TSTP Solution File: LCL784-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL784-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 : 600s
% DateTime : Sun Jul 17 12:55:59 EDT 2022
% Result : Unsatisfiable 0.62s 0.79s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 32
% Syntax : Number of clauses : 69 ( 36 unt; 0 nHn; 64 RR)
% Number of literals : 119 ( 106 equ; 53 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 29 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_subst__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ).
cnf(cls_foldl__Nil_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ).
cnf(cls_CHAINED_0,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB) ).
cnf(cls_CHAINED_0_01,axiom,
v_n____ = v_i____ ).
cnf(cls_CHAINED_0_02,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ).
cnf(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____))) ).
cnf(refute_0_0,plain,
c_Lambda_OdB_OVar(v_n____) = c_Lambda_OdB_OVar(v_n____),
introduced(tautology,[refl,[$fot(c_Lambda_OdB_OVar(v_n____))]]) ).
cnf(refute_0_1,plain,
( c_Lambda_OdB_OVar(v_n____) != c_Lambda_OdB_OVar(v_n____)
| v_n____ != v_i____
| c_Lambda_OdB_OVar(v_n____) = c_Lambda_OdB_OVar(v_i____) ),
introduced(tautology,[equality,[$cnf( $equal(c_Lambda_OdB_OVar(v_n____),c_Lambda_OdB_OVar(v_n____)) ),[1,0],$fot(v_i____)]]) ).
cnf(refute_0_2,plain,
( v_n____ != v_i____
| c_Lambda_OdB_OVar(v_n____) = c_Lambda_OdB_OVar(v_i____) ),
inference(resolve,[$cnf( $equal(c_Lambda_OdB_OVar(v_n____),c_Lambda_OdB_OVar(v_n____)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
c_Lambda_OdB_OVar(v_n____) = c_Lambda_OdB_OVar(v_i____),
inference(resolve,[$cnf( $equal(v_n____,v_i____) )],[cls_CHAINED_0_01,refute_0_2]) ).
cnf(refute_0_4,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),
introduced(tautology,[refl,[$fot(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))]]) ).
cnf(refute_0_5,plain,
( c_Lambda_OdB_OVar(v_n____) != c_Lambda_OdB_OVar(v_i____)
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(tautology,[equality,[$cnf( $equal(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) ),[1,1],$fot(c_Lambda_OdB_OVar(v_i____))]]) ).
cnf(refute_0_6,plain,
( c_Lambda_OdB_OVar(v_n____) != c_Lambda_OdB_OVar(v_i____)
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(resolve,[$cnf( $equal(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),
inference(resolve,[$cnf( $equal(c_Lambda_OdB_OVar(v_n____),c_Lambda_OdB_OVar(v_i____)) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) = hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),
introduced(tautology,[refl,[$fot(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)))]]) ).
cnf(refute_0_9,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)
| 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)) != 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))
| 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)) = hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))) ),[1,1],$fot(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))]]) ).
cnf(refute_0_10,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)
| 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)) = hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) ),
inference(resolve,[$cnf( $equal(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) = hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),
inference(resolve,[$cnf( $equal(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) = hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),
introduced(tautology,[refl,[$fot(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____))]]) ).
cnf(refute_0_13,plain,
( 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)) != hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))
| 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____) != 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____)
| 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____) = hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____)) ),[1,0],$fot(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)))]]) ).
cnf(refute_0_14,plain,
( 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)) != hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))
| 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____) = hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) ),
inference(resolve,[$cnf( $equal(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) = hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),
inference(resolve,[$cnf( $equal(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),
introduced(tautology,[refl,[$fot(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____))]]) ).
cnf(refute_0_17,plain,
( 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____) != hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____)
| 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____) != 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____)
| 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____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) ),[1,0],$fot(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____))]]) ).
cnf(refute_0_18,plain,
( 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____) != hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____)
| 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____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) ),
inference(resolve,[$cnf( $equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),
inference(resolve,[$cnf( $equal(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) = hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),
introduced(tautology,[refl,[$fot(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____)))]]) ).
cnf(refute_0_21,plain,
( 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____)) != 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____))
| 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____) != hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)
| 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____)) = hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),[1,1],$fot(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))]]) ).
cnf(refute_0_22,plain,
( 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____) != hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)
| 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____)) = hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) ),
inference(resolve,[$cnf( $equal(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) = hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),
inference(resolve,[$cnf( $equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) != hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),
introduced(tautology,[equality,[$cnf( ~ 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____))) ),[0],$fot(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))]]) ).
cnf(refute_0_25,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),
inference(resolve,[$cnf( $equal(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(resolve,[$cnf( 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____))) )],[refute_0_25,cls_conjecture_0]) ).
cnf(refute_0_27,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____) = v_u____,
inference(subst,[],[cls_subst__eq_0:[bind(V_k,$fot(v_i____)),bind(V_u,$fot(v_u____))]]) ).
cnf(refute_0_28,plain,
c_List_Ofoldl(X_65,X_64,c_List_Olist_ONil(tc_Lambda_OdB),X_62,tc_Lambda_OdB) = X_64,
inference(subst,[],[cls_foldl__Nil_0:[bind(T_a,$fot(X_62)),bind(T_b,$fot(tc_Lambda_OdB)),bind(V_a,$fot(X_64)),bind(V_f,$fot(X_65))]]) ).
cnf(refute_0_29,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_30,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_31,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( v_rs____ != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olist_ONil(tc_Lambda_OdB) = v_rs____ ),
inference(subst,[],[refute_0_31:[bind(X,$fot(v_rs____)),bind(Y,$fot(c_List_Olist_ONil(tc_Lambda_OdB)))]]) ).
cnf(refute_0_33,plain,
c_List_Olist_ONil(tc_Lambda_OdB) = v_rs____,
inference(resolve,[$cnf( $equal(v_rs____,c_List_Olist_ONil(tc_Lambda_OdB)) )],[cls_CHAINED_0,refute_0_32]) ).
cnf(refute_0_34,plain,
( c_List_Ofoldl(X_65,X_64,c_List_Olist_ONil(tc_Lambda_OdB),X_62,tc_Lambda_OdB) != X_64
| c_List_Olist_ONil(tc_Lambda_OdB) != v_rs____
| c_List_Ofoldl(X_65,X_64,v_rs____,X_62,tc_Lambda_OdB) = X_64 ),
introduced(tautology,[equality,[$cnf( $equal(c_List_Ofoldl(X_65,X_64,c_List_Olist_ONil(tc_Lambda_OdB),X_62,tc_Lambda_OdB),X_64) ),[0,2],$fot(v_rs____)]]) ).
cnf(refute_0_35,plain,
( c_List_Ofoldl(X_65,X_64,c_List_Olist_ONil(tc_Lambda_OdB),X_62,tc_Lambda_OdB) != X_64
| c_List_Ofoldl(X_65,X_64,v_rs____,X_62,tc_Lambda_OdB) = X_64 ),
inference(resolve,[$cnf( $equal(c_List_Olist_ONil(tc_Lambda_OdB),v_rs____) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
c_List_Ofoldl(X_65,X_64,v_rs____,X_62,tc_Lambda_OdB) = X_64,
inference(resolve,[$cnf( $equal(c_List_Ofoldl(X_65,X_64,c_List_Olist_ONil(tc_Lambda_OdB),X_62,tc_Lambda_OdB),X_64) )],[refute_0_28,refute_0_35]) ).
cnf(refute_0_37,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OVar(v_i____),
inference(subst,[],[refute_0_36:[bind(X_62,$fot(tc_Lambda_OdB)),bind(X_64,$fot(c_Lambda_OdB_OVar(v_i____))),bind(X_65,$fot(c_Lambda_OdB_OApp))]]) ).
cnf(refute_0_38,plain,
hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) = hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),
introduced(tautology,[refl,[$fot(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)))]]) ).
cnf(refute_0_39,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(v_i____)
| hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) != hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))
| hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) = hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))) ),[1,1],$fot(c_Lambda_OdB_OVar(v_i____))]]) ).
cnf(refute_0_40,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(v_i____)
| hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) = hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)) ),
inference(resolve,[$cnf( $equal(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) = hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),
inference(resolve,[$cnf( $equal(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),c_Lambda_OdB_OVar(v_i____)) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) = hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),
introduced(tautology,[refl,[$fot(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____))]]) ).
cnf(refute_0_43,plain,
( hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) != hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____))
| hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) != hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____)
| hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) = hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____)) ),[1,0],$fot(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)))]]) ).
cnf(refute_0_44,plain,
( hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) != hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____))
| hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) = hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____) ),
inference(resolve,[$cnf( $equal(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) = hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),
inference(resolve,[$cnf( $equal(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),
introduced(tautology,[refl,[$fot(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))]]) ).
cnf(refute_0_47,plain,
( hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) != hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) != hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) ),[1,0],$fot(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____))]]) ).
cnf(refute_0_48,plain,
( hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) != hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____) ),
inference(resolve,[$cnf( $equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____),
inference(resolve,[$cnf( $equal(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_51,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_31,refute_0_50]) ).
cnf(refute_0_52,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____) != v_u____
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) != hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = v_u____ ),
inference(subst,[],[refute_0_51:[bind(X,$fot(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),bind(Y,$fot(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____))),bind(Z,$fot(v_u____))]]) ).
cnf(refute_0_53,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____) != v_u____
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = v_u____ ),
inference(resolve,[$cnf( $equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = v_u____,
inference(resolve,[$cnf( $equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____),v_u____) )],[refute_0_27,refute_0_53]) ).
cnf(refute_0_55,plain,
hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) = hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),
introduced(tautology,[refl,[$fot(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))]]) ).
cnf(refute_0_56,plain,
( hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) != hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) != v_u____
| hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) = hAPP(c_InductTermi_OIT,v_u____) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),[1,1],$fot(v_u____)]]) ).
cnf(refute_0_57,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) != v_u____
| hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) = hAPP(c_InductTermi_OIT,v_u____) ),
inference(resolve,[$cnf( $equal(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) = hAPP(c_InductTermi_OIT,v_u____),
inference(resolve,[$cnf( $equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),v_u____) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
( hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)) != hAPP(c_InductTermi_OIT,v_u____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_u____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),
introduced(tautology,[equality,[$cnf( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),[0],$fot(hAPP(c_InductTermi_OIT,v_u____))]]) ).
cnf(refute_0_60,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,v_u____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),
inference(resolve,[$cnf( $equal(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),hAPP(c_InductTermi_OIT,v_u____)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(resolve,[$cnf( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) )],[refute_0_60,refute_0_26]) ).
cnf(refute_0_62,plain,
$false,
inference(resolve,[$cnf( hBOOL(hAPP(c_InductTermi_OIT,v_u____)) )],[cls_CHAINED_0_02,refute_0_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL784-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n013.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 : 600
% 0.13/0.34 % DateTime : Sun Jul 3 02:30:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.62/0.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.79
% 0.62/0.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.62/0.80
%------------------------------------------------------------------------------