TSTP Solution File: LAT263-2 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n032.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 : 600s
% DateTime : Sun Jul 17 06:05:38 EDT 2022
% Result : Unsatisfiable 1.42s 1.54s
% Output : Proof 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.10 % Command : moca.sh %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Wed Jun 29 05:42:58 EDT 2022
% 0.10/0.29 % CPUTime :
% 1.42/1.54 % SZS status Unsatisfiable
% 1.42/1.54 % SZS output start Proof
% 1.42/1.54 The input problem is unsatisfiable because
% 1.42/1.54
% 1.42/1.54 [1] the following set of Horn clauses is unsatisfiable:
% 1.42/1.54
% 1.42/1.54 c_lessequals(v_S, v_A, tc_set(t_a))
% 1.42/1.54 c_in(c_Tarski_Oglb(v_S, v_cl, t_a), v_A, t_a) ==> \bottom
% 1.42/1.54 v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit)
% 1.42/1.54 c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) & c_in(V_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) & c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), tc_set(T_a)) ==> c_in(c_Tarski_Olub(V_S, V_cl, T_a), c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), T_a)
% 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit))
% 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit))
% 1.42/1.54 c_Tarski_Oglb(V_S, V_cl, T_a) = c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a)
% 1.42/1.54 c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit)
% 1.42/1.54
% 1.42/1.54 This holds because
% 1.42/1.54
% 1.42/1.54 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.42/1.54
% 1.42/1.54 E:
% 1.42/1.54 c_Tarski_Oglb(V_S, V_cl, T_a) = c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a)
% 1.42/1.54 c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit)
% 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true__
% 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true__
% 1.42/1.54 c_lessequals(v_S, v_A, tc_set(t_a)) = true__
% 1.42/1.54 f1(c_in(c_Tarski_Oglb(v_S, v_cl, t_a), v_A, t_a)) = true__
% 1.42/1.54 f1(true__) = false__
% 1.42/1.54 f2(true__, V_S, V_cl, T_a) = c_in(c_Tarski_Olub(V_S, V_cl, T_a), c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), T_a)
% 1.42/1.54 f3(true__, V_cl, T_a, V_S) = f2(c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_S, V_cl, T_a)
% 1.42/1.54 f4(c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), tc_set(T_a)), V_cl, T_a, V_S) = true__
% 1.42/1.54 f4(true__, V_cl, T_a, V_S) = f3(c_in(V_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_cl, T_a, V_S)
% 1.42/1.54 v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit)
% 1.42/1.54 G:
% 1.42/1.54 true__ = false__
% 1.42/1.54
% 1.42/1.54 This holds because
% 1.42/1.54
% 1.42/1.54 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.42/1.54
% 1.42/1.54 c_in(c_Tarski_Oglb(Y0, X0, Y2), c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), Y2) = f2(true__, Y0, c_Tarski_Odual(X0, Y2), Y2)
% 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(X0, Y2), Y2), c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), Y2) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2)
% 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), Y2) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2)
% 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2), c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), Y2) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2), Y2)
% 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), v_A, t_a) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), t_a)
% 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(v_cl, t_a), t_a), v_A, t_a) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a)
% 1.42/1.54 c_in(c_Tarski_Oglb(Y0, v_cl, t_a), v_A, t_a) = f4(true__, c_Tarski_Odual(v_cl, t_a), t_a, Y0)
% 1.42/1.54 c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a) -> c_Tarski_Oglb(V_S, V_cl, T_a)
% 1.42/1.54 c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit) -> c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit)
% 1.42/1.54 c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) -> v_A
% 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) -> true__
% 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) -> true__
% 1.42/1.54 c_in(c_Tarski_Oglb(v_S, v_cl, t_a), v_A, t_a) -> true__
% 1.42/1.54 c_in(c_Tarski_Olub(V_S, V_cl, T_a), c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), T_a) -> f2(true__, V_S, V_cl, T_a)
% 1.42/1.54 c_in(c_Tarski_Olub(Y0, v_cl, t_a), v_A, t_a) -> f2(true__, Y0, v_cl, t_a)
% 1.42/1.54 c_lessequals(v_S, v_A, tc_set(t_a)) -> true__
% 1.42/1.54 f1(c_in(c_Tarski_Oglb(v_S, v_cl, t_a), v_A, t_a)) -> true__
% 1.42/1.54 f1(true__) -> false__
% 1.42/1.54 f2(c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_S, V_cl, T_a) -> f3(true__, V_cl, T_a, V_S)
% 1.42/1.54 f2(true__, Y2, c_Tarski_Odual(v_cl, t_a), t_a) -> f3(true__, c_Tarski_Odual(v_cl, t_a), t_a, Y2)
% 1.42/1.54 f3(c_in(V_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_cl, T_a, V_S) -> f4(true__, V_cl, T_a, V_S)
% 1.42/1.54 f3(true__, c_Tarski_Odual(v_cl, t_a), t_a, Y2) -> f4(true__, c_Tarski_Odual(v_cl, t_a), t_a, Y2)
% 1.42/1.54 f4(c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), tc_set(T_a)), V_cl, T_a, V_S) -> true__
% 1.42/1.54 f4(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_Tarski_Odual(X0, Y2), Y2, Y0) -> true__
% 1.42/1.54 f4(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2, Y0) -> true__
% 1.42/1.54 f4(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2, Y0) -> true__
% 1.42/1.54 f4(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2), Y2, Y0) -> true__
% 1.42/1.54 f4(c_lessequals(Y0, v_A, tc_set(t_a)), c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), t_a, Y0) -> true__
% 1.42/1.54 f4(c_lessequals(Y0, v_A, tc_set(t_a)), c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a, Y0) -> true__
% 1.42/1.54 f4(c_lessequals(Y0, v_A, tc_set(t_a)), c_Tarski_Odual(v_cl, t_a), t_a, Y0) -> true__
% 1.42/1.54 f4(c_lessequals(Y0, v_A, tc_set(t_a)), v_cl, t_a, Y0) -> true__
% 1.42/1.54 f4(true__, c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a, v_S) -> true__
% 1.42/1.54 f4(true__, v_cl, t_a, v_S) -> true__
% 1.42/1.54 false__ -> true__
% 1.42/1.54 with the LPO induced by
% 1.42/1.54 c_Tarski_Odual > c_in > f2 > f3 > c_Tarski_OCompleteLattice > f4 > tc_Product__Type_Ounit > v_A > t_a > c_Tarski_Opotype_Opset > c_Tarski_OPartialOrder > tc_Tarski_Opotype_Opotype__ext__type > c_Tarski_Olub > c_Tarski_Oglb > v_cl > f1 > tc_set > v_S > c_lessequals > false__ > true__
% 1.42/1.54
% 1.42/1.54 % SZS output end Proof
% 1.42/1.54
%------------------------------------------------------------------------------