TSTP Solution File: SEU413+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU413+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : n021.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 17:52:40 EDT 2023
% Result : Theorem 45.27s 6.24s
% Output : Proof 45.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU413+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : n021.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 : Wed Aug 23 18:38:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 45.27/6.24 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 45.27/6.24
% 45.27/6.24 % SZS status Theorem
% 45.27/6.24
% 45.27/6.25 % SZS output start Proof
% 45.27/6.25 Take the following subset of the input axioms:
% 45.27/6.25 fof(d9_orders_2, axiom, ![A2]: (l1_orders_2(A2) => ![B]: (m1_subset_1(B, u1_struct_0(A2)) => ![C]: (m1_subset_1(C, u1_struct_0(A2)) => (r1_orders_2(A2, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A2))))))).
% 45.27/6.25 fof(dt_k1_latsum_1, axiom, ![B2, A2_2]: ((l1_orders_2(A2_2) & l1_orders_2(B2)) => (v1_orders_2(k1_latsum_1(A2_2, B2)) & l1_orders_2(k1_latsum_1(A2_2, B2))))).
% 45.27/6.25 fof(t21_latsum_1, axiom, ![A2_2]: (l1_orders_2(A2_2) => ![B2]: (l1_orders_2(B2) => ![D, C2]: ((v12_waybel_0(k3_xboole_0(u1_struct_0(A2_2), u1_struct_0(B2)), B2) & (m1_subset_1(k3_xboole_0(u1_struct_0(A2_2), u1_struct_0(B2)), k1_zfmisc_1(u1_struct_0(B2))) & (r2_hidden(k4_tarski(C2, D), u1_orders_2(k1_latsum_1(A2_2, B2))) & r2_hidden(D, u1_struct_0(A2_2))))) => r2_hidden(C2, u1_struct_0(A2_2)))))).
% 45.27/6.25 fof(t23_latsum_1, conjecture, ![A]: (l1_orders_2(A) => ![B2]: (l1_orders_2(B2) => ![C2]: (m1_subset_1(C2, u1_struct_0(k1_latsum_1(A, B2))) => ![D2]: (m1_subset_1(D2, u1_struct_0(k1_latsum_1(A, B2))) => ((v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B2)), B2) & (m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B2)), k1_zfmisc_1(u1_struct_0(B2))) & (r1_orders_2(k1_latsum_1(A, B2), C2, D2) & r2_hidden(D2, u1_struct_0(A))))) => r2_hidden(C2, u1_struct_0(A)))))))).
% 45.27/6.25
% 45.27/6.25 Now clausify the problem and encode Horn clauses using encoding 3 of
% 45.27/6.25 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 45.27/6.25 We repeatedly replace C & s=t => u=v by the two clauses:
% 45.27/6.25 fresh(y, y, x1...xn) = u
% 45.27/6.25 C => fresh(s, t, x1...xn) = v
% 45.27/6.25 where fresh is a fresh function symbol and x1..xn are the free
% 45.27/6.25 variables of u and v.
% 45.27/6.25 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 45.27/6.25 input problem has no model of domain size 1).
% 45.27/6.25
% 45.27/6.25 The encoding turns the above axioms into the following unit equations and goals:
% 45.27/6.25
% 45.27/6.25 Axiom 1 (t23_latsum_1): l1_orders_2(a5) = true2.
% 45.27/6.25 Axiom 2 (t23_latsum_1_1): l1_orders_2(b2) = true2.
% 45.27/6.25 Axiom 3 (t23_latsum_1_7): r2_hidden(d, u1_struct_0(a5)) = true2.
% 45.27/6.25 Axiom 4 (t21_latsum_1): fresh32(X, X, Y, Z) = true2.
% 45.27/6.25 Axiom 5 (t21_latsum_1): fresh30(X, X, Y, Z) = r2_hidden(Z, u1_struct_0(Y)).
% 45.27/6.25 Axiom 6 (dt_k1_latsum_1): fresh22(X, X, Y, Z) = l1_orders_2(k1_latsum_1(Y, Z)).
% 45.27/6.25 Axiom 7 (dt_k1_latsum_1): fresh21(X, X, Y, Z) = true2.
% 45.27/6.25 Axiom 8 (d9_orders_2): fresh36(X, X, Y, Z, W) = true2.
% 45.27/6.25 Axiom 9 (t21_latsum_1): fresh31(X, X, Y, Z, W) = fresh32(l1_orders_2(Y), true2, Y, W).
% 45.27/6.25 Axiom 10 (t21_latsum_1): fresh29(X, X, Y, Z, W) = fresh30(l1_orders_2(Z), true2, Y, W).
% 45.27/6.25 Axiom 11 (dt_k1_latsum_1): fresh22(l1_orders_2(X), true2, Y, X) = fresh21(l1_orders_2(Y), true2, Y, X).
% 45.27/6.25 Axiom 12 (t23_latsum_1_6): r1_orders_2(k1_latsum_1(a5, b2), c3, d) = true2.
% 45.27/6.25 Axiom 13 (d9_orders_2): fresh34(X, X, Y, Z, W) = r2_hidden(k4_tarski(Z, W), u1_orders_2(Y)).
% 45.27/6.25 Axiom 14 (t23_latsum_1_3): m1_subset_1(c3, u1_struct_0(k1_latsum_1(a5, b2))) = true2.
% 45.27/6.25 Axiom 15 (t23_latsum_1_4): m1_subset_1(d, u1_struct_0(k1_latsum_1(a5, b2))) = true2.
% 45.27/6.25 Axiom 16 (t23_latsum_1_5): v12_waybel_0(k3_xboole_0(u1_struct_0(a5), u1_struct_0(b2)), b2) = true2.
% 45.27/6.25 Axiom 17 (d9_orders_2): fresh35(X, X, Y, Z, W) = fresh36(l1_orders_2(Y), true2, Y, Z, W).
% 45.27/6.25 Axiom 18 (d9_orders_2): fresh33(X, X, Y, Z, W) = fresh34(m1_subset_1(Z, u1_struct_0(Y)), true2, Y, Z, W).
% 45.27/6.25 Axiom 19 (d9_orders_2): fresh33(r1_orders_2(X, Y, Z), true2, X, Y, Z) = fresh35(m1_subset_1(Z, u1_struct_0(X)), true2, X, Y, Z).
% 45.27/6.25 Axiom 20 (t21_latsum_1): fresh27(X, X, Y, Z, W, V) = fresh28(r2_hidden(V, u1_struct_0(Y)), true2, Y, Z, W).
% 45.27/6.25 Axiom 21 (t23_latsum_1_2): m1_subset_1(k3_xboole_0(u1_struct_0(a5), u1_struct_0(b2)), k1_zfmisc_1(u1_struct_0(b2))) = true2.
% 45.27/6.25 Axiom 22 (t21_latsum_1): fresh28(X, X, Y, Z, W) = fresh29(v12_waybel_0(k3_xboole_0(u1_struct_0(Y), u1_struct_0(Z)), Z), true2, Y, Z, W).
% 45.27/6.25 Axiom 23 (t21_latsum_1): fresh27(r2_hidden(k4_tarski(X, Y), u1_orders_2(k1_latsum_1(Z, W))), true2, Z, W, X, Y) = fresh31(m1_subset_1(k3_xboole_0(u1_struct_0(Z), u1_struct_0(W)), k1_zfmisc_1(u1_struct_0(W))), true2, Z, W, X).
% 45.27/6.25
% 45.27/6.25 Goal 1 (t23_latsum_1_8): r2_hidden(c3, u1_struct_0(a5)) = true2.
% 45.27/6.25 Proof:
% 45.27/6.25 r2_hidden(c3, u1_struct_0(a5))
% 45.27/6.25 = { by axiom 5 (t21_latsum_1) R->L }
% 45.27/6.25 fresh30(true2, true2, a5, c3)
% 45.27/6.25 = { by axiom 2 (t23_latsum_1_1) R->L }
% 45.27/6.25 fresh30(l1_orders_2(b2), true2, a5, c3)
% 45.27/6.25 = { by axiom 10 (t21_latsum_1) R->L }
% 45.27/6.25 fresh29(true2, true2, a5, b2, c3)
% 45.27/6.25 = { by axiom 16 (t23_latsum_1_5) R->L }
% 45.27/6.25 fresh29(v12_waybel_0(k3_xboole_0(u1_struct_0(a5), u1_struct_0(b2)), b2), true2, a5, b2, c3)
% 45.27/6.25 = { by axiom 22 (t21_latsum_1) R->L }
% 45.27/6.25 fresh28(true2, true2, a5, b2, c3)
% 45.27/6.25 = { by axiom 3 (t23_latsum_1_7) R->L }
% 45.27/6.25 fresh28(r2_hidden(d, u1_struct_0(a5)), true2, a5, b2, c3)
% 45.27/6.25 = { by axiom 20 (t21_latsum_1) R->L }
% 45.27/6.25 fresh27(true2, true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 8 (d9_orders_2) R->L }
% 45.27/6.26 fresh27(fresh36(true2, true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 7 (dt_k1_latsum_1) R->L }
% 45.27/6.26 fresh27(fresh36(fresh21(true2, true2, a5, b2), true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 1 (t23_latsum_1) R->L }
% 45.27/6.26 fresh27(fresh36(fresh21(l1_orders_2(a5), true2, a5, b2), true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 11 (dt_k1_latsum_1) R->L }
% 45.27/6.26 fresh27(fresh36(fresh22(l1_orders_2(b2), true2, a5, b2), true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 2 (t23_latsum_1_1) }
% 45.27/6.26 fresh27(fresh36(fresh22(true2, true2, a5, b2), true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 6 (dt_k1_latsum_1) }
% 45.27/6.26 fresh27(fresh36(l1_orders_2(k1_latsum_1(a5, b2)), true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 17 (d9_orders_2) R->L }
% 45.27/6.26 fresh27(fresh35(true2, true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 15 (t23_latsum_1_4) R->L }
% 45.27/6.26 fresh27(fresh35(m1_subset_1(d, u1_struct_0(k1_latsum_1(a5, b2))), true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 19 (d9_orders_2) R->L }
% 45.27/6.26 fresh27(fresh33(r1_orders_2(k1_latsum_1(a5, b2), c3, d), true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 12 (t23_latsum_1_6) }
% 45.27/6.26 fresh27(fresh33(true2, true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 18 (d9_orders_2) }
% 45.27/6.26 fresh27(fresh34(m1_subset_1(c3, u1_struct_0(k1_latsum_1(a5, b2))), true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 14 (t23_latsum_1_3) }
% 45.27/6.26 fresh27(fresh34(true2, true2, k1_latsum_1(a5, b2), c3, d), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 13 (d9_orders_2) }
% 45.27/6.26 fresh27(r2_hidden(k4_tarski(c3, d), u1_orders_2(k1_latsum_1(a5, b2))), true2, a5, b2, c3, d)
% 45.27/6.26 = { by axiom 23 (t21_latsum_1) }
% 45.27/6.26 fresh31(m1_subset_1(k3_xboole_0(u1_struct_0(a5), u1_struct_0(b2)), k1_zfmisc_1(u1_struct_0(b2))), true2, a5, b2, c3)
% 45.27/6.26 = { by axiom 21 (t23_latsum_1_2) }
% 45.27/6.26 fresh31(true2, true2, a5, b2, c3)
% 45.27/6.26 = { by axiom 9 (t21_latsum_1) }
% 45.27/6.26 fresh32(l1_orders_2(a5), true2, a5, c3)
% 45.27/6.26 = { by axiom 1 (t23_latsum_1) }
% 45.27/6.26 fresh32(true2, true2, a5, c3)
% 45.27/6.26 = { by axiom 4 (t21_latsum_1) }
% 45.27/6.26 true2
% 45.27/6.26 % SZS output end Proof
% 45.27/6.26
% 45.27/6.26 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------