TSTP Solution File: SWV225+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV225+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 : n018.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 0.20s 0.60s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV225+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % 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 : n018.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 : Tue Aug 29 06:04:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.60 Command-line arguments: --no-flatten-goal
% 0.20/0.60
% 0.20/0.60 % SZS status Theorem
% 0.20/0.60
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 Take the following subset of the input axioms:
% 0.20/0.73 fof(quaternion_ds1_symm_0561, 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 & n2=F) & (~(n0=E & n3=F) & (~(n0=E & n4=F) & (~(n0=E & n5=F) & (~(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=F & n3=E))))))))))))))))))))))))))))))))) => n0=a_select2(xinit_noise, n1)))).
% 0.20/0.73 fof(succ_plus_1_r, axiom, ![X]: plus(X, n1)=succ(X)).
% 0.20/0.73 fof(succ_plus_2_r, axiom, ![X2]: plus(X2, n2)=succ(succ(X2))).
% 0.20/0.73 fof(successor_1, axiom, succ(n0)=n1).
% 0.20/0.73 fof(successor_4, axiom, succ(succ(succ(succ(n0))))=n4).
% 0.20/0.73 fof(successor_5, axiom, succ(succ(succ(succ(succ(n0)))))=n5).
% 0.20/0.73
% 0.20/0.73 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.73 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.73 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.73 fresh(y, y, x1...xn) = u
% 0.20/0.73 C => fresh(s, t, x1...xn) = v
% 0.20/0.73 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.73 variables of u and v.
% 0.20/0.73 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.73 input problem has no model of domain size 1).
% 0.20/0.73
% 0.20/0.73 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.73
% 0.20/0.73 Axiom 1 (quaternion_ds1_symm_0561): n1 = f.
% 0.20/0.73 Axiom 2 (quaternion_ds1_symm_0561_2): n2 = f.
% 0.20/0.73 Axiom 3 (quaternion_ds1_symm_0561_1): n1 = e.
% 0.20/0.73 Axiom 4 (quaternion_ds1_symm_0561_3): n3 = e.
% 0.20/0.73 Axiom 5 (successor_1): succ(n0) = n1.
% 0.20/0.73 Axiom 6 (succ_plus_1_r): plus(X, n1) = succ(X).
% 0.20/0.73 Axiom 7 (succ_plus_2_r): plus(X, n2) = succ(succ(X)).
% 0.20/0.73 Axiom 8 (successor_4): succ(succ(succ(succ(n0)))) = n4.
% 0.20/0.73 Axiom 9 (successor_5): succ(succ(succ(succ(succ(n0))))) = n5.
% 0.20/0.73
% 0.20/0.73 Lemma 10: n2 = n1.
% 0.20/0.73 Proof:
% 0.20/0.73 n2
% 0.20/0.73 = { by axiom 2 (quaternion_ds1_symm_0561_2) }
% 0.20/0.73 f
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) R->L }
% 0.20/0.73 n1
% 0.20/0.73
% 0.20/0.73 Lemma 11: succ(succ(X)) = succ(X).
% 0.20/0.73 Proof:
% 0.20/0.73 succ(succ(X))
% 0.20/0.73 = { by axiom 7 (succ_plus_2_r) R->L }
% 0.20/0.73 plus(X, n2)
% 0.20/0.73 = { by lemma 10 }
% 0.20/0.73 plus(X, n1)
% 0.20/0.73 = { by axiom 6 (succ_plus_1_r) }
% 0.20/0.73 succ(X)
% 0.20/0.73
% 0.20/0.73 Lemma 12: n5 = n1.
% 0.20/0.73 Proof:
% 0.20/0.73 n5
% 0.20/0.73 = { by axiom 9 (successor_5) R->L }
% 0.20/0.73 succ(succ(succ(succ(succ(n0)))))
% 0.20/0.73 = { by lemma 11 }
% 0.20/0.73 succ(succ(succ(succ(n0))))
% 0.20/0.73 = { by lemma 11 }
% 0.20/0.73 succ(succ(succ(n0)))
% 0.20/0.73 = { by lemma 11 }
% 0.20/0.73 succ(succ(n0))
% 0.20/0.73 = { by lemma 11 }
% 0.20/0.73 succ(n0)
% 0.20/0.73 = { by axiom 5 (successor_1) }
% 0.20/0.73 n1
% 0.20/0.73
% 0.20/0.73 Lemma 13: n3 = n1.
% 0.20/0.73 Proof:
% 0.20/0.73 n3
% 0.20/0.73 = { by axiom 4 (quaternion_ds1_symm_0561_3) }
% 0.20/0.73 e
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) R->L }
% 0.20/0.73 n1
% 0.20/0.73
% 0.20/0.73 Lemma 14: n4 = n1.
% 0.20/0.73 Proof:
% 0.20/0.73 n4
% 0.20/0.73 = { by axiom 8 (successor_4) R->L }
% 0.20/0.73 succ(succ(succ(succ(n0))))
% 0.20/0.73 = { by lemma 11 }
% 0.20/0.73 succ(succ(succ(n0)))
% 0.20/0.73 = { by lemma 11 }
% 0.20/0.73 succ(succ(n0))
% 0.20/0.73 = { by lemma 11 }
% 0.20/0.73 succ(n0)
% 0.20/0.73 = { by axiom 5 (successor_1) }
% 0.20/0.73 n1
% 0.20/0.73
% 0.20/0.73 Goal 1 (quaternion_ds1_symm_0561_38): tuple2(n5, n5) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n5, n5)
% 0.20/0.73 = { by lemma 12 }
% 0.20/0.73 tuple2(n1, n5)
% 0.20/0.73 = { by lemma 12 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(n1, e)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(f, e)
% 0.20/0.73
% 0.20/0.73 Goal 2 (quaternion_ds1_symm_0561_37): tuple2(n4, n5) = tuple2(e, f).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n4, n5)
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 tuple2(n1, n5)
% 0.20/0.73 = { by lemma 12 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(e, n1)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(e, f)
% 0.20/0.73
% 0.20/0.73 Goal 3 (quaternion_ds1_symm_0561_36): tuple2(n4, n5) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n4, n5)
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 tuple2(n1, n5)
% 0.20/0.73 = { by lemma 12 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(n1, e)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(f, e)
% 0.20/0.73
% 0.20/0.73 Goal 4 (quaternion_ds1_symm_0561_35): tuple2(n4, n4) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n4, n4)
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 tuple2(n1, n4)
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(n1, e)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(f, e)
% 0.20/0.73
% 0.20/0.73 Goal 5 (quaternion_ds1_symm_0561_34): tuple2(n3, n5) = tuple2(e, f).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n3, n5)
% 0.20/0.73 = { by lemma 13 }
% 0.20/0.73 tuple2(n1, n5)
% 0.20/0.73 = { by lemma 12 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(e, n1)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(e, f)
% 0.20/0.73
% 0.20/0.73 Goal 6 (quaternion_ds1_symm_0561_33): tuple2(n3, n4) = tuple2(e, f).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n3, n4)
% 0.20/0.73 = { by lemma 13 }
% 0.20/0.73 tuple2(n1, n4)
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(e, n1)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(e, f)
% 0.20/0.73
% 0.20/0.73 Goal 7 (quaternion_ds1_symm_0561_32): tuple2(n3, n5) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n3, n5)
% 0.20/0.73 = { by lemma 13 }
% 0.20/0.73 tuple2(n1, n5)
% 0.20/0.73 = { by lemma 12 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(n1, e)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(f, e)
% 0.20/0.73
% 0.20/0.73 Goal 8 (quaternion_ds1_symm_0561_31): tuple2(n3, n4) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n3, n4)
% 0.20/0.73 = { by lemma 13 }
% 0.20/0.73 tuple2(n1, n4)
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(n1, e)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(f, e)
% 0.20/0.73
% 0.20/0.73 Goal 9 (quaternion_ds1_symm_0561_30): tuple2(n3, n3) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n3, n3)
% 0.20/0.73 = { by lemma 13 }
% 0.20/0.73 tuple2(n1, n3)
% 0.20/0.73 = { by lemma 13 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(n1, e)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(f, e)
% 0.20/0.73
% 0.20/0.73 Goal 10 (quaternion_ds1_symm_0561_29): tuple2(n2, n5) = tuple2(e, f).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n2, n5)
% 0.20/0.73 = { by lemma 10 }
% 0.20/0.73 tuple2(n1, n5)
% 0.20/0.73 = { by lemma 12 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(e, n1)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(e, f)
% 0.20/0.73
% 0.20/0.73 Goal 11 (quaternion_ds1_symm_0561_28): tuple2(n2, n4) = tuple2(e, f).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n2, n4)
% 0.20/0.73 = { by lemma 10 }
% 0.20/0.73 tuple2(n1, n4)
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(e, n1)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(e, f)
% 0.20/0.73
% 0.20/0.73 Goal 12 (quaternion_ds1_symm_0561_27): tuple2(n2, n3) = tuple2(e, f).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n2, n3)
% 0.20/0.73 = { by lemma 10 }
% 0.20/0.73 tuple2(n1, n3)
% 0.20/0.73 = { by lemma 13 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(e, n1)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(e, f)
% 0.20/0.73
% 0.20/0.73 Goal 13 (quaternion_ds1_symm_0561_26): tuple2(n2, n5) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n2, n5)
% 0.20/0.73 = { by lemma 10 }
% 0.20/0.73 tuple2(n1, n5)
% 0.20/0.73 = { by lemma 12 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(n1, e)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(f, e)
% 0.20/0.73
% 0.20/0.73 Goal 14 (quaternion_ds1_symm_0561_25): tuple2(n2, n4) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n2, n4)
% 0.20/0.73 = { by lemma 10 }
% 0.20/0.73 tuple2(n1, n4)
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(n1, e)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(f, e)
% 0.20/0.73
% 0.20/0.73 Goal 15 (quaternion_ds1_symm_0561_24): tuple2(n2, n3) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.73 tuple2(n2, n3)
% 0.20/0.73 = { by lemma 10 }
% 0.20/0.73 tuple2(n1, n3)
% 0.20/0.73 = { by lemma 13 }
% 0.20/0.73 tuple2(n1, n1)
% 0.20/0.73 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.73 tuple2(n1, e)
% 0.20/0.73 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.73 tuple2(f, e)
% 0.20/0.73
% 0.20/0.73 Goal 16 (quaternion_ds1_symm_0561_23): tuple2(n2, n2) = tuple2(f, e).
% 0.20/0.73 Proof:
% 0.20/0.74 tuple2(n2, n2)
% 0.20/0.74 = { by lemma 10 }
% 0.20/0.74 tuple2(n1, n2)
% 0.20/0.74 = { by lemma 10 }
% 0.20/0.74 tuple2(n1, n1)
% 0.20/0.74 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.74 tuple2(n1, e)
% 0.20/0.74 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.74 tuple2(f, e)
% 0.20/0.74
% 0.20/0.74 Goal 17 (quaternion_ds1_symm_0561_22): tuple2(n1, n5) = tuple2(e, f).
% 0.20/0.74 Proof:
% 0.20/0.74 tuple2(n1, n5)
% 0.20/0.74 = { by lemma 12 }
% 0.20/0.74 tuple2(n1, n1)
% 0.20/0.74 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.74 tuple2(e, n1)
% 0.20/0.74 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.74 tuple2(e, f)
% 0.20/0.74
% 0.20/0.74 Goal 18 (quaternion_ds1_symm_0561_21): tuple2(n1, n4) = tuple2(e, f).
% 0.20/0.74 Proof:
% 0.20/0.74 tuple2(n1, n4)
% 0.20/0.74 = { by lemma 14 }
% 0.20/0.74 tuple2(n1, n1)
% 0.20/0.74 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.74 tuple2(e, n1)
% 0.20/0.74 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.74 tuple2(e, f)
% 0.20/0.74
% 0.20/0.74 Goal 19 (quaternion_ds1_symm_0561_20): tuple2(n1, n3) = tuple2(e, f).
% 0.20/0.74 Proof:
% 0.20/0.74 tuple2(n1, n3)
% 0.20/0.74 = { by lemma 13 }
% 0.20/0.74 tuple2(n1, n1)
% 0.20/0.74 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.74 tuple2(e, n1)
% 0.20/0.74 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.74 tuple2(e, f)
% 0.20/0.74
% 0.20/0.74 Goal 20 (quaternion_ds1_symm_0561_19): tuple2(n1, n2) = tuple2(e, f).
% 0.20/0.74 Proof:
% 0.20/0.74 tuple2(n1, n2)
% 0.20/0.74 = { by lemma 10 }
% 0.20/0.74 tuple2(n1, n1)
% 0.20/0.74 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.74 tuple2(e, n1)
% 0.20/0.74 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.74 tuple2(e, f)
% 0.20/0.74
% 0.20/0.74 Goal 21 (quaternion_ds1_symm_0561_18): tuple2(n1, n5) = tuple2(f, e).
% 0.20/0.74 Proof:
% 0.20/0.74 tuple2(n1, n5)
% 0.20/0.74 = { by lemma 12 }
% 0.20/0.74 tuple2(n1, n1)
% 0.20/0.74 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.74 tuple2(n1, e)
% 0.20/0.74 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.74 tuple2(f, e)
% 0.20/0.74
% 0.20/0.74 Goal 22 (quaternion_ds1_symm_0561_17): tuple2(n1, n4) = tuple2(f, e).
% 0.20/0.74 Proof:
% 0.20/0.74 tuple2(n1, n4)
% 0.20/0.74 = { by lemma 14 }
% 0.20/0.74 tuple2(n1, n1)
% 0.20/0.74 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.74 tuple2(n1, e)
% 0.20/0.74 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.74 tuple2(f, e)
% 0.20/0.74
% 0.20/0.74 Goal 23 (quaternion_ds1_symm_0561_16): tuple2(n1, n3) = tuple2(f, e).
% 0.20/0.74 Proof:
% 0.20/0.74 tuple2(n1, n3)
% 0.20/0.74 = { by lemma 13 }
% 0.20/0.74 tuple2(n1, n1)
% 0.20/0.74 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.74 tuple2(n1, e)
% 0.20/0.74 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.74 tuple2(f, e)
% 0.20/0.74
% 0.20/0.74 Goal 24 (quaternion_ds1_symm_0561_15): tuple2(n1, n2) = tuple2(f, e).
% 0.20/0.74 Proof:
% 0.20/0.74 tuple2(n1, n2)
% 0.20/0.74 = { by lemma 10 }
% 0.20/0.74 tuple2(n1, n1)
% 0.20/0.74 = { by axiom 3 (quaternion_ds1_symm_0561_1) }
% 0.20/0.74 tuple2(n1, e)
% 0.20/0.74 = { by axiom 1 (quaternion_ds1_symm_0561) }
% 0.20/0.74 tuple2(f, e)
% 0.20/0.74 % SZS output end Proof
% 0.20/0.74
% 0.20/0.74 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------