TSTP Solution File: SWV633-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV633-1 : 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 125.52s 16.62s
% Output : Proof 125.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV633-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % 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 : n031.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 07:12:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 125.52/16.62 Command-line arguments: --no-flatten-goal
% 125.52/16.62
% 125.52/16.62 % SZS status Unsatisfiable
% 125.52/16.62
% 125.52/16.63 % SZS output start Proof
% 125.52/16.63 Take the following subset of the input axioms:
% 125.52/16.63 fof(cls_One__nat__def_0, axiom, c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 125.52/16.63 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(v_i, c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)!=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)).
% 125.52/16.63 fof(cls_nat__mult__2__right_0, axiom, ![V_z]: c_HOL_Otimes__class_Otimes(V_z, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), tc_nat)=c_HOL_Oplus__class_Oplus(V_z, V_z, tc_nat)).
% 125.52/16.63 fof(cls_nat__mult__assoc_0, axiom, ![V_n, V_m, V_k]: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), V_k, tc_nat)=c_HOL_Otimes__class_Otimes(V_m, c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat)).
% 125.52/16.63 fof(cls_nat__mult__commute_0, axiom, ![V_n2, V_m2]: c_HOL_Otimes__class_Otimes(V_m2, V_n2, tc_nat)=c_HOL_Otimes__class_Otimes(V_n2, V_m2, tc_nat)).
% 125.52/16.63 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)))).
% 125.52/16.63
% 125.52/16.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 125.52/16.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 125.52/16.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 125.52/16.63 fresh(y, y, x1...xn) = u
% 125.52/16.63 C => fresh(s, t, x1...xn) = v
% 125.52/16.63 where fresh is a fresh function symbol and x1..xn are the free
% 125.52/16.63 variables of u and v.
% 125.52/16.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 125.52/16.63 input problem has no model of domain size 1).
% 125.52/16.63
% 125.52/16.63 The encoding turns the above axioms into the following unit equations and goals:
% 125.52/16.63
% 125.52/16.63 Axiom 1 (cls_One__nat__def_0): c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 125.52/16.63 Axiom 2 (cls_nat__mult__commute_0): c_HOL_Otimes__class_Otimes(X, Y, tc_nat) = c_HOL_Otimes__class_Otimes(Y, X, tc_nat).
% 125.52/16.63 Axiom 3 (cls_one__add__one__is__two_0): fresh304(X, X, Y) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), Y).
% 125.52/16.63 Axiom 4 (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))).
% 125.52/16.63 Axiom 5 (cls_nat__mult__assoc_0): c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X, Y, tc_nat), Z, tc_nat) = c_HOL_Otimes__class_Otimes(X, c_HOL_Otimes__class_Otimes(Y, Z, tc_nat), tc_nat).
% 125.52/16.63 Axiom 6 (cls_nat__mult__2__right_0): c_HOL_Otimes__class_Otimes(X, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), tc_nat) = c_HOL_Oplus__class_Oplus(X, X, tc_nat).
% 125.52/16.63
% 125.52/16.63 Lemma 7: fresh304(X, X, tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)).
% 125.52/16.63 Proof:
% 125.52/16.63 fresh304(X, X, tc_nat)
% 125.52/16.63 = { by axiom 3 (cls_one__add__one__is__two_0) }
% 125.52/16.63 c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)
% 125.52/16.63 = { by axiom 4 (cls_numeral__2__eq__2_0) }
% 125.52/16.63 c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
% 125.52/16.63 = { by axiom 1 (cls_One__nat__def_0) R->L }
% 125.52/16.63 c_Suc(c_HOL_Oone__class_Oone(tc_nat))
% 125.52/16.63
% 125.52/16.63 Lemma 8: c_HOL_Otimes__class_Otimes(X, c_Suc(c_HOL_Oone__class_Oone(tc_nat)), tc_nat) = c_HOL_Oplus__class_Oplus(X, X, tc_nat).
% 125.52/16.63 Proof:
% 125.52/16.63 c_HOL_Otimes__class_Otimes(X, c_Suc(c_HOL_Oone__class_Oone(tc_nat)), tc_nat)
% 125.52/16.63 = { by lemma 7 R->L }
% 125.52/16.63 c_HOL_Otimes__class_Otimes(X, fresh304(Y, Y, tc_nat), tc_nat)
% 125.52/16.63 = { by axiom 3 (cls_one__add__one__is__two_0) }
% 125.52/16.63 c_HOL_Otimes__class_Otimes(X, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), tc_nat)
% 125.52/16.63 = { by axiom 6 (cls_nat__mult__2__right_0) }
% 125.52/16.63 c_HOL_Oplus__class_Oplus(X, X, tc_nat)
% 125.52/16.63
% 125.52/16.63 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(v_i, c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), v_j, tc_nat), tc_nat), tc_Complex_Ocomplex) = 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).
% 125.52/16.63 Proof:
% 125.52/16.63 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(v_i, c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by axiom 3 (cls_one__add__one__is__two_0) R->L }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(fresh304(X, X, tc_nat), v_m, tc_nat)), c_HOL_Otimes__class_Otimes(v_i, c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by axiom 3 (cls_one__add__one__is__two_0) R->L }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(fresh304(X, X, tc_nat), v_m, tc_nat)), c_HOL_Otimes__class_Otimes(v_i, c_HOL_Otimes__class_Otimes(fresh304(Y, Y, tc_nat), v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by lemma 7 }
% 125.52/16.63 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(v_i, c_HOL_Otimes__class_Otimes(fresh304(Y, Y, tc_nat), v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by lemma 7 }
% 125.52/16.63 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(v_i, c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)), v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by axiom 2 (cls_nat__mult__commute_0) }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m, c_Suc(c_HOL_Oone__class_Oone(tc_nat)), tc_nat)), c_HOL_Otimes__class_Otimes(v_i, c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)), v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by lemma 8 }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m, v_m, tc_nat)), c_HOL_Otimes__class_Otimes(v_i, c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)), v_j, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by axiom 2 (cls_nat__mult__commute_0) }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m, v_m, tc_nat)), c_HOL_Otimes__class_Otimes(v_i, c_HOL_Otimes__class_Otimes(v_j, c_Suc(c_HOL_Oone__class_Oone(tc_nat)), tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by axiom 5 (cls_nat__mult__assoc_0) R->L }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m, v_m, tc_nat)), c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), c_Suc(c_HOL_Oone__class_Oone(tc_nat)), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by lemma 8 R->L }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m, c_Suc(c_HOL_Oone__class_Oone(tc_nat)), tc_nat)), c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), c_Suc(c_HOL_Oone__class_Oone(tc_nat)), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by lemma 7 R->L }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m, fresh304(Z, Z, tc_nat), tc_nat)), c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), c_Suc(c_HOL_Oone__class_Oone(tc_nat)), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by lemma 7 R->L }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m, fresh304(Z, Z, tc_nat), tc_nat)), c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), fresh304(W, W, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by axiom 3 (cls_one__add__one__is__two_0) }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), tc_nat)), c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), fresh304(W, W, tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by axiom 3 (cls_one__add__one__is__two_0) }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), tc_nat)), c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i, v_j, tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), tc_nat), tc_Complex_Ocomplex)
% 125.52/16.63 = { by axiom 2 (cls_nat__mult__commute_0) R->L }
% 125.52/16.63 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat), 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)
% 125.52/16.63 = { by axiom 2 (cls_nat__mult__commute_0) R->L }
% 125.52/16.64 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)
% 125.52/16.64 % SZS output end Proof
% 125.52/16.64
% 125.52/16.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------