TSTP Solution File: LCL798-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL798-1 : 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 : n031.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 08:20:42 EDT 2023
% Result : Unsatisfiable 0.19s 0.63s
% Output : Proof 0.19s
% 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 : LCL798-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % 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 : n031.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 05:02:36 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.63 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.63
% 0.19/0.63 % SZS status Unsatisfiable
% 0.19/0.63
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 Take the following subset of the input axioms:
% 0.19/0.64 fof(cls_CHAINED_0, axiom, ![V_i, V_u, V_e, V_T_H]: (c_InductTermi_OIT(c_Lambda_Osubst(v_a____, V_u, V_i)) | (~c_Type_Otyping(V_e, V_u, v_T____) | (~c_InductTermi_OIT(V_u) | ~c_Type_Otyping(c_Type_Oshift(V_e, V_i, v_T____, tc_Type_Otype), v_a____, V_T_H))))).
% 0.19/0.64 fof(cls_CHAINED_0_01, axiom, c_Type_Otyping(v_e____, v_u____, v_T____)).
% 0.19/0.64 fof(cls_CHAINED_0_03, axiom, c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_T_H_H____)).
% 0.19/0.64 fof(cls_conjecture_0, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_Osubst(v_a____, v_u____, v_i____))).
% 0.19/0.64 fof(cls_uIT_0, axiom, c_InductTermi_OIT(v_u____)).
% 0.19/0.64
% 0.19/0.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.64 fresh(y, y, x1...xn) = u
% 0.19/0.64 C => fresh(s, t, x1...xn) = v
% 0.19/0.64 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.64 variables of u and v.
% 0.19/0.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.64 input problem has no model of domain size 1).
% 0.19/0.64
% 0.19/0.64 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.64
% 0.19/0.64 Axiom 1 (cls_uIT_0): c_InductTermi_OIT(v_u____) = true2.
% 0.19/0.64 Axiom 2 (cls_CHAINED_0_01): c_Type_Otyping(v_e____, v_u____, v_T____) = true2.
% 0.19/0.64 Axiom 3 (cls_CHAINED_0): fresh31(X, X, Y, Z) = true2.
% 0.19/0.64 Axiom 4 (cls_CHAINED_0): fresh29(X, X, Y, Z) = c_InductTermi_OIT(c_Lambda_Osubst(v_a____, Y, Z)).
% 0.19/0.64 Axiom 5 (cls_CHAINED_0): fresh30(X, X, Y, Z, W) = fresh31(c_InductTermi_OIT(Y), true2, Y, Z).
% 0.19/0.64 Axiom 6 (cls_CHAINED_0_03): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_T_H_H____) = true2.
% 0.19/0.64 Axiom 7 (cls_CHAINED_0): fresh30(c_Type_Otyping(c_Type_Oshift(X, Y, v_T____, tc_Type_Otype), v_a____, Z), true2, W, Y, X) = fresh29(c_Type_Otyping(X, W, v_T____), true2, W, Y).
% 0.19/0.64
% 0.19/0.64 Goal 1 (cls_conjecture_0): c_InductTermi_OIT(c_Lambda_Osubst(v_a____, v_u____, v_i____)) = true2.
% 0.19/0.64 Proof:
% 0.19/0.64 c_InductTermi_OIT(c_Lambda_Osubst(v_a____, v_u____, v_i____))
% 0.19/0.64 = { by axiom 4 (cls_CHAINED_0) R->L }
% 0.19/0.64 fresh29(true2, true2, v_u____, v_i____)
% 0.19/0.64 = { by axiom 2 (cls_CHAINED_0_01) R->L }
% 0.19/0.64 fresh29(c_Type_Otyping(v_e____, v_u____, v_T____), true2, v_u____, v_i____)
% 0.19/0.64 = { by axiom 7 (cls_CHAINED_0) R->L }
% 0.19/0.64 fresh30(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_T_H_H____), true2, v_u____, v_i____, v_e____)
% 0.19/0.64 = { by axiom 6 (cls_CHAINED_0_03) }
% 0.19/0.64 fresh30(true2, true2, v_u____, v_i____, v_e____)
% 0.19/0.64 = { by axiom 5 (cls_CHAINED_0) }
% 0.19/0.64 fresh31(c_InductTermi_OIT(v_u____), true2, v_u____, v_i____)
% 0.19/0.64 = { by axiom 1 (cls_uIT_0) }
% 0.19/0.64 fresh31(true2, true2, v_u____, v_i____)
% 0.19/0.64 = { by axiom 3 (cls_CHAINED_0) }
% 0.19/0.64 true2
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64
% 0.19/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
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