TSTP Solution File: LCL443-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL443-2 : 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 : n031.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 08:19:00 EDT 2023
% Result : Unsatisfiable 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL443-2 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n031.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 : 300
% 0.13/0.35 % DateTime : Fri Aug 25 07:12:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.47
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 Take the following subset of the input axioms:
% 0.19/0.48 fof(cls_PropLog_Odeduction_0, axiom, ![V_p, V_H, T_a, V_q]: (~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)))).
% 0.19/0.48 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)))).
% 0.19/0.48 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))))).
% 0.19/0.48 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)))).
% 0.19/0.48 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)).
% 0.19/0.48 fof(cls_conjecture_0, negated_conjecture, c_in(v_p, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))).
% 0.19/0.48 fof(cls_conjecture_1, negated_conjecture, c_in(c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))).
% 0.19/0.48 fof(cls_conjecture_2, negated_conjecture, ~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_Ofalse, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))).
% 0.19/0.48
% 0.19/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.48 fresh(y, y, x1...xn) = u
% 0.19/0.48 C => fresh(s, t, x1...xn) = v
% 0.19/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.48 variables of u and v.
% 0.19/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.48 input problem has no model of domain size 1).
% 0.19/0.48
% 0.19/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.48
% 0.19/0.48 Axiom 1 (cls_PropLog_Othms_OH_0): fresh5(X, X, Y, Z, W) = true.
% 0.19/0.48 Axiom 2 (cls_PropLog_Othms_OMP_0): fresh2(X, X, Y, Z, W) = true.
% 0.19/0.48 Axiom 3 (cls_Set_OinsertCI_1): c_in(X, c_insert(X, Y, Z), Z) = true.
% 0.19/0.48 Axiom 4 (cls_conjecture_0): c_in(v_p, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)) = true.
% 0.19/0.48 Axiom 5 (cls_PropLog_Oweaken__left__insert_0): fresh(X, X, Y, Z, W, V) = true.
% 0.19/0.48 Axiom 6 (cls_PropLog_Odeduction_0): fresh4(X, X, Y, Z, W, V) = true.
% 0.19/0.48 Axiom 7 (cls_PropLog_Othms_OMP_0): fresh3(X, X, Y, Z, W, V) = c_in(V, c_PropLog_Othms(Z, W), tc_PropLog_Opl(W)).
% 0.19/0.48 Axiom 8 (cls_conjecture_1): c_in(c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)) = true.
% 0.19/0.48 Axiom 9 (cls_PropLog_Othms_OH_0): fresh5(c_in(X, Y, tc_PropLog_Opl(Z)), true, X, Y, Z) = c_in(X, c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)).
% 0.19/0.48 Axiom 10 (cls_PropLog_Oweaken__left__insert_0): fresh(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)).
% 0.19/0.48 Axiom 11 (cls_PropLog_Othms_OMP_0): fresh3(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) = fresh2(c_in(X, c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)), true, W, Z, Y).
% 0.19/0.48 Axiom 12 (cls_PropLog_Odeduction_0): fresh4(c_in(X, c_PropLog_Othms(c_insert(Y, Z, tc_PropLog_Opl(W)), W), tc_PropLog_Opl(W)), true, X, Y, Z, W) = c_in(c_PropLog_Opl_Oop_A_N_62(Y, X, W), c_PropLog_Othms(Z, W), tc_PropLog_Opl(W)).
% 0.19/0.48
% 0.19/0.48 Goal 1 (cls_conjecture_2): 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_Ofalse, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)) = true.
% 0.19/0.48 Proof:
% 0.19/0.48 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_Ofalse, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))
% 0.19/0.48 = { by axiom 12 (cls_PropLog_Odeduction_0) R->L }
% 0.19/0.48 fresh4(c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.48 = { by axiom 7 (cls_PropLog_Othms_OMP_0) R->L }
% 0.19/0.48 fresh4(fresh3(true, true, v_q, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.48 = { by axiom 5 (cls_PropLog_Oweaken__left__insert_0) R->L }
% 0.19/0.48 fresh4(fresh3(fresh(true, true, c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), v_H, t_a, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a)), true, v_q, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.48 = { by axiom 8 (cls_conjecture_1) R->L }
% 0.19/0.48 fresh4(fresh3(fresh(c_in(c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), v_H, t_a, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a)), true, v_q, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.48 = { by axiom 10 (cls_PropLog_Oweaken__left__insert_0) }
% 0.19/0.48 fresh4(fresh3(c_in(c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, v_q, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.48 = { by axiom 11 (cls_PropLog_Othms_OMP_0) }
% 0.19/0.48 fresh4(fresh2(c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.48 = { by axiom 7 (cls_PropLog_Othms_OMP_0) R->L }
% 0.19/0.48 fresh4(fresh2(fresh3(true, true, v_p, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, v_q), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.48 = { by axiom 1 (cls_PropLog_Othms_OH_0) R->L }
% 0.19/0.48 fresh4(fresh2(fresh3(fresh5(true, true, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), true, v_p, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, v_q), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.48 = { by axiom 3 (cls_Set_OinsertCI_1) R->L }
% 0.19/0.48 fresh4(fresh2(fresh3(fresh5(c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a)), true, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), true, v_p, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, v_q), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.48 = { by axiom 9 (cls_PropLog_Othms_OH_0) }
% 0.19/0.49 fresh4(fresh2(fresh3(c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, v_p, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, v_q), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.49 = { by axiom 11 (cls_PropLog_Othms_OMP_0) }
% 0.19/0.49 fresh4(fresh2(fresh2(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, v_q), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.49 = { by axiom 10 (cls_PropLog_Oweaken__left__insert_0) R->L }
% 0.19/0.49 fresh4(fresh2(fresh2(fresh(c_in(v_p, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, v_p, v_H, t_a, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a)), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, v_q), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.49 = { by axiom 4 (cls_conjecture_0) }
% 0.19/0.49 fresh4(fresh2(fresh2(fresh(true, true, v_p, v_H, t_a, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a)), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, v_q), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.49 = { by axiom 5 (cls_PropLog_Oweaken__left__insert_0) }
% 0.19/0.49 fresh4(fresh2(fresh2(true, true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, v_q), true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.49 = { by axiom 2 (cls_PropLog_Othms_OMP_0) }
% 0.19/0.49 fresh4(fresh2(true, true, c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a, c_PropLog_Opl_Ofalse), true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.49 = { by axiom 2 (cls_PropLog_Othms_OMP_0) }
% 0.19/0.49 fresh4(true, true, c_PropLog_Opl_Ofalse, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, t_a)
% 0.19/0.49 = { by axiom 6 (cls_PropLog_Odeduction_0) }
% 0.19/0.49 true
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49
% 0.19/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------