TSTP Solution File: ALG425-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG425-1 : 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 : n025.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 : Wed Aug 30 16:43:15 EDT 2023
% Result : Unsatisfiable 33.98s 4.77s
% Output : Proof 33.98s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG425-1 : 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 : n025.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 : Mon Aug 28 04:59:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 33.98/4.77 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 33.98/4.77
% 33.98/4.77 % SZS status Unsatisfiable
% 33.98/4.77
% 33.98/4.77 % SZS output start Proof
% 33.98/4.77 Take the following subset of the input axioms:
% 33.98/4.78 fof(cls_CHAINED_0, axiom, c_Power_Opower__class_Opower(v_qa____, v_na____, tc_Polynomial_Opoly(tc_Complex_Ocomplex))=c_HOL_Otimes__class_Otimes(v_pa____, c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), v_c____, tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex), c_Power_Opower__class_Opower(v_qa____, v_na____, tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 33.98/4.78 fof(cls_Suc__n__not__n_0, axiom, ![V_n]: c_Suc(V_n)!=V_n).
% 33.98/4.78 fof(cls_Suc__neq__Zero_0, axiom, ![V_m]: c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat)).
% 33.98/4.78 fof(cls_Zero__neq__Suc_0, axiom, ![V_m2]: c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m2)).
% 33.98/4.78 fof(cls_abs__not__less__zero_0, axiom, ![T_a, V_a]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a))).
% 33.98/4.78 fof(cls_conjecture_0, negated_conjecture, ![V_x]: c_Power_Opower__class_Opower(v_qa____, v_na____, tc_Polynomial_Opoly(tc_Complex_Ocomplex))!=c_HOL_Otimes__class_Otimes(v_pa____, V_x, tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 33.98/4.78 fof(cls_exa_0, axiom, ![V_x2]: c_Polynomial_Opoly(v_pa____, V_x2, tc_Complex_Ocomplex)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 33.98/4.78 fof(cls_linorder__neq__iff_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 33.98/4.78 fof(cls_n__not__Suc__n_0, axiom, ![V_n2]: V_n2!=c_Suc(V_n2)).
% 33.98/4.78 fof(cls_nat_Osimps_I2_J_0, axiom, ![V_nat_H]: c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H)).
% 33.98/4.78 fof(cls_nat_Osimps_I3_J_0, axiom, ![V_nat_H2]: c_Suc(V_nat_H2)!=c_HOL_Ozero__class_Ozero(tc_nat)).
% 33.98/4.78 fof(cls_not__less__iff__gr__or__eq_1, axiom, ![V_y, T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y, T_a2) | ~c_HOL_Oord__class_Oless(V_y, V_x2, T_a2)))).
% 33.98/4.78 fof(cls_not__one__less__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 33.98/4.78 fof(cls_not__pos__poly__0_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | ~c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)), T_a2))).
% 33.98/4.78 fof(cls_not__square__less__zero_0, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a2, V_a2, T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 33.98/4.78 fof(cls_not__sum__squares__lt__zero_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x2, V_x2, T_a2), c_HOL_Otimes__class_Otimes(V_y2, V_y2, T_a2), T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 33.98/4.78 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))).
% 33.98/4.78 fof(cls_order__less__asym_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2)))).
% 33.98/4.78 fof(cls_order__less__asym_H_0, axiom, ![V_b, T_a2, V_a2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_b, V_a2, T_a2) | ~c_HOL_Oord__class_Oless(V_a2, V_b, T_a2)))).
% 33.98/4.78 fof(cls_order__less__irrefl_0, axiom, ![T_a2, V_x2]: (~class_Orderings_Opreorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 33.98/4.78 fof(cls_order__less__le_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Oorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 33.98/4.78 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) | c_Power_Opower__class_Opower(V_a2, c_HOL_Ozero__class_Ozero(tc_nat), T_a2)!=c_HOL_Ozero__class_Ozero(T_a2)))))).
% 33.98/4.78 fof(cls_sum__squares__gt__zero__iff_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2), T_a2), T_a2))).
% 33.98/4.78 fof(cls_xt1_I9_J_0, axiom, ![T_a2, V_a2, V_b2]: (~class_Orderings_Oorder(T_a2) | (~c_HOL_Oord__class_Oless(V_a2, V_b2, T_a2) | ~c_HOL_Oord__class_Oless(V_b2, V_a2, T_a2)))).
% 33.98/4.78 fof(cls_zero__less__abs__iff_0, axiom, ![T_a2]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a2), T_a2), T_a2))).
% 33.98/4.78 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))).
% 33.98/4.78
% 33.98/4.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 33.98/4.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 33.98/4.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 33.98/4.78 fresh(y, y, x1...xn) = u
% 33.98/4.78 C => fresh(s, t, x1...xn) = v
% 33.98/4.78 where fresh is a fresh function symbol and x1..xn are the free
% 33.98/4.78 variables of u and v.
% 33.98/4.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 33.98/4.78 input problem has no model of domain size 1).
% 33.98/4.78
% 33.98/4.78 The encoding turns the above axioms into the following unit equations and goals:
% 33.98/4.78
% 33.98/4.78 Axiom 1 (cls_CHAINED_0): c_Power_Opower__class_Opower(v_qa____, v_na____, tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_pa____, c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), v_c____, tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex), c_Power_Opower__class_Opower(v_qa____, v_na____, tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 33.98/4.78
% 33.98/4.78 Goal 1 (cls_conjecture_0): c_Power_Opower__class_Opower(v_qa____, v_na____, tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_pa____, X, tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 33.98/4.78 The goal is true when:
% 33.98/4.78 X = c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), v_c____, tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex), c_Power_Opower__class_Opower(v_qa____, v_na____, tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 33.98/4.78
% 33.98/4.78 Proof:
% 33.98/4.78 c_Power_Opower__class_Opower(v_qa____, v_na____, tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 33.98/4.78 = { by axiom 1 (cls_CHAINED_0) }
% 33.98/4.78 c_HOL_Otimes__class_Otimes(v_pa____, c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), v_c____, tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex), c_Power_Opower__class_Opower(v_qa____, v_na____, tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 33.98/4.78 % SZS output end Proof
% 33.98/4.78
% 33.98/4.78 RESULT: Unsatisfiable (the axioms are contradictory).
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