TSTP Solution File: ALG376-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG376-1 : 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 : n019.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 16:43:07 EDT 2023
% Result : Unsatisfiable 89.57s 12.10s
% Output : Proof 89.57s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : ALG376-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 04:21:43 EDT 2023
% 0.14/0.37 % CPUTime :
% 89.57/12.10 Command-line arguments: --no-flatten-goal
% 89.57/12.10
% 89.57/12.10 % SZS status Unsatisfiable
% 89.57/12.10
% 89.57/12.10 % SZS output start Proof
% 89.57/12.10 Take the following subset of the input axioms:
% 89.57/12.10 fof(cls_CHAINED_0, axiom, ![V_wa]: (c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p, V_wa, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_wa, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____, tc_RealDef_Oreal))).
% 89.57/12.10 fof(cls_N1_0, axiom, ![V_n]: (c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_g____(v_f____(V_n)), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____, tc_RealDef_Oreal) | ~c_lessequals(v_N1____, V_n, tc_nat))).
% 89.57/12.10 fof(cls_conjecture_0, negated_conjecture, ~c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p, v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_Complex_Ocomplex), c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 89.57/12.10 fof(cls_le__add1_0, axiom, ![V_m, V_n2]: c_lessequals(V_n2, c_HOL_Oplus__class_Oplus(V_n2, V_m, tc_nat), tc_nat)).
% 89.57/12.10
% 89.57/12.10 Now clausify the problem and encode Horn clauses using encoding 3 of
% 89.57/12.10 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 89.57/12.10 We repeatedly replace C & s=t => u=v by the two clauses:
% 89.57/12.10 fresh(y, y, x1...xn) = u
% 89.57/12.10 C => fresh(s, t, x1...xn) = v
% 89.57/12.10 where fresh is a fresh function symbol and x1..xn are the free
% 89.57/12.10 variables of u and v.
% 89.57/12.10 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 89.57/12.10 input problem has no model of domain size 1).
% 89.57/12.10
% 89.57/12.10 The encoding turns the above axioms into the following unit equations and goals:
% 89.57/12.10
% 89.57/12.10 Axiom 1 (cls_CHAINED_0): fresh820(X, X, Y) = true2.
% 89.57/12.10 Axiom 2 (cls_N1_0): fresh816(X, X, Y) = true2.
% 89.57/12.10 Axiom 3 (cls_le__add1_0): c_lessequals(X, c_HOL_Oplus__class_Oplus(X, Y, tc_nat), tc_nat) = true2.
% 89.57/12.10 Axiom 4 (cls_N1_0): fresh816(c_lessequals(v_N1____, X, tc_nat), true2, X) = c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_g____(v_f____(X)), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____, tc_RealDef_Oreal).
% 89.57/12.10 Axiom 5 (cls_CHAINED_0): fresh820(c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____, tc_RealDef_Oreal), true2, X) = c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p, X, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal).
% 89.57/12.10
% 89.57/12.10 Goal 1 (cls_conjecture_0): c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p, v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_Complex_Ocomplex), c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 89.57/12.10 Proof:
% 89.57/12.10 c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p, v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_Complex_Ocomplex), c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 89.57/12.10 = { by axiom 5 (cls_CHAINED_0) R->L }
% 89.57/12.10 fresh820(c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____, tc_RealDef_Oreal), true2, v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))))
% 89.57/12.10 = { by axiom 4 (cls_N1_0) R->L }
% 89.57/12.10 fresh820(fresh816(c_lessequals(v_N1____, c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat), tc_nat), true2, c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), true2, v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))))
% 89.57/12.10 = { by axiom 3 (cls_le__add1_0) }
% 89.57/12.10 fresh820(fresh816(true2, true2, c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), true2, v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))))
% 89.57/12.10 = { by axiom 2 (cls_N1_0) }
% 89.57/12.10 fresh820(true2, true2, v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))))
% 89.57/12.10 = { by axiom 1 (cls_CHAINED_0) }
% 89.57/12.10 true2
% 89.57/12.10 % SZS output end Proof
% 89.57/12.10
% 89.57/12.10 RESULT: Unsatisfiable (the axioms are contradictory).
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