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LisaST---0.9.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : LisaST---0.9
% Problem  : GEO562+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 07:15:24 AM UTC 2026

% Result   : Theorem 1.32s 8.79s
% Output   : CNFRefutation 1.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  115 (  30 unt;   0 def)
%            Number of atoms       :  257 (   0 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  229 (  87   ~;  83   |;  30   &)
%                                         (   0 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-8 aty)
%            Number of functors    :    7 (   7 usr;   7 con; 0-0 aty)
%            Number of variables   :  475 (  45 sgn 158   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
    ! [X0,X1,X2] :
      ( coll(X0,X1,X2)
     => coll(X0,X2,X1) ) ).

fof(ruleD2,axiom,
    ! [X0,X1,X2] :
      ( coll(X0,X1,X2)
     => coll(X1,X0,X2) ) ).

fof(ruleD3,axiom,
    ! [X0,X1,X2,X3] :
      ( ( coll(X0,X1,X3)
        & coll(X0,X1,X2) )
     => coll(X2,X3,X0) ) ).

fof(ruleD7,axiom,
    ! [X0,X1,X2,X3] :
      ( perp(X0,X1,X2,X3)
     => perp(X0,X1,X3,X2) ) ).

fof(ruleD8,axiom,
    ! [X0,X1,X2,X3] :
      ( perp(X0,X1,X2,X3)
     => perp(X2,X3,X0,X1) ) ).

fof(ruleD9,axiom,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( perp(X2,X3,X4,X5)
        & perp(X0,X1,X2,X3) )
     => para(X0,X1,X4,X5) ) ).

fof(ruleD14,axiom,
    ! [X0,X1,X2,X3] :
      ( cyclic(X0,X1,X2,X3)
     => cyclic(X0,X1,X3,X2) ) ).

fof(ruleD15,axiom,
    ! [X0,X1,X2,X3] :
      ( cyclic(X0,X1,X2,X3)
     => cyclic(X0,X2,X1,X3) ) ).

fof(ruleD16,axiom,
    ! [X0,X1,X2,X3] :
      ( cyclic(X0,X1,X2,X3)
     => cyclic(X1,X0,X2,X3) ) ).

fof(ruleD18,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
     => eqangle(X1,X0,X2,X3,X4,X5,X6,X7) ) ).

fof(ruleD19,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
     => eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ) ).

fof(ruleD21,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
     => eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ) ).

fof(ruleD22,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
      ( ( eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
        & eqangle(X0,X1,X2,X3,X4,X5,X6,X7) )
     => eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ) ).

fof(ruleD23,axiom,
    ! [X0,X1,X2,X3] :
      ( cong(X0,X1,X2,X3)
     => cong(X0,X1,X3,X2) ) ).

fof(ruleD24,axiom,
    ! [X0,X1,X2,X3] :
      ( cong(X0,X1,X2,X3)
     => cong(X2,X3,X0,X1) ) ).

fof(ruleD39,axiom,
    ! [X0,X1,X2,X3,X4,X5] :
      ( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
     => para(X0,X1,X2,X3) ) ).

fof(ruleD40,axiom,
    ! [X0,X1,X2,X3,X4,X5] :
      ( para(X0,X1,X2,X3)
     => eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ) ).

fof(ruleD41,axiom,
    ! [X0,X1,X2,X3] :
      ( cyclic(X0,X1,X2,X3)
     => eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ) ).

fof(ruleD42b,axiom,
    ! [X0,X1,X2,X3] :
      ( ( coll(X2,X3,X1)
        & eqangle(X2,X0,X2,X1,X3,X0,X3,X1) )
     => cyclic(X0,X1,X2,X3) ) ).

fof(ruleD43,axiom,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
        & cyclic(X0,X1,X2,X5)
        & cyclic(X0,X1,X2,X4)
        & cyclic(X0,X1,X2,X3) )
     => cong(X0,X1,X3,X4) ) ).

fof(ruleD44,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( ( midp(X4,X0,X2)
        & midp(X3,X0,X1) )
     => para(X3,X4,X1,X2) ) ).

fof(ruleD52,axiom,
    ! [X0,X1,X2,X3] :
      ( ( midp(X3,X0,X2)
        & perp(X0,X1,X1,X2) )
     => cong(X0,X3,X1,X3) ) ).

fof(ruleD56,axiom,
    ! [X0,X1,X2,X3] :
      ( ( cong(X0,X3,X1,X3)
        & cong(X0,X2,X1,X2) )
     => perp(X0,X1,X2,X3) ) ).

fof(ruleD66,axiom,
    ! [X0,X1,X2] :
      ( para(X0,X1,X0,X2)
     => coll(X0,X1,X2) ) ).

fof(ruleD67,axiom,
    ! [X0,X1,X2] :
      ( ( coll(X0,X1,X2)
        & cong(X0,X1,X0,X2) )
     => midp(X0,X1,X2) ) ).

fof(ruleD68,axiom,
    ! [X0,X1,X2] :
      ( midp(X0,X1,X2)
     => cong(X0,X1,X0,X2) ) ).

fof(ruleD74,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ( perp(X4,X5,X6,X7)
        & eqangle(X0,X1,X2,X3,X4,X5,X6,X7) )
     => perp(X0,X1,X2,X3) ) ).

fof(exemplo6GDDFULL214023,conjecture,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
      ( ( coll(X8,X1,X6)
        & coll(X8,X0,X4)
        & coll(X7,X1,X2)
        & coll(X7,X0,X4)
        & circle(X3,X0,X6,X10)
        & coll(X5,X0,X4)
        & coll(X5,X1,X3)
        & circle(X3,X0,X4,X9)
        & perp(X1,X3,X0,X4)
        & circle(X3,X0,X1,X2) )
     => eqangle(X0,X8,X8,X1,X1,X2,X2,X6) ) ).

fof(negated_conjecture,negated_conjecture,
    ~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
        ( ( coll(X8,X1,X6)
          & coll(X8,X0,X4)
          & coll(X7,X1,X2)
          & coll(X7,X0,X4)
          & circle(X3,X0,X6,X10)
          & coll(X5,X0,X4)
          & coll(X5,X1,X3)
          & circle(X3,X0,X4,X9)
          & perp(X1,X3,X0,X4)
          & circle(X3,X0,X1,X2) )
       => eqangle(X0,X8,X8,X1,X1,X2,X2,X6) ),
    inference(negate_conjecture,[status(cth)],[exemplo6GDDFULL214023]) ).

cnf(c0,plain,
    ( coll(X0,X2,X1)
    | ~ coll(X0,X1,X2) ),
    inference(clausification,[status(esa)],[ruleD1]) ).

cnf(c1,plain,
    ( coll(X1,X0,X2)
    | ~ coll(X0,X1,X2) ),
    inference(clausification,[status(esa)],[ruleD2]) ).

cnf(c2,plain,
    ( coll(X2,X3,X0)
    | ~ coll(X0,X1,X3)
    | ~ coll(X0,X1,X2) ),
    inference(clausification,[status(esa)],[ruleD3]) ).

cnf(c6,plain,
    ( perp(X0,X1,X3,X2)
    | ~ perp(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD7]) ).

cnf(c7,plain,
    ( perp(X2,X3,X0,X1)
    | ~ perp(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD8]) ).

cnf(c8,plain,
    ( para(X0,X1,X4,X5)
    | ~ perp(X2,X3,X4,X5)
    | ~ perp(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD9]) ).

cnf(c13,plain,
    ( cyclic(X0,X1,X3,X2)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD14]) ).

cnf(c14,plain,
    ( cyclic(X0,X2,X1,X3)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD15]) ).

cnf(c15,plain,
    ( cyclic(X1,X0,X2,X3)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD16]) ).

cnf(c17,plain,
    ( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
    | ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(clausification,[status(esa)],[ruleD18]) ).

cnf(c18,plain,
    ( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
    | ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(clausification,[status(esa)],[ruleD19]) ).

cnf(c20,plain,
    ( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
    | ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(clausification,[status(esa)],[ruleD21]) ).

cnf(c21,plain,
    ( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
    | ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
    | ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(clausification,[status(esa)],[ruleD22]) ).

cnf(c22,plain,
    ( cong(X0,X1,X3,X2)
    | ~ cong(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD23]) ).

cnf(c23,plain,
    ( cong(X2,X3,X0,X1)
    | ~ cong(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD24]) ).

cnf(c38,plain,
    ( para(X0,X1,X4,X5)
    | ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD39]) ).

cnf(c39,plain,
    ( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
    | ~ para(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD40]) ).

cnf(c40,plain,
    ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD41]) ).

cnf(c42,plain,
    ( cyclic(X1,X2,X0,X3)
    | ~ coll(X0,X3,X2)
    | ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
    inference(clausification,[status(esa)],[ruleD42b]) ).

cnf(c43,plain,
    ( ~ eqangle(X2,X0,X2,X1,X5,X4,X5,X3)
    | ~ cyclic(X0,X1,X2,X5)
    | ~ cyclic(X0,X1,X2,X4)
    | cong(X0,X1,X4,X3)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(clausification,[status(esa)],[ruleD43]) ).

cnf(c44,plain,
    ( para(X0,X3,X2,X4)
    | ~ midp(X3,X1,X4)
    | ~ midp(X0,X1,X2) ),
    inference(clausification,[status(esa)],[ruleD44]) ).

cnf(c52,plain,
    ( cong(X0,X3,X1,X3)
    | ~ midp(X3,X0,X2)
    | ~ perp(X0,X1,X1,X2) ),
    inference(clausification,[status(esa)],[ruleD52]) ).

cnf(c56,plain,
    ( perp(X0,X2,X1,X3)
    | ~ cong(X0,X3,X2,X3)
    | ~ cong(X0,X1,X2,X1) ),
    inference(clausification,[status(esa)],[ruleD56]) ).

cnf(c66,plain,
    ( coll(X0,X1,X2)
    | ~ para(X0,X1,X0,X2) ),
    inference(clausification,[status(esa)],[ruleD66]) ).

cnf(c67,plain,
    ( midp(X0,X1,X2)
    | ~ coll(X0,X1,X2)
    | ~ cong(X0,X1,X0,X2) ),
    inference(clausification,[status(esa)],[ruleD67]) ).

cnf(c68,plain,
    ( cong(X0,X1,X0,X2)
    | ~ midp(X0,X1,X2) ),
    inference(clausification,[status(esa)],[ruleD68]) ).

cnf(c74,plain,
    ( perp(X0,X1,X2,X3)
    | ~ perp(X4,X5,X6,X7)
    | ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(clausification,[status(esa)],[ruleD74]) ).

cnf(c114,plain,
    perp(sK523,sK525,sK522,sK526),
    inference(clausification,[status(esa)],[negated_conjecture]) ).

cnf(c123,plain,
    ~ eqangle(sK522,sK530,sK530,sK523,sK523,sK524,sK524,sK528),
    inference(clausification,[status(esa)],[negated_conjecture]) ).

cnf(d0,plain,
    ( eqangle(X0,X1,X4,X5,X6,X7,X8,X9)
    | ~ eqangle(X2,X3,X4,X5,X6,X7,X8,X9)
    | ~ para(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[c39,c21]) ).

cnf(d1,plain,
    ( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
    | ~ para(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[c39,c18]) ).

cnf(d2,plain,
    ( eqangle(X4,X5,X0,X1,X6,X7,X2,X3)
    | ~ para(X4,X5,X6,X7)
    | ~ para(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[d1,d0]) ).

cnf(d3,plain,
    ( ~ para(sK530,sK523,sK524,sK528)
    | ~ para(sK522,sK530,sK523,sK524) ),
    inference(resolution,[status(thm)],[d2,c123]) ).

cnf(d4,plain,
    ( eqangle(X0,X2,X2,X1,X3,X0,X3,X1)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[c40,c17]) ).

cnf(d5,plain,
    ( eqangle(X2,X1,X0,X2,X3,X1,X3,X0)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[d4,c18]) ).

cnf(d6,plain,
    ( ~ cyclic(X1,X0,X0,X0)
    | ~ cyclic(X1,X0,X0,X2)
    | ~ cyclic(X1,X0,X0,X1)
    | cong(X1,X0,X1,X0)
    | ~ cyclic(X0,X1,X0,X2) ),
    inference(resolution,[status(thm)],[d5,c43]) ).

cnf(d7,plain,
    ( eqangle(X1,X0,X4,X5,X2,X3,X4,X5)
    | ~ para(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[c39,c17]) ).

cnf(d8,plain,
    ( eqangle(X4,X5,X1,X0,X4,X5,X2,X3)
    | ~ para(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[d7,c18]) ).

cnf(d9,plain,
    ( cyclic(X2,X0,X1,X1)
    | ~ coll(X1,X1,X0)
    | ~ para(X0,X1,X1,X0) ),
    inference(resolution,[status(thm)],[d8,c42]) ).

cnf(d10,plain,
    ( para(X2,X3,X2,X3)
    | ~ para(X0,X1,X0,X1) ),
    inference(resolution,[status(thm)],[d1,c38]) ).

cnf(d11,plain,
    perp(sK522,sK526,sK523,sK525),
    inference(resolution,[status(thm)],[c114,c7]) ).

cnf(d12,plain,
    ( ~ perp(X0,X1,sK523,sK525)
    | para(X0,X1,sK522,sK526) ),
    inference(resolution,[status(thm)],[c114,c8]) ).

cnf(d13,plain,
    para(sK522,sK526,sK522,sK526),
    inference(resolution,[status(thm)],[d12,d11]) ).

cnf(d14,plain,
    para(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[d13,d10]) ).

cnf(d15,plain,
    coll(X0,X1,X1),
    inference(resolution,[status(thm)],[d14,c66]) ).

cnf(d16,plain,
    coll(X0,X1,X0),
    inference(resolution,[status(thm)],[d15,c1]) ).

cnf(d17,plain,
    coll(X0,X0,X1),
    inference(resolution,[status(thm)],[d16,c0]) ).

cnf(d18,plain,
    ( cyclic(X2,X0,X1,X1)
    | ~ para(X0,X1,X1,X0) ),
    inference(resolution,[status(thm)],[d17,d9]) ).

cnf(d19,plain,
    ( para(X1,X0,X2,X3)
    | ~ para(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[d7,c38]) ).

cnf(d20,plain,
    para(X0,X1,X1,X0),
    inference(resolution,[status(thm)],[d14,d19]) ).

cnf(d21,plain,
    cyclic(X0,X1,X2,X2),
    inference(resolution,[status(thm)],[d20,d18]) ).

cnf(d22,plain,
    cyclic(X0,X1,X2,X1),
    inference(resolution,[status(thm)],[d21,c14]) ).

cnf(d23,plain,
    cyclic(X0,X1,X1,X2),
    inference(resolution,[status(thm)],[d22,c13]) ).

cnf(d24,plain,
    ( ~ cyclic(X1,X0,X1,X2)
    | ~ cyclic(X0,X1,X1,X1)
    | ~ cyclic(X0,X1,X1,X0)
    | cong(X0,X1,X0,X1) ),
    inference(resolution,[status(thm)],[d23,d6]) ).

cnf(d25,plain,
    cyclic(X0,X1,X2,X0),
    inference(resolution,[status(thm)],[d22,c15]) ).

cnf(d26,plain,
    cyclic(X0,X1,X0,X2),
    inference(resolution,[status(thm)],[d25,c13]) ).

cnf(d27,plain,
    ( ~ cyclic(X0,X1,X1,X0)
    | ~ cyclic(X0,X1,X1,X1)
    | cong(X0,X1,X0,X1) ),
    inference(resolution,[status(thm)],[d26,d24]) ).

cnf(d28,plain,
    ( ~ cyclic(X0,X1,X1,X0)
    | cong(X0,X1,X0,X1) ),
    inference(resolution,[status(thm)],[d21,d27]) ).

cnf(d29,plain,
    cong(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[d25,d28]) ).

cnf(d30,plain,
    ( ~ coll(X2,X2,X0)
    | coll(X0,X1,X2) ),
    inference(resolution,[status(thm)],[d17,c2]) ).

cnf(d31,plain,
    coll(X0,X1,X2),
    inference(resolution,[status(thm)],[d17,d30]) ).

cnf(d32,plain,
    ( ~ cong(X0,X1,X0,X2)
    | midp(X0,X1,X2) ),
    inference(resolution,[status(thm)],[d31,c67]) ).

cnf(d33,plain,
    midp(X0,X1,X1),
    inference(resolution,[status(thm)],[d32,d29]) ).

cnf(d34,plain,
    ( ~ midp(X0,X3,X2)
    | para(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[d33,c44]) ).

cnf(d35,plain,
    ( ~ cong(X0,X2,X0,X2)
    | perp(X0,X0,X2,X1)
    | ~ midp(X0,X1,X1) ),
    inference(resolution,[status(thm)],[c68,c56]) ).

cnf(d36,plain,
    ( ~ midp(X0,X2,X2)
    | perp(X0,X0,X1,X2) ),
    inference(resolution,[status(thm)],[d29,d35]) ).

cnf(d37,plain,
    perp(X0,X0,X1,X2),
    inference(resolution,[status(thm)],[d33,d36]) ).

cnf(d38,plain,
    perp(X0,X1,X2,X2),
    inference(resolution,[status(thm)],[d37,c7]) ).

cnf(d39,plain,
    ( eqangle(X2,X0,X3,X0,X2,X1,X3,X1)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[c40,c20]) ).

cnf(d40,plain,
    ( eqangle(X2,X0,X2,X1,X4,X5,X6,X7)
    | ~ eqangle(X3,X0,X3,X1,X4,X5,X6,X7)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[c40,c21]) ).

cnf(d41,plain,
    ( ~ cyclic(X0,X3,X2,X2)
    | eqangle(X1,X0,X1,X0,X2,X3,X2,X3)
    | ~ cyclic(X0,X0,X1,X2) ),
    inference(resolution,[status(thm)],[d40,d39]) ).

cnf(d42,plain,
    ( perp(X3,X0,X3,X0)
    | ~ perp(X2,X1,X2,X1)
    | ~ cyclic(X0,X0,X3,X2)
    | ~ cyclic(X0,X1,X2,X2) ),
    inference(resolution,[status(thm)],[d41,c74]) ).

cnf(d43,plain,
    cyclic(X0,X0,X1,X2),
    inference(resolution,[status(thm)],[d26,c14]) ).

cnf(d44,plain,
    ( ~ cyclic(X1,X3,X2,X2)
    | ~ perp(X2,X3,X2,X3)
    | perp(X0,X1,X0,X1) ),
    inference(resolution,[status(thm)],[d43,d42]) ).

cnf(d45,plain,
    ( perp(X2,X3,X2,X3)
    | ~ perp(X0,X1,X0,X1) ),
    inference(resolution,[status(thm)],[d21,d44]) ).

cnf(d46,plain,
    perp(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[d45,d38]) ).

cnf(d47,plain,
    perp(X0,X1,X1,X0),
    inference(resolution,[status(thm)],[d46,c6]) ).

cnf(d48,plain,
    ( cong(X1,X0,X2,X0)
    | ~ midp(X0,X1,X1) ),
    inference(resolution,[status(thm)],[d47,c52]) ).

cnf(d49,plain,
    cong(X0,X1,X2,X1),
    inference(resolution,[status(thm)],[d33,d48]) ).

cnf(d50,plain,
    cong(X0,X1,X1,X2),
    inference(resolution,[status(thm)],[d49,c22]) ).

cnf(d51,plain,
    cong(X0,X1,X2,X0),
    inference(resolution,[status(thm)],[d50,c23]) ).

cnf(d52,plain,
    cong(X0,X1,X0,X2),
    inference(resolution,[status(thm)],[d51,c22]) ).

cnf(d53,plain,
    midp(X0,X1,X2),
    inference(resolution,[status(thm)],[d52,d32]) ).

cnf(d54,plain,
    para(X0,X1,X2,X3),
    inference(resolution,[status(thm)],[d53,d34]) ).

cnf(d55,plain,
    ~ para(sK530,sK523,sK524,sK528),
    inference(resolution,[status(thm)],[d54,d3]) ).

cnf(d56,plain,
    $false,
    inference(resolution,[status(thm)],[d54,d55]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : GEO562+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03  % Command  : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35  % Computer : n016.cluster.edu
% 0.08/0.35  % Model    : x86_64 x86_64
% 0.08/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35  % Memory   : 8046.5625MB
% 0.08/0.35  % OS       : Linux 6.8.0-71-generic
% 0.08/0.35  % CPULimit : 300
% 0.08/0.35  % WCLimit  : 300
% 0.08/0.35  % DateTime : Fri Sep 25 13:46:32 UTC 2026
% 0.08/0.35  % CPUTime  : 
% 0.08/0.35  Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.32/8.79  % SZS status Theorem for theBenchmark.p
% 1.32/8.79  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------