TSTP Solution File: LCL430-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL430-2 : 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 : 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 : 300s
% DateTime : Thu Aug 31 08:18:55 EDT 2023
% Result : Unsatisfiable 0.22s 0.46s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL430-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.35 % Computer : n020.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Fri Aug 25 05:29:45 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.22/0.46 Command-line arguments: --no-flatten-goal
% 0.22/0.46
% 0.22/0.46 % SZS status Unsatisfiable
% 0.22/0.46
% 0.22/0.47 % SZS output start Proof
% 0.22/0.47 Take the following subset of the input axioms:
% 0.22/0.47 fof(cls_PropLog_ODiff__weaken__left_0, axiom, ![V_p, V_A, V_B, T_a, V_C]: (~c_in(V_p, c_PropLog_Othms(c_minus(V_A, V_B, tc_set(tc_PropLog_Opl(T_a))), T_a), tc_PropLog_Opl(T_a)) | (~c_lessequals(V_A, V_C, tc_set(tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_minus(V_C, V_B, tc_set(tc_PropLog_Opl(T_a))), T_a), tc_PropLog_Opl(T_a))))).
% 0.22/0.47 fof(cls_PropLog_Ohyps__insert_0, axiom, ![V_v, V_t, V_p2, T_a2]: c_lessequals(c_PropLog_Ohyps(V_p2, c_insert(V_v, V_t, T_a2), T_a2), c_insert(c_PropLog_Opl_Ovar(V_v, T_a2), c_minus(c_PropLog_Ohyps(V_p2, V_t, T_a2), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(V_v, T_a2), c_PropLog_Opl_Ofalse, T_a2), c_emptyset, tc_PropLog_Opl(T_a2)), tc_set(tc_PropLog_Opl(T_a2))), tc_PropLog_Opl(T_a2)), tc_set(tc_PropLog_Opl(T_a2)))).
% 0.22/0.47 fof(cls_PropLog_Oinsert__Diff__same_0, axiom, ![V_a, T_a2, V_B2, V_C2]: c_lessequals(c_minus(V_B2, V_C2, tc_set(T_a2)), c_insert(V_a, c_minus(V_B2, c_insert(V_a, V_C2, T_a2), tc_set(T_a2)), T_a2), tc_set(T_a2))).
% 0.22/0.47 fof(cls_PropLog_Oinsert__Diff__subset2_0, axiom, ![V_c, V_D, T_a2, V_B2, V_a2]: c_lessequals(c_minus(c_insert(V_a2, c_minus(V_B2, c_insert(V_c, c_emptyset, T_a2), tc_set(T_a2)), T_a2), V_D, tc_set(T_a2)), c_insert(V_a2, c_minus(V_B2, c_insert(V_c, V_D, T_a2), tc_set(T_a2)), T_a2), tc_set(T_a2))).
% 0.22/0.47 fof(cls_PropLog_Othms__excluded__middle__rule_0, axiom, ![V_q, V_H, V_p2, T_a2]: (~c_in(V_q, c_PropLog_Othms(c_insert(V_p2, V_H, tc_PropLog_Opl(T_a2)), T_a2), tc_PropLog_Opl(T_a2)) | (~c_in(V_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V_p2, c_PropLog_Opl_Ofalse, T_a2), V_H, tc_PropLog_Opl(T_a2)), T_a2), tc_PropLog_Opl(T_a2)) | c_in(V_q, c_PropLog_Othms(V_H, T_a2), tc_PropLog_Opl(T_a2))))).
% 0.22/0.47 fof(cls_PropLog_Oweaken__left_0, axiom, ![V_G, V_p2, T_a2, V_H2]: (~c_in(V_p2, c_PropLog_Othms(V_G, T_a2), tc_PropLog_Opl(T_a2)) | (~c_lessequals(V_G, V_H2, tc_set(tc_PropLog_Opl(T_a2))) | c_in(V_p2, c_PropLog_Othms(V_H2, T_a2), tc_PropLog_Opl(T_a2))))).
% 0.22/0.47 fof(cls_conjecture_3, negated_conjecture, ![V_U]: c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, V_U, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a))).
% 0.22/0.47 fof(cls_conjecture_5, negated_conjecture, ~c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a))).
% 0.22/0.47
% 0.22/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.47 fresh(y, y, x1...xn) = u
% 0.22/0.47 C => fresh(s, t, x1...xn) = v
% 0.22/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.47 variables of u and v.
% 0.22/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.47 input problem has no model of domain size 1).
% 0.22/0.47
% 0.22/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.47
% 0.22/0.47 Axiom 1 (cls_PropLog_Oweaken__left_0): fresh(X, X, Y, Z, W) = true.
% 0.22/0.47 Axiom 2 (cls_PropLog_Othms__excluded__middle__rule_0): fresh3(X, X, Y, Z, W) = true.
% 0.22/0.47 Axiom 3 (cls_PropLog_ODiff__weaken__left_0): fresh6(X, X, Y, Z, W, V) = true.
% 0.22/0.47 Axiom 4 (cls_PropLog_Othms__excluded__middle__rule_0): fresh4(X, X, Y, Z, W, V) = c_in(Y, c_PropLog_Othms(W, V), tc_PropLog_Opl(V)).
% 0.22/0.47 Axiom 5 (cls_PropLog_Oweaken__left_0): fresh2(X, X, Y, Z, W, V) = c_in(Y, c_PropLog_Othms(V, W), tc_PropLog_Opl(W)).
% 0.22/0.47 Axiom 6 (cls_PropLog_Oweaken__left_0): fresh2(c_lessequals(X, Y, tc_set(tc_PropLog_Opl(Z))), true, W, X, Z, Y) = fresh(c_in(W, c_PropLog_Othms(X, Z), tc_PropLog_Opl(Z)), true, W, Z, Y).
% 0.22/0.47 Axiom 7 (cls_PropLog_ODiff__weaken__left_0): fresh5(X, X, Y, Z, W, V, U) = c_in(Y, c_PropLog_Othms(c_minus(U, W, tc_set(tc_PropLog_Opl(V))), V), tc_PropLog_Opl(V)).
% 0.22/0.47 Axiom 8 (cls_conjecture_3): c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, X, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)) = true.
% 0.22/0.47 Axiom 9 (cls_PropLog_ODiff__weaken__left_0): fresh5(c_lessequals(X, Y, tc_set(tc_PropLog_Opl(Z))), true, W, X, V, Z, Y) = fresh6(c_in(W, c_PropLog_Othms(c_minus(X, V, tc_set(tc_PropLog_Opl(Z))), Z), tc_PropLog_Opl(Z)), true, W, V, Z, Y).
% 0.22/0.47 Axiom 10 (cls_PropLog_Oinsert__Diff__same_0): c_lessequals(c_minus(X, Y, tc_set(Z)), c_insert(W, c_minus(X, c_insert(W, Y, Z), tc_set(Z)), Z), tc_set(Z)) = true.
% 0.22/0.47 Axiom 11 (cls_PropLog_Othms__excluded__middle__rule_0): fresh4(c_in(X, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(Y, c_PropLog_Opl_Ofalse, Z), W, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z)), true, X, Y, W, Z) = fresh3(c_in(X, c_PropLog_Othms(c_insert(Y, W, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z)), true, X, W, Z).
% 0.22/0.47 Axiom 12 (cls_PropLog_Oinsert__Diff__subset2_0): c_lessequals(c_minus(c_insert(X, c_minus(Y, c_insert(Z, c_emptyset, W), tc_set(W)), W), V, tc_set(W)), c_insert(X, c_minus(Y, c_insert(Z, V, W), tc_set(W)), W), tc_set(W)) = true.
% 0.22/0.47 Axiom 13 (cls_PropLog_Ohyps__insert_0): c_lessequals(c_PropLog_Ohyps(X, c_insert(Y, Z, W), W), c_insert(c_PropLog_Opl_Ovar(Y, W), c_minus(c_PropLog_Ohyps(X, Z, W), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(Y, W), c_PropLog_Opl_Ofalse, W), c_emptyset, tc_PropLog_Opl(W)), tc_set(tc_PropLog_Opl(W))), tc_PropLog_Opl(W)), tc_set(tc_PropLog_Opl(W))) = true.
% 0.22/0.47
% 0.22/0.47 Lemma 14: fresh2(X, X, Y, Z, W, V) = fresh4(U, U, Y, T, V, W).
% 0.22/0.47 Proof:
% 0.22/0.47 fresh2(X, X, Y, Z, W, V)
% 0.22/0.47 = { by axiom 5 (cls_PropLog_Oweaken__left_0) }
% 0.22/0.47 c_in(Y, c_PropLog_Othms(V, W), tc_PropLog_Opl(W))
% 0.22/0.47 = { by axiom 4 (cls_PropLog_Othms__excluded__middle__rule_0) R->L }
% 0.22/0.47 fresh4(U, U, Y, T, V, W)
% 0.22/0.47
% 0.22/0.47 Lemma 15: fresh4(X, X, Y, Z, c_minus(W, V, tc_set(tc_PropLog_Opl(U))), U) = fresh5(T, T, Y, S, V, U, W).
% 0.22/0.47 Proof:
% 0.22/0.47 fresh4(X, X, Y, Z, c_minus(W, V, tc_set(tc_PropLog_Opl(U))), U)
% 0.22/0.47 = { by axiom 4 (cls_PropLog_Othms__excluded__middle__rule_0) }
% 0.22/0.47 c_in(Y, c_PropLog_Othms(c_minus(W, V, tc_set(tc_PropLog_Opl(U))), U), tc_PropLog_Opl(U))
% 0.22/0.47 = { by axiom 7 (cls_PropLog_ODiff__weaken__left_0) R->L }
% 0.22/0.47 fresh5(T, T, Y, S, V, U, W)
% 0.22/0.47
% 0.22/0.47 Lemma 16: fresh5(X, X, v_p, Y, v_F, t_a, c_PropLog_Ohyps(v_p, Z, t_a)) = true.
% 0.22/0.47 Proof:
% 0.22/0.47 fresh5(X, X, v_p, Y, v_F, t_a, c_PropLog_Ohyps(v_p, Z, t_a))
% 0.22/0.47 = { by lemma 15 R->L }
% 0.22/0.47 fresh4(W, W, v_p, V, c_minus(c_PropLog_Ohyps(v_p, Z, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.47 = { by axiom 4 (cls_PropLog_Othms__excluded__middle__rule_0) }
% 0.22/0.47 c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, Z, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a))
% 0.22/0.47 = { by axiom 8 (cls_conjecture_3) }
% 0.22/0.47 true
% 0.22/0.47
% 0.22/0.47 Lemma 17: fresh2(c_lessequals(X, Y, tc_set(tc_PropLog_Opl(Z))), true, W, X, Z, Y) = fresh(fresh4(V, V, W, U, X, Z), true, W, Z, Y).
% 0.22/0.47 Proof:
% 0.22/0.47 fresh2(c_lessequals(X, Y, tc_set(tc_PropLog_Opl(Z))), true, W, X, Z, Y)
% 0.22/0.47 = { by axiom 6 (cls_PropLog_Oweaken__left_0) }
% 0.22/0.47 fresh(c_in(W, c_PropLog_Othms(X, Z), tc_PropLog_Opl(Z)), true, W, Z, Y)
% 0.22/0.47 = { by axiom 4 (cls_PropLog_Othms__excluded__middle__rule_0) R->L }
% 0.22/0.48 fresh(fresh4(V, V, W, U, X, Z), true, W, Z, Y)
% 0.22/0.48
% 0.22/0.48 Goal 1 (cls_conjecture_5): c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)) = true.
% 0.22/0.48 Proof:
% 0.22/0.48 c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a))
% 0.22/0.48 = { by axiom 4 (cls_PropLog_Othms__excluded__middle__rule_0) R->L }
% 0.22/0.48 fresh4(true, true, v_p, c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 1 (cls_PropLog_Oweaken__left_0) R->L }
% 0.22/0.48 fresh4(fresh(true, true, v_p, t_a, c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by lemma 16 R->L }
% 0.22/0.48 fresh4(fresh(fresh5(X, X, v_p, Y, v_F, t_a, c_PropLog_Ohyps(v_p, v_t, t_a)), true, v_p, t_a, c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by lemma 15 R->L }
% 0.22/0.48 fresh4(fresh(fresh4(Z, Z, v_p, W, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), true, v_p, t_a, c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by lemma 17 R->L }
% 0.22/0.48 fresh4(fresh2(c_lessequals(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a, c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 10 (cls_PropLog_Oinsert__Diff__same_0) }
% 0.22/0.48 fresh4(fresh2(true, true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a, c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by lemma 14 }
% 0.22/0.48 fresh4(fresh4(V, V, v_p, U, c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), true, v_p, c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 4 (cls_PropLog_Othms__excluded__middle__rule_0) }
% 0.22/0.48 fresh4(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, v_p, c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 11 (cls_PropLog_Othms__excluded__middle__rule_0) }
% 0.22/0.48 fresh3(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 4 (cls_PropLog_Othms__excluded__middle__rule_0) R->L }
% 0.22/0.48 fresh3(fresh4(T, T, v_p, S, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by lemma 14 R->L }
% 0.22/0.48 fresh3(fresh2(true, true, v_p, c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 12 (cls_PropLog_Oinsert__Diff__subset2_0) R->L }
% 0.22/0.48 fresh3(fresh2(c_lessequals(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by lemma 17 }
% 0.22/0.48 fresh3(fresh(fresh4(X2, X2, v_p, Y2, c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), true, v_p, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by lemma 15 }
% 0.22/0.48 fresh3(fresh(fresh5(true, true, v_p, c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a), v_F, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 13 (cls_PropLog_Ohyps__insert_0) R->L }
% 0.22/0.48 fresh3(fresh(fresh5(c_lessequals(c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, v_p, c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a), v_F, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 9 (cls_PropLog_ODiff__weaken__left_0) }
% 0.22/0.48 fresh3(fresh(fresh6(c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true, v_p, v_F, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 4 (cls_PropLog_Othms__excluded__middle__rule_0) R->L }
% 0.22/0.48 fresh3(fresh(fresh6(fresh4(Z2, Z2, v_p, W2, c_minus(c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), true, v_p, v_F, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by lemma 15 }
% 0.22/0.48 fresh3(fresh(fresh6(fresh5(V2, V2, v_p, U2, v_F, t_a, c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a)), true, v_p, v_F, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by lemma 16 }
% 0.22/0.48 fresh3(fresh(fresh6(true, true, v_p, v_F, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 3 (cls_PropLog_ODiff__weaken__left_0) }
% 0.22/0.48 fresh3(fresh(true, true, v_p, t_a, c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a))), true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 1 (cls_PropLog_Oweaken__left_0) }
% 0.22/0.48 fresh3(true, true, v_p, c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a)
% 0.22/0.48 = { by axiom 2 (cls_PropLog_Othms__excluded__middle__rule_0) }
% 0.22/0.48 true
% 0.22/0.48 % SZS output end Proof
% 0.22/0.48
% 0.22/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------