TSTP Solution File: ALG350-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG350-1 : 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 16:43:02 EDT 2023
% Result : Unsatisfiable 10.30s 1.72s
% Output : Proof 10.30s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG350-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % 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 : n008.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 05:14:02 EDT 2023
% 0.14/0.36 % CPUTime :
% 10.30/1.72 Command-line arguments: --no-flatten-goal
% 10.30/1.72
% 10.30/1.72 % SZS status Unsatisfiable
% 10.30/1.72
% 10.30/1.72 % SZS output start Proof
% 10.30/1.72 Take the following subset of the input axioms:
% 10.30/1.72 fof(cls_CHAINED_0, axiom, ![V_x]: (c_HOL_Oord__class_Oless(V_x, v_Y____, tc_RealDef_Oreal) | ~hBOOL(hAPP(v_P, V_x)))).
% 10.30/1.72 fof(cls_conjecture_0, negated_conjecture, hBOOL(hAPP(v_P, v_xa))).
% 10.30/1.72 fof(cls_conjecture_1, negated_conjecture, ~c_lessequals(v_xa, v_Y____, tc_RealDef_Oreal)).
% 10.30/1.72 fof(cls_real__less__def_0, axiom, ![V_y, V_x2]: (c_lessequals(V_x2, V_y, tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(V_x2, V_y, tc_RealDef_Oreal))).
% 10.30/1.72
% 10.30/1.72 Now clausify the problem and encode Horn clauses using encoding 3 of
% 10.30/1.72 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 10.30/1.72 We repeatedly replace C & s=t => u=v by the two clauses:
% 10.30/1.72 fresh(y, y, x1...xn) = u
% 10.30/1.72 C => fresh(s, t, x1...xn) = v
% 10.30/1.72 where fresh is a fresh function symbol and x1..xn are the free
% 10.30/1.72 variables of u and v.
% 10.30/1.72 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 10.30/1.72 input problem has no model of domain size 1).
% 10.30/1.72
% 10.30/1.72 The encoding turns the above axioms into the following unit equations and goals:
% 10.30/1.72
% 10.30/1.72 Axiom 1 (cls_CHAINED_0): fresh411(X, X, Y) = true2.
% 10.30/1.72 Axiom 2 (cls_conjecture_0): hBOOL(hAPP(v_P, v_xa)) = true2.
% 10.30/1.72 Axiom 3 (cls_real__less__def_0): fresh84(X, X, Y, Z) = true2.
% 10.30/1.72 Axiom 4 (cls_CHAINED_0): fresh411(hBOOL(hAPP(v_P, X)), true2, X) = c_HOL_Oord__class_Oless(X, v_Y____, tc_RealDef_Oreal).
% 10.30/1.72 Axiom 5 (cls_real__less__def_0): fresh84(c_HOL_Oord__class_Oless(X, Y, tc_RealDef_Oreal), true2, X, Y) = c_lessequals(X, Y, tc_RealDef_Oreal).
% 10.30/1.72
% 10.30/1.72 Goal 1 (cls_conjecture_1): c_lessequals(v_xa, v_Y____, tc_RealDef_Oreal) = true2.
% 10.30/1.72 Proof:
% 10.30/1.72 c_lessequals(v_xa, v_Y____, tc_RealDef_Oreal)
% 10.30/1.72 = { by axiom 5 (cls_real__less__def_0) R->L }
% 10.30/1.72 fresh84(c_HOL_Oord__class_Oless(v_xa, v_Y____, tc_RealDef_Oreal), true2, v_xa, v_Y____)
% 10.30/1.72 = { by axiom 4 (cls_CHAINED_0) R->L }
% 10.30/1.72 fresh84(fresh411(hBOOL(hAPP(v_P, v_xa)), true2, v_xa), true2, v_xa, v_Y____)
% 10.30/1.72 = { by axiom 2 (cls_conjecture_0) }
% 10.30/1.72 fresh84(fresh411(true2, true2, v_xa), true2, v_xa, v_Y____)
% 10.30/1.72 = { by axiom 1 (cls_CHAINED_0) }
% 10.30/1.72 fresh84(true2, true2, v_xa, v_Y____)
% 10.30/1.72 = { by axiom 3 (cls_real__less__def_0) }
% 10.30/1.72 true2
% 10.30/1.72 % SZS output end Proof
% 10.30/1.72
% 10.30/1.72 RESULT: Unsatisfiable (the axioms are contradictory).
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