%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:43:43 PM UTC 2026
% Result : Unsatisfiable 0.33s 0.56s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 5 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 4 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_IT__implies__termi_0,axiom,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
cnf(cls_type__implies__IT_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Type_Otyping(v_e,v_t,v_T) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ).
cnf(refute_0_0,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ),
inference(subst,[],[cls_IT__implies__termi_0:[bind(V_t,$fot(v_t))]]) ).
cnf(refute_0_1,plain,
( ~ c_Type_Otyping(v_e,v_t,v_T)
| hBOOL(hAPP(c_InductTermi_OIT,v_t)) ),
inference(subst,[],[cls_type__implies__IT_0:[bind(V_T,$fot(v_T)),bind(V_e,$fot(v_e)),bind(V_t,$fot(v_t))]]) ).
cnf(refute_0_2,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(resolve,[$cnf( c_Type_Otyping(v_e,v_t,v_T) )],[cls_conjecture_0,refute_0_1]) ).
cnf(refute_0_3,plain,
c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
inference(resolve,[$cnf( hBOOL(hAPP(c_InductTermi_OIT,v_t)) )],[refute_0_2,refute_0_0]) ).
cnf(refute_0_4,plain,
$false,
inference(resolve,[$cnf( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) )],[refute_0_3,cls_conjecture_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 03:22:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.33/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.56
% 0.33/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.33/0.56
%------------------------------------------------------------------------------