TSTP Solution File: SWV693-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV693-1 : 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 23:05:55 EDT 2023
% Result : Unsatisfiable 182.20s 23.31s
% Output : Proof 182.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV693-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % 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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 11:00:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 182.20/23.31 Command-line arguments: --no-flatten-goal
% 182.20/23.31
% 182.20/23.31 % SZS status Unsatisfiable
% 182.20/23.31
% 182.20/23.31 % SZS output start Proof
% 182.20/23.31 Take the following subset of the input axioms:
% 182.80/23.31 fof(cls_assms_0, axiom, hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i, tc_nat), v_n))).
% 182.80/23.31 fof(cls_conjecture_0, negated_conjecture, hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), c_SetInterval_Oord__class_OatLeastLessThan(v_i, v_n, tc_nat))!=hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i, c_Orderings_Obot__class_Obot(tc_fun(tc_nat, tc_bool)), tc_nat), c_SetInterval_Oord__class_OgreaterThanLessThan(v_i, v_n, tc_nat), tc_fun(tc_nat, tc_bool)))).
% 182.80/23.32 fof(cls_ivl__disj__un_I3_J_0, axiom, ![T_a, V_u, V_l]: (~class_Orderings_Olinorder(T_a) | (c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l, c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_bool)), T_a), c_SetInterval_Oord__class_OgreaterThanLessThan(V_l, V_u, T_a), tc_fun(T_a, tc_bool))=c_SetInterval_Oord__class_OatLeastLessThan(V_l, V_u, T_a) | ~hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l, T_a), V_u))))).
% 182.80/23.32 fof(clsarity_nat__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_nat)).
% 182.80/23.32
% 182.80/23.32 Now clausify the problem and encode Horn clauses using encoding 3 of
% 182.80/23.32 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 182.80/23.32 We repeatedly replace C & s=t => u=v by the two clauses:
% 182.80/23.32 fresh(y, y, x1...xn) = u
% 182.80/23.32 C => fresh(s, t, x1...xn) = v
% 182.80/23.32 where fresh is a fresh function symbol and x1..xn are the free
% 182.80/23.32 variables of u and v.
% 182.80/23.32 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 182.80/23.32 input problem has no model of domain size 1).
% 182.80/23.32
% 182.80/23.32 The encoding turns the above axioms into the following unit equations and goals:
% 182.80/23.32
% 182.80/23.32 Axiom 1 (clsarity_nat__Orderings_Olinorder): class_Orderings_Olinorder(tc_nat) = true2.
% 182.80/23.32 Axiom 2 (cls_ivl__disj__un_I3_J_0): fresh793(X, X, Y, Z, W) = c_SetInterval_Oord__class_OatLeastLessThan(Z, W, Y).
% 182.80/23.32 Axiom 3 (cls_assms_0): hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i, tc_nat), v_n)) = true2.
% 182.80/23.32 Axiom 4 (cls_ivl__disj__un_I3_J_0): fresh792(X, X, Y, Z, W) = fresh793(hBOOL(hAPP(c_HOL_Oord__class_Oless(Z, Y), W)), true2, Y, Z, W).
% 182.80/23.32 Axiom 5 (cls_ivl__disj__un_I3_J_0): fresh792(class_Orderings_Olinorder(X), true2, X, Y, Z) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(Y, c_Orderings_Obot__class_Obot(tc_fun(X, tc_bool)), X), c_SetInterval_Oord__class_OgreaterThanLessThan(Y, Z, X), tc_fun(X, tc_bool)).
% 182.80/23.32
% 182.80/23.32 Goal 1 (cls_conjecture_0): hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), c_SetInterval_Oord__class_OatLeastLessThan(v_i, v_n, tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i, c_Orderings_Obot__class_Obot(tc_fun(tc_nat, tc_bool)), tc_nat), c_SetInterval_Oord__class_OgreaterThanLessThan(v_i, v_n, tc_nat), tc_fun(tc_nat, tc_bool))).
% 182.80/23.32 Proof:
% 182.80/23.32 hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), c_SetInterval_Oord__class_OatLeastLessThan(v_i, v_n, tc_nat))
% 182.80/23.32 = { by axiom 2 (cls_ivl__disj__un_I3_J_0) R->L }
% 182.80/23.32 hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), fresh793(true2, true2, tc_nat, v_i, v_n))
% 182.80/23.32 = { by axiom 3 (cls_assms_0) R->L }
% 182.80/23.32 hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), fresh793(hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i, tc_nat), v_n)), true2, tc_nat, v_i, v_n))
% 182.80/23.32 = { by axiom 4 (cls_ivl__disj__un_I3_J_0) R->L }
% 182.80/23.32 hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), fresh792(true2, true2, tc_nat, v_i, v_n))
% 182.80/23.32 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 182.80/23.32 hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), fresh792(class_Orderings_Olinorder(tc_nat), true2, tc_nat, v_i, v_n))
% 182.80/23.32 = { by axiom 5 (cls_ivl__disj__un_I3_J_0) }
% 182.80/23.32 hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex), c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_Complex_Ocomplex, tc_Complex_Ocomplex), tc_nat), c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)), hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat, tc_Complex_Ocomplex), tc_fun(tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), tc_nat), c_Finite__Set_Osetsum(tc_nat, tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex, tc_fun(tc_nat, tc_Complex_Ocomplex), tc_nat), c_Power_Opower__class_Opower(tc_Complex_Ocomplex)), hAPP(hAPP(c_COMBB(tc_nat, tc_Complex_Ocomplex, tc_nat), hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n))), hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat), tc_nat, tc_nat, tc_nat), v_i)))), tc_nat, tc_fun(tc_nat, tc_bool), tc_Complex_Ocomplex), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), v_n, tc_nat))), v_a, tc_nat, tc_Complex_Ocomplex, tc_Complex_Ocomplex)), c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i, c_Orderings_Obot__class_Obot(tc_fun(tc_nat, tc_bool)), tc_nat), c_SetInterval_Oord__class_OgreaterThanLessThan(v_i, v_n, tc_nat), tc_fun(tc_nat, tc_bool)))
% 182.80/23.32 % SZS output end Proof
% 182.80/23.32
% 182.80/23.32 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------