TSTP Solution File: GEO603+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO603+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 05:27:37 EDT 2022

% Result   : Theorem 14.55s 14.81s
% Output   : CNFRefutation 14.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   95 (  31 unt;   0 def)
%            Number of atoms       :  210 (   0 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  189 (  74   ~;  69   |;  36   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-3 aty)
%            Number of variables   :  163 (   2 sgn 115   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
    ! [A,B,C] :
      ( coll(A,B,C)
     => coll(A,C,B) ) ).

fof(ruleD2,axiom,
    ! [A,B,C] :
      ( coll(A,B,C)
     => coll(B,A,C) ) ).

fof(ruleD3,axiom,
    ! [A,B,C,D] :
      ( ( coll(A,B,C)
        & coll(A,B,D) )
     => coll(C,D,A) ) ).

fof(ruleD7,axiom,
    ! [A,B,C,D] :
      ( perp(A,B,C,D)
     => perp(A,B,D,C) ) ).

fof(ruleD8,axiom,
    ! [A,B,C,D] :
      ( perp(A,B,C,D)
     => perp(C,D,A,B) ) ).

fof(ruleX10,axiom,
    ! [A,B,C,H] :
    ? [P,Q] :
      ( ( perp(A,H,B,C)
        & perp(B,H,A,C) )
     => ( coll(P,C,B)
        & perp(A,P,C,B)
        & coll(Q,C,A)
        & perp(B,Q,C,A) ) ) ).

fof(ruleX11,axiom,
    ! [A,B,C,O] :
    ? [P] :
      ( circle(O,A,B,C)
     => perp(P,A,A,O) ) ).

fof(exemplo6GDDFULL618065,conjecture,
    ! [A,B,C,D,E,F,G] :
      ( ( circle(D,A,B,C)
        & coll(E,A,B)
        & para(B,C,F,E)
        & coll(F,A,C)
        & circle(G,A,E,F) )
     => coll(A,G,D) ) ).

fof(subgoal_0,plain,
    ! [A,B,C,D,E,F,G] :
      ( ( circle(D,A,B,C)
        & coll(E,A,B)
        & para(B,C,F,E)
        & coll(F,A,C)
        & circle(G,A,E,F) )
     => coll(A,G,D) ),
    inference(strip,[],[exemplo6GDDFULL618065]) ).

fof(negate_0_0,plain,
    ~ ! [A,B,C,D,E,F,G] :
        ( ( circle(D,A,B,C)
          & coll(E,A,B)
          & para(B,C,F,E)
          & coll(F,A,C)
          & circle(G,A,E,F) )
       => coll(A,G,D) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A,B,C] :
      ( ~ coll(A,B,C)
      | coll(A,C,B) ),
    inference(canonicalize,[],[ruleD1]) ).

fof(normalize_0_1,plain,
    ! [A,B,C] :
      ( ~ coll(A,B,C)
      | coll(A,C,B) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A,B,C] :
      ( ~ coll(A,B,C)
      | coll(B,A,C) ),
    inference(canonicalize,[],[ruleD2]) ).

fof(normalize_0_3,plain,
    ! [A,B,C] :
      ( ~ coll(A,B,C)
      | coll(B,A,C) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [A,B,C,D] :
      ( ~ coll(A,B,C)
      | ~ coll(A,B,D)
      | coll(C,D,A) ),
    inference(canonicalize,[],[ruleD3]) ).

fof(normalize_0_5,plain,
    ! [A,B,C,D] :
      ( ~ coll(A,B,C)
      | ~ coll(A,B,D)
      | coll(C,D,A) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [A,B,C,D] :
      ( ~ perp(A,B,C,D)
      | perp(A,B,D,C) ),
    inference(canonicalize,[],[ruleD7]) ).

fof(normalize_0_7,plain,
    ! [A,B,C,D] :
      ( ~ perp(A,B,C,D)
      | perp(A,B,D,C) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [A,B,C,H] :
      ( ~ perp(A,H,B,C)
      | ~ perp(B,H,A,C)
      | ? [P,Q] :
          ( coll(P,C,B)
          & coll(Q,C,A)
          & perp(A,P,C,B)
          & perp(B,Q,C,A) ) ),
    inference(canonicalize,[],[ruleX10]) ).

fof(normalize_0_9,plain,
    ! [A,B,C,H] :
      ( ~ perp(A,H,B,C)
      | ~ perp(B,H,A,C)
      | ? [P,Q] :
          ( coll(P,C,B)
          & coll(Q,C,A)
          & perp(A,P,C,B)
          & perp(B,Q,C,A) ) ),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [A,B,C,H] :
      ( ( ~ perp(A,H,B,C)
        | ~ perp(B,H,A,C)
        | coll(skolemFOFtoCNF_P_3(A,B,C),C,B) )
      & ( ~ perp(A,H,B,C)
        | ~ perp(B,H,A,C)
        | coll(skolemFOFtoCNF_Q_1(A,B,C),C,A) )
      & ( ~ perp(A,H,B,C)
        | ~ perp(B,H,A,C)
        | perp(A,skolemFOFtoCNF_P_3(A,B,C),C,B) )
      & ( ~ perp(A,H,B,C)
        | ~ perp(B,H,A,C)
        | perp(B,skolemFOFtoCNF_Q_1(A,B,C),C,A) ) ),
    inference(clausify,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [A,B,C,H] :
      ( ~ perp(A,H,B,C)
      | ~ perp(B,H,A,C)
      | perp(A,skolemFOFtoCNF_P_3(A,B,C),C,B) ),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [A,B,C,D] :
      ( ~ perp(A,B,C,D)
      | perp(C,D,A,B) ),
    inference(canonicalize,[],[ruleD8]) ).

fof(normalize_0_13,plain,
    ! [A,B,C,D] :
      ( ~ perp(A,B,C,D)
      | perp(C,D,A,B) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ? [A,B,C,D,E,F,G] :
      ( ~ coll(A,G,D)
      & circle(D,A,B,C)
      & circle(G,A,E,F)
      & coll(E,A,B)
      & coll(F,A,C)
      & para(B,C,F,E) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_15,plain,
    ( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
    & circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    & circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F)
    & coll(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
    & coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
    & para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_E) ),
    inference(skolemize,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [A,B,C,O] :
      ( ~ circle(O,A,B,C)
      | ? [P] : perp(P,A,A,O) ),
    inference(canonicalize,[],[ruleX11]) ).

fof(normalize_0_18,plain,
    ! [A,B,C,O] :
      ( ~ circle(O,A,B,C)
      | ? [P] : perp(P,A,A,O) ),
    inference(specialize,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    ! [A,B,C,O] :
      ( ~ circle(O,A,B,C)
      | perp(skolemFOFtoCNF_P_4(A,O),A,A,O) ),
    inference(clausify,[],[normalize_0_18]) ).

fof(normalize_0_20,plain,
    ! [A,B,C,H] :
      ( ~ perp(A,H,B,C)
      | ~ perp(B,H,A,C)
      | coll(skolemFOFtoCNF_P_3(A,B,C),C,B) ),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_21,plain,
    circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_22,plain,
    ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
    inference(conjunct,[],[normalize_0_15]) ).

cnf(refute_0_0,plain,
    ( ~ coll(A,B,C)
    | coll(A,C,B) ),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_G)
    | coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D) ),
    inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).

cnf(refute_0_2,plain,
    ( ~ coll(A,B,C)
    | coll(B,A,C) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    ( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_G)
    | coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_G) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).

cnf(refute_0_4,plain,
    ( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_A)
    | coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
    inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_5,plain,
    ( ~ coll(A,B,C)
    | ~ coll(A,B,D)
    | coll(C,D,A) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_6,plain,
    ( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A)
    | coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
    inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_7,plain,
    ( ~ coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A)
    | coll(skolemFOFtoCNF_G,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_8,plain,
    ( ~ perp(A,B,C,D)
    | perp(A,B,D,C) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A)
    | perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_10,plain,
    ( ~ perp(A,H,B,C)
    | ~ perp(B,H,A,C)
    | perp(A,skolemFOFtoCNF_P_3(A,B,C),C,B) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_11,plain,
    ( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G)
    | perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_G)),bind(H,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)))]]) ).

cnf(refute_0_12,plain,
    ( ~ perp(A,B,C,D)
    | perp(C,D,A,B) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_13,plain,
    ( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G))
    | perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
    inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)))]]) ).

cnf(refute_0_14,plain,
    ( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A)
    | perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(D,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_15,plain,
    ( ~ perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G)
    | perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).

cnf(refute_0_16,plain,
    circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_17,plain,
    ( ~ circle(O,A,B,C)
    | perp(skolemFOFtoCNF_P_4(A,O),A,A,O) ),
    inference(canonicalize,[],[normalize_0_19]) ).

cnf(refute_0_18,plain,
    ( ~ circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F)
    | perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
    inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_F)),bind(O,$fot(skolemFOFtoCNF_G))]]) ).

cnf(refute_0_19,plain,
    perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),
    inference(resolve,[$cnf( circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F) )],[refute_0_16,refute_0_18]) ).

cnf(refute_0_20,plain,
    perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_19,refute_0_15]) ).

cnf(refute_0_21,plain,
    perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A) )],[refute_0_20,refute_0_14]) ).

cnf(refute_0_22,plain,
    perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)) )],[refute_0_21,refute_0_13]) ).

cnf(refute_0_23,plain,
    perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_22,refute_0_11]) ).

cnf(refute_0_24,plain,
    perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A) )],[refute_0_23,refute_0_9]) ).

cnf(refute_0_25,plain,
    ( ~ perp(A,H,B,C)
    | ~ perp(B,H,A,C)
    | coll(skolemFOFtoCNF_P_3(A,B,C),C,B) ),
    inference(canonicalize,[],[normalize_0_20]) ).

cnf(refute_0_26,plain,
    ( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G)
    | coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_G)),bind(H,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G)))]]) ).

cnf(refute_0_27,plain,
    coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_24,refute_0_26]) ).

cnf(refute_0_28,plain,
    coll(skolemFOFtoCNF_G,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A),
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A) )],[refute_0_27,refute_0_7]) ).

cnf(refute_0_29,plain,
    coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A) )],[refute_0_28,refute_0_6]) ).

cnf(refute_0_30,plain,
    ( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A)
    | coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
    inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_31,plain,
    ( ~ coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A)
    | coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_32,plain,
    ( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A)
    | perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_33,plain,
    ( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D)
    | perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D)),bind(H,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)))]]) ).

cnf(refute_0_34,plain,
    ( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A)
    | perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_35,plain,
    ( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))
    | perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)))]]) ).

cnf(refute_0_36,plain,
    ( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A)
    | perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(D,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_37,plain,
    ( ~ perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
    | perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_38,plain,
    ( ~ perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
    | perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).

cnf(refute_0_39,plain,
    circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
    inference(canonicalize,[],[normalize_0_21]) ).

cnf(refute_0_40,plain,
    ( ~ circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
    inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(O,$fot(skolemFOFtoCNF_D))]]) ).

cnf(refute_0_41,plain,
    perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
    inference(resolve,[$cnf( circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_41,refute_0_38]) ).

cnf(refute_0_43,plain,
    perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_42,refute_0_37]) ).

cnf(refute_0_44,plain,
    perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A) )],[refute_0_43,refute_0_36]) ).

cnf(refute_0_45,plain,
    perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)) )],[refute_0_44,refute_0_35]) ).

cnf(refute_0_46,plain,
    perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_45,refute_0_34]) ).

cnf(refute_0_47,plain,
    perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_46,refute_0_33]) ).

cnf(refute_0_48,plain,
    perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_47,refute_0_32]) ).

cnf(refute_0_49,plain,
    ( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D)
    | coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D)),bind(H,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D)))]]) ).

cnf(refute_0_50,plain,
    coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A),
    inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A),
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_50,refute_0_31]) ).

cnf(refute_0_52,plain,
    coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A) )],[refute_0_51,refute_0_30]) ).

cnf(refute_0_53,plain,
    ( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_396)
    | ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
    | coll(skolemFOFtoCNF_D,X_396,skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_396))]]) ).

cnf(refute_0_54,plain,
    ( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_396)
    | coll(skolemFOFtoCNF_D,X_396,skolemFOFtoCNF_A) ),
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    ( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G)
    | coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_A) ),
    inference(subst,[],[refute_0_54:[bind(X_396,$fot(skolemFOFtoCNF_G))]]) ).

cnf(refute_0_56,plain,
    coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_A),
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_29,refute_0_55]) ).

cnf(refute_0_57,plain,
    coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_G),
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_A) )],[refute_0_56,refute_0_4]) ).

cnf(refute_0_58,plain,
    coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_G),
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_57,refute_0_3]) ).

cnf(refute_0_59,plain,
    coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_G) )],[refute_0_58,refute_0_1]) ).

cnf(refute_0_60,plain,
    ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_61,plain,
    $false,
    inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D) )],[refute_0_59,refute_0_60]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GEO603+1 : TPTP v8.1.0. Released v7.5.0.
% 0.08/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.36  % Computer : n007.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sat Jun 18 04:49:43 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.37  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 14.55/14.81  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.55/14.81  
% 14.55/14.81  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.55/14.82  
%------------------------------------------------------------------------------