TSTP Solution File: SWW219+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWW219+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n004.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 : Fri Sep 1 00:54:27 EDT 2023
% Result : Theorem 126.28s 16.57s
% Output : Proof 127.32s
% 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 : SWW219+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 21:40:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 126.28/16.57 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 126.28/16.57
% 126.28/16.57 % SZS status Theorem
% 126.28/16.57
% 126.28/16.57 % SZS output start Proof
% 126.28/16.57 Take the following subset of the input axioms:
% 126.28/16.58 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____))).
% 126.28/16.58 fof(conj_1, conjecture, v_thesis____).
% 126.28/16.58 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))))))).
% 126.28/16.58
% 126.28/16.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 126.28/16.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 126.28/16.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 126.28/16.58 fresh(y, y, x1...xn) = u
% 126.28/16.58 C => fresh(s, t, x1...xn) = v
% 126.28/16.58 where fresh is a fresh function symbol and x1..xn are the free
% 126.28/16.59 variables of u and v.
% 126.28/16.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 127.32/16.60 input problem has no model of domain size 1).
% 127.32/16.60
% 127.32/16.60 The encoding turns the above axioms into the following unit equations and goals:
% 127.32/16.60
% 127.32/16.60 Axiom 1 (conj_0): fresh1097(X, X) = true2.
% 127.32/16.60 Axiom 2 (conj_0): fresh1098(X, X, Y) = v_thesis____.
% 127.32/16.60 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.
% 127.32/16.60 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.
% 127.32/16.60 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).
% 127.32/16.60
% 127.32/16.60 Goal 1 (conj_1): v_thesis____ = true2.
% 127.32/16.60 Proof:
% 127.32/16.60 v_thesis____
% 127.32/16.60 = { by axiom 2 (conj_0) R->L }
% 127.32/16.60 fresh1098(true2, true2, b_f)
% 127.32/16.60 = { 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 }
% 127.32/16.60 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)
% 127.32/16.60 = { by axiom 5 (conj_0) }
% 127.32/16.60 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)
% 127.32/16.60 = { 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) }
% 127.32/16.60 fresh1097(true2, true2)
% 127.32/16.60 = { by axiom 1 (conj_0) }
% 127.32/16.60 true2
% 127.32/16.60 % SZS output end Proof
% 127.32/16.60
% 127.32/16.60 RESULT: Theorem (the conjecture is true).
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