TSTP Solution File: KRS010-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS010-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:18:25 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of clauses : 87 ( 14 unt; 28 nHn; 87 RR)
% Number of literals : 241 ( 0 equ; 131 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_1,negated_conjecture,
e(exist) ).
cnf(clause_2,negated_conjecture,
~ f(exist) ).
cnf(clause_3,axiom,
( c(X1)
| d(X1)
| ~ a(X1) ) ).
cnf(clause_6,axiom,
( equalish(X4,X3)
| ~ e(X1)
| ~ r(X1,X4)
| ~ r(X1,X3)
| ~ c(X4)
| ~ c(X3) ) ).
cnf(clause_7,axiom,
( r3least(X1)
| ~ e(X1) ) ).
cnf(clause_8,axiom,
( a(X2)
| ~ e(X1)
| ~ r(X1,X2) ) ).
cnf(clause_19,axiom,
( ~ r3least(X1)
| ~ equalish(u2r2(X1),u2r1(X1)) ) ).
cnf(clause_20,axiom,
( ~ r3least(X1)
| ~ equalish(u2r3(X1),u2r1(X1)) ) ).
cnf(clause_21,axiom,
( ~ r3least(X1)
| ~ equalish(u2r3(X1),u2r2(X1)) ) ).
cnf(clause_22,axiom,
( r(X1,u2r1(X1))
| ~ r3least(X1) ) ).
cnf(clause_23,axiom,
( r(X1,u2r2(X1))
| ~ r3least(X1) ) ).
cnf(clause_24,axiom,
( r(X1,u2r3(X1))
| ~ r3least(X1) ) ).
cnf(clause_31,axiom,
( f(X1)
| equalish(X3,X2)
| ~ r(X1,X3)
| ~ r(X1,X2)
| ~ d(X3)
| ~ d(X2) ) ).
cnf(refute_0_0,plain,
( ~ equalish(u2r2(exist),u2r1(exist))
| ~ r3least(exist) ),
inference(subst,[],[clause_19:[bind(X1,$fot(exist))]]) ).
cnf(refute_0_1,plain,
( ~ e(exist)
| r3least(exist) ),
inference(subst,[],[clause_7:[bind(X1,$fot(exist))]]) ).
cnf(refute_0_2,plain,
r3least(exist),
inference(resolve,[$cnf( e(exist) )],[clause_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r3least(exist)
| r(exist,u2r2(exist)) ),
inference(subst,[],[clause_23:[bind(X1,$fot(exist))]]) ).
cnf(refute_0_4,plain,
r(exist,u2r2(exist)),
inference(resolve,[$cnf( r3least(exist) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ r3least(exist)
| r(exist,u2r1(exist)) ),
inference(subst,[],[clause_22:[bind(X1,$fot(exist))]]) ).
cnf(refute_0_6,plain,
r(exist,u2r1(exist)),
inference(resolve,[$cnf( r3least(exist) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ c(X_35)
| ~ c(u2r1(exist))
| ~ e(exist)
| ~ r(exist,X_35)
| ~ r(exist,u2r1(exist))
| equalish(X_35,u2r1(exist)) ),
inference(subst,[],[clause_6:[bind(X1,$fot(exist)),bind(X3,$fot(u2r1(exist))),bind(X4,$fot(X_35))]]) ).
cnf(refute_0_8,plain,
( ~ c(X_35)
| ~ c(u2r1(exist))
| ~ e(exist)
| ~ r(exist,X_35)
| equalish(X_35,u2r1(exist)) ),
inference(resolve,[$cnf( r(exist,u2r1(exist)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ c(X_35)
| ~ c(u2r1(exist))
| ~ r(exist,X_35)
| equalish(X_35,u2r1(exist)) ),
inference(resolve,[$cnf( e(exist) )],[clause_1,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ c(u2r1(exist))
| ~ c(u2r2(exist))
| ~ r(exist,u2r2(exist))
| equalish(u2r2(exist),u2r1(exist)) ),
inference(subst,[],[refute_0_9:[bind(X_35,$fot(u2r2(exist)))]]) ).
cnf(refute_0_11,plain,
( ~ c(u2r1(exist))
| ~ c(u2r2(exist))
| equalish(u2r2(exist),u2r1(exist)) ),
inference(resolve,[$cnf( r(exist,u2r2(exist)) )],[refute_0_4,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ equalish(u2r3(exist),u2r1(exist))
| ~ r3least(exist) ),
inference(subst,[],[clause_20:[bind(X1,$fot(exist))]]) ).
cnf(refute_0_13,plain,
( ~ r3least(exist)
| r(exist,u2r3(exist)) ),
inference(subst,[],[clause_24:[bind(X1,$fot(exist))]]) ).
cnf(refute_0_14,plain,
r(exist,u2r3(exist)),
inference(resolve,[$cnf( r3least(exist) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ c(u2r1(exist))
| ~ c(u2r3(exist))
| ~ r(exist,u2r3(exist))
| equalish(u2r3(exist),u2r1(exist)) ),
inference(subst,[],[refute_0_9:[bind(X_35,$fot(u2r3(exist)))]]) ).
cnf(refute_0_16,plain,
( ~ c(u2r1(exist))
| ~ c(u2r3(exist))
| equalish(u2r3(exist),u2r1(exist)) ),
inference(resolve,[$cnf( r(exist,u2r3(exist)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ equalish(u2r3(exist),u2r2(exist))
| ~ r3least(exist) ),
inference(subst,[],[clause_21:[bind(X1,$fot(exist))]]) ).
cnf(refute_0_18,plain,
( ~ a(u2r2(exist))
| c(u2r2(exist))
| d(u2r2(exist)) ),
inference(subst,[],[clause_3:[bind(X1,$fot(u2r2(exist)))]]) ).
cnf(refute_0_19,plain,
( ~ e(exist)
| ~ r(exist,u2r2(exist))
| a(u2r2(exist)) ),
inference(subst,[],[clause_8:[bind(X1,$fot(exist)),bind(X2,$fot(u2r2(exist)))]]) ).
cnf(refute_0_20,plain,
( ~ e(exist)
| a(u2r2(exist)) ),
inference(resolve,[$cnf( r(exist,u2r2(exist)) )],[refute_0_4,refute_0_19]) ).
cnf(refute_0_21,plain,
a(u2r2(exist)),
inference(resolve,[$cnf( e(exist) )],[clause_1,refute_0_20]) ).
cnf(refute_0_22,plain,
( c(u2r2(exist))
| d(u2r2(exist)) ),
inference(resolve,[$cnf( a(u2r2(exist)) )],[refute_0_21,refute_0_18]) ).
cnf(refute_0_23,plain,
( ~ a(u2r3(exist))
| c(u2r3(exist))
| d(u2r3(exist)) ),
inference(subst,[],[clause_3:[bind(X1,$fot(u2r3(exist)))]]) ).
cnf(refute_0_24,plain,
( ~ e(exist)
| ~ r(exist,u2r3(exist))
| a(u2r3(exist)) ),
inference(subst,[],[clause_8:[bind(X1,$fot(exist)),bind(X2,$fot(u2r3(exist)))]]) ).
cnf(refute_0_25,plain,
( ~ e(exist)
| a(u2r3(exist)) ),
inference(resolve,[$cnf( r(exist,u2r3(exist)) )],[refute_0_14,refute_0_24]) ).
cnf(refute_0_26,plain,
a(u2r3(exist)),
inference(resolve,[$cnf( e(exist) )],[clause_1,refute_0_25]) ).
cnf(refute_0_27,plain,
( c(u2r3(exist))
| d(u2r3(exist)) ),
inference(resolve,[$cnf( a(u2r3(exist)) )],[refute_0_26,refute_0_23]) ).
cnf(refute_0_28,plain,
( ~ d(X_44)
| ~ d(u2r2(exist))
| ~ r(exist,X_44)
| ~ r(exist,u2r2(exist))
| equalish(X_44,u2r2(exist))
| f(exist) ),
inference(subst,[],[clause_31:[bind(X1,$fot(exist)),bind(X2,$fot(u2r2(exist))),bind(X3,$fot(X_44))]]) ).
cnf(refute_0_29,plain,
( ~ d(X_44)
| ~ d(u2r2(exist))
| ~ r(exist,X_44)
| equalish(X_44,u2r2(exist))
| f(exist) ),
inference(resolve,[$cnf( r(exist,u2r2(exist)) )],[refute_0_4,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ d(X_44)
| ~ d(u2r2(exist))
| ~ r(exist,X_44)
| equalish(X_44,u2r2(exist)) ),
inference(resolve,[$cnf( f(exist) )],[refute_0_29,clause_2]) ).
cnf(refute_0_31,plain,
( ~ d(u2r2(exist))
| ~ d(u2r3(exist))
| ~ r(exist,u2r3(exist))
| equalish(u2r3(exist),u2r2(exist)) ),
inference(subst,[],[refute_0_30:[bind(X_44,$fot(u2r3(exist)))]]) ).
cnf(refute_0_32,plain,
( ~ d(u2r2(exist))
| ~ d(u2r3(exist))
| equalish(u2r3(exist),u2r2(exist)) ),
inference(resolve,[$cnf( r(exist,u2r3(exist)) )],[refute_0_14,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ d(u2r2(exist))
| equalish(u2r3(exist),u2r2(exist))
| c(u2r3(exist)) ),
inference(resolve,[$cnf( d(u2r3(exist)) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
( equalish(u2r3(exist),u2r2(exist))
| c(u2r2(exist))
| c(u2r3(exist)) ),
inference(resolve,[$cnf( d(u2r2(exist)) )],[refute_0_22,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ r3least(exist)
| c(u2r2(exist))
| c(u2r3(exist)) ),
inference(resolve,[$cnf( equalish(u2r3(exist),u2r2(exist)) )],[refute_0_34,refute_0_17]) ).
cnf(refute_0_36,plain,
( c(u2r2(exist))
| c(u2r3(exist)) ),
inference(resolve,[$cnf( r3least(exist) )],[refute_0_2,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ c(u2r1(exist))
| equalish(u2r3(exist),u2r1(exist))
| c(u2r2(exist)) ),
inference(resolve,[$cnf( c(u2r3(exist)) )],[refute_0_36,refute_0_16]) ).
cnf(refute_0_38,plain,
( ~ a(u2r1(exist))
| c(u2r1(exist))
| d(u2r1(exist)) ),
inference(subst,[],[clause_3:[bind(X1,$fot(u2r1(exist)))]]) ).
cnf(refute_0_39,plain,
( ~ e(exist)
| ~ r(exist,u2r1(exist))
| a(u2r1(exist)) ),
inference(subst,[],[clause_8:[bind(X1,$fot(exist)),bind(X2,$fot(u2r1(exist)))]]) ).
cnf(refute_0_40,plain,
( ~ e(exist)
| a(u2r1(exist)) ),
inference(resolve,[$cnf( r(exist,u2r1(exist)) )],[refute_0_6,refute_0_39]) ).
cnf(refute_0_41,plain,
a(u2r1(exist)),
inference(resolve,[$cnf( e(exist) )],[clause_1,refute_0_40]) ).
cnf(refute_0_42,plain,
( c(u2r1(exist))
| d(u2r1(exist)) ),
inference(resolve,[$cnf( a(u2r1(exist)) )],[refute_0_41,refute_0_38]) ).
cnf(refute_0_43,plain,
( ~ d(X_44)
| ~ d(u2r1(exist))
| ~ r(exist,X_44)
| ~ r(exist,u2r1(exist))
| equalish(X_44,u2r1(exist))
| f(exist) ),
inference(subst,[],[clause_31:[bind(X1,$fot(exist)),bind(X2,$fot(u2r1(exist))),bind(X3,$fot(X_44))]]) ).
cnf(refute_0_44,plain,
( ~ d(X_44)
| ~ d(u2r1(exist))
| ~ r(exist,X_44)
| equalish(X_44,u2r1(exist))
| f(exist) ),
inference(resolve,[$cnf( r(exist,u2r1(exist)) )],[refute_0_6,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ d(X_44)
| ~ d(u2r1(exist))
| ~ r(exist,X_44)
| equalish(X_44,u2r1(exist)) ),
inference(resolve,[$cnf( f(exist) )],[refute_0_44,clause_2]) ).
cnf(refute_0_46,plain,
( ~ d(u2r1(exist))
| ~ d(u2r2(exist))
| ~ r(exist,u2r2(exist))
| equalish(u2r2(exist),u2r1(exist)) ),
inference(subst,[],[refute_0_45:[bind(X_44,$fot(u2r2(exist)))]]) ).
cnf(refute_0_47,plain,
( ~ d(u2r1(exist))
| ~ d(u2r2(exist))
| equalish(u2r2(exist),u2r1(exist)) ),
inference(resolve,[$cnf( r(exist,u2r2(exist)) )],[refute_0_4,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ d(u2r1(exist))
| equalish(u2r2(exist),u2r1(exist))
| c(u2r2(exist)) ),
inference(resolve,[$cnf( d(u2r2(exist)) )],[refute_0_22,refute_0_47]) ).
cnf(refute_0_49,plain,
( equalish(u2r2(exist),u2r1(exist))
| c(u2r1(exist))
| c(u2r2(exist)) ),
inference(resolve,[$cnf( d(u2r1(exist)) )],[refute_0_42,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ r3least(exist)
| c(u2r1(exist))
| c(u2r2(exist)) ),
inference(resolve,[$cnf( equalish(u2r2(exist),u2r1(exist)) )],[refute_0_49,refute_0_0]) ).
cnf(refute_0_51,plain,
( c(u2r1(exist))
| c(u2r2(exist)) ),
inference(resolve,[$cnf( r3least(exist) )],[refute_0_2,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ c(X_35)
| ~ c(u2r2(exist))
| ~ e(exist)
| ~ r(exist,X_35)
| ~ r(exist,u2r2(exist))
| equalish(X_35,u2r2(exist)) ),
inference(subst,[],[clause_6:[bind(X1,$fot(exist)),bind(X3,$fot(u2r2(exist))),bind(X4,$fot(X_35))]]) ).
cnf(refute_0_53,plain,
( ~ c(X_35)
| ~ c(u2r2(exist))
| ~ e(exist)
| ~ r(exist,X_35)
| equalish(X_35,u2r2(exist)) ),
inference(resolve,[$cnf( r(exist,u2r2(exist)) )],[refute_0_4,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ c(X_35)
| ~ c(u2r2(exist))
| ~ r(exist,X_35)
| equalish(X_35,u2r2(exist)) ),
inference(resolve,[$cnf( e(exist) )],[clause_1,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ c(u2r2(exist))
| ~ c(u2r3(exist))
| ~ r(exist,u2r3(exist))
| equalish(u2r3(exist),u2r2(exist)) ),
inference(subst,[],[refute_0_54:[bind(X_35,$fot(u2r3(exist)))]]) ).
cnf(refute_0_56,plain,
( ~ c(u2r2(exist))
| ~ c(u2r3(exist))
| equalish(u2r3(exist),u2r2(exist)) ),
inference(resolve,[$cnf( r(exist,u2r3(exist)) )],[refute_0_14,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ d(u2r1(exist))
| ~ d(u2r3(exist))
| ~ r(exist,u2r3(exist))
| equalish(u2r3(exist),u2r1(exist)) ),
inference(subst,[],[refute_0_45:[bind(X_44,$fot(u2r3(exist)))]]) ).
cnf(refute_0_58,plain,
( ~ d(u2r1(exist))
| ~ d(u2r3(exist))
| equalish(u2r3(exist),u2r1(exist)) ),
inference(resolve,[$cnf( r(exist,u2r3(exist)) )],[refute_0_14,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ d(u2r1(exist))
| equalish(u2r3(exist),u2r1(exist))
| c(u2r3(exist)) ),
inference(resolve,[$cnf( d(u2r3(exist)) )],[refute_0_27,refute_0_58]) ).
cnf(refute_0_60,plain,
( equalish(u2r3(exist),u2r1(exist))
| c(u2r1(exist))
| c(u2r3(exist)) ),
inference(resolve,[$cnf( d(u2r1(exist)) )],[refute_0_42,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ r3least(exist)
| c(u2r1(exist))
| c(u2r3(exist)) ),
inference(resolve,[$cnf( equalish(u2r3(exist),u2r1(exist)) )],[refute_0_60,refute_0_12]) ).
cnf(refute_0_62,plain,
( c(u2r1(exist))
| c(u2r3(exist)) ),
inference(resolve,[$cnf( r3least(exist) )],[refute_0_2,refute_0_61]) ).
cnf(refute_0_63,plain,
( ~ c(u2r2(exist))
| equalish(u2r3(exist),u2r2(exist))
| c(u2r1(exist)) ),
inference(resolve,[$cnf( c(u2r3(exist)) )],[refute_0_62,refute_0_56]) ).
cnf(refute_0_64,plain,
( equalish(u2r3(exist),u2r2(exist))
| c(u2r1(exist)) ),
inference(resolve,[$cnf( c(u2r2(exist)) )],[refute_0_51,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ r3least(exist)
| c(u2r1(exist)) ),
inference(resolve,[$cnf( equalish(u2r3(exist),u2r2(exist)) )],[refute_0_64,refute_0_17]) ).
cnf(refute_0_66,plain,
c(u2r1(exist)),
inference(resolve,[$cnf( r3least(exist) )],[refute_0_2,refute_0_65]) ).
cnf(refute_0_67,plain,
( equalish(u2r3(exist),u2r1(exist))
| c(u2r2(exist)) ),
inference(resolve,[$cnf( c(u2r1(exist)) )],[refute_0_66,refute_0_37]) ).
cnf(refute_0_68,plain,
( ~ r3least(exist)
| c(u2r2(exist)) ),
inference(resolve,[$cnf( equalish(u2r3(exist),u2r1(exist)) )],[refute_0_67,refute_0_12]) ).
cnf(refute_0_69,plain,
c(u2r2(exist)),
inference(resolve,[$cnf( r3least(exist) )],[refute_0_2,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ c(u2r1(exist))
| equalish(u2r2(exist),u2r1(exist)) ),
inference(resolve,[$cnf( c(u2r2(exist)) )],[refute_0_69,refute_0_11]) ).
cnf(refute_0_71,plain,
equalish(u2r2(exist),u2r1(exist)),
inference(resolve,[$cnf( c(u2r1(exist)) )],[refute_0_66,refute_0_70]) ).
cnf(refute_0_72,plain,
~ r3least(exist),
inference(resolve,[$cnf( equalish(u2r2(exist),u2r1(exist)) )],[refute_0_71,refute_0_0]) ).
cnf(refute_0_73,plain,
$false,
inference(resolve,[$cnf( r3least(exist) )],[refute_0_2,refute_0_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS010-1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Tue Jun 7 07:15:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------