 Axiom 1 (involutory_quandle): product(X, X) = X.
% 0.21/0.44 Axiom 2 (knot_03): a3 = product(a1, a2).
% 0.21/0.44 Axiom 3 (knot_06): a6 = product(a5, a4).
% 0.21/0.44 Axiom 4 (knot_10): a4 = product(a10, a3).
% 0.21/0.44 Axiom 5 (knot_07): a7 = product(a6, a1).
% 0.21/0.44 Axiom 6 (knot): a1 = product(a9, a7).
% 0.21/0.44 Axiom 7 (knot_08): a8 = product(a7, a4).
% 0.21/0.44 Axiom 8 (knot_04): a2 = product(a3, a4).
% 0.21/0.44 Axiom 9 (knot_05): a5 = product(a2, a10).
% 0.21/0.44 Axiom 10 (knot_09): a10 = product(a8, a9).
% 0.21/0.44 Axiom 11 (knot_11): a9 = product(a4, a8).
% 0.21/0.44 Axiom 12 (involutory_quandle_01): product(product(X, Y), Y) = X.
% 0.21/0.44 Axiom 13 (involutory_quandle_02): product(product(X, Y), Z) = product(product(X, Z), product(Y, Z)).
% 0.21/0.44
% 0.21/0.44 Lemma 14: product(product(X, Y), X) = product(X, product(Y, X)).
% 0.21/0.44 Proof:
% 0.21/0.44 product(product(X, Y), X)
% 0.21/0.44 = { by axiom 13 (involutory_quandle_02) }
% 0.21/0.44 product(product(X, X), product(Y, X))
% 0.21/0.44 = { by axiom 1 (involutory_quandle) }
% 0.21/0.44 product(X, product(Y, X))
% 0.21/0.44
% 0.21/0.44 Lemma 15: product(a4, a3) = a10.
% 0.21/0.44 Proof:
% 0.21/0.44 product(a4, a3)
% 0.21/0.44 = { by axiom 4 (knot_10) }
% 0.21/0.44 product(product(a10, a3), a3)
% 0.21/0.44 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.44 a10
% 0.21/0.44
% 0.21/0.44 Lemma 16: a2 = a7.
% 0.21/0.44 Proof:
% 0.21/0.44 a2
% 0.21/0.44 = { by axiom 1 (involutory_quandle) R->L }
% 0.21/0.44 product(a2, a2)
% 0.21/0.44 = { by axiom 8 (knot_04) }
% 0.21/0.44 product(product(a3, a4), a2)
% 0.21/0.44 = { by axiom 4 (knot_10) }
% 0.21/0.44 product(product(a3, product(a10, a3)), a2)
% 0.21/0.44 = { by lemma 14 R->L }
% 0.21/0.44 product(product(product(a3, a10), a3), a2)
% 0.21/0.44 = { by lemma 15 R->L }
% 0.21/0.44 product(product(product(a3, product(a4, a3)), a3), a2)
% 0.21/0.44 = { by lemma 14 R->L }
% 0.21/0.44 product(product(product(product(a3, a4), a3), a3), a2)
% 0.21/0.44 = { by axiom 8 (knot_04) R->L }
% 0.21/0.44 product(product(product(a2, a3), a3), a2)
% 0.21/0.44 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.44 product(product(product(product(product(a2, a10), a10), a3), a3), a2)
% 0.21/0.44 = { by axiom 9 (knot_05) R->L }
% 0.21/0.44 product(product(product(product(a5, a10), a3), a3), a2)
% 0.21/0.44 = { by axiom 13 (involutory_quandle_02) }
% 0.21/0.44 product(product(product(product(a5, a3), product(a10, a3)), a3), a2)
% 0.21/0.44 = { by axiom 4 (knot_10) R->L }
% 0.21/0.44 product(product(product(product(a5, a3), a4), a3), a2)
% 0.21/0.44 = { by axiom 13 (involutory_quandle_02) }
% 0.21/0.44 product(product(product(product(a5, a4), product(a3, a4)), a3), a2)
% 0.21/0.44 = { by axiom 3 (knot_06) R->L }
% 0.21/0.44 product(product(product(a6, product(a3, a4)), a3), a2)
% 0.21/0.44 = { by axiom 8 (knot_04) R->L }
% 0.21/0.44 product(product(product(a6, a2), a3), a2)
% 0.21/0.44 = { by axiom 2 (knot_03) }
% 0.21/0.44 product(product(product(a6, a2), product(a1, a2)), a2)
% 0.21/0.44 = { by axiom 13 (involutory_quandle_02) R->L }
% 0.21/0.44 product(product(product(a6, a1), a2), a2)
% 0.21/0.44 = { by axiom 5 (knot_07) R->L }
% 0.21/0.44 product(product(a7, a2), a2)
% 0.21/0.44 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.44 a7
% 0.21/0.44
% 0.21/0.44 Lemma 17: product(a2, a4) = a3.
% 0.21/0.44 Proof:
% 0.21/0.44 product(a2, a4)
% 0.21/0.44 = { by axiom 8 (knot_04) }
% 0.21/0.44 product(product(a3, a4), a4)
% 0.21/0.44 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.44 a3
% 0.21/0.44
% 0.21/0.44 Lemma 18: a3 = a9.
% 0.21/0.44 Proof:
% 0.21/0.44 a3
% 0.21/0.44 = { by axiom 2 (knot_03) }
% 0.21/0.44 product(a1, a2)
% 0.21/0.44 = { by lemma 16 }
% 0.21/0.44 product(a1, a7)
% 0.21/0.44 = { by axiom 6 (knot) }
% 0.21/0.44 product(product(a9, a7), a7)
% 0.21/0.44 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.44 a9
% 0.21/0.44
% 0.21/0.44 Lemma 19: a8 = a9.
% 0.21/0.44 Proof:
% 0.21/0.44 a8
% 0.21/0.44 = { by axiom 7 (knot_08) }
% 0.21/0.44 product(a7, a4)
% 0.21/0.44 = { by lemma 16 R->L }
% 0.21/0.44 product(a2, a4)
% 0.21/0.44 = { by lemma 17 }
% 0.21/0.44 a3
% 0.21/0.44 = { by lemma 18 }
% 0.21/0.44 a9
% 0.21/0.44
% 0.21/0.44 Lemma 20: a4 = a8.
% 0.21/0.44 Proof:
% 0.21/0.44 a4
% 0.21/0.44 = { by axiom 4 (knot_10) }
% 0.21/0.44 product(a10, a3)
% 0.21/0.44 = { by lemma 18 }
% 0.21/0.44 product(a10, a9)
% 0.21/0.44 = { by axiom 10 (knot_09) }
% 0.21/0.44 product(product(a8, a9), a9)
% 0.21/0.44 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.44 a8
% 0.21/0.44
% 0.21/0.44 Lemma 21: product(a8, a4) = a7.
% 0.21/0.44 Proof:
% 0.21/0.44 product(a8, a4)
% 0.21/0.44 = { by axiom 7 (knot_08) }
% 0.21/0.44 product(product(a7, a4), a4)
% 0.21/0.44 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.44 a7
% 0.21/0.44
% 0.21/0.44 Lemma 22: a9 = a10.
% 0.21/0.44 Proof:
% 0.21/0.44 a9
% 0.21/0.44 = { by lemma 19 R->L }
% 0.21/0.44 a8
% 0.21/0.44 = { by axiom 7 (knot_08) }
% 0.21/0.44 product(a7, a4)
% 0.21/0.44 = { by lemma 20 }
% 0.21/0.44 product(a7, a8)
% 0.21/0.44 = { by lemma 21 R->L }
% 0.21/0.44 product(product(a8, a4), a8)
% 0.21/0.44 = { by lemma 14 }
% 0.21/0.44 product(a8, product(a4, a8))
% 0.21/0.44 = { by axiom 11 (knot_11) R->L }
% 0.21/0.44 product(a8, a9)
% 0.21/0.44 = { by axiom 10 (knot_09) R->L }
% 0.21/0.44 a10
% 0.21/0.44
% 0.21/0.44 Lemma 23: product(a9, a8) = a4.
% 0.21/0.44 Proof:
% 0.21/0.44 product(a9, a8)
% 0.21/0.44 = { by axiom 11 (knot_11) }
% 0.21/0.44 product(product(a4, a8), a8)
% 0.21/0.44 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.44 a4
% 0.21/0.44
% 0.21/0.44 Lemma 24: a7 = a10.
% 0.21/0.44 Proof:
% 0.21/0.44 a7
% 0.21/0.44 = { by lemma 16 R->L }
% 0.21/0.44 a2
% 0.21/0.44 = { by axiom 8 (knot_04) }
% 0.21/0.45 product(a3, a4)
% 0.21/0.45 = { by lemma 20 }
% 0.21/0.45 product(a3, a8)
% 0.21/0.45 = { by lemma 18 }
% 0.21/0.45 product(a9, a8)
% 0.21/0.45 = { by lemma 23 }
% 0.21/0.45 a4
% 0.21/0.45 = { by lemma 20 }
% 0.21/0.45 a8
% 0.21/0.45 = { by lemma 19 }
% 0.21/0.45 a9
% 0.21/0.45 = { by lemma 22 }
% 0.21/0.45 a10
% 0.21/0.45
% 0.21/0.45 Lemma 25: a10 = a1.
% 0.21/0.45 Proof:
% 0.21/0.45 a10
% 0.21/0.45 = { by axiom 1 (involutory_quandle) R->L }
% 0.21/0.45 product(a10, a10)
% 0.21/0.45 = { by lemma 24 R->L }
% 0.21/0.45 product(a10, a7)
% 0.21/0.45 = { by lemma 21 R->L }
% 0.21/0.45 product(a10, product(a8, a4))
% 0.21/0.45 = { by lemma 23 R->L }
% 0.21/0.45 product(a10, product(a8, product(a9, a8)))
% 0.21/0.45 = { by lemma 14 R->L }
% 0.21/0.45 product(a10, product(product(a8, a9), a8))
% 0.21/0.45 = { by axiom 10 (knot_09) R->L }
% 0.21/0.45 product(a10, product(a10, a8))
% 0.21/0.45 = { by lemma 24 R->L }
% 0.21/0.45 product(a7, product(a10, a8))
% 0.21/0.45 = { by lemma 16 R->L }
% 0.21/0.45 product(a2, product(a10, a8))
% 0.21/0.45 = { by lemma 20 R->L }
% 0.21/0.45 product(a2, product(a10, a4))
% 0.21/0.45 = { by lemma 15 R->L }
% 0.21/0.45 product(a2, product(product(a4, a3), a4))
% 0.21/0.45 = { by lemma 14 }
% 0.21/0.45 product(a2, product(a4, product(a3, a4)))
% 0.21/0.45 = { by axiom 8 (knot_04) R->L }
% 0.21/0.45 product(a2, product(a4, a2))
% 0.21/0.45 = { by lemma 14 R->L }
% 0.21/0.45 product(product(a2, a4), a2)
% 0.21/0.45 = { by lemma 17 }
% 0.21/0.45 product(a3, a2)
% 0.21/0.45 = { by axiom 2 (knot_03) }
% 0.21/0.45 product(product(a1, a2), a2)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.45 a1
% 0.21/0.45
% 0.21/0.45 Lemma 26: a5 = a1.
% 0.21/0.45 Proof:
% 0.21/0.45 a5
% 0.21/0.45 = { by axiom 9 (knot_05) }
% 0.21/0.45 product(a2, a10)
% 0.21/0.45 = { by lemma 16 }
% 0.21/0.45 product(a7, a10)
% 0.21/0.45 = { by lemma 24 }
% 0.21/0.45 product(a10, a10)
% 0.21/0.45 = { by axiom 1 (involutory_quandle) }
% 0.21/0.45 a10
% 0.21/0.45 = { by lemma 25 }
% 0.21/0.45 a1
% 0.21/0.45
% 0.21/0.45 Lemma 27: a6 = a5.
% 0.21/0.45 Proof:
% 0.21/0.45 a6
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.45 product(product(a6, a1), a1)
% 0.21/0.45 = { by axiom 5 (knot_07) R->L }
% 0.21/0.45 product(a7, a1)
% 0.21/0.45 = { by lemma 16 R->L }
% 0.21/0.45 product(a2, a1)
% 0.21/0.45 = { by lemma 25 R->L }
% 0.21/0.45 product(a2, a10)
% 0.21/0.45 = { by axiom 9 (knot_05) R->L }
% 0.21/0.45 a5
% 0.21/0.45
% 0.21/0.45 Goal 1 (goal): tuple(a1, a9, a8, a6, a7, a2, a3, a4, a5) = tuple(a2, a10, a9, a7, a8, a3, a4, a5, a6).
% 0.21/0.45 Proof:
% 0.21/0.45 tuple(a1, a9, a8, a6, a7, a2, a3, a4, a5)
% 0.21/0.45 = { by lemma 16 }
% 0.21/0.45 tuple(a1, a9, a8, a6, a7, a7, a3, a4, a5)
% 0.21/0.45 = { by lemma 18 }
% 0.21/0.45 tuple(a1, a9, a8, a6, a7, a7, a9, a4, a5)
% 0.21/0.45 = { by lemma 20 }
% 0.21/0.45 tuple(a1, a9, a8, a6, a7, a7, a9, a8, a5)
% 0.21/0.45 = { by lemma 19 }
% 0.21/0.45 tuple(a1, a9, a9, a6, a7, a7, a9, a8, a5)
% 0.21/0.45 = { by lemma 19 }
% 0.21/0.45 tuple(a1, a9, a9, a6, a7, a7, a9, a9, a5)
% 0.21/0.45 = { by lemma 22 }
% 0.21/0.45 tuple(a1, a10, a9, a6, a7, a7, a9, a9, a5)
% 0.21/0.45 = { by lemma 22 }
% 0.21/0.45 tuple(a1, a10, a10, a6, a7, a7, a9, a9, a5)
% 0.21/0.45 = { by lemma 22 }
% 0.21/0.45 tuple(a1, a10, a10, a6, a7, a7, a10, a9, a5)
% 0.21/0.45 = { by lemma 22 }
% 0.21/0.45 tuple(a1, a10, a10, a6, a7, a7, a10, a10, a5)
% 0.21/0.45 = { by lemma 24 }
% 0.21/0.45 tuple(a1, a10, a10, a6, a10, a7, a10, a10, a5)
% 0.21/0.45 = { by lemma 24 }
% 0.21/0.45 tuple(a1, a10, a10, a6, a10, a10, a10, a10, a5)
% 0.21/0.45 = { by lemma 25 }
% 0.21/0.45 tuple(a1, a1, a10, a6, a10, a10, a10, a10, a5)
% 0.21/0.45 = { by lemma 25 }
% 0.21/0.45 tuple(a1, a1, a1, a6, a10, a10, a10, a10, a5)
% 0.21/0.45 = { by lemma 25 }
% 0.21/0.45 tuple(a1, a1, a1, a6, a1, a10, a10, a10, a5)
% 0.21/0.45 = { by lemma 25 }
% 0.21/0.45 tuple(a1, a1, a1, a6, a1, a1, a10, a10, a5)
% 0.21/0.45 = { by lemma 25 }
% 0.21/0.45 tuple(a1, a1, a1, a6, a1, a1, a1, a10, a5)
% 0.21/0.45 = { by lemma 25 }
% 0.21/0.45 tuple(a1, a1, a1, a6, a1, a1, a1, a1, a5)
% 0.21/0.45 = { by lemma 27 }
% 0.21/0.45 tuple(a1, a1, a1, a5, a1, a1, a1, a1, a5)
% 0.21/0.45 = { by lemma 26 }
% 0.21/0.45 tuple(a1, a1, a1, a1, a1, a1, a1, a1, a5)
% 0.21/0.45 = { by lemma 26 }
% 0.21/0.45 tuple(a1, a1, a1, a1, a1, a1, a1, a1, a1)
% 0.21/0.45 = { by lemma 26 R->L }
% 0.21/0.45 tuple(a1, a1, a1, a1, a1, a1, a1, a5, a1)
% 0.21/0.45 = { by lemma 26 R->L }
% 0.21/0.45 tuple(a1, a1, a1, a1, a1, a1, a1, a5, a5)
% 0.21/0.45 = { by lemma 27 R->L }
% 0.21/0.45 tuple(a1, a1, a1, a1, a1, a1, a1, a5, a6)
% 0.21/0.45 = { by lemma 25 R->L }
% 0.21/0.45 tuple(a10, a1, a1, a1, a1, a1, a1, a5, a6)
% 0.21/0.45 = { by lemma 25 R->L }
% 0.21/0.45 tuple(a10, a10, a1, a1, a1, a1, a1, a5, a6)
% 0.21/0.45 = { by lemma 25 R->L }
% 0.21/0.45 tuple(a10, a10, a10, a1, a1, a1, a1, a5, a6)
% 0.21/0.45 = { by lemma 25 R->L }
% 0.21/0.45 tuple(a10, a10, a10, a10, a1, a1, a1, a5, a6)
% 0.21/0.45 = { by lemma 25 R->L }
% 0.21/0.45 tuple(a10, a10, a10, a10, a10, a1, a1, a5, a6)
% 0.21/0.45 = { by lemma 25 R->L }
% 0.21/0.45 tuple(a10, a10, a10, a10, a10, a10, a1, a5, a6)
% 0.21/0.45 = { by lemma 25 R->L }
% 0.21/0.45 tuple(a10, a10, a10, a10, a10, a10, a10, a5, a6)
% 0.21/0.45 = { by lemma 24 R->L }
% 0.21/0.45 tuple(a7, a10, a10, a10, a10, a10, a10, a5, a6)
% 0.21/0.45 = { by lemma 24 R->L }
% 0.21/0.45 tuple(a7, a10, a10, a7, a10, a10, a10, a5, a6)
% 0.21/0.45 = { by lemma 22 R->L }
% 0.21/0.45 tuple(a7, a10, a9, a7, a10, a10, a10, a5, a6)
% 0.21/0.45 = { by lemma 22 R->L }
% 0.21/0.45 tuple(a7, a10, a9, a7, a9, a10, a10, a5, a6)
% 0.21/0.45 = { by lemma 22 R->L }
% 0.21/0.45 tuple(a7, a10, a9, a7, a9, a9, a10, a5, a6)
% 0.21/0.45 = { by lemma 22 R->L }
% 0.21/0.45 tuple(a7, a10, a9, a7, a9, a9, a9, a5, a6)
% 0.21/0.45 = { by lemma 19 R->L }
% 0.21/0.45 tuple(a7, a10, a9, a7, a8, a9, a9, a5, a6)
% 0.21/0.45 = { by lemma 19 R->L }
% 0.21/0.45 tuple(a7, a10, a9, a7, a8, a9, a8, a5, a6)
% 0.21/0.45 = { by lemma 20 R->L }
% 0.21/0.45 tuple(a7, a10, a9, a7, a8, a9, a4, a5, a6)
% 0.21/0.45 = { by lemma 18 R->L }
% 0.21/0.45 tuple(a7, a10, a9, a7, a8, a3, a4, a5, a6)
% 0.21/0.45 = { by lemma 16 R->L }
% 0.21/0.45 tuple(a2, a10, a9, a7, a8, a3, a4, a5, a6)
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45
% 0.21/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------