TSTP Solution File: HWV052-1.001.001 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : HWV052-1.001.001 : 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 18:30:22 EDT 2022

% Result   : Unsatisfiable 0.19s 0.36s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   34
% Syntax   : Number of clauses     :  105 (  35 unt;  25 nHn;  97 RR)
%            Number of literals    :  210 ( 209 equ;  83 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   27 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(bit_domain,axiom,
    ( X = o
    | X = i ) ).

cnf(bit_inverse,axiom,
    inv(X) != X ).

cnf(unpack1,axiom,
    unpack1(X1,pack1(X1)) = X1 ).

cnf(unpack1_01,axiom,
    unpack1(inv(X1),pack1(X1)) = X1 ).

cnf(unpack1_02,axiom,
    unpack1(X1,inv(pack1(X1))) = X1 ).

cnf(refute_0_0,plain,
    ( inv(X) = i
    | inv(X) = o ),
    inference(subst,[],[bit_domain:[bind(X,$fot(inv(X)))]]) ).

cnf(refute_0_1,plain,
    ( i != X
    | inv(X) != i
    | inv(X) = X ),
    introduced(tautology,[equality,[$cnf( $equal(inv(X),i) ),[1],$fot(X)]]) ).

cnf(refute_0_2,plain,
    ( i != X
    | inv(X) = X
    | inv(X) = o ),
    inference(resolve,[$cnf( $equal(inv(X),i) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( i != X
    | inv(X) = o ),
    inference(resolve,[$cnf( $equal(inv(X),X) )],[refute_0_2,bit_inverse]) ).

cnf(refute_0_4,plain,
    ( i != i
    | inv(i) = o ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(i))]]) ).

cnf(refute_0_5,plain,
    i = i,
    introduced(tautology,[refl,[$fot(i)]]) ).

cnf(refute_0_6,plain,
    inv(i) = o,
    inference(resolve,[$cnf( $equal(i,i) )],[refute_0_5,refute_0_4]) ).

cnf(refute_0_7,plain,
    unpack1(inv(o),pack1(o)) = o,
    inference(subst,[],[unpack1_01:[bind(X1,$fot(o))]]) ).

cnf(refute_0_8,plain,
    ( inv(X) != o
    | o != X
    | inv(X) = X ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inv(X),X) ),[0],$fot(o)]]) ).

cnf(refute_0_9,plain,
    ( o != X
    | inv(X) = X
    | inv(X) = i ),
    inference(resolve,[$cnf( $equal(inv(X),o) )],[refute_0_0,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( o != X
    | inv(X) = i ),
    inference(resolve,[$cnf( $equal(inv(X),X) )],[refute_0_9,bit_inverse]) ).

cnf(refute_0_11,plain,
    ( o != o
    | inv(o) = i ),
    inference(subst,[],[refute_0_10:[bind(X,$fot(o))]]) ).

cnf(refute_0_12,plain,
    o = o,
    introduced(tautology,[refl,[$fot(o)]]) ).

cnf(refute_0_13,plain,
    inv(o) = i,
    inference(resolve,[$cnf( $equal(o,o) )],[refute_0_12,refute_0_11]) ).

cnf(refute_0_14,plain,
    ( inv(o) != i
    | unpack1(inv(o),pack1(o)) != o
    | unpack1(i,pack1(o)) = o ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(inv(o),pack1(o)),o) ),[0,0],$fot(i)]]) ).

cnf(refute_0_15,plain,
    ( unpack1(inv(o),pack1(o)) != o
    | unpack1(i,pack1(o)) = o ),
    inference(resolve,[$cnf( $equal(inv(o),i) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    unpack1(i,pack1(o)) = o,
    inference(resolve,[$cnf( $equal(unpack1(inv(o),pack1(o)),o) )],[refute_0_7,refute_0_15]) ).

cnf(refute_0_17,plain,
    unpack1(i,inv(pack1(i))) = i,
    inference(subst,[],[unpack1_02:[bind(X1,$fot(i))]]) ).

cnf(refute_0_18,plain,
    unpack1(inv(i),pack1(i)) = i,
    inference(subst,[],[unpack1_01:[bind(X1,$fot(i))]]) ).

cnf(refute_0_19,plain,
    ( inv(i) != o
    | unpack1(inv(i),pack1(i)) != i
    | unpack1(o,pack1(i)) = i ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(inv(i),pack1(i)),i) ),[0,0],$fot(o)]]) ).

cnf(refute_0_20,plain,
    ( unpack1(inv(i),pack1(i)) != i
    | unpack1(o,pack1(i)) = i ),
    inference(resolve,[$cnf( $equal(inv(i),o) )],[refute_0_6,refute_0_19]) ).

cnf(refute_0_21,plain,
    unpack1(o,pack1(i)) = i,
    inference(resolve,[$cnf( $equal(unpack1(inv(i),pack1(i)),i) )],[refute_0_18,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( pack1(i) = i
    | pack1(i) = o ),
    inference(subst,[],[bit_domain:[bind(X,$fot(pack1(i)))]]) ).

cnf(refute_0_23,plain,
    ( pack1(i) != i
    | unpack1(o,pack1(i)) != i
    | unpack1(o,i) = i ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(o,pack1(i)),i) ),[0,1],$fot(i)]]) ).

cnf(refute_0_24,plain,
    ( unpack1(o,pack1(i)) != i
    | pack1(i) = o
    | unpack1(o,i) = i ),
    inference(resolve,[$cnf( $equal(pack1(i),i) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( pack1(i) = o
    | unpack1(o,i) = i ),
    inference(resolve,[$cnf( $equal(unpack1(o,pack1(i)),i) )],[refute_0_21,refute_0_24]) ).

cnf(refute_0_26,plain,
    unpack1(o,inv(pack1(o))) = o,
    inference(subst,[],[unpack1_02:[bind(X1,$fot(o))]]) ).

cnf(refute_0_27,plain,
    ( pack1(o) = i
    | pack1(o) = o ),
    inference(subst,[],[bit_domain:[bind(X,$fot(pack1(o)))]]) ).

cnf(refute_0_28,plain,
    ( pack1(o) != i
    | unpack1(i,pack1(o)) != o
    | unpack1(i,i) = o ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,pack1(o)),o) ),[0,1],$fot(i)]]) ).

cnf(refute_0_29,plain,
    ( unpack1(i,pack1(o)) != o
    | pack1(o) = o
    | unpack1(i,i) = o ),
    inference(resolve,[$cnf( $equal(pack1(o),i) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( pack1(o) = o
    | unpack1(i,i) = o ),
    inference(resolve,[$cnf( $equal(unpack1(i,pack1(o)),o) )],[refute_0_16,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( pack1(X1) = i
    | pack1(X1) = o ),
    inference(subst,[],[bit_domain:[bind(X,$fot(pack1(X1)))]]) ).

cnf(refute_0_32,plain,
    ( pack1(X1) != i
    | unpack1(X1,pack1(X1)) != X1
    | unpack1(X1,i) = X1 ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(X1,pack1(X1)),X1) ),[0,1],$fot(i)]]) ).

cnf(refute_0_33,plain,
    ( unpack1(X1,pack1(X1)) != X1
    | pack1(X1) = o
    | unpack1(X1,i) = X1 ),
    inference(resolve,[$cnf( $equal(pack1(X1),i) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( pack1(X1) = o
    | unpack1(X1,i) = X1 ),
    inference(resolve,[$cnf( $equal(unpack1(X1,pack1(X1)),X1) )],[unpack1,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( pack1(i) = o
    | unpack1(i,i) = i ),
    inference(subst,[],[refute_0_34:[bind(X1,$fot(i))]]) ).

cnf(refute_0_36,plain,
    ( unpack1(i,i) != i
    | unpack1(i,i) != o
    | i = o ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,i),o) ),[0],$fot(i)]]) ).

cnf(refute_0_37,plain,
    ( unpack1(i,i) != o
    | i = o
    | pack1(i) = o ),
    inference(resolve,[$cnf( $equal(unpack1(i,i),i) )],[refute_0_35,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( i = o
    | pack1(i) = o
    | pack1(o) = o ),
    inference(resolve,[$cnf( $equal(unpack1(i,i),o) )],[refute_0_30,refute_0_37]) ).

cnf(refute_0_39,plain,
    inv(i) != i,
    inference(subst,[],[bit_inverse:[bind(X,$fot(i))]]) ).

cnf(refute_0_40,plain,
    ( inv(i) != o
    | o != i
    | inv(i) = i ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inv(i),i) ),[0],$fot(o)]]) ).

cnf(refute_0_41,plain,
    ( o != i
    | inv(i) = i ),
    inference(resolve,[$cnf( $equal(inv(i),o) )],[refute_0_6,refute_0_40]) ).

cnf(refute_0_42,plain,
    o != i,
    inference(resolve,[$cnf( $equal(inv(i),i) )],[refute_0_41,refute_0_39]) ).

cnf(refute_0_43,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_44,plain,
    ( X0 != X0
    | X0 != Y
    | Y = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).

cnf(refute_0_45,plain,
    ( X0 != Y
    | Y = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_43,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( i != o
    | o = i ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(i)),bind(Y,$fot(o))]]) ).

cnf(refute_0_47,plain,
    i != o,
    inference(resolve,[$cnf( $equal(o,i) )],[refute_0_46,refute_0_42]) ).

cnf(refute_0_48,plain,
    ( pack1(i) = o
    | pack1(o) = o ),
    inference(resolve,[$cnf( $equal(i,o) )],[refute_0_38,refute_0_47]) ).

cnf(refute_0_49,plain,
    ( pack1(o) != o
    | unpack1(o,inv(pack1(o))) != o
    | unpack1(o,inv(o)) = o ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(o,inv(pack1(o))),o) ),[0,1,0],$fot(o)]]) ).

cnf(refute_0_50,plain,
    ( unpack1(o,inv(pack1(o))) != o
    | pack1(i) = o
    | unpack1(o,inv(o)) = o ),
    inference(resolve,[$cnf( $equal(pack1(o),o) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( pack1(i) = o
    | unpack1(o,inv(o)) = o ),
    inference(resolve,[$cnf( $equal(unpack1(o,inv(pack1(o))),o) )],[refute_0_26,refute_0_50]) ).

cnf(refute_0_52,plain,
    unpack1(o,inv(o)) = unpack1(o,inv(o)),
    introduced(tautology,[refl,[$fot(unpack1(o,inv(o)))]]) ).

cnf(refute_0_53,plain,
    ( inv(o) != i
    | unpack1(o,inv(o)) != unpack1(o,inv(o))
    | unpack1(o,inv(o)) = unpack1(o,i) ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(o,inv(o)),unpack1(o,inv(o))) ),[1,1],$fot(i)]]) ).

cnf(refute_0_54,plain,
    ( inv(o) != i
    | unpack1(o,inv(o)) = unpack1(o,i) ),
    inference(resolve,[$cnf( $equal(unpack1(o,inv(o)),unpack1(o,inv(o))) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    unpack1(o,inv(o)) = unpack1(o,i),
    inference(resolve,[$cnf( $equal(inv(o),i) )],[refute_0_13,refute_0_54]) ).

cnf(refute_0_56,plain,
    ( unpack1(o,inv(o)) != o
    | unpack1(o,inv(o)) != unpack1(o,i)
    | unpack1(o,i) = o ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(o,inv(o)),o) ),[0],$fot(unpack1(o,i))]]) ).

cnf(refute_0_57,plain,
    ( unpack1(o,inv(o)) != o
    | unpack1(o,i) = o ),
    inference(resolve,[$cnf( $equal(unpack1(o,inv(o)),unpack1(o,i)) )],[refute_0_55,refute_0_56]) ).

cnf(refute_0_58,plain,
    ( pack1(i) = o
    | unpack1(o,i) = o ),
    inference(resolve,[$cnf( $equal(unpack1(o,inv(o)),o) )],[refute_0_51,refute_0_57]) ).

cnf(refute_0_59,plain,
    ( unpack1(o,i) != i
    | unpack1(o,i) != o
    | o = i ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(o,i),i) ),[0],$fot(o)]]) ).

cnf(refute_0_60,plain,
    ( unpack1(o,i) != i
    | o = i
    | pack1(i) = o ),
    inference(resolve,[$cnf( $equal(unpack1(o,i),o) )],[refute_0_58,refute_0_59]) ).

cnf(refute_0_61,plain,
    ( o = i
    | pack1(i) = o ),
    inference(resolve,[$cnf( $equal(unpack1(o,i),i) )],[refute_0_25,refute_0_60]) ).

cnf(refute_0_62,plain,
    pack1(i) = o,
    inference(resolve,[$cnf( $equal(o,i) )],[refute_0_61,refute_0_42]) ).

cnf(refute_0_63,plain,
    ( pack1(i) != o
    | unpack1(i,inv(pack1(i))) != i
    | unpack1(i,inv(o)) = i ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,inv(pack1(i))),i) ),[0,1,0],$fot(o)]]) ).

cnf(refute_0_64,plain,
    ( unpack1(i,inv(pack1(i))) != i
    | unpack1(i,inv(o)) = i ),
    inference(resolve,[$cnf( $equal(pack1(i),o) )],[refute_0_62,refute_0_63]) ).

cnf(refute_0_65,plain,
    unpack1(i,inv(o)) = i,
    inference(resolve,[$cnf( $equal(unpack1(i,inv(pack1(i))),i) )],[refute_0_17,refute_0_64]) ).

cnf(refute_0_66,plain,
    unpack1(i,inv(o)) = unpack1(i,inv(o)),
    introduced(tautology,[refl,[$fot(unpack1(i,inv(o)))]]) ).

cnf(refute_0_67,plain,
    ( inv(o) != i
    | unpack1(i,inv(o)) != unpack1(i,inv(o))
    | unpack1(i,inv(o)) = unpack1(i,i) ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,inv(o)),unpack1(i,inv(o))) ),[1,1],$fot(i)]]) ).

cnf(refute_0_68,plain,
    ( inv(o) != i
    | unpack1(i,inv(o)) = unpack1(i,i) ),
    inference(resolve,[$cnf( $equal(unpack1(i,inv(o)),unpack1(i,inv(o))) )],[refute_0_66,refute_0_67]) ).

cnf(refute_0_69,plain,
    unpack1(i,inv(o)) = unpack1(i,i),
    inference(resolve,[$cnf( $equal(inv(o),i) )],[refute_0_13,refute_0_68]) ).

cnf(refute_0_70,plain,
    ( unpack1(i,inv(o)) != i
    | unpack1(i,inv(o)) != unpack1(i,i)
    | unpack1(i,i) = i ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,inv(o)),i) ),[0],$fot(unpack1(i,i))]]) ).

cnf(refute_0_71,plain,
    ( unpack1(i,inv(o)) != i
    | unpack1(i,i) = i ),
    inference(resolve,[$cnf( $equal(unpack1(i,inv(o)),unpack1(i,i)) )],[refute_0_69,refute_0_70]) ).

cnf(refute_0_72,plain,
    unpack1(i,i) = i,
    inference(resolve,[$cnf( $equal(unpack1(i,inv(o)),i) )],[refute_0_65,refute_0_71]) ).

cnf(refute_0_73,plain,
    ( pack1(o) != o
    | unpack1(i,pack1(o)) != o
    | unpack1(i,o) = o ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,pack1(o)),o) ),[0,1],$fot(o)]]) ).

cnf(refute_0_74,plain,
    ( unpack1(i,pack1(o)) != o
    | pack1(o) = i
    | unpack1(i,o) = o ),
    inference(resolve,[$cnf( $equal(pack1(o),o) )],[refute_0_27,refute_0_73]) ).

cnf(refute_0_75,plain,
    ( pack1(o) = i
    | unpack1(i,o) = o ),
    inference(resolve,[$cnf( $equal(unpack1(i,pack1(o)),o) )],[refute_0_16,refute_0_74]) ).

cnf(refute_0_76,plain,
    unpack1(i,pack1(i)) = i,
    inference(subst,[],[unpack1:[bind(X1,$fot(i))]]) ).

cnf(refute_0_77,plain,
    ( pack1(i) != o
    | unpack1(i,pack1(i)) != i
    | unpack1(i,o) = i ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,pack1(i)),i) ),[0,1],$fot(o)]]) ).

cnf(refute_0_78,plain,
    ( unpack1(i,pack1(i)) != i
    | unpack1(i,o) = i ),
    inference(resolve,[$cnf( $equal(pack1(i),o) )],[refute_0_62,refute_0_77]) ).

cnf(refute_0_79,plain,
    unpack1(i,o) = i,
    inference(resolve,[$cnf( $equal(unpack1(i,pack1(i)),i) )],[refute_0_76,refute_0_78]) ).

cnf(refute_0_80,plain,
    ( unpack1(i,o) != i
    | unpack1(i,o) != o
    | i = o ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,o),o) ),[0],$fot(i)]]) ).

cnf(refute_0_81,plain,
    ( unpack1(i,o) != o
    | i = o ),
    inference(resolve,[$cnf( $equal(unpack1(i,o),i) )],[refute_0_79,refute_0_80]) ).

cnf(refute_0_82,plain,
    ( i = o
    | pack1(o) = i ),
    inference(resolve,[$cnf( $equal(unpack1(i,o),o) )],[refute_0_75,refute_0_81]) ).

cnf(refute_0_83,plain,
    pack1(o) = i,
    inference(resolve,[$cnf( $equal(i,o) )],[refute_0_82,refute_0_47]) ).

cnf(refute_0_84,plain,
    unpack1(i,pack1(o)) = unpack1(i,pack1(o)),
    introduced(tautology,[refl,[$fot(unpack1(i,pack1(o)))]]) ).

cnf(refute_0_85,plain,
    ( pack1(o) != i
    | unpack1(i,pack1(o)) != unpack1(i,pack1(o))
    | unpack1(i,pack1(o)) = unpack1(i,i) ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,pack1(o)),unpack1(i,pack1(o))) ),[1,1],$fot(i)]]) ).

cnf(refute_0_86,plain,
    ( pack1(o) != i
    | unpack1(i,pack1(o)) = unpack1(i,i) ),
    inference(resolve,[$cnf( $equal(unpack1(i,pack1(o)),unpack1(i,pack1(o))) )],[refute_0_84,refute_0_85]) ).

cnf(refute_0_87,plain,
    unpack1(i,pack1(o)) = unpack1(i,i),
    inference(resolve,[$cnf( $equal(pack1(o),i) )],[refute_0_83,refute_0_86]) ).

cnf(refute_0_88,plain,
    ( Y != X0
    | Y != Z
    | X0 = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).

cnf(refute_0_89,plain,
    ( X0 != Y
    | Y != Z
    | X0 = Z ),
    inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_45,refute_0_88]) ).

cnf(refute_0_90,plain,
    ( unpack1(i,i) != i
    | unpack1(i,pack1(o)) != unpack1(i,i)
    | unpack1(i,pack1(o)) = i ),
    inference(subst,[],[refute_0_89:[bind(X0,$fot(unpack1(i,pack1(o)))),bind(Y,$fot(unpack1(i,i))),bind(Z,$fot(i))]]) ).

cnf(refute_0_91,plain,
    ( unpack1(i,i) != i
    | unpack1(i,pack1(o)) = i ),
    inference(resolve,[$cnf( $equal(unpack1(i,pack1(o)),unpack1(i,i)) )],[refute_0_87,refute_0_90]) ).

cnf(refute_0_92,plain,
    unpack1(i,pack1(o)) = i,
    inference(resolve,[$cnf( $equal(unpack1(i,i),i) )],[refute_0_72,refute_0_91]) ).

cnf(refute_0_93,plain,
    ( unpack1(i,pack1(o)) != i
    | unpack1(i,pack1(o)) != o
    | i = o ),
    introduced(tautology,[equality,[$cnf( $equal(unpack1(i,pack1(o)),o) ),[0],$fot(i)]]) ).

cnf(refute_0_94,plain,
    ( unpack1(i,pack1(o)) != o
    | i = o ),
    inference(resolve,[$cnf( $equal(unpack1(i,pack1(o)),i) )],[refute_0_92,refute_0_93]) ).

cnf(refute_0_95,plain,
    i = o,
    inference(resolve,[$cnf( $equal(unpack1(i,pack1(o)),o) )],[refute_0_16,refute_0_94]) ).

cnf(refute_0_96,plain,
    o = i,
    inference(resolve,[$cnf( $equal(i,o) )],[refute_0_95,refute_0_46]) ).

cnf(refute_0_97,plain,
    ( inv(i) != o
    | inv(i) = i ),
    inference(resolve,[$cnf( $equal(o,i) )],[refute_0_96,refute_0_40]) ).

cnf(refute_0_98,plain,
    inv(i) = i,
    inference(resolve,[$cnf( $equal(inv(i),o) )],[refute_0_6,refute_0_97]) ).

cnf(refute_0_99,plain,
    $false,
    inference(resolve,[$cnf( $equal(inv(i),i) )],[refute_0_98,refute_0_39]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : HWV052-1.001.001 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 : Fri Jun 17 04:32:13 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36  
% 0.19/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37  
%------------------------------------------------------------------------------