TSTP Solution File: SWV634-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV634-1 : 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 : n031.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 23:05:42 EDT 2023
% Result : Unsatisfiable 180.90s 23.50s
% Output : Proof 180.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV634-1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33 % Computer : n031.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Aug 29 08:17:10 EDT 2023
% 0.11/0.33 % CPUTime :
% 180.90/23.50 Command-line arguments: --no-flatten-goal
% 180.90/23.50
% 180.90/23.50 % SZS status Unsatisfiable
% 180.90/23.50
% 180.90/23.51 % SZS output start Proof
% 180.90/23.51 Take the following subset of the input axioms:
% 180.90/23.51 fof(cls_One__nat__def_0, axiom, c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 180.90/23.51 fof(cls_conjecture_0, negated_conjecture, c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), v_m, tc_nat)), c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)!=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_Complex_Ocomplex)).
% 180.90/23.51 fof(cls_gr0__conv__Suc_1, axiom, ![V_x]: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(V_x), tc_nat)).
% 180.90/23.51 fof(cls_numeral__2__eq__2_0, axiom, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))).
% 180.90/23.51 fof(cls_root__cancel_0, axiom, ![V_n, V_k, V_d]: (c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d, V_n, tc_nat)), c_HOL_Otimes__class_Otimes(V_d, V_k, tc_nat), tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n), V_k, tc_Complex_Ocomplex) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_d, tc_nat))).
% 180.90/23.51
% 180.90/23.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 180.90/23.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 180.90/23.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 180.90/23.51 fresh(y, y, x1...xn) = u
% 180.90/23.51 C => fresh(s, t, x1...xn) = v
% 180.90/23.51 where fresh is a fresh function symbol and x1..xn are the free
% 180.90/23.51 variables of u and v.
% 180.90/23.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 180.90/23.51 input problem has no model of domain size 1).
% 180.90/23.51
% 180.90/23.51 The encoding turns the above axioms into the following unit equations and goals:
% 180.90/23.51
% 180.90/23.51 Axiom 1 (cls_One__nat__def_0): c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.90/23.52 Axiom 2 (cls_one__add__one__is__two_0): fresh295(X, X, Y) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), Y).
% 180.90/23.52 Axiom 3 (cls_numeral__2__eq__2_0): c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat) = c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 180.90/23.52 Axiom 4 (cls_root__cancel_0): fresh218(X, X, Y, Z, W) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(Z), W, tc_Complex_Ocomplex).
% 180.90/23.52 Axiom 5 (cls_gr0__conv__Suc_1): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat) = true2.
% 180.90/23.52 Axiom 6 (cls_root__cancel_0): fresh218(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), X, tc_nat), true2, X, Y, Z) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X, Y, tc_nat)), c_HOL_Otimes__class_Otimes(X, Z, tc_nat), tc_Complex_Ocomplex).
% 180.90/23.52
% 180.90/23.52 Lemma 7: fresh295(X, X, tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)).
% 180.90/23.52 Proof:
% 180.90/23.52 fresh295(X, X, tc_nat)
% 180.90/23.52 = { by axiom 2 (cls_one__add__one__is__two_0) }
% 180.90/23.52 c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)
% 180.90/23.52 = { by axiom 3 (cls_numeral__2__eq__2_0) }
% 180.90/23.52 c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
% 180.90/23.52 = { by axiom 1 (cls_One__nat__def_0) R->L }
% 180.90/23.52 c_Suc(c_HOL_Oone__class_Oone(tc_nat))
% 180.90/23.52
% 180.90/23.52 Goal 1 (cls_conjecture_0): c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), v_m, tc_nat)), c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_nat), tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_Complex_Ocomplex).
% 180.90/23.52 Proof:
% 180.90/23.52 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), v_m, tc_nat)), c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 180.90/23.52 = { by axiom 2 (cls_one__add__one__is__two_0) R->L }
% 180.90/23.52 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(fresh295(X, X, tc_nat), v_m, tc_nat)), c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 180.90/23.52 = { by axiom 2 (cls_one__add__one__is__two_0) R->L }
% 180.90/23.52 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(fresh295(X, X, tc_nat), v_m, tc_nat)), c_HOL_Otimes__class_Otimes(fresh295(Y, Y, tc_nat), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 180.90/23.52 = { by lemma 7 }
% 180.90/23.52 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)), v_m, tc_nat)), c_HOL_Otimes__class_Otimes(fresh295(Y, Y, tc_nat), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 180.90/23.52 = { by lemma 7 }
% 180.90/23.52 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)), v_m, tc_nat)), c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 180.90/23.52 = { by axiom 6 (cls_root__cancel_0) R->L }
% 180.90/23.52 fresh218(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(c_HOL_Oone__class_Oone(tc_nat)), tc_nat), true2, c_Suc(c_HOL_Oone__class_Oone(tc_nat)), v_m, c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat))
% 180.90/23.52 = { by axiom 5 (cls_gr0__conv__Suc_1) }
% 180.90/23.52 fresh218(true2, true2, c_Suc(c_HOL_Oone__class_Oone(tc_nat)), v_m, c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat))
% 180.90/23.52 = { by axiom 4 (cls_root__cancel_0) }
% 180.90/23.52 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m), c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), tc_Complex_Ocomplex)
% 180.90/23.52 % SZS output end Proof
% 180.90/23.52
% 180.90/23.52 RESULT: Unsatisfiable (the axioms are contradictory).
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