TSTP Solution File: ALG410-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG410-1 : 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 : n027.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 16:43:13 EDT 2023
% Result : Unsatisfiable 35.72s 5.06s
% Output : Proof 35.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG410-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon Aug 28 06:22:37 EDT 2023
% 0.17/0.35 % CPUTime :
% 35.72/5.05 Command-line arguments: --no-flatten-goal
% 35.72/5.06
% 35.72/5.06 % SZS status Unsatisfiable
% 35.72/5.06
% 35.72/5.06 % SZS output start Proof
% 35.72/5.06 Take the following subset of the input axioms:
% 35.72/5.06 fof(cls_CHAINED_0, axiom, c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____, tc_Complex_Ocomplex), v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 35.72/5.06 fof(cls_conjecture_0, negated_conjecture, ![V_x]: ~c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), V_x, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 35.72/5.06 fof(cls_less__le__not__le_1, axiom, ![T_a, V_y, V_x2]: (~class_Orderings_Opreorder(T_a) | (~c_lessequals(V_y, V_x2, T_a) | ~c_HOL_Oord__class_Oless(V_x2, V_y, T_a)))).
% 35.72/5.06 fof(cls_linorder__antisym__conv2_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | (~c_lessequals(V_x2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2)))).
% 35.72/5.06 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))).
% 35.72/5.06 fof(cls_linorder__not__le_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_lessequals(V_x2, V_y2, T_a2) | ~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2)))).
% 35.72/5.06 fof(cls_linorder__not__less_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2) | ~c_lessequals(V_y2, V_x2, T_a2)))).
% 35.72/5.06 fof(cls_norm__not__less__zero_0, axiom, ![T_a2, V_x2]: (~class_RealVector_Oreal__normed__vector(T_a2) | ~c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x2, T_a2), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal))).
% 35.72/5.06 fof(cls_not__less__iff__gr__or__eq_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2) | ~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2)))).
% 35.72/5.06 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))).
% 35.72/5.06 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))).
% 35.72/5.06 fof(cls_not__square__less__zero_0, axiom, ![V_a, T_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_a, T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 35.72/5.06 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))).
% 35.72/5.06 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))).
% 35.72/5.06 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)))).
% 35.72/5.06 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)))).
% 35.72/5.06 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))).
% 35.72/5.06 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))).
% 35.72/5.06 fof(cls_real__less__def_1, axiom, ![V_x2]: ~c_HOL_Oord__class_Oless(V_x2, V_x2, tc_RealDef_Oreal)).
% 35.72/5.06 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))).
% 35.72/5.06 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)))).
% 35.72/5.07 fof(cls_zero__less__norm__iff_0, axiom, ![T_a2]: (~class_RealVector_Oreal__normed__vector(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a2), T_a2), tc_RealDef_Oreal))).
% 35.72/5.07 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))).
% 35.72/5.07
% 35.72/5.07 Now clausify the problem and encode Horn clauses using encoding 3 of
% 35.72/5.07 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 35.72/5.07 We repeatedly replace C & s=t => u=v by the two clauses:
% 35.72/5.07 fresh(y, y, x1...xn) = u
% 35.72/5.07 C => fresh(s, t, x1...xn) = v
% 35.72/5.07 where fresh is a fresh function symbol and x1..xn are the free
% 35.72/5.07 variables of u and v.
% 35.72/5.07 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 35.72/5.07 input problem has no model of domain size 1).
% 35.72/5.07
% 35.72/5.07 The encoding turns the above axioms into the following unit equations and goals:
% 35.72/5.07
% 35.72/5.07 Axiom 1 (cls_CHAINED_0): c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____, tc_Complex_Ocomplex), v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 35.72/5.07
% 35.72/5.07 Goal 1 (cls_conjecture_0): c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), X, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 35.72/5.07 The goal is true when:
% 35.72/5.07 X = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____, tc_Complex_Ocomplex), v_w____, tc_Complex_Ocomplex)
% 35.72/5.07
% 35.72/5.07 Proof:
% 35.72/5.07 c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____, tc_Complex_Ocomplex), v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 35.72/5.07 = { by axiom 1 (cls_CHAINED_0) }
% 35.72/5.07 true2
% 35.72/5.07 % SZS output end Proof
% 35.72/5.07
% 35.72/5.07 RESULT: Unsatisfiable (the axioms are contradictory).
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