TSTP Solution File: LCL433-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL433-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n001.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 : 300s
% DateTime : Thu Aug 31 08:18:56 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL433-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 21:27:12 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --ground-connectedness --complete-subsets
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Take the following subset of the input axioms:
% 0.19/0.41 fof(cls_PropLog_Osat__imp_0, axiom, ![V_p, V_H, T_a, V_q]: (~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))).
% 0.19/0.41 fof(cls_PropLog_Othms_OH_0, axiom, ![T_a2, V_p2, V_H2]: (~c_in(V_p2, V_H2, tc_PropLog_Opl(T_a2)) | c_in(V_p2, c_PropLog_Othms(V_H2, T_a2), tc_PropLog_Opl(T_a2)))).
% 0.19/0.41 fof(cls_PropLog_Othms_OMP_0, axiom, ![T_a2, V_p2, V_H2, V_q2]: (~c_in(V_p2, c_PropLog_Othms(V_H2, T_a2), tc_PropLog_Opl(T_a2)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p2, V_q2, T_a2), c_PropLog_Othms(V_H2, T_a2), tc_PropLog_Opl(T_a2)) | c_in(V_q2, c_PropLog_Othms(V_H2, T_a2), tc_PropLog_Opl(T_a2))))).
% 0.19/0.41 fof(cls_PropLog_Oweaken__left__insert_0, axiom, ![V_G, V_a, T_a2, V_p2]: (~c_in(V_p2, c_PropLog_Othms(V_G, T_a2), tc_PropLog_Opl(T_a2)) | c_in(V_p2, c_PropLog_Othms(c_insert(V_a, V_G, tc_PropLog_Opl(T_a2)), T_a2), tc_PropLog_Opl(T_a2)))).
% 0.19/0.41 fof(cls_Set_OinsertCI_1, axiom, ![V_x, V_B, T_a2]: c_in(V_x, c_insert(V_x, V_B, T_a2), T_a2)).
% 0.19/0.41 fof(cls_conjecture_2, negated_conjecture, c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a)).
% 0.19/0.41 fof(cls_conjecture_3, negated_conjecture, ~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))).
% 0.19/0.41 fof(cls_conjecture_4, negated_conjecture, ![V_U]: (c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)) | ~c_PropLog_Osat(v_F, V_U, t_a))).
% 0.19/0.41
% 0.19/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.41 fresh(y, y, x1...xn) = u
% 0.19/0.41 C => fresh(s, t, x1...xn) = v
% 0.19/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.41 variables of u and v.
% 0.19/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.41 input problem has no model of domain size 1).
% 0.19/0.41
% 0.19/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.41
% 0.19/0.41 Axiom 1 (cls_conjecture_4): fresh(X, X, Y) = true.
% 0.19/0.42 Axiom 2 (cls_PropLog_Othms_OH_0): fresh6(X, X, Y, Z, W) = true.
% 0.19/0.42 Axiom 3 (cls_PropLog_Othms_OMP_0): fresh3(X, X, Y, Z, W) = true.
% 0.19/0.42 Axiom 4 (cls_PropLog_Osat__imp_0): fresh5(X, X, Y, Z, W, V) = true.
% 0.19/0.42 Axiom 5 (cls_PropLog_Oweaken__left__insert_0): fresh2(X, X, Y, Z, W, V) = true.
% 0.19/0.42 Axiom 6 (cls_conjecture_4): fresh(c_PropLog_Osat(v_F, X, t_a), true, X) = c_in(X, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)).
% 0.19/0.42 Axiom 7 (cls_Set_OinsertCI_1): c_in(X, c_insert(X, Y, Z), Z) = true.
% 0.19/0.42 Axiom 8 (cls_PropLog_Othms_OMP_0): fresh4(X, X, Y, Z, W, V) = c_in(V, c_PropLog_Othms(Z, W), tc_PropLog_Opl(W)).
% 0.19/0.42 Axiom 9 (cls_conjecture_2): c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a) = true.
% 0.19/0.42 Axiom 10 (cls_PropLog_Othms_OH_0): fresh6(c_in(X, Y, tc_PropLog_Opl(Z)), true, X, Y, Z) = c_in(X, c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)).
% 0.19/0.42 Axiom 11 (cls_PropLog_Oweaken__left__insert_0): fresh2(c_in(X, c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)), true, X, Y, Z, W) = c_in(X, c_PropLog_Othms(c_insert(W, Y, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z)).
% 0.19/0.42 Axiom 12 (cls_PropLog_Osat__imp_0): fresh5(c_PropLog_Osat(c_insert(X, Y, tc_PropLog_Opl(Z)), W, Z), true, X, Y, Z, W) = c_PropLog_Osat(Y, c_PropLog_Opl_Oop_A_N_62(X, W, Z), Z).
% 0.19/0.42 Axiom 13 (cls_PropLog_Othms_OMP_0): fresh4(c_in(c_PropLog_Opl_Oop_A_N_62(X, Y, Z), c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)), true, X, W, Z, Y) = fresh3(c_in(X, c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)), true, W, Z, Y).
% 0.19/0.42
% 0.19/0.42 Goal 1 (cls_conjecture_3): 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.
% 0.19/0.42 Proof:
% 0.19/0.42 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))
% 0.19/0.42 = { by axiom 8 (cls_PropLog_Othms_OMP_0) R->L }
% 0.19/0.42 fresh4(true, true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 5 (cls_PropLog_Oweaken__left__insert_0) R->L }
% 0.19/0.42 fresh4(fresh2(true, true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), v_F, t_a, v_x), true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 1 (cls_conjecture_4) R->L }
% 0.19/0.42 fresh4(fresh2(fresh(true, true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a)), true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), v_F, t_a, v_x), true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 4 (cls_PropLog_Osat__imp_0) R->L }
% 0.19/0.42 fresh4(fresh2(fresh(fresh5(true, true, v_x, v_F, t_a, v_xa), true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a)), true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), v_F, t_a, v_x), true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 9 (cls_conjecture_2) R->L }
% 0.19/0.42 fresh4(fresh2(fresh(fresh5(c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a), true, v_x, v_F, t_a, v_xa), true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a)), true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), v_F, t_a, v_x), true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 12 (cls_PropLog_Osat__imp_0) }
% 0.19/0.42 fresh4(fresh2(fresh(c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a), true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a)), true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), v_F, t_a, v_x), true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 6 (cls_conjecture_4) }
% 0.19/0.42 fresh4(fresh2(c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), true, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), v_F, t_a, v_x), true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 11 (cls_PropLog_Oweaken__left__insert_0) }
% 0.19/0.42 fresh4(c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 13 (cls_PropLog_Othms_OMP_0) }
% 0.19/0.42 fresh3(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 10 (cls_PropLog_Othms_OH_0) R->L }
% 0.19/0.42 fresh3(fresh6(c_in(v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a)), true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), true, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 7 (cls_Set_OinsertCI_1) }
% 0.19/0.42 fresh3(fresh6(true, true, v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), true, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 2 (cls_PropLog_Othms_OH_0) }
% 0.19/0.42 fresh3(true, true, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a, v_xa)
% 0.19/0.42 = { by axiom 3 (cls_PropLog_Othms_OMP_0) }
% 0.19/0.42 true
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------