TSTP Solution File: SWV882-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV882-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n005.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 23:06:37 EDT 2023
% Result : Unsatisfiable 38.35s 6.33s
% Output : Proof 38.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV882-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 03:14:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 38.35/6.33 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 38.35/6.33
% 38.35/6.33 % SZS status Unsatisfiable
% 38.35/6.33
% 38.51/6.34 % SZS output start Proof
% 38.51/6.34 Take the following subset of the input axioms:
% 38.51/6.34 fof(cls_Diff__cancel_0, axiom, ![T_a, V_A]: c_HOL_Ominus__class_Ominus(V_A, V_A, tc_fun(T_a, tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_bool))).
% 38.51/6.34 fof(cls_assms_I1_J_0, axiom, ![V_G, V_ts]: (hBOOL(hAPP(hAPP(v_P, V_G), V_ts)) | ~c_lessequals(V_ts, V_G, tc_fun(t_a, tc_bool)))).
% 38.51/6.34 fof(cls_conjecture_5, negated_conjecture, c_in(hAPP(v_mgt__call, v_pn), v_G, t_a)).
% 38.51/6.34 fof(cls_conjecture_6, negated_conjecture, ~hBOOL(hAPP(hAPP(v_P, v_G), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)))).
% 38.51/6.34 fof(cls_diff__single__insert_0, axiom, ![V_x, V_B, T_a2, V_A2]: (c_lessequals(V_A2, c_Set_Oinsert(V_x, V_B, T_a2), tc_fun(T_a2, tc_bool)) | (~c_in(V_x, V_A2, T_a2) | ~c_lessequals(c_HOL_Ominus__class_Ominus(V_A2, c_Set_Oinsert(V_x, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2), tc_fun(T_a2, tc_bool)), V_B, tc_fun(T_a2, tc_bool))))).
% 38.51/6.34 fof(cls_empty__subsetI_0, axiom, ![T_a2, V_A2]: c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), V_A2, tc_fun(T_a2, tc_bool))).
% 38.51/6.34 fof(cls_insert__absorb_0, axiom, ![V_a, T_a2, V_A2]: (c_Set_Oinsert(V_a, V_A2, T_a2)=V_A2 | ~c_in(V_a, V_A2, T_a2))).
% 38.51/6.34 fof(cls_insert__iff_1, axiom, ![T_a2, V_x2, V_A2]: c_in(V_x2, c_Set_Oinsert(V_x2, V_A2, T_a2), T_a2)).
% 38.51/6.34
% 38.51/6.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 38.51/6.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 38.51/6.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 38.51/6.34 fresh(y, y, x1...xn) = u
% 38.51/6.34 C => fresh(s, t, x1...xn) = v
% 38.51/6.34 where fresh is a fresh function symbol and x1..xn are the free
% 38.51/6.34 variables of u and v.
% 38.51/6.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 38.51/6.34 input problem has no model of domain size 1).
% 38.51/6.34
% 38.51/6.34 The encoding turns the above axioms into the following unit equations and goals:
% 38.51/6.34
% 38.51/6.34 Axiom 1 (cls_Diff__cancel_0): c_HOL_Ominus__class_Ominus(X, X, tc_fun(Y, tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(Y, tc_bool)).
% 38.51/6.34 Axiom 2 (cls_conjecture_5): c_in(hAPP(v_mgt__call, v_pn), v_G, t_a) = true2.
% 38.51/6.34 Axiom 3 (cls_assms_I1_J_0): fresh381(X, X, Y, Z) = true2.
% 38.51/6.34 Axiom 4 (cls_insert__iff_1): c_in(X, c_Set_Oinsert(X, Y, Z), Z) = true2.
% 38.51/6.34 Axiom 5 (cls_insert__absorb_0): fresh10(X, X, Y, Z, W) = Z.
% 38.51/6.34 Axiom 6 (cls_empty__subsetI_0): c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X, tc_bool)), Y, tc_fun(X, tc_bool)) = true2.
% 38.51/6.34 Axiom 7 (cls_diff__single__insert_0): fresh329(X, X, Y, Z, W, V) = c_lessequals(Y, c_Set_Oinsert(Z, W, V), tc_fun(V, tc_bool)).
% 38.51/6.34 Axiom 8 (cls_diff__single__insert_0): fresh328(X, X, Y, Z, W, V) = true2.
% 38.51/6.34 Axiom 9 (cls_assms_I1_J_0): fresh381(c_lessequals(X, Y, tc_fun(t_a, tc_bool)), true2, Y, X) = hBOOL(hAPP(hAPP(v_P, Y), X)).
% 38.51/6.34 Axiom 10 (cls_insert__absorb_0): fresh10(c_in(X, Y, Z), true2, X, Y, Z) = c_Set_Oinsert(X, Y, Z).
% 38.51/6.34 Axiom 11 (cls_diff__single__insert_0): fresh329(c_in(X, Y, Z), true2, Y, X, W, Z) = fresh328(c_lessequals(c_HOL_Ominus__class_Ominus(Y, c_Set_Oinsert(X, c_Orderings_Obot__class_Obot(tc_fun(Z, tc_bool)), Z), tc_fun(Z, tc_bool)), W, tc_fun(Z, tc_bool)), true2, Y, X, W, Z).
% 38.51/6.34
% 38.51/6.34 Goal 1 (cls_conjecture_6): hBOOL(hAPP(hAPP(v_P, v_G), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))) = true2.
% 38.51/6.34 Proof:
% 38.51/6.34 hBOOL(hAPP(hAPP(v_P, v_G), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a)))
% 38.51/6.34 = { by axiom 9 (cls_assms_I1_J_0) R->L }
% 38.51/6.34 fresh381(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), v_G, tc_fun(t_a, tc_bool)), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.34 = { by axiom 5 (cls_insert__absorb_0) R->L }
% 38.51/6.34 fresh381(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), fresh10(true2, true2, hAPP(v_mgt__call, v_pn), v_G, t_a), tc_fun(t_a, tc_bool)), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.34 = { by axiom 2 (cls_conjecture_5) R->L }
% 38.51/6.34 fresh381(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), fresh10(c_in(hAPP(v_mgt__call, v_pn), v_G, t_a), true2, hAPP(v_mgt__call, v_pn), v_G, t_a), tc_fun(t_a, tc_bool)), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.34 = { by axiom 10 (cls_insert__absorb_0) }
% 38.51/6.34 fresh381(c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), v_G, t_a), tc_fun(t_a, tc_bool)), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.34 = { by axiom 7 (cls_diff__single__insert_0) R->L }
% 38.51/6.34 fresh381(fresh329(true2, true2, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), hAPP(v_mgt__call, v_pn), v_G, t_a), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.34 = { by axiom 4 (cls_insert__iff_1) R->L }
% 38.51/6.35 fresh381(fresh329(c_in(hAPP(v_mgt__call, v_pn), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), t_a), true2, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), hAPP(v_mgt__call, v_pn), v_G, t_a), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.35 = { by axiom 11 (cls_diff__single__insert_0) }
% 38.51/6.35 fresh381(fresh328(c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), tc_fun(t_a, tc_bool)), v_G, tc_fun(t_a, tc_bool)), true2, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), hAPP(v_mgt__call, v_pn), v_G, t_a), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.35 = { by axiom 1 (cls_Diff__cancel_0) }
% 38.51/6.35 fresh381(fresh328(c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), v_G, tc_fun(t_a, tc_bool)), true2, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), hAPP(v_mgt__call, v_pn), v_G, t_a), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.35 = { by axiom 6 (cls_empty__subsetI_0) }
% 38.51/6.35 fresh381(fresh328(true2, true2, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a), hAPP(v_mgt__call, v_pn), v_G, t_a), true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.35 = { by axiom 8 (cls_diff__single__insert_0) }
% 38.51/6.35 fresh381(true2, true2, v_G, c_Set_Oinsert(hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a))
% 38.51/6.35 = { by axiom 3 (cls_assms_I1_J_0) }
% 38.51/6.35 true2
% 38.51/6.35 % SZS output end Proof
% 38.51/6.35
% 38.51/6.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------