TSTP Solution File: LCL806-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL806-1 : 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 : n015.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 : Thu Aug 31 08:20:44 EDT 2023
% Result : Unsatisfiable 10.99s 1.82s
% Output : Proof 10.99s
% 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 : LCL806-1 : 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
% 0.13/0.34 % Computer : n015.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 : Fri Aug 25 05:51:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 10.99/1.82 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 10.99/1.82
% 10.99/1.82 % SZS status Unsatisfiable
% 10.99/1.82
% 10.99/1.82 % SZS output start Proof
% 10.99/1.82 Take the following subset of the input axioms:
% 10.99/1.82 fof(cls_CHAINED_0_02, axiom, ![V_u, V_ia, V_ea, V_T_H]: (hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_b____), V_u), V_ia))) | (~hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, V_ea), V_u), v_T____)) | (~hBOOL(hAPP(c_InductTermi_OIT, V_u)) | ~hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype), V_ea), V_ia), v_T____)), v_b____), V_T_H)))))).
% 10.99/1.82 fof(cls_conjecture_0, negated_conjecture, hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype), v_x), v_xc), v_T____)), v_b____), v_xa))).
% 10.99/1.82 fof(cls_conjecture_1, negated_conjecture, hBOOL(hAPP(c_InductTermi_OIT, v_xb))).
% 10.99/1.82 fof(cls_conjecture_2, negated_conjecture, hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, v_x), v_xb), v_T____))).
% 10.99/1.82 fof(cls_conjecture_3, negated_conjecture, ~hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_b____), v_xb), v_xc)))).
% 10.99/1.82
% 10.99/1.82 Now clausify the problem and encode Horn clauses using encoding 3 of
% 10.99/1.82 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 10.99/1.82 We repeatedly replace C & s=t => u=v by the two clauses:
% 10.99/1.82 fresh(y, y, x1...xn) = u
% 10.99/1.82 C => fresh(s, t, x1...xn) = v
% 10.99/1.82 where fresh is a fresh function symbol and x1..xn are the free
% 10.99/1.82 variables of u and v.
% 10.99/1.82 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 10.99/1.82 input problem has no model of domain size 1).
% 10.99/1.82
% 10.99/1.82 The encoding turns the above axioms into the following unit equations and goals:
% 10.99/1.82
% 10.99/1.82 Axiom 1 (cls_conjecture_1): hBOOL(hAPP(c_InductTermi_OIT, v_xb)) = true2.
% 10.99/1.82 Axiom 2 (cls_CHAINED_0_02): fresh237(X, X, Y, Z) = true2.
% 10.99/1.82 Axiom 3 (cls_conjecture_2): hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, v_x), v_xb), v_T____)) = true2.
% 10.99/1.82 Axiom 4 (cls_CHAINED_0_02): fresh232(X, X, Y, Z, W) = hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_b____), Y), Z))).
% 10.99/1.82 Axiom 5 (cls_CHAINED_0_02): fresh236(X, X, Y, Z, W, V) = fresh237(hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, W), Y), v_T____)), true2, Y, Z).
% 10.99/1.82 Axiom 6 (cls_conjecture_0): hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype), v_x), v_xc), v_T____)), v_b____), v_xa)) = true2.
% 10.99/1.82 Axiom 7 (cls_CHAINED_0_02): fresh236(hBOOL(hAPP(c_InductTermi_OIT, X)), true2, X, Y, Z, W) = fresh232(hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype), Z), Y), v_T____)), v_b____), W)), true2, X, Y, Z).
% 10.99/1.82
% 10.99/1.82 Goal 1 (cls_conjecture_3): hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_b____), v_xb), v_xc))) = true2.
% 10.99/1.82 Proof:
% 10.99/1.82 hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_b____), v_xb), v_xc)))
% 10.99/1.82 = { by axiom 4 (cls_CHAINED_0_02) R->L }
% 10.99/1.82 fresh232(true2, true2, v_xb, v_xc, v_x)
% 10.99/1.82 = { by axiom 6 (cls_conjecture_0) R->L }
% 10.99/1.82 fresh232(hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype), v_x), v_xc), v_T____)), v_b____), v_xa)), true2, v_xb, v_xc, v_x)
% 10.99/1.82 = { by axiom 7 (cls_CHAINED_0_02) R->L }
% 10.99/1.82 fresh236(hBOOL(hAPP(c_InductTermi_OIT, v_xb)), true2, v_xb, v_xc, v_x, v_xa)
% 10.99/1.82 = { by axiom 1 (cls_conjecture_1) }
% 10.99/1.82 fresh236(true2, true2, v_xb, v_xc, v_x, v_xa)
% 10.99/1.82 = { by axiom 5 (cls_CHAINED_0_02) }
% 10.99/1.82 fresh237(hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping, v_x), v_xb), v_T____)), true2, v_xb, v_xc)
% 10.99/1.82 = { by axiom 3 (cls_conjecture_2) }
% 10.99/1.82 fresh237(true2, true2, v_xb, v_xc)
% 10.99/1.82 = { by axiom 2 (cls_CHAINED_0_02) }
% 10.99/1.82 true2
% 10.99/1.82 % SZS output end Proof
% 10.99/1.82
% 10.99/1.82 RESULT: Unsatisfiable (the axioms are contradictory).
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