TSTP Solution File: SWV216+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV216+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 23:03:02 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV216+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 04:55:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.61 Command-line arguments: --no-flatten-goal
% 0.20/0.61
% 0.20/0.61 % SZS status Theorem
% 0.20/0.61
% 0.20/0.62 % SZS output start Proof
% 0.20/0.62 Take the following subset of the input axioms:
% 0.20/0.66 fof(quaternion_ds1_symm_0201, conjecture, ![A, B]: ((leq(n0, A) & (leq(n0, B) & (leq(A, n5) & leq(B, n5)))) => ((~(n0=A & n3=B) & (~(n0=A & n4=B) & (~(n0=A & n5=B) & (~(n0=B & n5=A) & (~(n1=A & n3=B) & (~(n1=A & n4=B) & (~(n1=A & n5=B) & (~(n1=B & n5=A) & (~(n2=A & n3=B) & (~(n2=A & n4=B) & (~(n2=A & n5=B) & (~(n2=B & n3=A) & (~(n2=B & n4=A) & (~(n2=B & n5=A) & (~(n3=A & n3=B) & (~(n3=A & n4=B) & (~(n3=A & n5=B) & (~(n3=B & n4=A) & (~(n3=B & n5=A) & (~(n4=A & n4=B) & (~(n4=A & n5=B) & (~(n4=B & n5=A) & (~(n5=A & n5=B) & (n1=B & (n2=A & (n2=B & n4=A)))))))))))))))))))))))))) => n0=times(divide(n1, n400), a_select2(sigma, n2))))).
% 0.20/0.66 fof(succ_plus_1_r, axiom, ![X]: plus(X, n1)=succ(X)).
% 0.20/0.66 fof(succ_plus_2_r, axiom, ![X2]: plus(X2, n2)=succ(succ(X2))).
% 0.20/0.66 fof(successor_1, axiom, succ(n0)=n1).
% 0.20/0.66 fof(successor_3, axiom, succ(succ(succ(n0)))=n3).
% 0.20/0.66 fof(successor_5, axiom, succ(succ(succ(succ(succ(n0)))))=n5).
% 0.20/0.66
% 0.20/0.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.66 fresh(y, y, x1...xn) = u
% 0.20/0.66 C => fresh(s, t, x1...xn) = v
% 0.20/0.66 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.66 variables of u and v.
% 0.20/0.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.66 input problem has no model of domain size 1).
% 0.20/0.66
% 0.20/0.66 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.66
% 0.20/0.66 Axiom 1 (quaternion_ds1_symm_0201): n1 = b.
% 0.20/0.66 Axiom 2 (quaternion_ds1_symm_0201_1): n2 = b.
% 0.20/0.66 Axiom 3 (quaternion_ds1_symm_0201_2): n2 = a.
% 0.20/0.66 Axiom 4 (quaternion_ds1_symm_0201_3): n4 = a.
% 0.20/0.66 Axiom 5 (successor_1): succ(n0) = n1.
% 0.20/0.66 Axiom 6 (succ_plus_1_r): plus(X, n1) = succ(X).
% 0.20/0.66 Axiom 7 (succ_plus_2_r): plus(X, n2) = succ(succ(X)).
% 0.20/0.66 Axiom 8 (successor_3): succ(succ(succ(n0))) = n3.
% 0.20/0.66 Axiom 9 (successor_5): succ(succ(succ(succ(succ(n0))))) = n5.
% 0.20/0.66
% 0.20/0.66 Lemma 10: n2 = n1.
% 0.20/0.66 Proof:
% 0.20/0.66 n2
% 0.20/0.66 = { by axiom 2 (quaternion_ds1_symm_0201_1) }
% 0.20/0.66 b
% 0.20/0.66 = { by axiom 1 (quaternion_ds1_symm_0201) R->L }
% 0.20/0.66 n1
% 0.20/0.66
% 0.20/0.66 Lemma 11: succ(succ(X)) = succ(X).
% 0.20/0.66 Proof:
% 0.20/0.66 succ(succ(X))
% 0.20/0.66 = { by axiom 7 (succ_plus_2_r) R->L }
% 0.20/0.66 plus(X, n2)
% 0.20/0.66 = { by lemma 10 }
% 0.20/0.66 plus(X, n1)
% 0.20/0.66 = { by axiom 6 (succ_plus_1_r) }
% 0.20/0.66 succ(X)
% 0.20/0.66
% 0.20/0.66 Lemma 12: n3 = n1.
% 0.20/0.66 Proof:
% 0.20/0.66 n3
% 0.20/0.66 = { by axiom 8 (successor_3) R->L }
% 0.20/0.66 succ(succ(succ(n0)))
% 0.20/0.66 = { by lemma 11 }
% 0.20/0.66 succ(succ(n0))
% 0.20/0.66 = { by lemma 11 }
% 0.20/0.66 succ(n0)
% 0.20/0.66 = { by axiom 5 (successor_1) }
% 0.20/0.66 n1
% 0.20/0.66
% 0.20/0.66 Lemma 13: a = n1.
% 0.20/0.66 Proof:
% 0.20/0.66 a
% 0.20/0.66 = { by axiom 3 (quaternion_ds1_symm_0201_2) R->L }
% 0.20/0.66 n2
% 0.20/0.66 = { by lemma 10 }
% 0.20/0.66 n1
% 0.20/0.66
% 0.20/0.66 Lemma 14: n4 = n1.
% 0.20/0.66 Proof:
% 0.20/0.66 n4
% 0.20/0.66 = { by axiom 4 (quaternion_ds1_symm_0201_3) }
% 0.20/0.66 a
% 0.20/0.66 = { by lemma 13 }
% 0.20/0.66 n1
% 0.20/0.66
% 0.20/0.66 Lemma 15: n5 = n1.
% 0.20/0.66 Proof:
% 0.20/0.66 n5
% 0.20/0.66 = { by axiom 9 (successor_5) R->L }
% 0.20/0.66 succ(succ(succ(succ(succ(n0)))))
% 0.20/0.66 = { by lemma 11 }
% 0.20/0.66 succ(succ(succ(succ(n0))))
% 0.20/0.66 = { by lemma 11 }
% 0.20/0.66 succ(succ(succ(n0)))
% 0.20/0.66 = { by lemma 11 }
% 0.20/0.66 succ(succ(n0))
% 0.20/0.66 = { by lemma 11 }
% 0.20/0.66 succ(n0)
% 0.20/0.66 = { by axiom 5 (successor_1) }
% 0.20/0.66 n1
% 0.20/0.66
% 0.20/0.66 Goal 1 (quaternion_ds1_symm_0201_31): tuple2(n5, n5) = tuple2(b, a).
% 0.20/0.66 Proof:
% 0.20/0.66 tuple2(n5, n5)
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 tuple2(n1, n5)
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 tuple2(n1, n1)
% 0.20/0.66 = { by lemma 13 R->L }
% 0.20/0.66 tuple2(n1, a)
% 0.20/0.66 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.66 tuple2(b, a)
% 0.20/0.66
% 0.20/0.66 Goal 2 (quaternion_ds1_symm_0201_30): tuple2(n4, n5) = tuple2(a, b).
% 0.20/0.66 Proof:
% 0.20/0.66 tuple2(n4, n5)
% 0.20/0.66 = { by lemma 14 }
% 0.20/0.66 tuple2(n1, n5)
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 tuple2(n1, n1)
% 0.20/0.66 = { by lemma 13 R->L }
% 0.20/0.66 tuple2(a, n1)
% 0.20/0.66 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.66 tuple2(a, b)
% 0.20/0.66
% 0.20/0.66 Goal 3 (quaternion_ds1_symm_0201_29): tuple2(n4, n5) = tuple2(b, a).
% 0.20/0.66 Proof:
% 0.20/0.66 tuple2(n4, n5)
% 0.20/0.66 = { by lemma 14 }
% 0.20/0.66 tuple2(n1, n5)
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 tuple2(n1, n1)
% 0.20/0.66 = { by lemma 13 R->L }
% 0.20/0.66 tuple2(n1, a)
% 0.20/0.66 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.66 tuple2(b, a)
% 0.20/0.66
% 0.20/0.66 Goal 4 (quaternion_ds1_symm_0201_28): tuple2(n4, n4) = tuple2(b, a).
% 0.20/0.66 Proof:
% 0.20/0.66 tuple2(n4, n4)
% 0.20/0.66 = { by lemma 14 }
% 0.20/0.66 tuple2(n1, n4)
% 0.20/0.66 = { by lemma 14 }
% 0.20/0.66 tuple2(n1, n1)
% 0.20/0.66 = { by lemma 13 R->L }
% 0.20/0.66 tuple2(n1, a)
% 0.20/0.66 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.66 tuple2(b, a)
% 0.20/0.66
% 0.20/0.66 Goal 5 (quaternion_ds1_symm_0201_27): tuple2(n3, n5) = tuple2(a, b).
% 0.20/0.66 Proof:
% 0.20/0.66 tuple2(n3, n5)
% 0.20/0.66 = { by lemma 12 }
% 0.20/0.66 tuple2(n1, n5)
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 tuple2(n1, n1)
% 0.20/0.66 = { by lemma 13 R->L }
% 0.20/0.66 tuple2(a, n1)
% 0.20/0.66 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.66 tuple2(a, b)
% 0.20/0.66
% 0.20/0.66 Goal 6 (quaternion_ds1_symm_0201_26): tuple2(n3, n4) = tuple2(a, b).
% 0.20/0.66 Proof:
% 0.20/0.66 tuple2(n3, n4)
% 0.20/0.66 = { by lemma 14 }
% 0.20/0.66 tuple2(n3, n1)
% 0.20/0.66 = { by lemma 12 }
% 0.20/0.66 tuple2(n1, n1)
% 0.20/0.66 = { by lemma 13 R->L }
% 0.20/0.66 tuple2(a, n1)
% 0.20/0.66 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.66 tuple2(a, b)
% 0.20/0.66
% 0.20/0.66 Goal 7 (quaternion_ds1_symm_0201_25): tuple2(n3, n5) = tuple2(b, a).
% 0.20/0.66 Proof:
% 0.20/0.66 tuple2(n3, n5)
% 0.20/0.66 = { by lemma 12 }
% 0.20/0.66 tuple2(n1, n5)
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 tuple2(n1, n1)
% 0.20/0.66 = { by lemma 13 R->L }
% 0.20/0.66 tuple2(n1, a)
% 0.20/0.66 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.66 tuple2(b, a)
% 0.20/0.66
% 0.20/0.67 Goal 8 (quaternion_ds1_symm_0201_24): tuple2(n3, n4) = tuple2(b, a).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n3, n4)
% 0.20/0.67 = { by lemma 14 }
% 0.20/0.67 tuple2(n3, n1)
% 0.20/0.67 = { by lemma 12 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(n1, a)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(b, a)
% 0.20/0.67
% 0.20/0.67 Goal 9 (quaternion_ds1_symm_0201_23): tuple2(n3, n3) = tuple2(b, a).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n3, n3)
% 0.20/0.67 = { by lemma 12 }
% 0.20/0.67 tuple2(n1, n3)
% 0.20/0.67 = { by lemma 12 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(n1, a)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(b, a)
% 0.20/0.67
% 0.20/0.67 Goal 10 (quaternion_ds1_symm_0201_22): tuple2(n2, n5) = tuple2(a, b).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n2, n5)
% 0.20/0.67 = { by lemma 10 }
% 0.20/0.67 tuple2(n1, n5)
% 0.20/0.67 = { by lemma 15 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(a, n1)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(a, b)
% 0.20/0.67
% 0.20/0.67 Goal 11 (quaternion_ds1_symm_0201_21): tuple2(n2, n4) = tuple2(a, b).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n2, n4)
% 0.20/0.67 = { by lemma 10 }
% 0.20/0.67 tuple2(n1, n4)
% 0.20/0.67 = { by lemma 14 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(a, n1)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(a, b)
% 0.20/0.67
% 0.20/0.67 Goal 12 (quaternion_ds1_symm_0201_20): tuple2(n2, n3) = tuple2(a, b).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n2, n3)
% 0.20/0.67 = { by lemma 10 }
% 0.20/0.67 tuple2(n1, n3)
% 0.20/0.67 = { by lemma 12 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(a, n1)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(a, b)
% 0.20/0.67
% 0.20/0.67 Goal 13 (quaternion_ds1_symm_0201_19): tuple2(n2, n5) = tuple2(b, a).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n2, n5)
% 0.20/0.67 = { by lemma 10 }
% 0.20/0.67 tuple2(n1, n5)
% 0.20/0.67 = { by lemma 15 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(n1, a)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(b, a)
% 0.20/0.67
% 0.20/0.67 Goal 14 (quaternion_ds1_symm_0201_18): tuple2(n2, n4) = tuple2(b, a).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n2, n4)
% 0.20/0.67 = { by lemma 10 }
% 0.20/0.67 tuple2(n1, n4)
% 0.20/0.67 = { by lemma 14 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(n1, a)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(b, a)
% 0.20/0.67
% 0.20/0.67 Goal 15 (quaternion_ds1_symm_0201_17): tuple2(n2, n3) = tuple2(b, a).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n2, n3)
% 0.20/0.67 = { by lemma 10 }
% 0.20/0.67 tuple2(n1, n3)
% 0.20/0.67 = { by lemma 12 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(n1, a)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(b, a)
% 0.20/0.67
% 0.20/0.67 Goal 16 (quaternion_ds1_symm_0201_16): tuple2(n1, n5) = tuple2(a, b).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n1, n5)
% 0.20/0.67 = { by lemma 15 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(a, n1)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(a, b)
% 0.20/0.67
% 0.20/0.67 Goal 17 (quaternion_ds1_symm_0201_15): tuple2(n1, n4) = tuple2(a, b).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n1, n4)
% 0.20/0.67 = { by lemma 14 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(a, n1)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(a, b)
% 0.20/0.67
% 0.20/0.67 Goal 18 (quaternion_ds1_symm_0201_14): tuple2(n1, n3) = tuple2(a, b).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n1, n3)
% 0.20/0.67 = { by lemma 12 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(a, n1)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(a, b)
% 0.20/0.67
% 0.20/0.67 Goal 19 (quaternion_ds1_symm_0201_13): tuple2(n1, n5) = tuple2(b, a).
% 0.20/0.67 Proof:
% 0.20/0.67 tuple2(n1, n5)
% 0.20/0.67 = { by lemma 15 }
% 0.20/0.67 tuple2(n1, n1)
% 0.20/0.67 = { by lemma 13 R->L }
% 0.20/0.67 tuple2(n1, a)
% 0.20/0.67 = { by axiom 1 (quaternion_ds1_symm_0201) }
% 0.20/0.67 tuple2(b, a)
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67
% 0.20/0.67 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------