TSTP Solution File: HWV052-1.002.001 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HWV052-1.002.001 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 : Sat Jul 16 18:30:23 EDT 2022
% Result : Unsatisfiable 0.22s 0.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 45
% Syntax : Number of clauses : 134 ( 47 unt; 34 nHn; 109 RR)
% Number of literals : 265 ( 264 equ; 98 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(bit_domain,axiom,
( X = o
| X = i ) ).
cnf(bit_inverse,axiom,
inv(X) != X ).
cnf(unpack1,axiom,
unpack1(X1,X2,pack1(X1,X2)) = X1 ).
cnf(unpack1_01,axiom,
unpack1(inv(X1),X2,pack1(X1,X2)) = X1 ).
cnf(unpack1_02,axiom,
unpack1(X1,inv(X2),pack1(X1,X2)) = X1 ).
cnf(unpack1_03,axiom,
unpack1(X1,X2,inv(pack1(X1,X2))) = X1 ).
cnf(unpack2,axiom,
unpack2(X1,X2,pack1(X1,X2)) = X2 ).
cnf(unpack2_05,axiom,
unpack2(X1,inv(X2),pack1(X1,X2)) = X2 ).
cnf(unpack2_06,axiom,
unpack2(X1,X2,inv(pack1(X1,X2))) = X2 ).
cnf(refute_0_0,plain,
unpack1(inv(o),i,pack1(o,i)) = o,
inference(subst,[],[unpack1_01:[bind(X1,$fot(o)),bind(X2,$fot(i))]]) ).
cnf(refute_0_1,plain,
unpack1(inv(o),X_7,pack1(o,X_7)) = o,
inference(subst,[],[unpack1_01:[bind(X1,$fot(o)),bind(X2,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
( inv(X) = i
| inv(X) = o ),
inference(subst,[],[bit_domain:[bind(X,$fot(inv(X)))]]) ).
cnf(refute_0_3,plain,
( inv(X) != o
| o != X
| inv(X) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(inv(X),X) ),[0],$fot(o)]]) ).
cnf(refute_0_4,plain,
( o != X
| inv(X) = X
| inv(X) = i ),
inference(resolve,[$cnf( $equal(inv(X),o) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( o != X
| inv(X) = i ),
inference(resolve,[$cnf( $equal(inv(X),X) )],[refute_0_4,bit_inverse]) ).
cnf(refute_0_6,plain,
( o != o
| inv(o) = i ),
inference(subst,[],[refute_0_5:[bind(X,$fot(o))]]) ).
cnf(refute_0_7,plain,
o = o,
introduced(tautology,[refl,[$fot(o)]]) ).
cnf(refute_0_8,plain,
inv(o) = i,
inference(resolve,[$cnf( $equal(o,o) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( inv(o) != i
| unpack1(inv(o),X_7,pack1(o,X_7)) != o
| unpack1(i,X_7,pack1(o,X_7)) = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(inv(o),X_7,pack1(o,X_7)),o) ),[0,0],$fot(i)]]) ).
cnf(refute_0_10,plain,
( unpack1(inv(o),X_7,pack1(o,X_7)) != o
| unpack1(i,X_7,pack1(o,X_7)) = o ),
inference(resolve,[$cnf( $equal(inv(o),i) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
unpack1(i,X_7,pack1(o,X_7)) = o,
inference(resolve,[$cnf( $equal(unpack1(inv(o),X_7,pack1(o,X_7)),o) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
unpack1(i,X_8,pack1(o,X_8)) = o,
inference(subst,[],[refute_0_11:[bind(X_7,$fot(X_8))]]) ).
cnf(refute_0_13,plain,
( pack1(o,X_8) = i
| pack1(o,X_8) = o ),
inference(subst,[],[bit_domain:[bind(X,$fot(pack1(o,X_8)))]]) ).
cnf(refute_0_14,plain,
( pack1(o,X_8) != o
| unpack1(i,X_8,pack1(o,X_8)) != o
| unpack1(i,X_8,o) = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(i,X_8,pack1(o,X_8)),o) ),[0,2],$fot(o)]]) ).
cnf(refute_0_15,plain,
( unpack1(i,X_8,pack1(o,X_8)) != o
| pack1(o,X_8) = i
| unpack1(i,X_8,o) = o ),
inference(resolve,[$cnf( $equal(pack1(o,X_8),o) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( pack1(o,X_8) = i
| unpack1(i,X_8,o) = o ),
inference(resolve,[$cnf( $equal(unpack1(i,X_8,pack1(o,X_8)),o) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
( pack1(o,i) = i
| unpack1(i,i,o) = o ),
inference(subst,[],[refute_0_16:[bind(X_8,$fot(i))]]) ).
cnf(refute_0_18,plain,
unpack1(i,i,inv(pack1(i,i))) = i,
inference(subst,[],[unpack1_03:[bind(X1,$fot(i)),bind(X2,$fot(i))]]) ).
cnf(refute_0_19,plain,
unpack2(o,o,pack1(o,o)) = o,
inference(subst,[],[unpack2:[bind(X1,$fot(o)),bind(X2,$fot(o))]]) ).
cnf(refute_0_20,plain,
( pack1(o,o) = i
| unpack1(i,o,o) = o ),
inference(subst,[],[refute_0_16:[bind(X_8,$fot(o))]]) ).
cnf(refute_0_21,plain,
unpack1(X_14,inv(i),pack1(X_14,i)) = X_14,
inference(subst,[],[unpack1_02:[bind(X1,$fot(X_14)),bind(X2,$fot(i))]]) ).
cnf(refute_0_22,plain,
( i != X
| inv(X) != i
| inv(X) = X ),
introduced(tautology,[equality,[$cnf( $equal(inv(X),i) ),[1],$fot(X)]]) ).
cnf(refute_0_23,plain,
( i != X
| inv(X) = X
| inv(X) = o ),
inference(resolve,[$cnf( $equal(inv(X),i) )],[refute_0_2,refute_0_22]) ).
cnf(refute_0_24,plain,
( i != X
| inv(X) = o ),
inference(resolve,[$cnf( $equal(inv(X),X) )],[refute_0_23,bit_inverse]) ).
cnf(refute_0_25,plain,
( i != i
| inv(i) = o ),
inference(subst,[],[refute_0_24:[bind(X,$fot(i))]]) ).
cnf(refute_0_26,plain,
i = i,
introduced(tautology,[refl,[$fot(i)]]) ).
cnf(refute_0_27,plain,
inv(i) = o,
inference(resolve,[$cnf( $equal(i,i) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
( inv(i) != o
| unpack1(X_14,inv(i),pack1(X_14,i)) != X_14
| unpack1(X_14,o,pack1(X_14,i)) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(X_14,inv(i),pack1(X_14,i)),X_14) ),[0,1],$fot(o)]]) ).
cnf(refute_0_29,plain,
( unpack1(X_14,inv(i),pack1(X_14,i)) != X_14
| unpack1(X_14,o,pack1(X_14,i)) = X_14 ),
inference(resolve,[$cnf( $equal(inv(i),o) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
unpack1(X_14,o,pack1(X_14,i)) = X_14,
inference(resolve,[$cnf( $equal(unpack1(X_14,inv(i),pack1(X_14,i)),X_14) )],[refute_0_21,refute_0_29]) ).
cnf(refute_0_31,plain,
unpack1(X_16,o,pack1(X_16,i)) = X_16,
inference(subst,[],[refute_0_30:[bind(X_14,$fot(X_16))]]) ).
cnf(refute_0_32,plain,
( pack1(X_16,i) = i
| pack1(X_16,i) = o ),
inference(subst,[],[bit_domain:[bind(X,$fot(pack1(X_16,i)))]]) ).
cnf(refute_0_33,plain,
( pack1(X_16,i) != o
| unpack1(X_16,o,pack1(X_16,i)) != X_16
| unpack1(X_16,o,o) = X_16 ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(X_16,o,pack1(X_16,i)),X_16) ),[0,2],$fot(o)]]) ).
cnf(refute_0_34,plain,
( unpack1(X_16,o,pack1(X_16,i)) != X_16
| pack1(X_16,i) = i
| unpack1(X_16,o,o) = X_16 ),
inference(resolve,[$cnf( $equal(pack1(X_16,i),o) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( pack1(X_16,i) = i
| unpack1(X_16,o,o) = X_16 ),
inference(resolve,[$cnf( $equal(unpack1(X_16,o,pack1(X_16,i)),X_16) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( pack1(i,i) = i
| unpack1(i,o,o) = i ),
inference(subst,[],[refute_0_35:[bind(X_16,$fot(i))]]) ).
cnf(refute_0_37,plain,
( unpack1(i,o,o) != i
| unpack1(i,o,o) != o
| i = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(i,o,o),o) ),[0],$fot(i)]]) ).
cnf(refute_0_38,plain,
( unpack1(i,o,o) != o
| i = o
| pack1(i,i) = i ),
inference(resolve,[$cnf( $equal(unpack1(i,o,o),i) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( i = o
| pack1(i,i) = i
| pack1(o,o) = i ),
inference(resolve,[$cnf( $equal(unpack1(i,o,o),o) )],[refute_0_20,refute_0_38]) ).
cnf(refute_0_40,plain,
inv(o) != o,
inference(subst,[],[bit_inverse:[bind(X,$fot(o))]]) ).
cnf(refute_0_41,plain,
( i != o
| inv(o) != i
| inv(o) = o ),
introduced(tautology,[equality,[$cnf( $equal(inv(o),i) ),[1],$fot(o)]]) ).
cnf(refute_0_42,plain,
( i != o
| inv(o) = o ),
inference(resolve,[$cnf( $equal(inv(o),i) )],[refute_0_8,refute_0_41]) ).
cnf(refute_0_43,plain,
i != o,
inference(resolve,[$cnf( $equal(inv(o),o) )],[refute_0_42,refute_0_40]) ).
cnf(refute_0_44,plain,
( pack1(i,i) = i
| pack1(o,o) = i ),
inference(resolve,[$cnf( $equal(i,o) )],[refute_0_39,refute_0_43]) ).
cnf(refute_0_45,plain,
( pack1(o,o) != i
| unpack2(o,o,pack1(o,o)) != o
| unpack2(o,o,i) = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(o,o,pack1(o,o)),o) ),[0,2],$fot(i)]]) ).
cnf(refute_0_46,plain,
( unpack2(o,o,pack1(o,o)) != o
| pack1(i,i) = i
| unpack2(o,o,i) = o ),
inference(resolve,[$cnf( $equal(pack1(o,o),i) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( pack1(i,i) = i
| unpack2(o,o,i) = o ),
inference(resolve,[$cnf( $equal(unpack2(o,o,pack1(o,o)),o) )],[refute_0_19,refute_0_46]) ).
cnf(refute_0_48,plain,
unpack2(o,inv(i),pack1(o,i)) = i,
inference(subst,[],[unpack2_05:[bind(X1,$fot(o)),bind(X2,$fot(i))]]) ).
cnf(refute_0_49,plain,
unpack2(o,o,inv(pack1(o,o))) = o,
inference(subst,[],[unpack2_06:[bind(X1,$fot(o)),bind(X2,$fot(o))]]) ).
cnf(refute_0_50,plain,
( pack1(o,o) != i
| unpack2(o,o,inv(pack1(o,o))) != o
| unpack2(o,o,inv(i)) = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(o,o,inv(pack1(o,o))),o) ),[0,2,0],$fot(i)]]) ).
cnf(refute_0_51,plain,
( unpack2(o,o,inv(pack1(o,o))) != o
| pack1(i,i) = i
| unpack2(o,o,inv(i)) = o ),
inference(resolve,[$cnf( $equal(pack1(o,o),i) )],[refute_0_44,refute_0_50]) ).
cnf(refute_0_52,plain,
( pack1(i,i) = i
| unpack2(o,o,inv(i)) = o ),
inference(resolve,[$cnf( $equal(unpack2(o,o,inv(pack1(o,o))),o) )],[refute_0_49,refute_0_51]) ).
cnf(refute_0_53,plain,
unpack2(o,o,inv(i)) = unpack2(o,o,inv(i)),
introduced(tautology,[refl,[$fot(unpack2(o,o,inv(i)))]]) ).
cnf(refute_0_54,plain,
( inv(i) != o
| unpack2(o,o,inv(i)) != unpack2(o,o,inv(i))
| unpack2(o,o,inv(i)) = unpack2(o,o,o) ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(o,o,inv(i)),unpack2(o,o,inv(i))) ),[1,2],$fot(o)]]) ).
cnf(refute_0_55,plain,
( inv(i) != o
| unpack2(o,o,inv(i)) = unpack2(o,o,o) ),
inference(resolve,[$cnf( $equal(unpack2(o,o,inv(i)),unpack2(o,o,inv(i))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
unpack2(o,o,inv(i)) = unpack2(o,o,o),
inference(resolve,[$cnf( $equal(inv(i),o) )],[refute_0_27,refute_0_55]) ).
cnf(refute_0_57,plain,
( unpack2(o,o,inv(i)) != o
| unpack2(o,o,inv(i)) != unpack2(o,o,o)
| unpack2(o,o,o) = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(o,o,inv(i)),o) ),[0],$fot(unpack2(o,o,o))]]) ).
cnf(refute_0_58,plain,
( unpack2(o,o,inv(i)) != o
| unpack2(o,o,o) = o ),
inference(resolve,[$cnf( $equal(unpack2(o,o,inv(i)),unpack2(o,o,o)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( pack1(i,i) = i
| unpack2(o,o,o) = o ),
inference(resolve,[$cnf( $equal(unpack2(o,o,inv(i)),o) )],[refute_0_52,refute_0_58]) ).
cnf(refute_0_60,plain,
unpack2(X_20,inv(i),pack1(X_20,i)) = i,
inference(subst,[],[unpack2_05:[bind(X1,$fot(X_20)),bind(X2,$fot(i))]]) ).
cnf(refute_0_61,plain,
( inv(i) != o
| unpack2(X_20,inv(i),pack1(X_20,i)) != i
| unpack2(X_20,o,pack1(X_20,i)) = i ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(X_20,inv(i),pack1(X_20,i)),i) ),[0,1],$fot(o)]]) ).
cnf(refute_0_62,plain,
( unpack2(X_20,inv(i),pack1(X_20,i)) != i
| unpack2(X_20,o,pack1(X_20,i)) = i ),
inference(resolve,[$cnf( $equal(inv(i),o) )],[refute_0_27,refute_0_61]) ).
cnf(refute_0_63,plain,
unpack2(X_20,o,pack1(X_20,i)) = i,
inference(resolve,[$cnf( $equal(unpack2(X_20,inv(i),pack1(X_20,i)),i) )],[refute_0_60,refute_0_62]) ).
cnf(refute_0_64,plain,
unpack2(X_23,o,pack1(X_23,i)) = i,
inference(subst,[],[refute_0_63:[bind(X_20,$fot(X_23))]]) ).
cnf(refute_0_65,plain,
( pack1(X_23,i) = i
| pack1(X_23,i) = o ),
inference(subst,[],[bit_domain:[bind(X,$fot(pack1(X_23,i)))]]) ).
cnf(refute_0_66,plain,
( pack1(X_23,i) != o
| unpack2(X_23,o,pack1(X_23,i)) != i
| unpack2(X_23,o,o) = i ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(X_23,o,pack1(X_23,i)),i) ),[0,2],$fot(o)]]) ).
cnf(refute_0_67,plain,
( unpack2(X_23,o,pack1(X_23,i)) != i
| pack1(X_23,i) = i
| unpack2(X_23,o,o) = i ),
inference(resolve,[$cnf( $equal(pack1(X_23,i),o) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( pack1(X_23,i) = i
| unpack2(X_23,o,o) = i ),
inference(resolve,[$cnf( $equal(unpack2(X_23,o,pack1(X_23,i)),i) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
( pack1(o,i) = i
| unpack2(o,o,o) = i ),
inference(subst,[],[refute_0_68:[bind(X_23,$fot(o))]]) ).
cnf(refute_0_70,plain,
( unpack2(o,o,o) != i
| unpack2(o,o,o) != o
| i = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(o,o,o),o) ),[0],$fot(i)]]) ).
cnf(refute_0_71,plain,
( unpack2(o,o,o) != o
| i = o
| pack1(o,i) = i ),
inference(resolve,[$cnf( $equal(unpack2(o,o,o),i) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( i = o
| pack1(i,i) = i
| pack1(o,i) = i ),
inference(resolve,[$cnf( $equal(unpack2(o,o,o),o) )],[refute_0_59,refute_0_71]) ).
cnf(refute_0_73,plain,
( pack1(i,i) = i
| pack1(o,i) = i ),
inference(resolve,[$cnf( $equal(i,o) )],[refute_0_72,refute_0_43]) ).
cnf(refute_0_74,plain,
( pack1(o,i) != i
| unpack2(o,inv(i),pack1(o,i)) != i
| unpack2(o,inv(i),i) = i ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(o,inv(i),pack1(o,i)),i) ),[0,2],$fot(i)]]) ).
cnf(refute_0_75,plain,
( unpack2(o,inv(i),pack1(o,i)) != i
| pack1(i,i) = i
| unpack2(o,inv(i),i) = i ),
inference(resolve,[$cnf( $equal(pack1(o,i),i) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( pack1(i,i) = i
| unpack2(o,inv(i),i) = i ),
inference(resolve,[$cnf( $equal(unpack2(o,inv(i),pack1(o,i)),i) )],[refute_0_48,refute_0_75]) ).
cnf(refute_0_77,plain,
unpack2(o,inv(i),i) = unpack2(o,inv(i),i),
introduced(tautology,[refl,[$fot(unpack2(o,inv(i),i))]]) ).
cnf(refute_0_78,plain,
( inv(i) != o
| unpack2(o,inv(i),i) != unpack2(o,inv(i),i)
| unpack2(o,inv(i),i) = unpack2(o,o,i) ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(o,inv(i),i),unpack2(o,inv(i),i)) ),[1,1],$fot(o)]]) ).
cnf(refute_0_79,plain,
( inv(i) != o
| unpack2(o,inv(i),i) = unpack2(o,o,i) ),
inference(resolve,[$cnf( $equal(unpack2(o,inv(i),i),unpack2(o,inv(i),i)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
unpack2(o,inv(i),i) = unpack2(o,o,i),
inference(resolve,[$cnf( $equal(inv(i),o) )],[refute_0_27,refute_0_79]) ).
cnf(refute_0_81,plain,
( unpack2(o,inv(i),i) != i
| unpack2(o,inv(i),i) != unpack2(o,o,i)
| unpack2(o,o,i) = i ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(o,inv(i),i),i) ),[0],$fot(unpack2(o,o,i))]]) ).
cnf(refute_0_82,plain,
( unpack2(o,inv(i),i) != i
| unpack2(o,o,i) = i ),
inference(resolve,[$cnf( $equal(unpack2(o,inv(i),i),unpack2(o,o,i)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( pack1(i,i) = i
| unpack2(o,o,i) = i ),
inference(resolve,[$cnf( $equal(unpack2(o,inv(i),i),i) )],[refute_0_76,refute_0_82]) ).
cnf(refute_0_84,plain,
( unpack2(o,o,i) != i
| unpack2(o,o,i) != o
| i = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack2(o,o,i),o) ),[0],$fot(i)]]) ).
cnf(refute_0_85,plain,
( unpack2(o,o,i) != o
| i = o
| pack1(i,i) = i ),
inference(resolve,[$cnf( $equal(unpack2(o,o,i),i) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( i = o
| pack1(i,i) = i ),
inference(resolve,[$cnf( $equal(unpack2(o,o,i),o) )],[refute_0_47,refute_0_85]) ).
cnf(refute_0_87,plain,
pack1(i,i) = i,
inference(resolve,[$cnf( $equal(i,o) )],[refute_0_86,refute_0_43]) ).
cnf(refute_0_88,plain,
( pack1(i,i) != i
| unpack1(i,i,inv(pack1(i,i))) != i
| unpack1(i,i,inv(i)) = i ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(i,i,inv(pack1(i,i))),i) ),[0,2,0],$fot(i)]]) ).
cnf(refute_0_89,plain,
( unpack1(i,i,inv(pack1(i,i))) != i
| unpack1(i,i,inv(i)) = i ),
inference(resolve,[$cnf( $equal(pack1(i,i),i) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
unpack1(i,i,inv(i)) = i,
inference(resolve,[$cnf( $equal(unpack1(i,i,inv(pack1(i,i))),i) )],[refute_0_18,refute_0_89]) ).
cnf(refute_0_91,plain,
unpack1(i,i,inv(i)) = unpack1(i,i,inv(i)),
introduced(tautology,[refl,[$fot(unpack1(i,i,inv(i)))]]) ).
cnf(refute_0_92,plain,
( inv(i) != o
| unpack1(i,i,inv(i)) != unpack1(i,i,inv(i))
| unpack1(i,i,inv(i)) = unpack1(i,i,o) ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(i,i,inv(i)),unpack1(i,i,inv(i))) ),[1,2],$fot(o)]]) ).
cnf(refute_0_93,plain,
( inv(i) != o
| unpack1(i,i,inv(i)) = unpack1(i,i,o) ),
inference(resolve,[$cnf( $equal(unpack1(i,i,inv(i)),unpack1(i,i,inv(i))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
unpack1(i,i,inv(i)) = unpack1(i,i,o),
inference(resolve,[$cnf( $equal(inv(i),o) )],[refute_0_27,refute_0_93]) ).
cnf(refute_0_95,plain,
( unpack1(i,i,inv(i)) != i
| unpack1(i,i,inv(i)) != unpack1(i,i,o)
| unpack1(i,i,o) = i ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(i,i,inv(i)),i) ),[0],$fot(unpack1(i,i,o))]]) ).
cnf(refute_0_96,plain,
( unpack1(i,i,inv(i)) != i
| unpack1(i,i,o) = i ),
inference(resolve,[$cnf( $equal(unpack1(i,i,inv(i)),unpack1(i,i,o)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
unpack1(i,i,o) = i,
inference(resolve,[$cnf( $equal(unpack1(i,i,inv(i)),i) )],[refute_0_90,refute_0_96]) ).
cnf(refute_0_98,plain,
( unpack1(i,i,o) != i
| unpack1(i,i,o) != o
| i = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(i,i,o),o) ),[0],$fot(i)]]) ).
cnf(refute_0_99,plain,
( unpack1(i,i,o) != o
| i = o ),
inference(resolve,[$cnf( $equal(unpack1(i,i,o),i) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( i = o
| pack1(o,i) = i ),
inference(resolve,[$cnf( $equal(unpack1(i,i,o),o) )],[refute_0_17,refute_0_99]) ).
cnf(refute_0_101,plain,
pack1(o,i) = i,
inference(resolve,[$cnf( $equal(i,o) )],[refute_0_100,refute_0_43]) ).
cnf(refute_0_102,plain,
( pack1(o,i) != i
| unpack1(inv(o),i,pack1(o,i)) != o
| unpack1(inv(o),i,i) = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(inv(o),i,pack1(o,i)),o) ),[0,2],$fot(i)]]) ).
cnf(refute_0_103,plain,
( unpack1(inv(o),i,pack1(o,i)) != o
| unpack1(inv(o),i,i) = o ),
inference(resolve,[$cnf( $equal(pack1(o,i),i) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
unpack1(inv(o),i,i) = o,
inference(resolve,[$cnf( $equal(unpack1(inv(o),i,pack1(o,i)),o) )],[refute_0_0,refute_0_103]) ).
cnf(refute_0_105,plain,
unpack1(i,i,pack1(i,i)) = i,
inference(subst,[],[unpack1:[bind(X1,$fot(i)),bind(X2,$fot(i))]]) ).
cnf(refute_0_106,plain,
( pack1(i,i) != i
| unpack1(i,i,pack1(i,i)) != i
| unpack1(i,i,i) = i ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(i,i,pack1(i,i)),i) ),[0,2],$fot(i)]]) ).
cnf(refute_0_107,plain,
( unpack1(i,i,pack1(i,i)) != i
| unpack1(i,i,i) = i ),
inference(resolve,[$cnf( $equal(pack1(i,i),i) )],[refute_0_87,refute_0_106]) ).
cnf(refute_0_108,plain,
unpack1(i,i,i) = i,
inference(resolve,[$cnf( $equal(unpack1(i,i,pack1(i,i)),i) )],[refute_0_105,refute_0_107]) ).
cnf(refute_0_109,plain,
unpack1(inv(o),i,i) = unpack1(inv(o),i,i),
introduced(tautology,[refl,[$fot(unpack1(inv(o),i,i))]]) ).
cnf(refute_0_110,plain,
( inv(o) != i
| unpack1(inv(o),i,i) != unpack1(inv(o),i,i)
| unpack1(inv(o),i,i) = unpack1(i,i,i) ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(inv(o),i,i),unpack1(inv(o),i,i)) ),[1,0],$fot(i)]]) ).
cnf(refute_0_111,plain,
( inv(o) != i
| unpack1(inv(o),i,i) = unpack1(i,i,i) ),
inference(resolve,[$cnf( $equal(unpack1(inv(o),i,i),unpack1(inv(o),i,i)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
unpack1(inv(o),i,i) = unpack1(i,i,i),
inference(resolve,[$cnf( $equal(inv(o),i) )],[refute_0_8,refute_0_111]) ).
cnf(refute_0_113,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_114,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_115,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_117,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
( unpack1(i,i,i) != i
| unpack1(inv(o),i,i) != unpack1(i,i,i)
| unpack1(inv(o),i,i) = i ),
inference(subst,[],[refute_0_117:[bind(X0,$fot(unpack1(inv(o),i,i))),bind(Y,$fot(unpack1(i,i,i))),bind(Z,$fot(i))]]) ).
cnf(refute_0_119,plain,
( unpack1(i,i,i) != i
| unpack1(inv(o),i,i) = i ),
inference(resolve,[$cnf( $equal(unpack1(inv(o),i,i),unpack1(i,i,i)) )],[refute_0_112,refute_0_118]) ).
cnf(refute_0_120,plain,
unpack1(inv(o),i,i) = i,
inference(resolve,[$cnf( $equal(unpack1(i,i,i),i) )],[refute_0_108,refute_0_119]) ).
cnf(refute_0_121,plain,
( unpack1(inv(o),i,i) != i
| unpack1(inv(o),i,i) != o
| i = o ),
introduced(tautology,[equality,[$cnf( $equal(unpack1(inv(o),i,i),o) ),[0],$fot(i)]]) ).
cnf(refute_0_122,plain,
( unpack1(inv(o),i,i) != o
| i = o ),
inference(resolve,[$cnf( $equal(unpack1(inv(o),i,i),i) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
i = o,
inference(resolve,[$cnf( $equal(unpack1(inv(o),i,i),o) )],[refute_0_104,refute_0_122]) ).
cnf(refute_0_124,plain,
$false,
inference(resolve,[$cnf( $equal(i,o) )],[refute_0_123,refute_0_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : HWV052-1.002.001 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.36 % Computer : n029.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 600
% 0.13/0.36 % DateTime : Fri Jun 17 06:22:43 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.41
% 0.22/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.43
%------------------------------------------------------------------------------