TSTP Solution File: LCL817-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL817-1 : 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 : n006.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 08:20:49 EDT 2023
% Result : Unsatisfiable 5.47s 1.09s
% Output : Proof 5.47s
% 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 : LCL817-1 : 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
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 06:16:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.47/1.09 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 5.47/1.09
% 5.47/1.09 % SZS status Unsatisfiable
% 5.47/1.09
% 5.47/1.09 % SZS output start Proof
% 5.47/1.09 Take the following subset of the input axioms:
% 5.47/1.09 fof(cls_argT_0, axiom, c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_T_H_H____)).
% 5.47/1.09 fof(cls_conjecture_0, negated_conjecture, ~c_Type_Otyping(v_e____, c_Lambda_Osubst(v_a____, v_u____, v_i____), v_T_H_H____)).
% 5.47/1.09 fof(cls_subst__lemma_0, axiom, ![V_t, V_u, V_T, V_i, V_U, V_e_H]: (~c_Type_Otyping(V_e_H, V_u, V_U) | (~c_Type_Otyping(c_Type_Oshift(V_e_H, V_i, V_U, tc_Type_Otype), V_t, V_T) | c_Type_Otyping(V_e_H, c_Lambda_Osubst(V_t, V_u, V_i), V_T)))).
% 5.47/1.09 fof(cls_uT_0, axiom, c_Type_Otyping(v_e____, v_u____, v_T____)).
% 5.47/1.09
% 5.47/1.09 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.47/1.09 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.47/1.09 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.47/1.09 fresh(y, y, x1...xn) = u
% 5.47/1.09 C => fresh(s, t, x1...xn) = v
% 5.47/1.09 where fresh is a fresh function symbol and x1..xn are the free
% 5.47/1.09 variables of u and v.
% 5.47/1.09 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.47/1.09 input problem has no model of domain size 1).
% 5.47/1.09
% 5.47/1.09 The encoding turns the above axioms into the following unit equations and goals:
% 5.47/1.09
% 5.47/1.09 Axiom 1 (cls_uT_0): c_Type_Otyping(v_e____, v_u____, v_T____) = true2.
% 5.47/1.09 Axiom 2 (cls_argT_0): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_T_H_H____) = true2.
% 5.47/1.09 Axiom 3 (cls_subst__lemma_0): fresh75(X, X, Y, Z, W, V, U) = true2.
% 5.47/1.09 Axiom 4 (cls_subst__lemma_0): fresh76(X, X, Y, Z, W, V, U, T) = c_Type_Otyping(Y, c_Lambda_Osubst(U, Z, V), T).
% 5.47/1.09 Axiom 5 (cls_subst__lemma_0): fresh76(c_Type_Otyping(c_Type_Oshift(X, Y, Z, tc_Type_Otype), W, V), true2, X, U, Z, Y, W, V) = fresh75(c_Type_Otyping(X, U, Z), true2, X, U, Y, W, V).
% 5.47/1.09
% 5.47/1.09 Goal 1 (cls_conjecture_0): c_Type_Otyping(v_e____, c_Lambda_Osubst(v_a____, v_u____, v_i____), v_T_H_H____) = true2.
% 5.47/1.09 Proof:
% 5.47/1.09 c_Type_Otyping(v_e____, c_Lambda_Osubst(v_a____, v_u____, v_i____), v_T_H_H____)
% 5.47/1.09 = { by axiom 4 (cls_subst__lemma_0) R->L }
% 5.47/1.09 fresh76(true2, true2, v_e____, v_u____, v_T____, v_i____, v_a____, v_T_H_H____)
% 5.47/1.09 = { by axiom 2 (cls_argT_0) R->L }
% 5.47/1.09 fresh76(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_T_H_H____), true2, v_e____, v_u____, v_T____, v_i____, v_a____, v_T_H_H____)
% 5.47/1.09 = { by axiom 5 (cls_subst__lemma_0) }
% 5.47/1.09 fresh75(c_Type_Otyping(v_e____, v_u____, v_T____), true2, v_e____, v_u____, v_i____, v_a____, v_T_H_H____)
% 5.47/1.09 = { by axiom 1 (cls_uT_0) }
% 5.47/1.09 fresh75(true2, true2, v_e____, v_u____, v_i____, v_a____, v_T_H_H____)
% 5.47/1.09 = { by axiom 3 (cls_subst__lemma_0) }
% 5.47/1.09 true2
% 5.47/1.09 % SZS output end Proof
% 5.47/1.09
% 5.47/1.09 RESULT: Unsatisfiable (the axioms are contradictory).
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