TSTP Solution File: LCL855-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL855-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 12:56:37 EDT 2022
% Result : Unsatisfiable 3.53s 3.75s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 28 ( 16 unt; 0 nHn; 21 RR)
% Number of literals : 47 ( 39 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 34 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_subst__lift_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ).
cnf(cls_subst__eq_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ).
cnf(cls_subst__App_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ).
cnf(cls_CHAINED_0,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)) ).
cnf(refute_0_0,plain,
c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)) = v_ta____,
inference(subst,[],[cls_subst__lift_0:[bind(V_k,$fot(c_HOL_Ozero__class_Ozero(tc_nat))),bind(V_s,$fot(v_s____)),bind(V_t,$fot(v_ta____))]]) ).
cnf(refute_0_1,plain,
c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
introduced(tautology,[refl,[$fot(c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))))]]) ).
cnf(refute_0_2,plain,
( c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) != c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))
| c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)) != v_ta____
| c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OApp(v_s____,v_ta____) ),
introduced(tautology,[equality,[$cnf( $equal(c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))) ),[1,1],$fot(v_ta____)]]) ).
cnf(refute_0_3,plain,
( c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)) != v_ta____
| c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OApp(v_s____,v_ta____) ),
inference(resolve,[$cnf( $equal(c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OApp(v_s____,v_ta____),
inference(resolve,[$cnf( $equal(c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)),v_ta____) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X_489),X_492),X_490,X_489) = c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_OdB_OVar(X_489),X_490,X_489),c_Lambda_Osubst(X_492,X_490,X_489)),
inference(subst,[],[cls_subst__App_0:[bind(V_k,$fot(X_489)),bind(V_s,$fot(X_490)),bind(V_t,$fot(c_Lambda_OdB_OVar(X_489))),bind(V_u,$fot(X_492))]]) ).
cnf(refute_0_6,plain,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X_489),X_490,X_489) = X_490,
inference(subst,[],[cls_subst__eq_0:[bind(V_k,$fot(X_489)),bind(V_u,$fot(X_490))]]) ).
cnf(refute_0_7,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X_489),X_492),X_490,X_489) != c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_OdB_OVar(X_489),X_490,X_489),c_Lambda_Osubst(X_492,X_490,X_489))
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X_489),X_490,X_489) != X_490
| c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X_489),X_492),X_490,X_489) = c_Lambda_OdB_OApp(X_490,c_Lambda_Osubst(X_492,X_490,X_489)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X_489),X_492),X_490,X_489),c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_OdB_OVar(X_489),X_490,X_489),c_Lambda_Osubst(X_492,X_490,X_489))) ),[1,0],$fot(X_490)]]) ).
cnf(refute_0_8,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X_489),X_492),X_490,X_489) != c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_OdB_OVar(X_489),X_490,X_489),c_Lambda_Osubst(X_492,X_490,X_489))
| c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X_489),X_492),X_490,X_489) = c_Lambda_OdB_OApp(X_490,c_Lambda_Osubst(X_492,X_490,X_489)) ),
inference(resolve,[$cnf( $equal(c_Lambda_Osubst(c_Lambda_OdB_OVar(X_489),X_490,X_489),X_490) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X_489),X_492),X_490,X_489) = c_Lambda_OdB_OApp(X_490,c_Lambda_Osubst(X_492,X_490,X_489)),
inference(resolve,[$cnf( $equal(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X_489),X_492),X_490,X_489),c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_OdB_OVar(X_489),X_490,X_489),c_Lambda_Osubst(X_492,X_490,X_489))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(subst,[],[refute_0_9:[bind(X_489,$fot(c_HOL_Ozero__class_Ozero(tc_nat))),bind(X_490,$fot(v_s____)),bind(X_492,$fot(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))))]]) ).
cnf(refute_0_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) != c_Lambda_OdB_OApp(v_s____,v_ta____)
| c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)) != c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))
| c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OApp(v_s____,v_ta____) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))),bind(Y,$fot(c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))))),bind(Z,$fot(c_Lambda_OdB_OApp(v_s____,v_ta____)))]]) ).
cnf(refute_0_17,plain,
( c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) != c_Lambda_OdB_OApp(v_s____,v_ta____)
| c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OApp(v_s____,v_ta____) ),
inference(resolve,[$cnf( $equal(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))) )],[refute_0_10,refute_0_16]) ).
cnf(refute_0_18,plain,
c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OApp(v_s____,v_ta____),
inference(resolve,[$cnf( $equal(c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OApp(v_s____,v_ta____)) )],[refute_0_4,refute_0_17]) ).
cnf(refute_0_19,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)) != c_Lambda_OdB_OApp(v_s____,v_ta____)
| ~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))
| c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)) ),
introduced(tautology,[equality,[$cnf( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) ),[0],$fot(c_Lambda_OdB_OApp(v_s____,v_ta____))]]) ).
cnf(refute_0_20,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))
| c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)) ),
inference(resolve,[$cnf( $equal(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OApp(v_s____,v_ta____)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
inference(resolve,[$cnf( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) )],[cls_CHAINED_0,refute_0_20]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)) )],[refute_0_21,cls_conjecture_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL855-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 06:42:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.53/3.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.53/3.75
% 3.53/3.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.53/3.75
%------------------------------------------------------------------------------