%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL850-1 : 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 12:43:42 PM UTC 2026
% Result : Unsatisfiable 2.37s 2.62s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 5 RR)
% Number of literals : 13 ( 3 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 26 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_shift__eq_0,axiom,
hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Otype_OFun(v_Ta____,v_U____)) ).
cnf(refute_0_0,plain,
c_Type_Otyping(c_Type_Oshift(X_220,V_x,X_219,X_218),c_Lambda_OdB_OVar(V_x),hAPP(c_Type_Oshift(X_220,V_x,X_219,X_218),V_x)),
inference(subst,[],[cls_typing_OVar_0:[bind(V_env,$fot(c_Type_Oshift(X_220,V_x,X_219,X_218)))]]) ).
cnf(refute_0_1,plain,
hAPP(c_Type_Oshift(X_220,V_x,X_219,X_218),V_x) = X_219,
inference(subst,[],[cls_shift__eq_0:[bind(T_a,$fot(X_218)),bind(V_T,$fot(X_219)),bind(V_e,$fot(X_220))]]) ).
cnf(refute_0_2,plain,
( hAPP(c_Type_Oshift(X_220,V_x,X_219,X_218),V_x) != X_219
| ~ c_Type_Otyping(c_Type_Oshift(X_220,V_x,X_219,X_218),c_Lambda_OdB_OVar(V_x),hAPP(c_Type_Oshift(X_220,V_x,X_219,X_218),V_x))
| c_Type_Otyping(c_Type_Oshift(X_220,V_x,X_219,X_218),c_Lambda_OdB_OVar(V_x),X_219) ),
introduced(tautology,[equality,[$cnf( c_Type_Otyping(c_Type_Oshift(X_220,V_x,X_219,X_218),c_Lambda_OdB_OVar(V_x),hAPP(c_Type_Oshift(X_220,V_x,X_219,X_218),V_x)) ),[2],$fot(X_219)]]) ).
cnf(refute_0_3,plain,
( ~ c_Type_Otyping(c_Type_Oshift(X_220,V_x,X_219,X_218),c_Lambda_OdB_OVar(V_x),hAPP(c_Type_Oshift(X_220,V_x,X_219,X_218),V_x))
| c_Type_Otyping(c_Type_Oshift(X_220,V_x,X_219,X_218),c_Lambda_OdB_OVar(V_x),X_219) ),
inference(resolve,[$cnf( $equal(hAPP(c_Type_Oshift(X_220,V_x,X_219,X_218),V_x),X_219) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
c_Type_Otyping(c_Type_Oshift(X_220,V_x,X_219,X_218),c_Lambda_OdB_OVar(V_x),X_219),
inference(resolve,[$cnf( c_Type_Otyping(c_Type_Oshift(X_220,V_x,X_219,X_218),c_Lambda_OdB_OVar(V_x),hAPP(c_Type_Oshift(X_220,V_x,X_219,X_218),V_x)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Otype_OFun(v_Ta____,v_U____)),
inference(subst,[],[refute_0_4:[bind(V_x,$fot(c_HOL_Ozero__class_Ozero(tc_nat))),bind(X_218,$fot(tc_Type_Otype)),bind(X_219,$fot(c_Type_Otype_OFun(v_Ta____,v_U____))),bind(X_220,$fot(v_ea____))]]) ).
cnf(refute_0_6,plain,
$false,
inference(resolve,[$cnf( c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Otype_OFun(v_Ta____,v_U____)) )],[refute_0_5,cls_conjecture_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL850-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 18:02:43 UTC 2026
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.37/2.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.37/2.62
% 2.37/2.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.37/2.63
%------------------------------------------------------------------------------