TSTP Solution File: SWV221+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV221+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 : n001.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 23:03:03 EDT 2023
% Result : Theorem 0.20s 0.79s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV221+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n001.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 08:36:51 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.79 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.79
% 0.20/0.79 % SZS status Theorem
% 0.20/0.79
% 0.20/0.79 % SZS output start Proof
% 0.20/0.79 Take the following subset of the input axioms:
% 0.20/0.80 fof(quaternion_ds1_symm_0401, conjecture, (leq(n0, pv5) & (leq(n0, pv57) & (leq(pv5, n998) & (leq(pv57, n5) & (leq(pv58, n5) & (gt(pv58, pv57) & (![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)))) => a_select3(pminus_ds1_filter, E, F)=a_select3(pminus_ds1_filter, F, E)) & (![G, H]: ((leq(n0, G) & (leq(n0, H) & (leq(G, n5) & leq(H, n5)))) => ((G=pv57 & gt(pv58, H)) => a_select3(id_ds1_filter, G, H)=a_select3(id_ds1_filter, H, G))) & (![I, J]: ((leq(n0, I) & (leq(n0, J) & (leq(I, n5) & leq(J, n5)))) => (gt(pv57, I) => a_select3(id_ds1_filter, I, J)=a_select3(id_ds1_filter, J, I))) & ![K]: ((leq(n0, K) & leq(K, pred(pv57))) => ![L]: ((leq(n0, L) & leq(L, n5)) => a_select3(id_ds1_filter, K, L)=a_select3(id_ds1_filter, L, K)))))))))))))) => ![M]: ((leq(n0, M) & leq(M, pred(pv57))) => ![N]: ((leq(n0, N) & leq(N, n5)) => ((~(pv57=N & N=M) & pv57!=M) => a_select3(id_ds1_filter, M, N)=a_select3(id_ds1_filter, N, M))))).
% 0.20/0.80
% 0.20/0.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.80 fresh(y, y, x1...xn) = u
% 0.20/0.80 C => fresh(s, t, x1...xn) = v
% 0.20/0.80 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.80 variables of u and v.
% 0.20/0.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.80 input problem has no model of domain size 1).
% 0.20/0.80
% 0.20/0.80 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.80
% 0.20/0.80 Axiom 1 (quaternion_ds1_symm_0401_4): leq(n0, n) = true3.
% 0.20/0.80 Axiom 2 (quaternion_ds1_symm_0401_3): leq(n0, m) = true3.
% 0.20/0.80 Axiom 3 (quaternion_ds1_symm_0401_9): leq(n, n5) = true3.
% 0.20/0.80 Axiom 4 (quaternion_ds1_symm_0401_8): leq(m, pred(pv57)) = true3.
% 0.20/0.80 Axiom 5 (quaternion_ds1_symm_0401_18): fresh44(X, X, Y, Z) = a_select3(id_ds1_filter, Y, Z).
% 0.20/0.80 Axiom 6 (quaternion_ds1_symm_0401_18): fresh11(X, X, Y, Z) = a_select3(id_ds1_filter, Z, Y).
% 0.20/0.80 Axiom 7 (quaternion_ds1_symm_0401_18): fresh43(X, X, Y, Z) = fresh44(leq(Z, n5), true3, Y, Z).
% 0.20/0.80 Axiom 8 (quaternion_ds1_symm_0401_18): fresh42(X, X, Y, Z) = fresh43(leq(n0, Y), true3, Y, Z).
% 0.20/0.80 Axiom 9 (quaternion_ds1_symm_0401_18): fresh42(leq(n0, X), true3, Y, X) = fresh11(leq(Y, pred(pv57)), true3, Y, X).
% 0.20/0.80
% 0.20/0.80 Goal 1 (quaternion_ds1_symm_0401_11): a_select3(id_ds1_filter, m, n) = a_select3(id_ds1_filter, n, m).
% 0.20/0.80 Proof:
% 0.20/0.80 a_select3(id_ds1_filter, m, n)
% 0.20/0.80 = { by axiom 5 (quaternion_ds1_symm_0401_18) R->L }
% 0.20/0.80 fresh44(true3, true3, m, n)
% 0.20/0.80 = { by axiom 3 (quaternion_ds1_symm_0401_9) R->L }
% 0.20/0.80 fresh44(leq(n, n5), true3, m, n)
% 0.20/0.80 = { by axiom 7 (quaternion_ds1_symm_0401_18) R->L }
% 0.20/0.80 fresh43(true3, true3, m, n)
% 0.20/0.80 = { by axiom 2 (quaternion_ds1_symm_0401_3) R->L }
% 0.20/0.80 fresh43(leq(n0, m), true3, m, n)
% 0.20/0.80 = { by axiom 8 (quaternion_ds1_symm_0401_18) R->L }
% 0.20/0.80 fresh42(true3, true3, m, n)
% 0.20/0.80 = { by axiom 1 (quaternion_ds1_symm_0401_4) R->L }
% 0.20/0.80 fresh42(leq(n0, n), true3, m, n)
% 0.20/0.80 = { by axiom 9 (quaternion_ds1_symm_0401_18) }
% 0.20/0.80 fresh11(leq(m, pred(pv57)), true3, m, n)
% 0.20/0.80 = { by axiom 4 (quaternion_ds1_symm_0401_8) }
% 0.20/0.80 fresh11(true3, true3, m, n)
% 0.20/0.80 = { by axiom 6 (quaternion_ds1_symm_0401_18) }
% 0.20/0.80 a_select3(id_ds1_filter, n, m)
% 0.20/0.80 % SZS output end Proof
% 0.20/0.80
% 0.20/0.80 RESULT: Theorem (the conjecture is true).
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