TSTP Solution File: SWV224+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV224+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 : n006.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 0.59s
% Output : Proof 2.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV224+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.13 % 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 : n006.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 09:54:51 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 Command-line arguments: --no-flatten-goal
% 0.20/0.59
% 0.20/0.59 % SZS status Theorem
% 0.20/0.59
% 0.20/0.61 % SZS output start Proof
% 0.20/0.61 Take the following subset of the input axioms:
% 2.11/0.64 fof(quaternion_ds1_symm_0521, 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 & n1=F) & (~(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 & n1=F) & (~(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) & (n0=F & (n3=E & (n3=F & n4=E))))))))))))))))))))))))))))))))))) => a_select2(xinit_noise, n3)=n0))).
% 2.11/0.64
% 2.11/0.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.11/0.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.11/0.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.11/0.64 fresh(y, y, x1...xn) = u
% 2.11/0.64 C => fresh(s, t, x1...xn) = v
% 2.11/0.64 where fresh is a fresh function symbol and x1..xn are the free
% 2.11/0.64 variables of u and v.
% 2.11/0.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.11/0.64 input problem has no model of domain size 1).
% 2.11/0.64
% 2.11/0.64 The encoding turns the above axioms into the following unit equations and goals:
% 2.11/0.64
% 2.11/0.64 Axiom 1 (quaternion_ds1_symm_0521_1): n3 = f.
% 2.11/0.64 Axiom 2 (quaternion_ds1_symm_0521_3): n4 = e.
% 2.11/0.64 Axiom 3 (quaternion_ds1_symm_0521_2): n3 = e.
% 2.11/0.64 Axiom 4 (quaternion_ds1_symm_0521): n0 = f.
% 2.11/0.64
% 2.11/0.64 Lemma 5: n3 = n4.
% 2.11/0.64 Proof:
% 2.11/0.64 n3
% 2.11/0.64 = { by axiom 3 (quaternion_ds1_symm_0521_2) }
% 2.11/0.64 e
% 2.11/0.64 = { by axiom 2 (quaternion_ds1_symm_0521_3) R->L }
% 2.11/0.64 n4
% 2.11/0.64
% 2.11/0.64 Lemma 6: n0 = n4.
% 2.11/0.64 Proof:
% 2.11/0.64 n0
% 2.11/0.64 = { by axiom 4 (quaternion_ds1_symm_0521) }
% 2.11/0.64 f
% 2.11/0.64 = { by axiom 1 (quaternion_ds1_symm_0521_1) R->L }
% 2.11/0.64 n3
% 2.11/0.64 = { by lemma 5 }
% 2.11/0.65 n4
% 2.11/0.65
% 2.11/0.65 Goal 1 (quaternion_ds1_symm_0521_37): tuple2(n4, n4) = tuple2(f, e).
% 2.11/0.65 Proof:
% 2.11/0.65 tuple2(n4, n4)
% 2.11/0.65 = { by lemma 5 R->L }
% 2.11/0.65 tuple2(n3, n4)
% 2.11/0.65 = { by axiom 2 (quaternion_ds1_symm_0521_3) }
% 2.11/0.65 tuple2(n3, e)
% 2.11/0.65 = { by axiom 1 (quaternion_ds1_symm_0521_1) }
% 2.11/0.65 tuple2(f, e)
% 2.11/0.65
% 2.11/0.65 Goal 2 (quaternion_ds1_symm_0521_35): tuple2(n3, n4) = tuple2(e, f).
% 2.11/0.65 Proof:
% 2.11/0.65 tuple2(n3, n4)
% 2.11/0.65 = { by lemma 5 }
% 2.11/0.65 tuple2(n4, n4)
% 2.11/0.65 = { by lemma 5 R->L }
% 2.11/0.65 tuple2(n4, n3)
% 2.11/0.65 = { by axiom 2 (quaternion_ds1_symm_0521_3) }
% 2.11/0.65 tuple2(e, n3)
% 2.11/0.65 = { by axiom 1 (quaternion_ds1_symm_0521_1) }
% 2.11/0.65 tuple2(e, f)
% 2.11/0.65
% 2.11/0.65 Goal 3 (quaternion_ds1_symm_0521_33): tuple2(n3, n4) = tuple2(f, e).
% 2.11/0.65 Proof:
% 2.11/0.65 tuple2(n3, n4)
% 2.11/0.65 = { by axiom 2 (quaternion_ds1_symm_0521_3) }
% 2.11/0.65 tuple2(n3, e)
% 2.11/0.65 = { by axiom 1 (quaternion_ds1_symm_0521_1) }
% 2.11/0.65 tuple2(f, e)
% 2.11/0.65
% 2.11/0.65 Goal 4 (quaternion_ds1_symm_0521_32): tuple2(n3, n3) = tuple2(f, e).
% 2.11/0.65 Proof:
% 2.11/0.65 tuple2(n3, n3)
% 2.11/0.65 = { by lemma 5 }
% 2.11/0.65 tuple2(n4, n3)
% 2.11/0.65 = { by lemma 5 }
% 2.11/0.65 tuple2(n4, n4)
% 2.11/0.65 = { by lemma 5 R->L }
% 2.11/0.65 tuple2(n3, n4)
% 2.11/0.65 = { by axiom 2 (quaternion_ds1_symm_0521_3) }
% 2.11/0.65 tuple2(n3, e)
% 2.11/0.65 = { by axiom 1 (quaternion_ds1_symm_0521_1) }
% 2.11/0.65 tuple2(f, e)
% 2.11/0.65
% 2.11/0.65 Goal 5 (quaternion_ds1_symm_0521_14): tuple2(n0, n4) = tuple2(e, f).
% 2.11/0.65 Proof:
% 2.11/0.65 tuple2(n0, n4)
% 2.11/0.65 = { by lemma 6 }
% 2.11/0.65 tuple2(n4, n4)
% 2.11/0.65 = { by lemma 5 R->L }
% 2.11/0.65 tuple2(n4, n3)
% 2.11/0.65 = { by axiom 2 (quaternion_ds1_symm_0521_3) }
% 2.11/0.65 tuple2(e, n3)
% 2.11/0.65 = { by axiom 1 (quaternion_ds1_symm_0521_1) }
% 2.11/0.65 tuple2(e, f)
% 2.11/0.65
% 2.11/0.65 Goal 6 (quaternion_ds1_symm_0521_13): tuple2(n0, n3) = tuple2(e, f).
% 2.11/0.65 Proof:
% 2.11/0.65 tuple2(n0, n3)
% 2.11/0.65 = { by lemma 5 }
% 2.11/0.65 tuple2(n0, n4)
% 2.11/0.65 = { by lemma 6 }
% 2.11/0.65 tuple2(n4, n4)
% 2.11/0.65 = { by lemma 5 R->L }
% 2.11/0.65 tuple2(n4, n3)
% 2.11/0.65 = { by axiom 2 (quaternion_ds1_symm_0521_3) }
% 2.11/0.65 tuple2(e, n3)
% 2.11/0.65 = { by axiom 1 (quaternion_ds1_symm_0521_1) }
% 2.11/0.65 tuple2(e, f)
% 2.11/0.65
% 2.11/0.65 Goal 7 (quaternion_ds1_symm_0521_9): tuple2(n0, n4) = tuple2(f, e).
% 2.11/0.65 Proof:
% 2.11/0.65 tuple2(n0, n4)
% 2.11/0.65 = { by lemma 6 }
% 2.11/0.65 tuple2(n4, n4)
% 2.11/0.65 = { by lemma 5 R->L }
% 2.11/0.65 tuple2(n3, n4)
% 2.11/0.65 = { by axiom 2 (quaternion_ds1_symm_0521_3) }
% 2.11/0.65 tuple2(n3, e)
% 2.11/0.65 = { by axiom 1 (quaternion_ds1_symm_0521_1) }
% 2.11/0.65 tuple2(f, e)
% 2.11/0.65 % SZS output end Proof
% 2.11/0.65
% 2.11/0.65 RESULT: Theorem (the conjecture is true).
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