TSTP Solution File: LAT271-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LAT271-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n026.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 06:05:44 EDT 2022
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT271-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 29 18:21:33 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 The input problem is unsatisfiable because
% 0.14/0.41
% 0.14/0.41 [1] the following set of Horn clauses is unsatisfiable:
% 0.14/0.41
% 0.14/0.41 c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))
% 0.14/0.41 c_in(v_x, v_S, t_a)
% 0.14/0.41 c_in(c_Pair(v_a, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a)) ==> \bottom
% 0.14/0.41 c_in(V_x, V_S, T_a) & c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)) ==> c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))
% 0.14/0.41
% 0.14/0.41 This holds because
% 0.14/0.41
% 0.14/0.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.14/0.41
% 0.14/0.41 E:
% 0.14/0.41 c_in(v_x, v_S, t_a) = true__
% 0.14/0.41 c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) = true__
% 0.14/0.41 f1(c_in(c_Pair(v_a, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))) = true__
% 0.14/0.41 f1(true__) = false__
% 0.14/0.41 f2(true__, V_a, V_x, T_a, V_r) = c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))
% 0.14/0.41 f3(c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)), V_x, V_S, T_a, V_a, V_r) = true__
% 0.14/0.41 f3(true__, V_x, V_S, T_a, V_a, V_r) = f2(c_in(V_x, V_S, T_a), V_a, V_x, T_a, V_r)
% 0.14/0.41 G:
% 0.14/0.41 true__ = false__
% 0.14/0.41
% 0.14/0.41 This holds because
% 0.14/0.41
% 0.14/0.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.14/0.41
% 0.14/0.41
% 0.14/0.41 c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) -> f2(true__, V_a, V_x, T_a, V_r)
% 0.14/0.41 c_in(v_x, v_S, t_a) -> true__
% 0.14/0.41 c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) -> true__
% 0.14/0.41 f1(c_in(c_Pair(v_a, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))) -> true__
% 0.14/0.41 f1(f2(true__, v_a, v_x, t_a, v_r)) -> true__
% 0.14/0.41 f1(true__) -> false__
% 0.14/0.41 f2(c_in(V_x, V_S, T_a), V_a, V_x, T_a, V_r) -> f3(true__, V_x, V_S, T_a, V_a, V_r)
% 0.14/0.41 f2(f2(true__, X0, X1, X2, Y1), Y3, c_Pair(X0, X1, X2, X2), tc_prod(X2, X2), Y4) -> f3(true__, c_Pair(X0, X1, X2, X2), Y1, tc_prod(X2, X2), Y3, Y4)
% 0.14/0.41 f2(f3(true__, v_x, v_S, t_a, Y0, Y3), Y4, c_Pair(Y0, v_x, t_a, t_a), tc_prod(t_a, t_a), Y5) -> f3(true__, c_Pair(Y0, v_x, t_a, t_a), Y3, tc_prod(t_a, t_a), Y4, Y5)
% 0.14/0.41 f2(true__, Y3, v_x, t_a, Y4) -> f3(true__, v_x, v_S, t_a, Y3, Y4)
% 0.14/0.41 f3(c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)), V_x, V_S, T_a, V_a, V_r) -> true__
% 0.14/0.41 f3(true__, Y5, v_S, t_a, v_a, v_r) -> true__
% 0.14/0.41 false__ -> true__
% 0.14/0.41 with the LPO induced by
% 0.14/0.41 c_in > f2 > f3 > c_Pair > tc_prod > f1 > v_x > tc_set > t_a > v_b > v_a > v_r > c_Tarski_Ointerval > v_S > c_lessequals > false__ > true__
% 0.14/0.41
% 0.14/0.41 % SZS output end Proof
% 0.14/0.41
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