TSTP Solution File: SWW215+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW215+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 : n020.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 00:54:26 EDT 2023
% Result : Theorem 257.33s 33.65s
% Output : Proof 257.33s
% 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 : SWW215+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 : n020.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 22:11:59 EDT 2023
% 0.13/0.34 % CPUTime :
% 257.33/33.65 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 257.33/33.65
% 257.33/33.65 % SZS status Theorem
% 257.33/33.65
% 257.33/33.66 % SZS output start Proof
% 257.33/33.66 Take the following subset of the input axioms:
% 257.33/33.66 fof(arity_RealDef__Oreal__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_RealDef_Oreal)).
% 257.33/33.66 fof(conj_0, conjecture, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 257.33/33.66 fof(fact_H_I2_J, axiom, c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 257.33/33.66 fof(fact_H_I5_J, axiom, c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), v_da____)).
% 257.33/33.66 fof(fact_less__eq__real__def, axiom, ![V_x_2, V_y_2]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, V_x_2, V_y_2) <=> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, V_x_2, V_y_2) | V_x_2=V_y_2))).
% 257.33/33.66 fof(fact_xt1_I6_J, axiom, ![T_a, V_x, V_z, V_y]: (class_Orderings_Oorder(T_a) => (c_Orderings_Oord__class_Oless__eq(T_a, V_y, V_x) => (c_Orderings_Oord__class_Oless__eq(T_a, V_z, V_y) => c_Orderings_Oord__class_Oless__eq(T_a, V_z, V_x))))).
% 257.33/33.66
% 257.33/33.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 257.33/33.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 257.33/33.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 257.33/33.66 fresh(y, y, x1...xn) = u
% 257.33/33.66 C => fresh(s, t, x1...xn) = v
% 257.33/33.66 where fresh is a fresh function symbol and x1..xn are the free
% 257.33/33.66 variables of u and v.
% 257.33/33.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 257.33/33.66 input problem has no model of domain size 1).
% 257.33/33.66
% 257.33/33.66 The encoding turns the above axioms into the following unit equations and goals:
% 257.33/33.66
% 257.33/33.66 Axiom 1 (arity_RealDef__Oreal__Orderings_Oorder): class_Orderings_Oorder(tc_RealDef_Oreal) = true2.
% 257.33/33.66 Axiom 2 (fact_H_I2_J): c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = true2.
% 257.33/33.66 Axiom 3 (fact_less__eq__real__def_1): fresh640(X, X, Y, Z) = true2.
% 257.33/33.66 Axiom 4 (fact_xt1_I6_J): fresh1873(X, X, Y, Z, W) = true2.
% 257.33/33.66 Axiom 5 (fact_H_I5_J): c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), v_da____) = true2.
% 257.33/33.66 Axiom 6 (fact_less__eq__real__def_1): fresh640(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, X, Y), true2, Y, X) = c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, X, Y).
% 257.33/33.66 Axiom 7 (fact_xt1_I6_J): fresh215(X, X, Y, Z, W, V) = c_Orderings_Oord__class_Oless__eq(V, Y, Z).
% 257.33/33.66 Axiom 8 (fact_xt1_I6_J): fresh1872(X, X, Y, Z, W, V) = fresh1873(c_Orderings_Oord__class_Oless__eq(V, Y, W), true2, Y, Z, V).
% 257.33/33.66 Axiom 9 (fact_xt1_I6_J): fresh1872(class_Orderings_Oorder(X), true2, Y, Z, W, X) = fresh215(c_Orderings_Oord__class_Oless__eq(X, W, Z), true2, Y, Z, W, X).
% 257.33/33.66
% 257.33/33.66 Goal 1 (conj_0): c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = true2.
% 257.33/33.66 Proof:
% 257.33/33.66 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 257.33/33.66 = { by axiom 7 (fact_xt1_I6_J) R->L }
% 257.33/33.66 fresh215(true2, true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), v_da____, tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 3 (fact_less__eq__real__def_1) R->L }
% 257.33/33.66 fresh215(fresh640(true2, true2, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), v_da____), true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), v_da____, tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 2 (fact_H_I2_J) R->L }
% 257.33/33.66 fresh215(fresh640(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), true2, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), v_da____), true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), v_da____, tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 6 (fact_less__eq__real__def_1) }
% 257.33/33.66 fresh215(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), v_da____, tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 9 (fact_xt1_I6_J) R->L }
% 257.33/33.66 fresh1872(class_Orderings_Oorder(tc_RealDef_Oreal), true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), v_da____, tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 1 (arity_RealDef__Oreal__Orderings_Oorder) }
% 257.33/33.66 fresh1872(true2, true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), v_da____, tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 8 (fact_xt1_I6_J) }
% 257.33/33.66 fresh1873(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), v_da____), true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 6 (fact_less__eq__real__def_1) R->L }
% 257.33/33.66 fresh1873(fresh640(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), v_da____), true2, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z))), true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 5 (fact_H_I5_J) }
% 257.33/33.66 fresh1873(fresh640(true2, true2, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z))), true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 3 (fact_less__eq__real__def_1) }
% 257.33/33.66 fresh1873(true2, true2, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 257.33/33.66 = { by axiom 4 (fact_xt1_I6_J) }
% 257.33/33.66 true2
% 257.33/33.66 % SZS output end Proof
% 257.33/33.66
% 257.33/33.66 RESULT: Theorem (the conjecture is true).
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