TSTP Solution File: LCL787-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL787-1 : 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 : n020.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 08:20:38 EDT 2023
% Result : Unsatisfiable 21.12s 3.12s
% Output : Proof 21.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL787-1 : 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 : n020.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 : Thu Aug 24 17:58:15 EDT 2023
% 0.14/0.36 % CPUTime :
% 21.12/3.12 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 21.12/3.12
% 21.12/3.12 % SZS status Unsatisfiable
% 21.12/3.12
% 21.12/3.13 % SZS output start Proof
% 21.12/3.13 Take the following subset of the input axioms:
% 21.12/3.13 fof(cls_True_0, axiom, v_n____=v_i____).
% 21.12/3.13 fof(cls_conjecture_0, negated_conjecture, ~v_thesis____).
% 21.12/3.13 fof(cls_headT_0, axiom, c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____)), v_a____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))).
% 21.12/3.13 fof(cls_that_0, axiom, ![V_T_H_H]: (v_thesis____ | (~c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, V_T_H_H) | ~c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_n____), hAPP(hAPP(c_Type_Otype_OFun, V_T_H_H), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)))))).
% 21.12/3.13 fof(cls_typing__elims_I2_J_0, axiom, ![V_u, V_t, V_e, V_T]: (c_Type_Otyping(V_e, V_t, hAPP(hAPP(c_Type_Otype_OFun, c_Type_Osko__Type__Xtyping__elims__2__1(V_T, V_e, V_t, V_u)), V_T)) | ~c_Type_Otyping(V_e, hAPP(hAPP(c_Lambda_OdB_OApp, V_t), V_u), V_T))).
% 21.12/3.13 fof(cls_typing__elims_I2_J_1, axiom, ![V_T2, V_u2, V_t2, V_e2]: (c_Type_Otyping(V_e2, V_u2, c_Type_Osko__Type__Xtyping__elims__2__1(V_T2, V_e2, V_t2, V_u2)) | ~c_Type_Otyping(V_e2, hAPP(hAPP(c_Lambda_OdB_OApp, V_t2), V_u2), V_T2))).
% 21.12/3.13
% 21.12/3.13 Now clausify the problem and encode Horn clauses using encoding 3 of
% 21.12/3.13 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 21.12/3.13 We repeatedly replace C & s=t => u=v by the two clauses:
% 21.12/3.13 fresh(y, y, x1...xn) = u
% 21.12/3.13 C => fresh(s, t, x1...xn) = v
% 21.12/3.13 where fresh is a fresh function symbol and x1..xn are the free
% 21.12/3.13 variables of u and v.
% 21.12/3.13 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 21.12/3.13 input problem has no model of domain size 1).
% 21.12/3.13
% 21.12/3.13 The encoding turns the above axioms into the following unit equations and goals:
% 21.12/3.13
% 21.12/3.13 Axiom 1 (cls_True_0): v_n____ = v_i____.
% 21.12/3.13 Axiom 2 (cls_that_0): fresh87(X, X) = true2.
% 21.12/3.13 Axiom 3 (cls_that_0): fresh88(X, X, Y) = v_thesis____.
% 21.12/3.13 Axiom 4 (cls_typing__elims_I2_J_0): fresh81(X, X, Y, Z, W, V) = true2.
% 21.12/3.13 Axiom 5 (cls_typing__elims_I2_J_1): fresh80(X, X, Y, Z, W, V) = true2.
% 21.12/3.13 Axiom 6 (cls_typing__elims_I2_J_0): fresh81(c_Type_Otyping(X, hAPP(hAPP(c_Lambda_OdB_OApp, Y), Z), W), true2, X, Y, W, Z) = c_Type_Otyping(X, Y, hAPP(hAPP(c_Type_Otype_OFun, c_Type_Osko__Type__Xtyping__elims__2__1(W, X, Y, Z)), W)).
% 21.12/3.13 Axiom 7 (cls_typing__elims_I2_J_1): fresh80(c_Type_Otyping(X, hAPP(hAPP(c_Lambda_OdB_OApp, Y), Z), W), true2, X, Z, W, Y) = c_Type_Otyping(X, Z, c_Type_Osko__Type__Xtyping__elims__2__1(W, X, Y, Z)).
% 21.12/3.13 Axiom 8 (cls_headT_0): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____)), v_a____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)) = true2.
% 21.12/3.13 Axiom 9 (cls_that_0): fresh88(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, X), true2, X) = fresh87(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_n____), hAPP(hAPP(c_Type_Otype_OFun, X), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))), true2).
% 21.12/3.13
% 21.12/3.13 Lemma 10: c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_i____)), v_a____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)) = true2.
% 21.12/3.13 Proof:
% 21.12/3.13 c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_i____)), v_a____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))
% 21.12/3.13 = { by axiom 1 (cls_True_0) R->L }
% 21.12/3.13 c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____)), v_a____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))
% 21.12/3.13 = { by axiom 8 (cls_headT_0) }
% 21.12/3.13 true2
% 21.12/3.13
% 21.12/3.13 Goal 1 (cls_conjecture_0): v_thesis____ = true2.
% 21.12/3.13 Proof:
% 21.12/3.13 v_thesis____
% 21.12/3.13 = { by axiom 3 (cls_that_0) R->L }
% 21.12/3.13 fresh88(true2, true2, c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), v_a____))
% 21.12/3.13 = { by axiom 5 (cls_typing__elims_I2_J_1) R->L }
% 21.12/3.13 fresh88(fresh80(true2, true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____)), true2, c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), v_a____))
% 21.12/3.13 = { by lemma 10 R->L }
% 21.12/3.13 fresh88(fresh80(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_i____)), v_a____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)), true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____)), true2, c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), v_a____))
% 21.12/3.13 = { by axiom 7 (cls_typing__elims_I2_J_1) }
% 21.12/3.13 fresh88(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), v_a____)), true2, c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), v_a____))
% 21.12/3.13 = { by axiom 9 (cls_that_0) }
% 21.12/3.13 fresh87(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_n____), hAPP(hAPP(c_Type_Otype_OFun, c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), v_a____)), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))), true2)
% 21.12/3.13 = { by axiom 1 (cls_True_0) }
% 21.12/3.13 fresh87(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), hAPP(hAPP(c_Type_Otype_OFun, c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), v_a____)), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))), true2)
% 21.12/3.13 = { by axiom 6 (cls_typing__elims_I2_J_0) R->L }
% 21.12/3.13 fresh87(fresh81(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_i____)), v_a____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)), true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), v_a____), true2)
% 21.12/3.13 = { by lemma 10 }
% 21.12/3.13 fresh87(fresh81(true2, true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), v_a____), true2)
% 21.12/3.13 = { by axiom 4 (cls_typing__elims_I2_J_0) }
% 21.12/3.13 fresh87(true2, true2)
% 21.12/3.13 = { by axiom 2 (cls_that_0) }
% 21.12/3.13 true2
% 21.12/3.13 % SZS output end Proof
% 21.12/3.13
% 21.12/3.13 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------