TSTP Solution File: LCL445-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL445-2 : 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 : n026.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 08:19:01 EDT 2023
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL445-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n026.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 : 300
% 0.12/0.33 % DateTime : Thu Aug 24 17:37:02 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.37 Command-line arguments: --no-flatten-goal
% 0.18/0.37
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 Take the following subset of the input axioms:
% 0.18/0.38 fof(cls_PropLog_Odeduction_0, axiom, ![V_q, V_p, V_H, T_a]: (~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)))).
% 0.18/0.38 fof(cls_PropLog_Othms_OMP_0, axiom, ![V_q2, V_p2, V_H2, T_a2]: (~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))))).
% 0.18/0.38 fof(cls_PropLog_Othms__excluded__middle_0, axiom, ![V_q2, V_p2, V_H2, T_a2]: c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p2, V_q2, T_a2), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p2, c_PropLog_Opl_Ofalse, T_a2), V_q2, T_a2), V_q2, T_a2), T_a2), c_PropLog_Othms(V_H2, T_a2), tc_PropLog_Opl(T_a2))).
% 0.18/0.38 fof(cls_conjecture_0, negated_conjecture, 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))).
% 0.18/0.39 fof(cls_conjecture_1, negated_conjecture, 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))).
% 0.18/0.39 fof(cls_conjecture_2, negated_conjecture, ~c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))).
% 0.18/0.39
% 0.18/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.39 fresh(y, y, x1...xn) = u
% 0.18/0.39 C => fresh(s, t, x1...xn) = v
% 0.18/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.39 variables of u and v.
% 0.18/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.39 input problem has no model of domain size 1).
% 0.18/0.39
% 0.18/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.39
% 0.18/0.39 Axiom 1 (cls_PropLog_Othms_OMP_0): fresh(X, X, Y, Z, W) = true.
% 0.18/0.39 Axiom 2 (cls_PropLog_Odeduction_0): fresh2(X, X, Y, Z, W, V) = true.
% 0.18/0.39 Axiom 3 (cls_PropLog_Othms_OMP_0): fresh3(X, X, Y, Z, W, V) = c_in(V, c_PropLog_Othms(Z, W), tc_PropLog_Opl(W)).
% 0.18/0.39 Axiom 4 (cls_conjecture_0): 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.
% 0.18/0.39 Axiom 5 (cls_conjecture_1): 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.
% 0.18/0.39 Axiom 6 (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) = fresh(c_in(X, c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)), true, W, Z, Y).
% 0.18/0.39 Axiom 7 (cls_PropLog_Odeduction_0): fresh2(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)).
% 0.18/0.39 Axiom 8 (cls_PropLog_Othms__excluded__middle_0): c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X, Y, Z), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X, c_PropLog_Opl_Ofalse, Z), Y, Z), Y, Z), Z), c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)) = true.
% 0.18/0.39
% 0.18/0.39 Lemma 9: fresh3(fresh3(X, X, Y, Z, W, c_PropLog_Opl_Oop_A_N_62(V, U, W)), true, V, Z, W, U) = fresh(fresh3(T, T, S, Z, W, V), true, Z, W, U).
% 0.18/0.39 Proof:
% 0.18/0.39 fresh3(fresh3(X, X, Y, Z, W, c_PropLog_Opl_Oop_A_N_62(V, U, W)), true, V, Z, W, U)
% 0.18/0.39 = { by axiom 3 (cls_PropLog_Othms_OMP_0) }
% 0.18/0.39 fresh3(c_in(c_PropLog_Opl_Oop_A_N_62(V, U, W), c_PropLog_Othms(Z, W), tc_PropLog_Opl(W)), true, V, Z, W, U)
% 0.18/0.39 = { by axiom 6 (cls_PropLog_Othms_OMP_0) }
% 0.18/0.39 fresh(c_in(V, c_PropLog_Othms(Z, W), tc_PropLog_Opl(W)), true, Z, W, U)
% 0.18/0.39 = { by axiom 3 (cls_PropLog_Othms_OMP_0) R->L }
% 0.18/0.39 fresh(fresh3(T, T, S, Z, W, V), true, Z, W, U)
% 0.18/0.39
% 0.18/0.39 Lemma 10: fresh2(fresh3(X, X, Y, c_insert(Z, W, tc_PropLog_Opl(V)), V, U), true, U, Z, W, V) = fresh3(T, T, S, W, V, c_PropLog_Opl_Oop_A_N_62(Z, U, V)).
% 0.18/0.39 Proof:
% 0.18/0.39 fresh2(fresh3(X, X, Y, c_insert(Z, W, tc_PropLog_Opl(V)), V, U), true, U, Z, W, V)
% 0.18/0.39 = { by axiom 3 (cls_PropLog_Othms_OMP_0) }
% 0.18/0.39 fresh2(c_in(U, c_PropLog_Othms(c_insert(Z, W, tc_PropLog_Opl(V)), V), tc_PropLog_Opl(V)), true, U, Z, W, V)
% 0.18/0.39 = { by axiom 7 (cls_PropLog_Odeduction_0) }
% 0.18/0.39 c_in(c_PropLog_Opl_Oop_A_N_62(Z, U, V), c_PropLog_Othms(W, V), tc_PropLog_Opl(V))
% 0.18/0.39 = { by axiom 3 (cls_PropLog_Othms_OMP_0) R->L }
% 0.18/0.39 fresh3(T, T, S, W, V, c_PropLog_Opl_Oop_A_N_62(Z, U, V))
% 0.18/0.39
% 0.18/0.39 Goal 1 (cls_conjecture_2): c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)) = true.
% 0.18/0.39 Proof:
% 0.18/0.39 c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))
% 0.18/0.39 = { by axiom 3 (cls_PropLog_Othms_OMP_0) R->L }
% 0.18/0.39 fresh3(true, 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, v_q)
% 0.18/0.39 = { by axiom 1 (cls_PropLog_Othms_OMP_0) R->L }
% 0.18/0.39 fresh3(fresh(true, true, v_H, 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)), 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, v_q)
% 0.18/0.39 = { by axiom 2 (cls_PropLog_Odeduction_0) R->L }
% 0.18/0.39 fresh3(fresh(fresh2(true, true, v_q, v_p, v_H, t_a), true, v_H, 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)), 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, v_q)
% 0.18/0.39 = { by axiom 4 (cls_conjecture_0) R->L }
% 0.18/0.39 fresh3(fresh(fresh2(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, v_q, v_p, v_H, t_a), true, v_H, 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)), 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, v_q)
% 0.18/0.39 = { by axiom 3 (cls_PropLog_Othms_OMP_0) R->L }
% 0.18/0.39 fresh3(fresh(fresh2(fresh3(X, X, Y, c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a, v_q), true, v_q, v_p, v_H, t_a), true, v_H, 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)), 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, v_q)
% 0.18/0.39 = { by lemma 10 }
% 0.18/0.39 fresh3(fresh(fresh3(Z, Z, W, v_H, t_a, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a)), true, v_H, 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)), 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, v_q)
% 0.18/0.39 = { by lemma 9 R->L }
% 0.18/0.39 fresh3(fresh3(fresh3(V, V, U, v_H, t_a, 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)), true, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, 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)), 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, v_q)
% 0.18/0.39 = { by axiom 3 (cls_PropLog_Othms_OMP_0) }
% 0.18/0.39 fresh3(fresh3(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, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, 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)), 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, v_q)
% 0.18/0.39 = { by axiom 8 (cls_PropLog_Othms__excluded__middle_0) }
% 0.18/0.39 fresh3(fresh3(true, true, c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, 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)), 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, v_q)
% 0.18/0.39 = { by lemma 9 }
% 0.18/0.39 fresh(fresh3(T, T, S, v_H, t_a, 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)), true, v_H, t_a, v_q)
% 0.18/0.39 = { by lemma 10 R->L }
% 0.18/0.39 fresh(fresh2(fresh3(X2, X2, Y2, 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, v_q), true, v_q, c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_H, t_a), true, v_H, t_a, v_q)
% 0.18/0.39 = { by axiom 3 (cls_PropLog_Othms_OMP_0) }
% 0.18/0.39 fresh(fresh2(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, v_q, c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_H, t_a), true, v_H, t_a, v_q)
% 0.18/0.39 = { by axiom 5 (cls_conjecture_1) }
% 0.18/0.39 fresh(fresh2(true, true, v_q, c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_H, t_a), true, v_H, t_a, v_q)
% 0.18/0.39 = { by axiom 2 (cls_PropLog_Odeduction_0) }
% 0.18/0.39 fresh(true, true, v_H, t_a, v_q)
% 0.18/0.39 = { by axiom 1 (cls_PropLog_Othms_OMP_0) }
% 0.18/0.39 true
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39
% 0.18/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------