TSTP Solution File: SWV842-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV842-1 : 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 : n018.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 23:06:29 EDT 2023
% Result : Unsatisfiable 18.49s 2.77s
% Output : Proof 18.49s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV842-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 07:13:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 18.49/2.77 Command-line arguments: --no-flatten-goal
% 18.49/2.77
% 18.49/2.77 % SZS status Unsatisfiable
% 18.49/2.77
% 18.49/2.77 % SZS output start Proof
% 18.49/2.77 Take the following subset of the input axioms:
% 18.49/2.78 fof(cls_conjecture_1, negated_conjecture, ~c_Hoare__Mirabelle_Ohoare__derivs(v_G, c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b), tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), v_P), v_c0, t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_b))), v_Q, t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_b)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a, tc_Hoare__Mirabelle_Otriple(t_b)), t_b)).
% 18.49/2.78 fof(cls_empty_0, axiom, ![T_a, V_G]: c_Hoare__Mirabelle_Ohoare__derivs(V_G, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a), tc_bool)), T_a)).
% 18.49/2.78 fof(cls_image__empty_0, axiom, ![T_b, V_f, T_a2]: c_Set_Oimage(V_f, c_Orderings_Obot__class_Obot(tc_fun(T_b, tc_bool)), T_b, T_a2)=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool))).
% 18.49/2.78
% 18.49/2.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 18.49/2.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 18.49/2.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 18.49/2.78 fresh(y, y, x1...xn) = u
% 18.49/2.78 C => fresh(s, t, x1...xn) = v
% 18.49/2.78 where fresh is a fresh function symbol and x1..xn are the free
% 18.49/2.78 variables of u and v.
% 18.49/2.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 18.49/2.78 input problem has no model of domain size 1).
% 18.49/2.78
% 18.49/2.78 The encoding turns the above axioms into the following unit equations and goals:
% 18.49/2.78
% 18.49/2.78 Axiom 1 (cls_empty_0): c_Hoare__Mirabelle_Ohoare__derivs(X, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(Y), tc_bool)), Y) = true2.
% 18.49/2.78 Axiom 2 (cls_image__empty_0): c_Set_Oimage(X, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_bool)), Y, Z) = c_Orderings_Obot__class_Obot(tc_fun(Z, tc_bool)).
% 18.49/2.78
% 18.49/2.78 Goal 1 (cls_conjecture_1): c_Hoare__Mirabelle_Ohoare__derivs(v_G, c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b), tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), v_P), v_c0, t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_b))), v_Q, t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_b)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a, tc_Hoare__Mirabelle_Otriple(t_b)), t_b) = true2.
% 18.49/2.78 Proof:
% 18.49/2.78 c_Hoare__Mirabelle_Ohoare__derivs(v_G, c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b), tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), v_P), v_c0, t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_b))), v_Q, t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_bool)), tc_Hoare__Mirabelle_Otriple(t_b)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_bool)), t_a, tc_Hoare__Mirabelle_Otriple(t_b)), t_b)
% 18.49/2.78 = { by axiom 2 (cls_image__empty_0) }
% 18.49/2.78 c_Hoare__Mirabelle_Ohoare__derivs(v_G, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_bool)), t_b)
% 18.49/2.78 = { by axiom 1 (cls_empty_0) }
% 18.49/2.78 true2
% 18.49/2.78 % SZS output end Proof
% 18.49/2.78
% 18.49/2.78 RESULT: Unsatisfiable (the axioms are contradictory).
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