TSTP Solution File: SWV226+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV226+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 : 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 : Thu Aug 31 23:03:04 EDT 2023
% Result : Theorem 1.64s 0.62s
% Output : Proof 2.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV226+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.04/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 08:12:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.64/0.62 Command-line arguments: --no-flatten-goal
% 1.64/0.62
% 1.64/0.62 % SZS status Theorem
% 1.64/0.62
% 2.17/0.64 % SZS output start Proof
% 2.17/0.64 Take the following subset of the input axioms:
% 2.48/0.72 fof(quaternion_ds1_symm_0601, conjecture, (![B, A2]: ((leq(n0, A2) & (leq(n0, B) & (leq(A2, n5) & leq(B, n5)))) => a_select3(q_ds1_filter, A2, B)=a_select3(q_ds1_filter, B, A2)) & ![C, D]: ((leq(n0, C) & (leq(n0, D) & (leq(C, n2) & leq(D, n2)))) => a_select3(r_ds1_filter, C, D)=a_select3(r_ds1_filter, D, C))) => ![E, F]: ((leq(n0, E) & (leq(n0, F) & (leq(E, n5) & leq(F, n5)))) => ((~(n0=E & n3=F) & (~(n0=E & n4=F) & (~(n0=E & n5=F) & (~(n0=F & n2=E) & (~(n0=F & n3=E) & (~(n0=F & n4=E) & (~(n0=F & n5=E) & (~(n1=E & n2=F) & (~(n1=E & n3=F) & (~(n1=E & n4=F) & (~(n1=E & n5=F) & (~(n1=F & n2=E) & (~(n1=F & n3=E) & (~(n1=F & n4=E) & (~(n1=F & n5=E) & (~(n2=E & n2=F) & (~(n2=E & n3=F) & (~(n2=E & n4=F) & (~(n2=E & n5=F) & (~(n2=F & n3=E) & (~(n2=F & n4=E) & (~(n2=F & n5=E) & (~(n3=E & n3=F) & (~(n3=E & n4=F) & (~(n3=E & n5=F) & (~(n3=F & n4=E) & (~(n3=F & n5=E) & (~(n4=E & n4=F) & (~(n4=E & n5=F) & (~(n4=F & n5=E) & (~(n5=E & n5=F) & (n1=E & (n1=F & (n2=E & n2=F)))))))))))))))))))))))))))))))))) => a_select2(xinit_noise, n1)=a_select2(xinit_noise, n2)))).
% 2.48/0.72 fof(succ_plus_1_r, axiom, ![X]: plus(X, n1)=succ(X)).
% 2.48/0.72 fof(succ_plus_2_r, axiom, ![X2]: plus(X2, n2)=succ(succ(X2))).
% 2.48/0.72 fof(successor_1, axiom, succ(n0)=n1).
% 2.48/0.72 fof(successor_3, axiom, succ(succ(succ(n0)))=n3).
% 2.48/0.72 fof(successor_4, axiom, succ(succ(succ(succ(n0))))=n4).
% 2.48/0.72 fof(successor_5, axiom, succ(succ(succ(succ(succ(n0)))))=n5).
% 2.48/0.72
% 2.48/0.72 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.48/0.72 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.48/0.72 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.48/0.72 fresh(y, y, x1...xn) = u
% 2.48/0.72 C => fresh(s, t, x1...xn) = v
% 2.48/0.72 where fresh is a fresh function symbol and x1..xn are the free
% 2.48/0.72 variables of u and v.
% 2.48/0.72 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.48/0.72 input problem has no model of domain size 1).
% 2.48/0.72
% 2.48/0.72 The encoding turns the above axioms into the following unit equations and goals:
% 2.48/0.72
% 2.48/0.72 Axiom 1 (quaternion_ds1_symm_0601): n1 = f.
% 2.48/0.72 Axiom 2 (quaternion_ds1_symm_0601_2): n2 = f.
% 2.48/0.72 Axiom 3 (quaternion_ds1_symm_0601_1): n1 = e.
% 2.48/0.72 Axiom 4 (successor_1): succ(n0) = n1.
% 2.48/0.72 Axiom 5 (succ_plus_1_r): plus(X, n1) = succ(X).
% 2.48/0.72 Axiom 6 (succ_plus_2_r): plus(X, n2) = succ(succ(X)).
% 2.48/0.72 Axiom 7 (successor_3): succ(succ(succ(n0))) = n3.
% 2.48/0.72 Axiom 8 (successor_4): succ(succ(succ(succ(n0)))) = n4.
% 2.48/0.72 Axiom 9 (successor_5): succ(succ(succ(succ(succ(n0))))) = n5.
% 2.48/0.72
% 2.48/0.72 Lemma 10: n2 = n1.
% 2.48/0.72 Proof:
% 2.48/0.72 n2
% 2.48/0.72 = { by axiom 2 (quaternion_ds1_symm_0601_2) }
% 2.48/0.72 f
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) R->L }
% 2.48/0.72 n1
% 2.48/0.72
% 2.48/0.72 Lemma 11: succ(succ(X)) = succ(X).
% 2.48/0.72 Proof:
% 2.48/0.72 succ(succ(X))
% 2.48/0.72 = { by axiom 6 (succ_plus_2_r) R->L }
% 2.48/0.72 plus(X, n2)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 plus(X, n1)
% 2.48/0.72 = { by axiom 5 (succ_plus_1_r) }
% 2.48/0.72 succ(X)
% 2.48/0.72
% 2.48/0.72 Lemma 12: n5 = n1.
% 2.48/0.72 Proof:
% 2.48/0.72 n5
% 2.48/0.72 = { by axiom 9 (successor_5) R->L }
% 2.48/0.72 succ(succ(succ(succ(succ(n0)))))
% 2.48/0.72 = { by lemma 11 }
% 2.48/0.72 succ(succ(succ(succ(n0))))
% 2.48/0.72 = { by lemma 11 }
% 2.48/0.72 succ(succ(succ(n0)))
% 2.48/0.72 = { by lemma 11 }
% 2.48/0.72 succ(succ(n0))
% 2.48/0.72 = { by lemma 11 }
% 2.48/0.72 succ(n0)
% 2.48/0.72 = { by axiom 4 (successor_1) }
% 2.48/0.72 n1
% 2.48/0.72
% 2.48/0.72 Lemma 13: n3 = n1.
% 2.48/0.72 Proof:
% 2.48/0.72 n3
% 2.48/0.72 = { by axiom 7 (successor_3) R->L }
% 2.48/0.72 succ(succ(succ(n0)))
% 2.48/0.72 = { by lemma 11 }
% 2.48/0.72 succ(succ(n0))
% 2.48/0.72 = { by lemma 11 }
% 2.48/0.72 succ(n0)
% 2.48/0.72 = { by axiom 4 (successor_1) }
% 2.48/0.72 n1
% 2.48/0.72
% 2.48/0.72 Lemma 14: n4 = n1.
% 2.48/0.72 Proof:
% 2.48/0.72 n4
% 2.48/0.72 = { by axiom 8 (successor_4) R->L }
% 2.48/0.72 succ(succ(succ(succ(n0))))
% 2.48/0.72 = { by lemma 11 }
% 2.48/0.72 succ(succ(succ(n0)))
% 2.48/0.72 = { by lemma 11 }
% 2.48/0.72 succ(succ(n0))
% 2.48/0.72 = { by lemma 11 }
% 2.48/0.72 succ(n0)
% 2.48/0.72 = { by axiom 4 (successor_1) }
% 2.48/0.72 n1
% 2.48/0.72
% 2.48/0.72 Goal 1 (quaternion_ds1_symm_0601_39): tuple2(n5, n5) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n5, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 2 (quaternion_ds1_symm_0601_38): tuple2(n4, n5) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n4, n5)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 3 (quaternion_ds1_symm_0601_37): tuple2(n4, n5) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n4, n5)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 4 (quaternion_ds1_symm_0601_36): tuple2(n4, n4) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n4, n4)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n4)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 5 (quaternion_ds1_symm_0601_35): tuple2(n3, n5) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n3, n5)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 6 (quaternion_ds1_symm_0601_34): tuple2(n3, n4) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n3, n4)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n4)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 7 (quaternion_ds1_symm_0601_33): tuple2(n3, n5) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n3, n5)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 8 (quaternion_ds1_symm_0601_32): tuple2(n3, n4) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n3, n4)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n4)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 9 (quaternion_ds1_symm_0601_31): tuple2(n3, n3) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n3, n3)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n3)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 10 (quaternion_ds1_symm_0601_30): tuple2(n2, n5) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n2, n5)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 11 (quaternion_ds1_symm_0601_29): tuple2(n2, n4) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n2, n4)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n4)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 12 (quaternion_ds1_symm_0601_28): tuple2(n2, n3) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n2, n3)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n3)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 13 (quaternion_ds1_symm_0601_27): tuple2(n2, n5) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n2, n5)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 14 (quaternion_ds1_symm_0601_26): tuple2(n2, n4) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n2, n4)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n4)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 15 (quaternion_ds1_symm_0601_25): tuple2(n2, n3) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n2, n3)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n3)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 16 (quaternion_ds1_symm_0601_24): tuple2(n2, n2) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n2, n2)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n2)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 17 (quaternion_ds1_symm_0601_23): tuple2(n1, n5) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n1, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 18 (quaternion_ds1_symm_0601_22): tuple2(n1, n4) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n1, n4)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 19 (quaternion_ds1_symm_0601_21): tuple2(n1, n3) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n1, n3)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 20 (quaternion_ds1_symm_0601_20): tuple2(n1, n2) = tuple2(e, f).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n1, n2)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(e, n1)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(e, f)
% 2.48/0.72
% 2.48/0.72 Goal 21 (quaternion_ds1_symm_0601_19): tuple2(n1, n5) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n1, n5)
% 2.48/0.72 = { by lemma 12 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 22 (quaternion_ds1_symm_0601_18): tuple2(n1, n4) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n1, n4)
% 2.48/0.72 = { by lemma 14 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 23 (quaternion_ds1_symm_0601_17): tuple2(n1, n3) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n1, n3)
% 2.48/0.72 = { by lemma 13 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 24 (quaternion_ds1_symm_0601_16): tuple2(n1, n2) = tuple2(f, e).
% 2.48/0.72 Proof:
% 2.48/0.72 tuple2(n1, n2)
% 2.48/0.72 = { by lemma 10 }
% 2.48/0.72 tuple2(n1, n1)
% 2.48/0.72 = { by axiom 3 (quaternion_ds1_symm_0601_1) }
% 2.48/0.72 tuple2(n1, e)
% 2.48/0.72 = { by axiom 1 (quaternion_ds1_symm_0601) }
% 2.48/0.72 tuple2(f, e)
% 2.48/0.72
% 2.48/0.72 Goal 25 (quaternion_ds1_symm_0601_15): a_select2(xinit_noise, n1) = a_select2(xinit_noise, n2).
% 2.48/0.72 Proof:
% 2.48/0.72 a_select2(xinit_noise, n1)
% 2.48/0.72 = { by lemma 10 R->L }
% 2.48/0.72 a_select2(xinit_noise, n2)
% 2.48/0.72 % SZS output end Proof
% 2.48/0.72
% 2.48/0.72 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------