TSTP Solution File: SWV857-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV857-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n024.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 23:06:32 EDT 2023
% Result : Unsatisfiable 38.83s 5.37s
% Output : Proof 38.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWV857-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 07:06:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 38.83/5.37 Command-line arguments: --no-flatten-goal
% 38.83/5.37
% 38.83/5.37 % SZS status Unsatisfiable
% 38.83/5.37
% 38.83/5.38 % SZS output start Proof
% 38.83/5.38 Take the following subset of the input axioms:
% 38.83/5.38 fof(cls_conjecture_0, negated_conjecture, c_lessequals(v_tsa, v_Ga, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool))).
% 38.83/5.38 fof(cls_conjecture_1, negated_conjecture, hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)), v_xa), v_tsa))).
% 38.83/5.38 fof(cls_conjecture_2, negated_conjecture, ~c_Hoare__Mirabelle_Otriple__valid(v_x, v_xa, t_a)).
% 38.83/5.38 fof(cls_conjecture_3, negated_conjecture, ![V_xb]: (c_Hoare__Mirabelle_Otriple__valid(v_x, V_xb, t_a) | ~hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)), V_xb), v_Ga)))).
% 38.83/5.38 fof(cls_le__funD_0, axiom, ![T_a, T_b, V_f, V_x, V_g]: (~class_HOL_Oord(T_b) | (c_lessequals(hAPP(V_f, V_x), hAPP(V_g, V_x), T_b) | ~c_lessequals(V_f, V_g, tc_fun(T_a, T_b))))).
% 38.83/5.38 fof(cls_le__funI_0, axiom, ![T_a2, T_b2, V_f2, V_g2]: (~class_HOL_Oord(T_b2) | (c_lessequals(V_f2, V_g2, tc_fun(T_a2, T_b2)) | ~c_lessequals(hAPP(V_f2, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(V_f2, V_g2, T_a2, T_b2)), hAPP(V_g2, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(V_f2, V_g2, T_a2, T_b2)), T_b2)))).
% 38.83/5.38 fof(cls_mem__def_0, axiom, ![V_S, T_a2, V_x2]: (hBOOL(hAPP(V_S, V_x2)) | ~hBOOL(hAPP(hAPP(c_in(T_a2), V_x2), V_S)))).
% 38.83/5.38 fof(cls_mem__def_1, axiom, ![T_a2, V_x2, V_S2]: (hBOOL(hAPP(hAPP(c_in(T_a2), V_x2), V_S2)) | ~hBOOL(hAPP(V_S2, V_x2)))).
% 38.83/5.38 fof(cls_predicate1D_0, axiom, ![V_P, V_Q, T_a2, V_x2]: (hBOOL(hAPP(V_Q, V_x2)) | (~hBOOL(hAPP(V_P, V_x2)) | ~c_lessequals(V_P, V_Q, tc_fun(T_a2, tc_bool))))).
% 38.83/5.38 fof(clsarity_bool__HOL_Oord, axiom, class_HOL_Oord(tc_bool)).
% 38.83/5.38
% 38.83/5.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 38.83/5.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 38.83/5.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 38.83/5.38 fresh(y, y, x1...xn) = u
% 38.83/5.38 C => fresh(s, t, x1...xn) = v
% 38.83/5.38 where fresh is a fresh function symbol and x1..xn are the free
% 38.83/5.38 variables of u and v.
% 38.83/5.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 38.83/5.38 input problem has no model of domain size 1).
% 38.83/5.38
% 38.83/5.38 The encoding turns the above axioms into the following unit equations and goals:
% 38.83/5.38
% 38.83/5.38 Axiom 1 (clsarity_bool__HOL_Oord): class_HOL_Oord(tc_bool) = true2.
% 38.83/5.38 Axiom 2 (cls_conjecture_3): fresh340(X, X, Y) = true2.
% 38.83/5.38 Axiom 3 (cls_mem__def_0): fresh191(X, X, Y, Z) = true2.
% 38.83/5.38 Axiom 4 (cls_predicate1D_0): fresh157(X, X, Y, Z) = true2.
% 38.83/5.38 Axiom 5 (cls_mem__def_1): fresh190(X, X, Y, Z, W) = true2.
% 38.83/5.38 Axiom 6 (cls_predicate1D_0): fresh158(X, X, Y, Z, W) = hBOOL(hAPP(Y, Z)).
% 38.83/5.38 Axiom 7 (cls_le__funD_0): fresh258(X, X, Y, Z, W, V) = true2.
% 38.83/5.38 Axiom 8 (cls_le__funI_0): fresh257(X, X, Y, Z, W, V) = c_lessequals(Z, W, tc_fun(V, Y)).
% 38.83/5.38 Axiom 9 (cls_le__funI_0): fresh256(X, X, Y, Z, W, V) = true2.
% 38.83/5.38 Axiom 10 (cls_conjecture_0): c_lessequals(v_tsa, v_Ga, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)) = true2.
% 38.83/5.38 Axiom 11 (cls_conjecture_1): hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)), v_xa), v_tsa)) = true2.
% 38.83/5.38 Axiom 12 (cls_le__funD_0): fresh259(X, X, Y, Z, W, V, U) = c_lessequals(hAPP(Z, W), hAPP(V, W), Y).
% 38.83/5.38 Axiom 13 (cls_mem__def_1): fresh190(hBOOL(hAPP(X, Y)), true2, Z, Y, X) = hBOOL(hAPP(hAPP(c_in(Z), Y), X)).
% 38.83/5.38 Axiom 14 (cls_conjecture_3): fresh340(hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)), X), v_Ga)), true2, X) = c_Hoare__Mirabelle_Otriple__valid(v_x, X, t_a).
% 38.83/5.38 Axiom 15 (cls_mem__def_0): fresh191(hBOOL(hAPP(hAPP(c_in(X), Y), Z)), true2, Z, Y) = hBOOL(hAPP(Z, Y)).
% 38.83/5.38 Axiom 16 (cls_predicate1D_0): fresh158(c_lessequals(X, Y, tc_fun(Z, tc_bool)), true2, Y, W, X) = fresh157(hBOOL(hAPP(X, W)), true2, Y, W).
% 38.83/5.38 Axiom 17 (cls_le__funD_0): fresh259(class_HOL_Oord(X), true2, X, Y, Z, W, V) = fresh258(c_lessequals(Y, W, tc_fun(V, X)), true2, X, Y, Z, W).
% 38.83/5.38 Axiom 18 (cls_le__funI_0): fresh257(class_HOL_Oord(X), true2, X, Y, Z, W) = fresh256(c_lessequals(hAPP(Y, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(Y, Z, W, X)), hAPP(Z, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(Y, Z, W, X)), X), true2, X, Y, Z, W).
% 38.83/5.38
% 38.83/5.38 Goal 1 (cls_conjecture_2): c_Hoare__Mirabelle_Otriple__valid(v_x, v_xa, t_a) = true2.
% 38.83/5.38 Proof:
% 38.83/5.38 c_Hoare__Mirabelle_Otriple__valid(v_x, v_xa, t_a)
% 38.83/5.38 = { by axiom 14 (cls_conjecture_3) R->L }
% 38.83/5.38 fresh340(hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)), v_xa), v_Ga)), true2, v_xa)
% 38.83/5.38 = { by axiom 13 (cls_mem__def_1) R->L }
% 38.83/5.38 fresh340(fresh190(hBOOL(hAPP(v_Ga, v_xa)), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 6 (cls_predicate1D_0) R->L }
% 38.83/5.38 fresh340(fresh190(fresh158(true2, true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 9 (cls_le__funI_0) R->L }
% 38.83/5.38 fresh340(fresh190(fresh158(fresh256(true2, true2, tc_bool, v_tsa, v_Ga, X), true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 7 (cls_le__funD_0) R->L }
% 38.83/5.38 fresh340(fresh190(fresh158(fresh256(fresh258(true2, true2, tc_bool, v_tsa, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(v_tsa, v_Ga, X, tc_bool), v_Ga), true2, tc_bool, v_tsa, v_Ga, X), true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 10 (cls_conjecture_0) R->L }
% 38.83/5.38 fresh340(fresh190(fresh158(fresh256(fresh258(c_lessequals(v_tsa, v_Ga, tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_bool)), true2, tc_bool, v_tsa, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(v_tsa, v_Ga, X, tc_bool), v_Ga), true2, tc_bool, v_tsa, v_Ga, X), true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 17 (cls_le__funD_0) R->L }
% 38.83/5.38 fresh340(fresh190(fresh158(fresh256(fresh259(class_HOL_Oord(tc_bool), true2, tc_bool, v_tsa, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(v_tsa, v_Ga, X, tc_bool), v_Ga, tc_Hoare__Mirabelle_Otriple(t_a)), true2, tc_bool, v_tsa, v_Ga, X), true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 1 (clsarity_bool__HOL_Oord) }
% 38.83/5.38 fresh340(fresh190(fresh158(fresh256(fresh259(true2, true2, tc_bool, v_tsa, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(v_tsa, v_Ga, X, tc_bool), v_Ga, tc_Hoare__Mirabelle_Otriple(t_a)), true2, tc_bool, v_tsa, v_Ga, X), true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 12 (cls_le__funD_0) }
% 38.83/5.38 fresh340(fresh190(fresh158(fresh256(c_lessequals(hAPP(v_tsa, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(v_tsa, v_Ga, X, tc_bool)), hAPP(v_Ga, c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(v_tsa, v_Ga, X, tc_bool)), tc_bool), true2, tc_bool, v_tsa, v_Ga, X), true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 18 (cls_le__funI_0) R->L }
% 38.83/5.38 fresh340(fresh190(fresh158(fresh257(class_HOL_Oord(tc_bool), true2, tc_bool, v_tsa, v_Ga, X), true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 1 (clsarity_bool__HOL_Oord) }
% 38.83/5.38 fresh340(fresh190(fresh158(fresh257(true2, true2, tc_bool, v_tsa, v_Ga, X), true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 8 (cls_le__funI_0) }
% 38.83/5.38 fresh340(fresh190(fresh158(c_lessequals(v_tsa, v_Ga, tc_fun(X, tc_bool)), true2, v_Ga, v_xa, v_tsa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 16 (cls_predicate1D_0) }
% 38.83/5.38 fresh340(fresh190(fresh157(hBOOL(hAPP(v_tsa, v_xa)), true2, v_Ga, v_xa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 15 (cls_mem__def_0) R->L }
% 38.83/5.38 fresh340(fresh190(fresh157(fresh191(hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)), v_xa), v_tsa)), true2, v_tsa, v_xa), true2, v_Ga, v_xa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 11 (cls_conjecture_1) }
% 38.83/5.38 fresh340(fresh190(fresh157(fresh191(true2, true2, v_tsa, v_xa), true2, v_Ga, v_xa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 3 (cls_mem__def_0) }
% 38.83/5.38 fresh340(fresh190(fresh157(true2, true2, v_Ga, v_xa), true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 4 (cls_predicate1D_0) }
% 38.83/5.38 fresh340(fresh190(true2, true2, tc_Hoare__Mirabelle_Otriple(t_a), v_xa, v_Ga), true2, v_xa)
% 38.83/5.38 = { by axiom 5 (cls_mem__def_1) }
% 38.83/5.38 fresh340(true2, true2, v_xa)
% 38.83/5.38 = { by axiom 2 (cls_conjecture_3) }
% 38.83/5.38 true2
% 38.83/5.38 % SZS output end Proof
% 38.83/5.38
% 38.83/5.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------