TSTP Solution File: LCL433-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL433-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.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 13:01:16 EDT 2022
% Result : Unsatisfiable 8.87s 8.83s
% Output : Proof 8.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL433-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 08:26:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 8.87/8.83 % SZS status Unsatisfiable
% 8.87/8.83 % SZS output start Proof
% 8.87/8.83 The input problem is unsatisfiable because
% 8.87/8.83
% 8.87/8.83 [1] the following set of Horn clauses is unsatisfiable:
% 8.87/8.83
% 8.87/8.83 c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a)
% 8.87/8.83 c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) ==> \bottom
% 8.87/8.83 c_PropLog_Osat(v_F, V_U, t_a) ==> c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))
% 8.87/8.83 c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a) ==> c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a)
% 8.87/8.83 c_in(V_p, V_H, tc_PropLog_Opl(T_a)) ==> c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))
% 8.87/8.83 c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) & c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) ==> c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))
% 8.87/8.83 c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a)) ==> c_in(V_p, c_PropLog_Othms(c_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))
% 8.87/8.83 c_in(V_x, c_insert(V_x, V_B, T_a), T_a)
% 8.87/8.83
% 8.87/8.83 This holds because
% 8.87/8.83
% 8.87/8.83 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.87/8.83
% 8.87/8.83 E:
% 8.87/8.83 c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a) = true__
% 8.87/8.83 c_in(V_x, c_insert(V_x, V_B, T_a), T_a) = true__
% 8.87/8.83 f1(c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) = true__
% 8.87/8.83 f1(true__) = false__
% 8.87/8.83 f2(c_PropLog_Osat(v_F, V_U, t_a), V_U) = true__
% 8.87/8.83 f2(true__, V_U) = c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))
% 8.87/8.83 f3(c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a), V_H, V_p, V_q, T_a) = true__
% 8.87/8.83 f3(true__, V_H, V_p, V_q, T_a) = c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a)
% 8.87/8.83 f4(c_in(V_p, V_H, tc_PropLog_Opl(T_a)), V_p, V_H, T_a) = true__
% 8.87/8.83 f4(true__, V_p, V_H, T_a) = c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))
% 8.87/8.83 f5(true__, V_q, V_H, T_a) = c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))
% 8.87/8.83 f6(c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)), V_p, V_H, T_a, V_q) = true__
% 8.87/8.83 f6(true__, V_p, V_H, T_a, V_q) = f5(c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)), V_q, V_H, T_a)
% 8.87/8.83 f7(c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a)), V_p, V_a, V_G, T_a) = true__
% 8.87/8.83 f7(true__, V_p, V_a, V_G, T_a) = c_in(V_p, c_PropLog_Othms(c_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))
% 8.87/8.83 G:
% 8.87/8.83 true__ = false__
% 8.87/8.83
% 8.87/8.83 This holds because
% 8.87/8.83
% 8.87/8.83 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.87/8.83
% 8.87/8.83
% 8.87/8.83 c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a) -> f3(true__, V_H, V_p, V_q, T_a)
% 8.87/8.83 c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a) -> true__
% 8.87/8.83 c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) -> f4(true__, V_p, V_H, T_a)
% 8.87/8.83 c_in(V_x, c_insert(V_x, V_B, T_a), T_a) -> true__
% 8.87/8.83 f1(f4(true__, v_xa, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a)) -> true__
% 8.87/8.83 f1(true__) -> false__
% 8.87/8.83 f2(c_PropLog_Osat(v_F, V_U, t_a), V_U) -> true__
% 8.87/8.83 f2(f3(true__, v_F, X1, X2, t_a), c_PropLog_Opl_Oop_A_N_62(X1, X2, t_a)) -> true__
% 8.87/8.83 f2(true__, V_U) -> f4(true__, V_U, v_F, t_a)
% 8.87/8.83 f3(c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a), V_H, V_p, V_q, T_a) -> true__
% 8.87/8.83 f3(f3(true__, c_insert(Y0, Y1, tc_PropLog_Opl(Y2)), X1, X2, Y2), Y1, Y0, c_PropLog_Opl_Oop_A_N_62(X1, X2, Y2), Y2) -> true__
% 8.87/8.83 f3(true__, v_F, v_x, v_xa, t_a) -> true__
% 8.87/8.83 f4(c_in(V_p, V_H, tc_PropLog_Opl(T_a)), V_p, V_H, T_a) -> true__
% 8.87/8.83 f4(f4(true__, Y0, X1, Y2), Y0, c_PropLog_Othms(X1, Y2), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_PropLog_Othms(c_PropLog_Othms(c_PropLog_Othms(c_PropLog_Othms(c_insert(Y0, X1, tc_PropLog_Opl(Y2)), Y2), Y2), Y2), Y2), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_PropLog_Othms(c_PropLog_Othms(c_PropLog_Othms(c_insert(Y0, X1, tc_PropLog_Opl(Y2)), Y2), Y2), Y2), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_PropLog_Othms(c_PropLog_Othms(c_insert(X1, c_insert(Y0, X2, tc_PropLog_Opl(Y2)), tc_PropLog_Opl(Y2)), Y2), Y2), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_PropLog_Othms(c_PropLog_Othms(c_insert(Y0, X1, tc_PropLog_Opl(Y2)), Y2), Y2), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_PropLog_Othms(c_insert(X1, c_PropLog_Othms(c_insert(Y0, X2, tc_PropLog_Opl(Y2)), Y2), tc_PropLog_Opl(Y2)), Y2), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_PropLog_Othms(c_insert(X1, c_insert(Y0, X2, tc_PropLog_Opl(Y2)), tc_PropLog_Opl(Y2)), Y2), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_PropLog_Othms(c_insert(Y0, X1, tc_PropLog_Opl(Y2)), Y2), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_insert(Y0, X1, tc_PropLog_Opl(Y2)), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_insert(Y3, c_PropLog_Othms(c_PropLog_Othms(c_insert(Y0, X1, tc_PropLog_Opl(Y2)), Y2), Y2), tc_PropLog_Opl(Y2)), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_insert(Y3, c_PropLog_Othms(c_insert(Y0, X1, tc_PropLog_Opl(Y2)), Y2), tc_PropLog_Opl(Y2)), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_insert(Y3, c_insert(X1, c_insert(Y0, X2, tc_PropLog_Opl(Y2)), tc_PropLog_Opl(Y2)), tc_PropLog_Opl(Y2)), Y2) -> true__
% 8.87/8.83 f4(true__, Y0, c_insert(Y3, c_insert(Y0, X1, tc_PropLog_Opl(Y2)), tc_PropLog_Opl(Y2)), Y2) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_PropLog_Othms(c_PropLog_Othms(c_PropLog_Othms(v_F, t_a), t_a), t_a), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_PropLog_Othms(c_PropLog_Othms(c_insert(X0, v_F, tc_PropLog_Opl(t_a)), t_a), t_a), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_PropLog_Othms(c_PropLog_Othms(v_F, t_a), t_a), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_PropLog_Othms(c_insert(X0, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), t_a), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_PropLog_Othms(c_insert(X0, v_F, tc_PropLog_Opl(t_a)), t_a), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_PropLog_Othms(v_F, t_a), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(X0, c_PropLog_Othms(c_PropLog_Othms(v_F, t_a), t_a), tc_PropLog_Opl(t_a)), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(X0, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(X0, c_insert(X1, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a)), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(X0, v_F, tc_PropLog_Opl(t_a)), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_insert(Y3, c_PropLog_Othms(c_PropLog_Othms(c_PropLog_Othms(v_F, t_a), t_a), t_a), tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_insert(Y3, c_PropLog_Othms(c_PropLog_Othms(v_F, t_a), t_a), tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_insert(Y3, c_PropLog_Othms(c_insert(X0, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_insert(Y3, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_insert(Y3, c_insert(X0, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_insert(Y3, c_insert(X0, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_insert(Y3, v_F, tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f4(true__, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), v_F, t_a) -> true__
% 8.87/8.83 f4(true__, v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), t_a) -> true__
% 8.87/8.83 f4(true__, v_xa, c_insert(Y3, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f4(true__, v_xa, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f5(f4(true__, v_x, c_PropLog_Othms(c_PropLog_Othms(v_F, t_a), t_a), t_a), v_xa, c_PropLog_Othms(c_PropLog_Othms(v_F, t_a), t_a), t_a) -> true__
% 8.87/8.83 f5(f4(true__, v_x, c_PropLog_Othms(v_F, t_a), t_a), v_xa, c_PropLog_Othms(v_F, t_a), t_a) -> true__
% 8.87/8.83 f5(f4(true__, v_x, c_insert(X0, v_F, tc_PropLog_Opl(t_a)), t_a), v_xa, c_insert(X0, v_F, tc_PropLog_Opl(t_a)), t_a) -> true__
% 8.87/8.83 f5(f4(true__, v_x, v_F, t_a), v_xa, v_F, t_a) -> true__
% 8.87/8.83 f5(true__, V_q, V_H, T_a) -> f4(true__, V_q, V_H, T_a)
% 8.87/8.83 f6(f4(true__, c_PropLog_Opl_Oop_A_N_62(Y0, Y1, Y2), Y3, Y2), Y0, Y3, Y2, Y1) -> true__
% 8.87/8.83 f6(true__, V_p, V_H, T_a, V_q) -> f5(f4(true__, V_p, V_H, T_a), V_q, V_H, T_a)
% 8.87/8.83 f7(f4(true__, Y0, Y1, Y2), Y0, Y3, Y1, Y2) -> true__
% 8.87/8.83 f7(true__, V_p, V_a, V_G, T_a) -> f4(true__, V_p, c_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a)
% 8.87/8.83 false__ -> true__
% 8.87/8.83 with the LPO induced by
% 8.87/8.83 f2 > t_a > v_F > f6 > f5 > f7 > c_in > f4 > tc_PropLog_Opl > c_PropLog_Othms > c_PropLog_Osat > f3 > c_PropLog_Opl_Oop_A_N_62 > c_insert > v_xa > v_x > f1 > false__ > true__
% 8.87/8.83
% 8.87/8.83 % SZS output end Proof
% 8.87/8.83
%------------------------------------------------------------------------------