TSTP Solution File: LCL784-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL784-1 : 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 : n009.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 08:20:37 EDT 2023
% Result : Unsatisfiable 5.33s 1.03s
% Output : Proof 5.33s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL784-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % 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 : n009.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 : Thu Aug 24 19:10:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.33/1.03 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 5.33/1.03
% 5.33/1.03 % SZS status Unsatisfiable
% 5.33/1.03
% 5.33/1.03 % SZS output start Proof
% 5.33/1.03 Take the following subset of the input axioms:
% 5.33/1.03 fof(cls_Nil_0, axiom, v_rs____=c_List_Olist_ONil(tc_Lambda_OdB)).
% 5.33/1.03 fof(cls_True_0, axiom, v_n____=v_i____).
% 5.33/1.03 fof(cls_conjecture_0, negated_conjecture, ~hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB)), v_u____), v_i____)))).
% 5.33/1.03 fof(cls_foldl__Nil_0, axiom, ![T_a, V_a, V_f, T_b]: c_List_Ofoldl(V_f, V_a, c_List_Olist_ONil(T_b), T_a, T_b)=V_a).
% 5.33/1.03 fof(cls_subst__eq_0, axiom, ![V_u, V_k]: hAPP(hAPP(hAPP(c_Lambda_Osubst, c_Lambda_OdB_OVar(V_k)), V_u), V_k)=V_u).
% 5.33/1.03 fof(cls_uIT_0, axiom, hBOOL(hAPP(c_InductTermi_OIT, v_u____))).
% 5.33/1.03
% 5.33/1.03 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.33/1.03 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.33/1.03 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.33/1.03 fresh(y, y, x1...xn) = u
% 5.33/1.03 C => fresh(s, t, x1...xn) = v
% 5.33/1.03 where fresh is a fresh function symbol and x1..xn are the free
% 5.33/1.03 variables of u and v.
% 5.33/1.03 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.33/1.03 input problem has no model of domain size 1).
% 5.33/1.03
% 5.33/1.03 The encoding turns the above axioms into the following unit equations and goals:
% 5.33/1.03
% 5.33/1.03 Axiom 1 (cls_True_0): v_n____ = v_i____.
% 5.33/1.03 Axiom 2 (cls_Nil_0): v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB).
% 5.33/1.03 Axiom 3 (cls_uIT_0): hBOOL(hAPP(c_InductTermi_OIT, v_u____)) = true2.
% 5.33/1.03 Axiom 4 (cls_subst__eq_0): hAPP(hAPP(hAPP(c_Lambda_Osubst, c_Lambda_OdB_OVar(X)), Y), X) = Y.
% 5.33/1.03 Axiom 5 (cls_foldl__Nil_0): c_List_Ofoldl(X, Y, c_List_Olist_ONil(Z), W, Z) = Y.
% 5.33/1.03
% 5.33/1.03 Goal 1 (cls_conjecture_0): hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB)), v_u____), v_i____))) = true2.
% 5.33/1.03 Proof:
% 5.33/1.03 hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB)), v_u____), v_i____)))
% 5.33/1.03 = { by axiom 1 (cls_True_0) R->L }
% 5.33/1.03 hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB)), v_u____), v_n____)))
% 5.33/1.03 = { by axiom 2 (cls_Nil_0) }
% 5.33/1.03 hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)), v_u____), v_n____)))
% 5.33/1.03 = { by axiom 5 (cls_foldl__Nil_0) }
% 5.33/1.03 hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, c_Lambda_OdB_OVar(v_n____)), v_u____), v_n____)))
% 5.33/1.03 = { by axiom 4 (cls_subst__eq_0) }
% 5.33/1.03 hBOOL(hAPP(c_InductTermi_OIT, v_u____))
% 5.33/1.03 = { by axiom 3 (cls_uIT_0) }
% 5.33/1.03 true2
% 5.33/1.03 % SZS output end Proof
% 5.33/1.03
% 5.33/1.03 RESULT: Unsatisfiable (the axioms are contradictory).
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