TSTP Solution File: LAT259-2 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LAT259-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 06:05:35 EDT 2022
% Result : Unsatisfiable 1.39s 1.47s
% Output : Proof 1.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT259-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n019.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 : 600
% 0.13/0.34 % DateTime : Thu Jun 30 12:19:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.39/1.47 % SZS status Unsatisfiable
% 1.39/1.47 % SZS output start Proof
% 1.39/1.47 The input problem is unsatisfiable because
% 1.39/1.47
% 1.39/1.47 [1] the following set of Horn clauses is unsatisfiable:
% 1.39/1.47
% 1.39/1.47 c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))
% 1.39/1.47 c_in(c_Pair(v_b, v_a, t_a, t_a), v_r, tc_prod(t_a, t_a))
% 1.39/1.47 v_a = v_b ==> \bottom
% 1.39/1.47 c_Relation_Oantisym(V_r, T_a) & c_in(c_Pair(V_V, V_U, T_a, T_a), V_r, tc_prod(T_a, T_a)) & c_in(c_Pair(V_U, V_V, T_a, T_a), V_r, tc_prod(T_a, T_a)) ==> V_U = V_V
% 1.39/1.47 c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) ==> c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a)
% 1.39/1.47 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit))
% 1.39/1.47 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)
% 1.39/1.47
% 1.39/1.47 This holds because
% 1.39/1.47
% 1.39/1.47 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.39/1.47
% 1.39/1.47 E:
% 1.39/1.47 c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true__
% 1.39/1.47 c_in(c_Pair(v_b, v_a, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true__
% 1.39/1.47 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true__
% 1.39/1.47 f1(v_a) = true__
% 1.39/1.47 f1(v_b) = false__
% 1.39/1.47 f2(true__, V_U, V_V) = V_U
% 1.39/1.47 f3(true__, V_r, T_a, V_U, V_V) = f2(c_Relation_Oantisym(V_r, T_a), V_U, V_V)
% 1.39/1.47 f4(c_in(c_Pair(V_U, V_V, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_V, V_U, T_a, V_r) = V_V
% 1.39/1.47 f4(true__, V_V, V_U, T_a, V_r) = f3(c_in(c_Pair(V_V, V_U, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_r, T_a, V_U, V_V)
% 1.39/1.47 f5(c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_P, T_a) = true__
% 1.39/1.47 f5(true__, V_P, T_a) = c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a)
% 1.39/1.47 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)
% 1.39/1.47 G:
% 1.39/1.47 true__ = false__
% 1.39/1.47
% 1.39/1.47 This holds because
% 1.39/1.47
% 1.39/1.47 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.39/1.47
% 1.39/1.47
% 1.39/1.47 c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) -> f5(true__, V_P, T_a)
% 1.39/1.47 c_Relation_Oantisym(v_r, t_a) -> f5(true__, v_cl, t_a)
% 1.39/1.47 c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) -> v_r
% 1.39/1.47 c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> true__
% 1.39/1.47 c_in(c_Pair(v_b, v_a, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> true__
% 1.39/1.47 c_in(c_Pair(v_b, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> true__
% 1.39/1.47 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) -> true__
% 1.39/1.47 f1(v_a) -> true__
% 1.39/1.47 f1(v_b) -> false__
% 1.39/1.47 f2(c_Relation_Oantisym(V_r, T_a), V_U, V_V) -> f3(true__, V_r, T_a, V_U, V_V)
% 1.39/1.47 f2(f5(true__, X0, Y1), Y2, Y3) -> f3(true__, c_Tarski_Opotype_Oorder(X0, Y1, tc_Product__Type_Ounit), Y1, Y2, Y3)
% 1.39/1.47 f2(true__, V_U, V_V) -> V_U
% 1.39/1.47 f3(c_in(c_Pair(V_V, V_U, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_r, T_a, V_U, V_V) -> f4(true__, V_V, V_U, T_a, V_r)
% 1.39/1.47 f3(true__, v_r, t_a, Y2, Y3) -> Y2
% 1.39/1.47 f3(true__, v_r, t_a, v_a, v_b) -> f4(true__, v_b, v_a, t_a, v_r)
% 1.39/1.47 f3(true__, v_r, t_a, v_b, v_a) -> f4(true__, v_a, v_b, t_a, v_r)
% 1.39/1.47 f4(c_in(c_Pair(V_U, V_V, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_V, V_U, T_a, V_r) -> V_V
% 1.39/1.47 f4(true__, v_a, v_b, t_a, v_r) -> v_a
% 1.39/1.47 f4(true__, v_b, v_a, t_a, v_r) -> v_b
% 1.39/1.47 f4(true__, v_b, v_b, t_a, v_r) -> v_b
% 1.39/1.47 f5(c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_P, T_a) -> true__
% 1.39/1.47 f5(true__, v_cl, t_a) -> true__
% 1.39/1.47 false__ -> true__
% 1.39/1.47 v_a -> v_b
% 1.39/1.47 with the LPO induced by
% 1.39/1.47 f2 > f3 > f4 > c_Relation_Oantisym > f5 > c_Tarski_Opotype_Oorder > v_r > v_cl > tc_Tarski_Opotype_Opotype__ext__type > c_Tarski_OPartialOrder > tc_Product__Type_Ounit > v_a > c_in > c_Pair > f1 > tc_prod > t_a > v_b > false__ > true__
% 1.39/1.47
% 1.39/1.47 % SZS output end Proof
% 1.39/1.47
%------------------------------------------------------------------------------