TSTP Solution File: ALG341-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG341-1 : 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 : 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 : Wed Aug 30 16:43:00 EDT 2023
% Result : Unsatisfiable 33.61s 4.84s
% Output : Proof 33.61s
% 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 : ALG341-1 : 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
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon Aug 28 04:03:47 EDT 2023
% 0.16/0.34 % CPUTime :
% 33.61/4.84 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 33.61/4.84
% 33.61/4.84 % SZS status Unsatisfiable
% 33.61/4.84
% 33.61/4.84 % SZS output start Proof
% 33.61/4.84 Take the following subset of the input axioms:
% 33.61/4.84 fof(cls_CHAINED_0, axiom, c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex), tc_RealDef_Oreal)).
% 33.61/4.84 fof(cls_CHAINED_0_01, axiom, c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal)).
% 33.61/4.84 fof(cls_conjecture_0, negated_conjecture, ~c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, tc_RealDef_Oreal)).
% 33.61/4.84 fof(cls_order__trans_0, axiom, ![T_a, V_x, V_y, V_z]: (~class_Orderings_Opreorder(T_a) | (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_y, V_z, T_a) | ~c_lessequals(V_x, V_y, T_a))))).
% 33.61/4.84 fof(clsarity_RealDef__Oreal__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_RealDef_Oreal)).
% 33.61/4.84
% 33.61/4.84 Now clausify the problem and encode Horn clauses using encoding 3 of
% 33.61/4.84 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 33.61/4.84 We repeatedly replace C & s=t => u=v by the two clauses:
% 33.61/4.84 fresh(y, y, x1...xn) = u
% 33.61/4.84 C => fresh(s, t, x1...xn) = v
% 33.61/4.84 where fresh is a fresh function symbol and x1..xn are the free
% 33.61/4.84 variables of u and v.
% 33.61/4.84 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 33.61/4.84 input problem has no model of domain size 1).
% 33.61/4.84
% 33.61/4.84 The encoding turns the above axioms into the following unit equations and goals:
% 33.61/4.84
% 33.61/4.84 Axiom 1 (clsarity_RealDef__Oreal__Orderings_Opreorder): class_Orderings_Opreorder(tc_RealDef_Oreal) = true2.
% 33.61/4.84 Axiom 2 (cls_CHAINED_0_01): c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal) = true2.
% 33.61/4.84 Axiom 3 (cls_order__trans_0): fresh478(X, X, Y, Z, W) = true2.
% 33.61/4.84 Axiom 4 (cls_CHAINED_0): c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex), tc_RealDef_Oreal) = true2.
% 33.61/4.84 Axiom 5 (cls_order__trans_0): fresh171(X, X, Y, Z, W, V) = c_lessequals(Z, W, Y).
% 33.61/4.84 Axiom 6 (cls_order__trans_0): fresh477(X, X, Y, Z, W, V) = fresh478(c_lessequals(Z, V, Y), true2, Y, Z, W).
% 33.61/4.84 Axiom 7 (cls_order__trans_0): fresh477(class_Orderings_Opreorder(X), true2, X, Y, Z, W) = fresh171(c_lessequals(W, Z, X), true2, X, Y, Z, W).
% 33.61/4.84
% 33.61/4.84 Goal 1 (cls_conjecture_0): c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, tc_RealDef_Oreal) = true2.
% 33.61/4.84 Proof:
% 33.61/4.84 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, tc_RealDef_Oreal)
% 33.61/4.84 = { by axiom 5 (cls_order__trans_0) R->L }
% 33.61/4.84 fresh171(true2, true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex))
% 33.61/4.84 = { by axiom 2 (cls_CHAINED_0_01) R->L }
% 33.61/4.84 fresh171(c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex))
% 33.61/4.84 = { by axiom 7 (cls_order__trans_0) R->L }
% 33.61/4.84 fresh477(class_Orderings_Opreorder(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex))
% 33.61/4.84 = { by axiom 1 (clsarity_RealDef__Oreal__Orderings_Opreorder) }
% 33.61/4.84 fresh477(true2, true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex))
% 33.61/4.84 = { by axiom 6 (cls_order__trans_0) }
% 33.61/4.84 fresh478(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_z____, tc_Complex_Ocomplex), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r)
% 33.61/4.84 = { by axiom 4 (cls_CHAINED_0) }
% 33.61/4.84 fresh478(true2, true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r)
% 33.61/4.84 = { by axiom 3 (cls_order__trans_0) }
% 33.61/4.84 true2
% 33.61/4.84 % SZS output end Proof
% 33.61/4.84
% 33.61/4.84 RESULT: Unsatisfiable (the axioms are contradictory).
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