TSTP Solution File: SWV659-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV659-1 : 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 : n013.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 23:05:48 EDT 2023
% Result : Unsatisfiable 63.27s 8.49s
% Output : Proof 63.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV659-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % 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 : n013.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 03:02:46 EDT 2023
% 0.12/0.34 % CPUTime :
% 63.27/8.49 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 63.27/8.49
% 63.27/8.49 % SZS status Unsatisfiable
% 63.27/8.49
% 63.27/8.49 % SZS output start Proof
% 63.27/8.49 Take the following subset of the input axioms:
% 63.27/8.50 fof(cls_COMBB__def_0, axiom, ![V_P, V_Q, T_b, T_c, T_a, V_R]: hAPP(c_COMBB(V_P, V_Q, T_b, T_a, T_c), V_R)=hAPP(V_P, hAPP(V_Q, V_R))).
% 63.27/8.50 fof(cls_COMBS__def_0, axiom, ![T_a2, V_P2, V_Q2, T_b2, T_c2, V_R2]: hAPP(c_COMBS(V_P2, V_Q2, T_b2, T_c2, T_a2), V_R2)=hAPP(hAPP(V_P2, V_R2), hAPP(V_Q2, V_R2))).
% 63.27/8.50 fof(cls_Suc__n__not__n_0, axiom, ![V_n]: hAPP(c_Suc, V_n)!=V_n).
% 63.27/8.50 fof(cls_Suc__neq__Zero_0, axiom, ![V_m]: hAPP(c_Suc, V_m)!=c_HOL_Ozero__class_Ozero(tc_nat)).
% 63.27/8.50 fof(cls_Zero__neq__Suc_0, axiom, ![V_m2]: c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc, V_m2)).
% 63.27/8.50 fof(cls_mult__1__left_0, axiom, ![V_a, T_a2]: (~class_OrderedGroup_Omonoid__mult(T_a2) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a2), c_HOL_Oone__class_Oone(T_a2)), V_a)=V_a)).
% 63.27/8.50 fof(cls_n__not__Suc__n_0, axiom, ![V_n2]: V_n2!=hAPP(c_Suc, V_n2)).
% 63.27/8.50 fof(cls_nat_Osimps_I2_J_0, axiom, ![V_nat_H]: c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc, V_nat_H)).
% 63.27/8.50 fof(cls_nat_Osimps_I3_J_0, axiom, ![V_nat_H2]: hAPP(c_Suc, V_nat_H2)!=c_HOL_Ozero__class_Ozero(tc_nat)).
% 63.27/8.50 fof(cls_not__one__le__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_lessequals(c_HOL_Oone__class_Oone(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 63.27/8.50 fof(cls_one__neq__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | c_HOL_Oone__class_Oone(T_a2)!=c_HOL_Ozero__class_Ozero(T_a2))).
% 63.27/8.50 fof(cls_plus__nat_Oadd__0_0, axiom, ![V_n2]: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat)), V_n2)=V_n2).
% 63.27/8.50 fof(cls_power__eq__0__iff_1, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | (~class_Ring__and__Field_Ono__zero__divisors(T_a2) | (~class_Ring__and__Field_Omult__zero(T_a2) | (~class_Power_Opower(T_a2) | hAPP(c_Power_Opower__class_Opower(V_a2, T_a2), c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(T_a2)))))).
% 63.27/8.50 fof(cls_power__eq__0__iff__number__of_1, axiom, ![V_w, T_a2, V_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | (~class_Ring__and__Field_Ono__zero__divisors(T_a2) | (~class_Ring__and__Field_Omult__zero(T_a2) | (~class_Power_Opower(T_a2) | (c_Int_Onumber__class_Onumber__of(V_w, tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(V_a2, T_a2), c_Int_Onumber__class_Onumber__of(V_w, tc_nat))!=c_HOL_Ozero__class_Ozero(T_a2))))))).
% 63.27/8.50 fof(cls_power__le__zero__eq_0, axiom, ![V_x, T_a2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | ~c_lessequals(hAPP(c_Power_Opower__class_Opower(V_x, T_a2), c_HOL_Ozero__class_Ozero(tc_nat)), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 63.27/8.50 fof(cls_power__le__zero__eq__number__of_0, axiom, ![T_a2, V_x2, V_w2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | (c_Int_Onumber__class_Onumber__of(V_w2, tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat) | ~c_lessequals(hAPP(c_Power_Opower__class_Opower(V_x2, T_a2), c_Int_Onumber__class_Onumber__of(V_w2, tc_nat)), c_HOL_Ozero__class_Ozero(T_a2), T_a2)))).
% 63.27/8.50 fof(cls_rel__simps_I39_J_0, axiom, ![V_l]: c_Int_OPls!=c_Int_OBit1(V_l)).
% 63.27/8.50 fof(cls_rel__simps_I42_J_0, axiom, ![V_l2]: c_Int_OMin!=c_Int_OBit0(V_l2)).
% 63.27/8.50 fof(cls_rel__simps_I45_J_0, axiom, ![V_k]: c_Int_OBit0(V_k)!=c_Int_OMin).
% 63.27/8.50 fof(cls_rel__simps_I46_J_0, axiom, ![V_k2]: c_Int_OBit1(V_k2)!=c_Int_OPls).
% 63.27/8.50 fof(cls_rel__simps_I49_J_0, axiom, ![V_k2, V_l2]: c_Int_OBit0(V_k2)!=c_Int_OBit1(V_l2)).
% 63.27/8.50 fof(cls_rel__simps_I50_J_0, axiom, ![V_k2, V_l2]: c_Int_OBit1(V_k2)!=c_Int_OBit0(V_l2)).
% 63.27/8.50 fof(cls_zero__neq__one_0, axiom, ![T_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | c_HOL_Ozero__class_Ozero(T_a2)!=c_HOL_Oone__class_Oone(T_a2))).
% 63.27/8.50 fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, axiom, class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)).
% 63.27/8.50
% 63.27/8.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 63.27/8.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 63.27/8.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 63.27/8.50 fresh(y, y, x1...xn) = u
% 63.27/8.50 C => fresh(s, t, x1...xn) = v
% 63.27/8.50 where fresh is a fresh function symbol and x1..xn are the free
% 63.27/8.50 variables of u and v.
% 63.27/8.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 63.27/8.50 input problem has no model of domain size 1).
% 63.27/8.50
% 63.27/8.50 The encoding turns the above axioms into the following unit equations and goals:
% 63.27/8.50
% 63.27/8.50 Axiom 1 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult): class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) = true2.
% 63.27/8.50 Axiom 2 (cls_mult__1__left_0): fresh23(X, X, Y, Z) = Z.
% 63.27/8.50 Axiom 3 (cls_plus__nat_Oadd__0_0): hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat)), X) = X.
% 63.27/8.50 Axiom 4 (cls_mult__1__left_0): fresh23(class_OrderedGroup_Omonoid__mult(X), true2, X, Y) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X), c_HOL_Oone__class_Oone(X)), Y).
% 63.27/8.50 Axiom 5 (cls_COMBB__def_0): hAPP(c_COMBB(X, Y, Z, W, V), U) = hAPP(X, hAPP(Y, U)).
% 63.27/8.50 Axiom 6 (cls_COMBS__def_0): hAPP(c_COMBS(X, Y, Z, W, V), U) = hAPP(hAPP(X, U), hAPP(Y, U)).
% 63.27/8.50
% 63.27/8.50 Lemma 7: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X) = X.
% 63.27/8.50 Proof:
% 63.27/8.50 hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X)
% 63.27/8.50 = { by axiom 4 (cls_mult__1__left_0) R->L }
% 63.27/8.50 fresh23(class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, X)
% 63.27/8.50 = { by axiom 1 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) }
% 63.27/8.50 fresh23(true2, true2, tc_Complex_Ocomplex, X)
% 63.27/8.50 = { by axiom 2 (cls_mult__1__left_0) }
% 63.27/8.50 X
% 63.27/8.50
% 63.27/8.50 Goal 1 (cls_n__not__Suc__n_0): X = hAPP(c_Suc, X).
% 63.27/8.50 The goal is true when:
% 63.27/8.50 X = hAPP(c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U))
% 63.27/8.50
% 63.27/8.50 Proof:
% 63.27/8.50 hAPP(c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U))
% 63.27/8.50 = { by axiom 6 (cls_COMBS__def_0) }
% 63.27/8.50 hAPP(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U)), hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U)))
% 63.27/8.50 = { by lemma 7 }
% 63.27/8.50 hAPP(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U)), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U))
% 63.27/8.50 = { by axiom 3 (cls_plus__nat_Oadd__0_0) R->L }
% 63.27/8.50 hAPP(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U)), hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat)), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U)))
% 63.27/8.50 = { by lemma 7 }
% 63.27/8.50 hAPP(c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U), hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat)), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U)))
% 63.27/8.50 = { by axiom 3 (cls_plus__nat_Oadd__0_0) }
% 63.27/8.50 hAPP(c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U))
% 63.27/8.50 = { by axiom 5 (cls_COMBB__def_0) }
% 63.27/8.50 hAPP(c_Suc, hAPP(c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), c_COMBB(c_Suc, c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)), X, Y, Z), W, V, U)))
% 63.27/8.50 % SZS output end Proof
% 63.27/8.50
% 63.27/8.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------