TSTP Solution File: SWW219+1 by Twee---2.5.0
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% File : Twee---2.5.0
% Problem : SWW219+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n008.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 : Mon Jun 24 18:26:35 EDT 2024
% Result : Theorem 145.05s 18.65s
% Output : Proof 145.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW219+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 08:30:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 145.05/18.65 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 145.05/18.65
% 145.05/18.65 % SZS status Theorem
% 145.05/18.65
% 145.43/18.65 % SZS output start Proof
% 145.43/18.65 Take the following subset of the input axioms:
% 145.43/18.66 fof(conj_0, hypothesis, ![B_g]: (![B_n]: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(B_g, B_n)), v_r) => (![B_n2]: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), hAPP(B_g, B_n2))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v_s____), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(B_n2))))) => v_thesis____))).
% 145.43/18.66 fof(conj_1, conjecture, v_thesis____).
% 145.43/18.66 fof(fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096, axiom, ?[B_f]: ![B_x]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(B_f, B_x)), v_r) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), hAPP(B_f, B_x))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v_s____), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(B_x))))))).
% 145.43/18.66
% 145.43/18.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 145.43/18.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 145.43/18.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 145.43/18.66 fresh(y, y, x1...xn) = u
% 145.43/18.66 C => fresh(s, t, x1...xn) = v
% 145.43/18.66 where fresh is a fresh function symbol and x1..xn are the free
% 145.43/18.66 variables of u and v.
% 145.43/18.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 145.43/18.66 input problem has no model of domain size 1).
% 145.43/18.66
% 145.43/18.66 The encoding turns the above axioms into the following unit equations and goals:
% 145.43/18.66
% 145.43/18.66 Axiom 1 (conj_0): fresh1097(X, X) = true2.
% 145.43/18.66 Axiom 2 (conj_0): fresh1098(X, X, Y) = v_thesis____.
% 145.43/18.66 Axiom 3 (fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096): c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(b_f, X)), v_r) = true2.
% 145.43/18.66 Axiom 4 (fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096_1): c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), hAPP(b_f, X))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v_s____), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(X))))) = true2.
% 145.43/18.66 Axiom 5 (conj_0): fresh1098(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), hAPP(X, b_n(X)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v_s____), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(b_n(X)))))), true2, X) = fresh1097(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(X, b_n2(X))), v_r), true2).
% 145.43/18.66
% 145.43/18.66 Goal 1 (conj_1): v_thesis____ = true2.
% 145.43/18.66 Proof:
% 145.43/18.66 v_thesis____
% 145.43/18.66 = { by axiom 2 (conj_0) R->L }
% 145.43/18.66 fresh1098(true2, true2, b_f)
% 145.43/18.66 = { by axiom 4 (fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096_1) R->L }
% 145.43/18.66 fresh1098(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), hAPP(b_f, b_n(b_f)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v_s____), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(b_n(b_f)))))), true2, b_f)
% 145.43/18.66 = { by axiom 5 (conj_0) }
% 145.43/18.66 fresh1097(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(b_f, b_n2(b_f))), v_r), true2)
% 145.43/18.66 = { by axiom 3 (fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096) }
% 145.43/18.66 fresh1097(true2, true2)
% 145.43/18.66 = { by axiom 1 (conj_0) }
% 145.43/18.66 true2
% 145.43/18.66 % SZS output end Proof
% 145.43/18.66
% 145.43/18.66 RESULT: Theorem (the conjecture is true).
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