TSTP Solution File: TOP051-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : TOP051-1 : 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 : n004.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 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP051-1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % 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 : n004.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 23:53:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.42 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.42
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 Axiom 1 (involutory_quandle): product(X, X) = X.
% 0.21/0.45 Axiom 2 (knot): product(a1, a6) = a2.
% 0.21/0.45 Axiom 3 (knot_09): product(a8, a6) = a9.
% 0.21/0.45 Axiom 4 (knot_03): product(a2, a7) = a3.
% 0.21/0.45 Axiom 5 (knot_08): product(a7, a3) = a8.
% 0.21/0.45 Axiom 6 (knot_04): product(a3, a1) = a4.
% 0.21/0.45 Axiom 7 (knot_05): product(a4, a10) = a5.
% 0.21/0.45 Axiom 8 (knot_11): product(a10, a5) = a11.
% 0.21/0.45 Axiom 9 (knot_06): product(a5, a9) = a6.
% 0.21/0.45 Axiom 10 (knot_10): product(a9, a4) = a10.
% 0.21/0.45 Axiom 11 (knot_07): product(a6, a2) = a7.
% 0.21/0.45 Axiom 12 (involutory_quandle_01): product(product(X, Y), Y) = X.
% 0.21/0.45 Axiom 13 (involutory_quandle_02): product(product(X, Y), Z) = product(product(X, Z), product(Y, Z)).
% 0.21/0.45
% 0.21/0.45 Lemma 14: product(a2, a6) = a1.
% 0.21/0.45 Proof:
% 0.21/0.45 product(a2, a6)
% 0.21/0.45 = { by axiom 2 (knot) R->L }
% 0.21/0.45 product(product(a1, a6), a6)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.45 a1
% 0.21/0.45
% 0.21/0.45 Lemma 15: product(product(X, Y), X) = product(X, product(Y, X)).
% 0.21/0.45 Proof:
% 0.21/0.45 product(product(X, Y), X)
% 0.21/0.45 = { by axiom 13 (involutory_quandle_02) }
% 0.21/0.45 product(product(X, X), product(Y, X))
% 0.21/0.45 = { by axiom 1 (involutory_quandle) }
% 0.21/0.45 product(X, product(Y, X))
% 0.21/0.45
% 0.21/0.45 Lemma 16: product(a1, a2) = a3.
% 0.21/0.45 Proof:
% 0.21/0.45 product(a1, a2)
% 0.21/0.45 = { by lemma 14 R->L }
% 0.21/0.45 product(product(a2, a6), a2)
% 0.21/0.45 = { by lemma 15 }
% 0.21/0.45 product(a2, product(a6, a2))
% 0.21/0.45 = { by axiom 11 (knot_07) }
% 0.21/0.45 product(a2, a7)
% 0.21/0.45 = { by axiom 4 (knot_03) }
% 0.21/0.45 a3
% 0.21/0.45
% 0.21/0.45 Lemma 17: product(a10, a4) = a9.
% 0.21/0.45 Proof:
% 0.21/0.45 product(a10, a4)
% 0.21/0.45 = { by axiom 10 (knot_10) R->L }
% 0.21/0.45 product(product(a9, a4), a4)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.45 a9
% 0.21/0.45
% 0.21/0.45 Lemma 18: product(a5, a10) = a4.
% 0.21/0.45 Proof:
% 0.21/0.45 product(a5, a10)
% 0.21/0.45 = { by axiom 7 (knot_05) R->L }
% 0.21/0.45 product(product(a4, a10), a10)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.45 a4
% 0.21/0.45
% 0.21/0.45 Lemma 19: product(a6, a9) = a5.
% 0.21/0.45 Proof:
% 0.21/0.45 product(a6, a9)
% 0.21/0.45 = { by axiom 9 (knot_06) R->L }
% 0.21/0.45 product(product(a5, a9), a9)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.45 a5
% 0.21/0.45
% 0.21/0.45 Lemma 20: product(product(a7, a8), a6) = a10.
% 0.21/0.45 Proof:
% 0.21/0.45 product(product(a7, a8), a6)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.45 product(product(product(product(a7, a3), a3), a8), a6)
% 0.21/0.45 = { by axiom 5 (knot_08) }
% 0.21/0.45 product(product(product(a8, a3), a8), a6)
% 0.21/0.45 = { by lemma 15 }
% 0.21/0.45 product(product(a8, product(a3, a8)), a6)
% 0.21/0.45 = { by axiom 5 (knot_08) R->L }
% 0.21/0.45 product(product(a8, product(a3, product(a7, a3))), a6)
% 0.21/0.45 = { by lemma 15 R->L }
% 0.21/0.45 product(product(a8, product(product(a3, a7), a3)), a6)
% 0.21/0.45 = { by axiom 4 (knot_03) R->L }
% 0.21/0.45 product(product(a8, product(product(product(a2, a7), a7), a3)), a6)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.45 product(product(a8, product(a2, a3)), a6)
% 0.21/0.45 = { by axiom 13 (involutory_quandle_02) }
% 0.21/0.45 product(product(a8, a6), product(product(a2, a3), a6))
% 0.21/0.45 = { by axiom 3 (knot_09) }
% 0.21/0.45 product(a9, product(product(a2, a3), a6))
% 0.21/0.45 = { by lemma 16 R->L }
% 0.21/0.45 product(a9, product(product(a2, product(a1, a2)), a6))
% 0.21/0.45 = { by lemma 15 R->L }
% 0.21/0.45 product(a9, product(product(product(a2, a1), a2), a6))
% 0.21/0.45 = { by lemma 14 R->L }
% 0.21/0.45 product(a9, product(product(product(a2, product(a2, a6)), a2), a6))
% 0.21/0.45 = { by axiom 2 (knot) R->L }
% 0.21/0.45 product(a9, product(product(product(product(a1, a6), product(a2, a6)), a2), a6))
% 0.21/0.45 = { by axiom 13 (involutory_quandle_02) R->L }
% 0.21/0.45 product(a9, product(product(product(product(a1, a2), a6), a2), a6))
% 0.21/0.45 = { by lemma 16 }
% 0.21/0.45 product(a9, product(product(product(a3, a6), a2), a6))
% 0.21/0.45 = { by axiom 2 (knot) R->L }
% 0.21/0.45 product(a9, product(product(product(a3, a6), product(a1, a6)), a6))
% 0.21/0.45 = { by axiom 13 (involutory_quandle_02) R->L }
% 0.21/0.45 product(a9, product(product(product(a3, a1), a6), a6))
% 0.21/0.45 = { by axiom 6 (knot_04) }
% 0.21/0.45 product(a9, product(product(a4, a6), a6))
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.45 product(a9, a4)
% 0.21/0.45 = { by axiom 10 (knot_10) }
% 0.21/0.45 a10
% 0.21/0.45
% 0.21/0.45 Lemma 21: a5 = a11.
% 0.21/0.45 Proof:
% 0.21/0.45 a5
% 0.21/0.45 = { by lemma 19 R->L }
% 0.21/0.45 product(a6, a9)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.45 product(product(product(a6, product(a7, a6)), product(a7, a6)), a9)
% 0.21/0.45 = { by lemma 15 R->L }
% 0.21/0.45 product(product(product(product(a6, a7), a6), product(a7, a6)), a9)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.45 product(product(product(product(product(product(a6, a2), a2), a7), a6), product(a7, a6)), a9)
% 0.21/0.45 = { by axiom 11 (knot_07) }
% 0.21/0.45 product(product(product(product(product(a7, a2), a7), a6), product(a7, a6)), a9)
% 0.21/0.45 = { by lemma 15 }
% 0.21/0.45 product(product(product(product(a7, product(a2, a7)), a6), product(a7, a6)), a9)
% 0.21/0.45 = { by axiom 4 (knot_03) }
% 0.21/0.45 product(product(product(product(a7, a3), a6), product(a7, a6)), a9)
% 0.21/0.45 = { by axiom 5 (knot_08) }
% 0.21/0.45 product(product(product(a8, a6), product(a7, a6)), a9)
% 0.21/0.45 = { by axiom 3 (knot_09) }
% 0.21/0.45 product(product(a9, product(a7, a6)), a9)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.45 product(product(a9, product(product(product(a7, a8), a8), a6)), a9)
% 0.21/0.45 = { by axiom 13 (involutory_quandle_02) }
% 0.21/0.45 product(product(a9, product(product(product(a7, a8), a6), product(a8, a6))), a9)
% 0.21/0.45 = { by axiom 3 (knot_09) }
% 0.21/0.45 product(product(a9, product(product(product(a7, a8), a6), a9)), a9)
% 0.21/0.45 = { by lemma 20 }
% 0.21/0.45 product(product(a9, product(a10, a9)), a9)
% 0.21/0.45 = { by lemma 15 R->L }
% 0.21/0.45 product(product(product(a9, a10), a9), a9)
% 0.21/0.45 = { by lemma 17 R->L }
% 0.21/0.45 product(product(product(product(a10, a4), a10), a9), a9)
% 0.21/0.45 = { by lemma 15 }
% 0.21/0.45 product(product(product(a10, product(a4, a10)), a9), a9)
% 0.21/0.45 = { by axiom 7 (knot_05) }
% 0.21/0.45 product(product(product(a10, a5), a9), a9)
% 0.21/0.45 = { by axiom 8 (knot_11) }
% 0.21/0.45 product(product(a11, a9), a9)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.45 a11
% 0.21/0.45
% 0.21/0.45 Lemma 22: a4 = a11.
% 0.21/0.45 Proof:
% 0.21/0.45 a4
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.45 product(product(a4, a11), a11)
% 0.21/0.45 = { by lemma 21 R->L }
% 0.21/0.45 product(product(a4, a5), a11)
% 0.21/0.45 = { by lemma 18 R->L }
% 0.21/0.45 product(product(product(a5, a10), a5), a11)
% 0.21/0.45 = { by lemma 15 }
% 0.21/0.45 product(product(a5, product(a10, a5)), a11)
% 0.21/0.45 = { by axiom 8 (knot_11) }
% 0.21/0.45 product(product(a5, a11), a11)
% 0.21/0.45 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.45 a5
% 0.21/0.45 = { by lemma 21 }
% 0.21/0.45 a11
% 0.21/0.45
% 0.21/0.45 Lemma 23: a9 = a11.
% 0.21/0.45 Proof:
% 0.21/0.45 a9
% 0.21/0.45 = { by lemma 17 R->L }
% 0.21/0.46 product(a10, a4)
% 0.21/0.46 = { by lemma 18 R->L }
% 0.21/0.46 product(a10, product(a5, a10))
% 0.21/0.46 = { by lemma 15 R->L }
% 0.21/0.46 product(product(a10, a5), a10)
% 0.21/0.46 = { by axiom 8 (knot_11) }
% 0.21/0.46 product(a11, a10)
% 0.21/0.46 = { by lemma 21 R->L }
% 0.21/0.46 product(a5, a10)
% 0.21/0.46 = { by lemma 18 }
% 0.21/0.46 a4
% 0.21/0.46 = { by lemma 22 }
% 0.21/0.46 a11
% 0.21/0.46
% 0.21/0.46 Lemma 24: a6 = a11.
% 0.21/0.46 Proof:
% 0.21/0.46 a6
% 0.21/0.46 = { by axiom 9 (knot_06) R->L }
% 0.21/0.46 product(a5, a9)
% 0.21/0.46 = { by lemma 23 }
% 0.21/0.46 product(a5, a11)
% 0.21/0.46 = { by lemma 21 }
% 0.21/0.46 product(a11, a11)
% 0.21/0.46 = { by axiom 1 (involutory_quandle) }
% 0.21/0.46 a11
% 0.21/0.46
% 0.21/0.46 Lemma 25: product(a2, a11) = a1.
% 0.21/0.46 Proof:
% 0.21/0.46 product(a2, a11)
% 0.21/0.46 = { by lemma 24 R->L }
% 0.21/0.46 product(a2, a6)
% 0.21/0.46 = { by lemma 14 }
% 0.21/0.46 a1
% 0.21/0.46
% 0.21/0.46 Lemma 26: a8 = a11.
% 0.21/0.46 Proof:
% 0.21/0.46 a8
% 0.21/0.46 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.46 product(product(a8, a11), a11)
% 0.21/0.46 = { by lemma 21 R->L }
% 0.21/0.46 product(product(a8, a11), a5)
% 0.21/0.46 = { by lemma 23 R->L }
% 0.21/0.46 product(product(a8, a9), a5)
% 0.21/0.46 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.46 product(product(product(product(a8, a6), a6), a9), a5)
% 0.21/0.46 = { by axiom 3 (knot_09) }
% 0.21/0.46 product(product(product(a9, a6), a9), a5)
% 0.21/0.46 = { by lemma 15 }
% 0.21/0.46 product(product(a9, product(a6, a9)), a5)
% 0.21/0.46 = { by lemma 19 }
% 0.21/0.46 product(product(a9, a5), a5)
% 0.21/0.46 = { by axiom 12 (involutory_quandle_01) }
% 0.21/0.46 a9
% 0.21/0.46 = { by lemma 23 }
% 0.21/0.46 a11
% 0.21/0.46
% 0.21/0.46 Lemma 27: a10 = a11.
% 0.21/0.46 Proof:
% 0.21/0.46 a10
% 0.21/0.46 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.46 product(product(a10, a5), a5)
% 0.21/0.46 = { by axiom 8 (knot_11) }
% 0.21/0.46 product(a11, a5)
% 0.21/0.46 = { by lemma 21 }
% 0.21/0.46 product(a11, a11)
% 0.21/0.46 = { by axiom 1 (involutory_quandle) }
% 0.21/0.46 a11
% 0.21/0.46
% 0.21/0.46 Lemma 28: a7 = a11.
% 0.21/0.46 Proof:
% 0.21/0.46 a7
% 0.21/0.46 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.46 product(product(a7, a11), a11)
% 0.21/0.46 = { by lemma 24 R->L }
% 0.21/0.46 product(product(a7, a11), a6)
% 0.21/0.46 = { by lemma 26 R->L }
% 0.21/0.46 product(product(a7, a8), a6)
% 0.21/0.46 = { by lemma 20 }
% 0.21/0.46 a10
% 0.21/0.46 = { by lemma 27 }
% 0.21/0.46 a11
% 0.21/0.46
% 0.21/0.46 Lemma 29: a3 = a1.
% 0.21/0.46 Proof:
% 0.21/0.46 a3
% 0.21/0.46 = { by lemma 16 R->L }
% 0.21/0.46 product(a1, a2)
% 0.21/0.46 = { by lemma 25 R->L }
% 0.21/0.46 product(product(a2, a11), a2)
% 0.21/0.46 = { by lemma 15 }
% 0.21/0.46 product(a2, product(a11, a2))
% 0.21/0.46 = { by lemma 24 R->L }
% 0.21/0.46 product(a2, product(a6, a2))
% 0.21/0.46 = { by axiom 11 (knot_07) }
% 0.21/0.46 product(a2, a7)
% 0.21/0.46 = { by lemma 28 }
% 0.21/0.46 product(a2, a11)
% 0.21/0.46 = { by lemma 25 }
% 0.21/0.46 a1
% 0.21/0.46
% 0.21/0.46 Lemma 30: a1 = a11.
% 0.21/0.46 Proof:
% 0.21/0.46 a1
% 0.21/0.46 = { by lemma 29 R->L }
% 0.21/0.46 a3
% 0.21/0.46 = { by axiom 12 (involutory_quandle_01) R->L }
% 0.21/0.46 product(product(a3, a1), a1)
% 0.21/0.46 = { by axiom 6 (knot_04) }
% 0.21/0.46 product(a4, a1)
% 0.21/0.46 = { by lemma 22 }
% 0.21/0.46 product(a11, a1)
% 0.21/0.46 = { by lemma 28 R->L }
% 0.21/0.46 product(a7, a1)
% 0.21/0.46 = { by lemma 29 R->L }
% 0.21/0.46 product(a7, a3)
% 0.21/0.46 = { by axiom 5 (knot_08) }
% 0.21/0.46 a8
% 0.21/0.46 = { by lemma 26 }
% 0.21/0.46 a11
% 0.21/0.46
% 0.21/0.46 Lemma 31: a2 = a11.
% 0.21/0.46 Proof:
% 0.21/0.46 a2
% 0.21/0.46 = { by axiom 2 (knot) R->L }
% 0.21/0.46 product(a1, a6)
% 0.21/0.46 = { by lemma 30 }
% 0.21/0.46 product(a11, a6)
% 0.21/0.46 = { by lemma 24 }
% 0.21/0.46 product(a11, a11)
% 0.21/0.46 = { by axiom 1 (involutory_quandle) }
% 0.21/0.46 a11
% 0.21/0.46
% 0.21/0.46 Goal 1 (goal): tuple(a1, a6, a5, a2, a7, a3, a4, a9, a10, a8) = tuple(a2, a7, a6, a3, a8, a4, a5, a10, a11, a9).
% 0.21/0.46 Proof:
% 0.21/0.46 tuple(a1, a6, a5, a2, a7, a3, a4, a9, a10, a8)
% 0.21/0.46 = { by lemma 21 }
% 0.21/0.46 tuple(a1, a6, a11, a2, a7, a3, a4, a9, a10, a8)
% 0.21/0.46 = { by lemma 27 }
% 0.21/0.46 tuple(a1, a6, a11, a2, a7, a3, a4, a9, a11, a8)
% 0.21/0.46 = { by lemma 22 }
% 0.21/0.46 tuple(a1, a6, a11, a2, a7, a3, a11, a9, a11, a8)
% 0.21/0.46 = { by lemma 23 }
% 0.21/0.46 tuple(a1, a6, a11, a2, a7, a3, a11, a11, a11, a8)
% 0.21/0.46 = { by lemma 24 }
% 0.21/0.46 tuple(a1, a11, a11, a2, a7, a3, a11, a11, a11, a8)
% 0.21/0.46 = { by lemma 26 }
% 0.21/0.46 tuple(a1, a11, a11, a2, a7, a3, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 28 }
% 0.21/0.46 tuple(a1, a11, a11, a2, a11, a3, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 29 }
% 0.21/0.46 tuple(a1, a11, a11, a2, a11, a1, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 30 }
% 0.21/0.46 tuple(a11, a11, a11, a2, a11, a1, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 30 }
% 0.21/0.46 tuple(a11, a11, a11, a2, a11, a11, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 31 }
% 0.21/0.46 tuple(a11, a11, a11, a11, a11, a11, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 31 R->L }
% 0.21/0.46 tuple(a2, a11, a11, a11, a11, a11, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 30 R->L }
% 0.21/0.46 tuple(a2, a11, a11, a1, a11, a11, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 29 R->L }
% 0.21/0.46 tuple(a2, a11, a11, a3, a11, a11, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 28 R->L }
% 0.21/0.46 tuple(a2, a7, a11, a3, a11, a11, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 26 R->L }
% 0.21/0.46 tuple(a2, a7, a11, a3, a8, a11, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 24 R->L }
% 0.21/0.46 tuple(a2, a7, a6, a3, a8, a11, a11, a11, a11, a11)
% 0.21/0.46 = { by lemma 23 R->L }
% 0.21/0.46 tuple(a2, a7, a6, a3, a8, a11, a11, a11, a11, a9)
% 0.21/0.46 = { by lemma 22 R->L }
% 0.21/0.46 tuple(a2, a7, a6, a3, a8, a4, a11, a11, a11, a9)
% 0.21/0.46 = { by lemma 27 R->L }
% 0.21/0.46 tuple(a2, a7, a6, a3, a8, a4, a11, a10, a11, a9)
% 0.21/0.46 = { by lemma 21 R->L }
% 0.21/0.46 tuple(a2, a7, a6, a3, a8, a4, a5, a10, a11, a9)
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46
% 0.21/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------