TSTP Solution File: LCL445-2 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL445-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n008.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 13:01:27 EDT 2022
% Result : Unsatisfiable 3.45s 3.50s
% Output : Proof 3.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : LCL445-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14 % Command : moca.sh %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 2 13:09:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.45/3.50 % SZS status Unsatisfiable
% 3.45/3.50 % SZS output start Proof
% 3.45/3.50 The input problem is unsatisfiable because
% 3.45/3.50
% 3.45/3.50 [1] the following set of Horn clauses is unsatisfiable:
% 3.45/3.50
% 3.45/3.50 c_in(v_q, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))
% 3.45/3.50 c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))
% 3.45/3.50 c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)) ==> \bottom
% 3.45/3.50 c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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))
% 3.45/3.50 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))
% 3.45/3.50 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), V_q, T_a), V_q, T_a), T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))
% 3.45/3.50
% 3.45/3.50 This holds because
% 3.45/3.50
% 3.45/3.50 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.45/3.50
% 3.45/3.50 E:
% 3.45/3.50 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), V_q, T_a), V_q, T_a), T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) = true__
% 3.45/3.50 c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) = true__
% 3.45/3.50 c_in(v_q, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) = true__
% 3.45/3.50 f1(c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))) = true__
% 3.45/3.50 f1(true__) = false__
% 3.45/3.50 f2(c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)), V_p, V_q, T_a, V_H) = true__
% 3.45/3.50 f2(true__, V_p, V_q, T_a, V_H) = 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))
% 3.45/3.50 f3(true__, V_q, V_H, T_a) = c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))
% 3.45/3.50 f4(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__
% 3.45/3.50 f4(true__, V_p, V_H, T_a, V_q) = f3(c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)), V_q, V_H, T_a)
% 3.45/3.50 G:
% 3.45/3.50 true__ = false__
% 3.45/3.50
% 3.45/3.50 This holds because
% 3.45/3.50
% 3.45/3.50 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.45/3.50
% 3.45/3.50
% 3.45/3.50 c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) -> f3(true__, V_q, V_H, T_a)
% 3.45/3.50 f1(f3(true__, v_q, v_H, t_a)) -> true__
% 3.45/3.50 f1(true__) -> false__
% 3.45/3.50 f2(f3(true__, Y0, c_insert(Y1, Y2, tc_PropLog_Opl(Y3)), Y3), Y1, Y0, Y3, Y2) -> true__
% 3.45/3.50 f2(true__, V_p, V_q, T_a, V_H) -> f3(true__, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), V_H, T_a)
% 3.45/3.50 f3(f3(true__, c_PropLog_Opl_Oop_A_N_62(X0, X1, Y2), Y3, Y2), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0, c_PropLog_Opl_Ofalse, Y2), X1, Y2), X1, Y2), Y3, Y2) -> true__
% 3.45/3.50 f3(f3(true__, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_H, t_a), v_q, v_H, t_a) -> true__
% 3.45/3.50 f3(f3(true__, c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_H, t_a), v_q, v_H, t_a) -> true__
% 3.45/3.50 f3(f3(true__, v_p, v_H, t_a), v_q, v_H, t_a) -> true__
% 3.45/3.50 f3(true__, c_PropLog_Opl_Oop_A_N_62(Y1, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0, X1, Y3), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0, c_PropLog_Opl_Ofalse, Y3), X1, Y3), X1, Y3), Y3), Y3), Y2, Y3) -> true__
% 3.45/3.50 f3(true__, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(Y0, Y1, Y2), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(Y0, c_PropLog_Opl_Ofalse, Y2), Y1, Y2), Y1, Y2), Y2), Y3, Y2) -> true__
% 3.45/3.50 f3(true__, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), v_H, t_a) -> true__
% 3.45/3.50 f3(true__, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), v_H, t_a) -> true__
% 3.45/3.50 f3(true__, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_H, t_a) -> true__
% 3.45/3.50 f3(true__, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a) -> true__
% 3.45/3.50 f3(true__, v_q, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_H, tc_PropLog_Opl(t_a)), t_a) -> true__
% 3.45/3.50 f3(true__, v_q, c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a) -> true__
% 3.45/3.50 f3(true__, v_q, v_H, t_a) -> true__
% 3.45/3.50 f4(f3(true__, c_PropLog_Opl_Oop_A_N_62(Y0, Y1, Y2), Y3, Y2), Y0, Y3, Y2, Y1) -> true__
% 3.45/3.50 f4(true__, V_p, V_H, T_a, V_q) -> f3(f3(true__, V_p, V_H, T_a), V_q, V_H, T_a)
% 3.45/3.50 false__ -> true__
% 3.45/3.50 with the LPO induced by
% 3.45/3.50 f2 > f4 > c_in > f3 > c_PropLog_Othms > c_PropLog_Opl_Ofalse > c_insert > v_p > c_PropLog_Opl_Oop_A_N_62 > tc_PropLog_Opl > t_a > v_H > v_q > f1 > false__ > true__
% 3.45/3.50
% 3.45/3.50 % SZS output end Proof
% 3.45/3.50
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