TSTP Solution File: SWV880-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV880-1 : 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 : n029.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 16.10s 2.39s
% Output : Proof 16.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV880-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Tue Aug 29 10:57:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 16.10/2.39 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 16.10/2.39
% 16.10/2.39 % SZS status Unsatisfiable
% 16.10/2.39
% 16.10/2.39 % SZS output start Proof
% 16.10/2.39 Take the following subset of the input axioms:
% 16.10/2.39 fof(cls_conjecture_1, negated_conjecture, v_G=c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a)).
% 16.10/2.39 fof(cls_conjecture_2, negated_conjecture, c_in(v_pn, v_U, tc_Com_Opname)).
% 16.10/2.39 fof(cls_conjecture_3, negated_conjecture, ~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_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))).
% 16.10/2.39 fof(cls_empty__subsetI_0, axiom, ![T_a, V_A]: c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_bool)), V_A, tc_fun(T_a, tc_bool))).
% 16.10/2.39 fof(cls_image__insert_0, axiom, ![V_f, T_b, V_B, V_a, T_a2]: c_Set_Oimage(V_f, c_Set_Oinsert(V_a, V_B, T_b), T_b, T_a2)=c_Set_Oinsert(hAPP(V_f, V_a), c_Set_Oimage(V_f, V_B, T_b, T_a2), T_a2)).
% 16.10/2.39 fof(cls_insert__absorb_0, axiom, ![T_a2, V_a2, V_A2]: (c_Set_Oinsert(V_a2, V_A2, T_a2)=V_A2 | ~c_in(V_a2, V_A2, T_a2))).
% 16.10/2.40 fof(cls_insert__mono_0, axiom, ![V_C, V_D, T_a2, V_a2]: (c_lessequals(c_Set_Oinsert(V_a2, V_C, T_a2), c_Set_Oinsert(V_a2, V_D, T_a2), tc_fun(T_a2, tc_bool)) | ~c_lessequals(V_C, V_D, tc_fun(T_a2, tc_bool)))).
% 16.10/2.40
% 16.10/2.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.10/2.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.10/2.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.10/2.40 fresh(y, y, x1...xn) = u
% 16.10/2.40 C => fresh(s, t, x1...xn) = v
% 16.10/2.40 where fresh is a fresh function symbol and x1..xn are the free
% 16.10/2.40 variables of u and v.
% 16.10/2.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.10/2.40 input problem has no model of domain size 1).
% 16.10/2.40
% 16.10/2.40 The encoding turns the above axioms into the following unit equations and goals:
% 16.10/2.40
% 16.10/2.40 Axiom 1 (cls_conjecture_2): c_in(v_pn, v_U, tc_Com_Opname) = true2.
% 16.10/2.40 Axiom 2 (cls_conjecture_1): v_G = c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a).
% 16.10/2.40 Axiom 3 (cls_insert__absorb_0): fresh5(X, X, Y, Z, W) = Z.
% 16.10/2.40 Axiom 4 (cls_empty__subsetI_0): c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X, tc_bool)), Y, tc_fun(X, tc_bool)) = true2.
% 16.10/2.40 Axiom 5 (cls_insert__mono_0): fresh269(X, X, Y, Z, W, V) = true2.
% 16.10/2.40 Axiom 6 (cls_image__insert_0): c_Set_Oimage(X, c_Set_Oinsert(Y, Z, W), W, V) = c_Set_Oinsert(hAPP(X, Y), c_Set_Oimage(X, Z, W, V), V).
% 16.10/2.40 Axiom 7 (cls_insert__absorb_0): fresh5(c_in(X, Y, Z), true2, X, Y, Z) = c_Set_Oinsert(X, Y, Z).
% 16.10/2.40 Axiom 8 (cls_insert__mono_0): fresh269(c_lessequals(X, Y, tc_fun(Z, tc_bool)), true2, W, X, Z, Y) = c_lessequals(c_Set_Oinsert(W, X, Z), c_Set_Oinsert(W, Y, Z), tc_fun(Z, tc_bool)).
% 16.10/2.40
% 16.10/2.40 Goal 1 (cls_conjecture_3): 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_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool)) = true2.
% 16.10/2.40 Proof:
% 16.10/2.40 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_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 16.10/2.40 = { by axiom 3 (cls_insert__absorb_0) R->L }
% 16.10/2.40 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_Oimage(v_mgt__call, fresh5(true2, true2, v_pn, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 16.10/2.40 = { by axiom 1 (cls_conjecture_2) R->L }
% 16.10/2.40 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_Oimage(v_mgt__call, fresh5(c_in(v_pn, v_U, tc_Com_Opname), true2, v_pn, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 16.10/2.40 = { by axiom 7 (cls_insert__absorb_0) }
% 16.10/2.40 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_Oimage(v_mgt__call, c_Set_Oinsert(v_pn, v_U, tc_Com_Opname), tc_Com_Opname, t_a), tc_fun(t_a, tc_bool))
% 16.10/2.40 = { by axiom 6 (cls_image__insert_0) }
% 16.10/2.40 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), c_Set_Oimage(v_mgt__call, v_U, tc_Com_Opname, t_a), t_a), tc_fun(t_a, tc_bool))
% 16.10/2.40 = { by axiom 2 (cls_conjecture_1) R->L }
% 16.10/2.40 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))
% 16.10/2.40 = { by axiom 8 (cls_insert__mono_0) R->L }
% 16.10/2.40 fresh269(c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), v_G, tc_fun(t_a, tc_bool)), true2, hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a, v_G)
% 16.10/2.40 = { by axiom 4 (cls_empty__subsetI_0) }
% 16.10/2.40 fresh269(true2, true2, hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a, v_G)
% 16.10/2.40 = { by axiom 5 (cls_insert__mono_0) }
% 16.10/2.40 true2
% 16.10/2.40 % SZS output end Proof
% 16.10/2.40
% 16.10/2.40 RESULT: Unsatisfiable (the axioms are contradictory).
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