↑ Up

Drodi---4.1.1.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : GEO652+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n005.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 : Thu Sep 24 12:25:28 PM UTC 2026

% Result   : Theorem 7.22s 1.48s
% Output   : CNFRefutation 7.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  112 (  16 unt;   4 def)
%            Number of atoms       :  330 (   0 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  338 ( 120   ~; 115   |;  80   &)
%                                         (   4 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   38 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   5 prp; 0-8 aty)
%            Number of functors    :   23 (  23 usr;  22 con; 0-2 aty)
%            Number of variables   :  433 ( 386   !;  47   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B,C] :
      ( coll(A,B,C)
     => coll(B,A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B,C,D] :
      ( perp(A,B,C,D)
     => perp(C,D,A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B,C,D,E,F] :
      ( ( perp(C,D,E,F)
        & perp(A,B,C,D) )
     => para(A,B,E,F) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [A,B,C,D,P,Q,U,V] :
      ( eqangle(A,B,C,D,P,Q,U,V)
     => eqangle(C,D,A,B,U,V,P,Q) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [A,B,C,D,P,Q,U,V] :
      ( eqangle(A,B,C,D,P,Q,U,V)
     => eqangle(A,B,P,Q,C,D,U,V) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f39,axiom,
    ! [A,B,C,D,P,Q] :
      ( eqangle(A,B,P,Q,C,D,P,Q)
     => para(A,B,C,D) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f40,axiom,
    ! [A,B,C,D,P,Q] :
      ( para(A,B,C,D)
     => eqangle(A,B,P,Q,C,D,P,Q) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f42,axiom,
    ! [A,B,P,Q] :
      ( ( ~ coll(P,Q,A)
        & eqangle(P,A,P,B,Q,A,Q,B) )
     => cyclic(A,B,P,Q) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f43,axiom,
    ! [A,B,P,Q] :
      ( ( coll(P,Q,B)
        & eqangle(P,A,P,B,Q,A,Q,B) )
     => cyclic(A,B,P,Q) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f44,axiom,
    ! [A,B,C,P,Q,R] :
      ( ( eqangle(C,A,C,B,R,P,R,Q)
        & cyclic(A,B,C,R)
        & cyclic(A,B,C,Q)
        & cyclic(A,B,C,P) )
     => cong(A,B,P,Q) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f46,axiom,
    ! [A,B,C,E,F] :
      ( ( coll(F,A,C)
        & para(E,F,B,C)
        & midp(E,A,B) )
     => midp(F,A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f57,axiom,
    ! [A,B,P,Q] :
      ( ( cong(A,Q,B,Q)
        & cong(A,P,B,P) )
     => perp(A,B,P,Q) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f65,axiom,
    ! [A,B,C,D,M] :
      ( ( para(A,D,B,C)
        & para(A,C,B,D)
        & midp(M,A,B) )
     => midp(M,C,D) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f67,axiom,
    ! [A,B,C] :
      ( para(A,B,A,C)
     => coll(A,B,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f68,axiom,
    ! [A,B,C] :
      ( ( coll(A,B,C)
        & cong(A,B,A,C) )
     => midp(A,B,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f69,axiom,
    ! [A,B,C] :
      ( midp(A,B,C)
     => cong(A,B,A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f87,axiom,
    ! [A,B,C,O] :
    ? [P] :
      ( circle(O,A,B,C)
     => perp(P,A,A,O) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f95,conjecture,
    ! [A,B,C,D,E,F,G,H,I,J,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
      ( ( circle(C,B,J,NWPNT21)
        & coll(B,G,J)
        & circle(C,D,I,NWPNT11)
        & coll(D,H,I)
        & circle(A,B,H,NWPNT01)
        & coll(B,F,H)
        & circle(A,D,G,NWPNT9)
        & coll(D,E,G)
        & circle(C,B,F,NWPNT8)
        & circle(C,B,E,NWPNT7)
        & circle(C,B,D,NWPNT6)
        & circle(A,B,D,NWPNT5)
        & circle(C,B,NWPNT3,NWPNT4)
        & circle(A,B,NWPNT1,NWPNT2) )
     => para(E,F,I,J) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f96,negated_conjecture,
    ~ ! [A,B,C,D,E,F,G,H,I,J,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
        ( ( circle(C,B,J,NWPNT21)
          & coll(B,G,J)
          & circle(C,D,I,NWPNT11)
          & coll(D,H,I)
          & circle(A,B,H,NWPNT01)
          & coll(B,F,H)
          & circle(A,D,G,NWPNT9)
          & coll(D,E,G)
          & circle(C,B,F,NWPNT8)
          & circle(C,B,E,NWPNT7)
          & circle(C,B,D,NWPNT6)
          & circle(A,B,D,NWPNT5)
          & circle(C,B,NWPNT3,NWPNT4)
          & circle(A,B,NWPNT1,NWPNT2) )
       => para(E,F,I,J) ),
    inference(negated_conjecture,[status(cth)],[f95]) ).

fof(f99,plain,
    ! [A,B,C] :
      ( coll(B,A,C)
      | ~ coll(A,B,C) ),
    inference(pre_NNF_transformation,[status(thm)],[f2]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( coll(X1,X0,X2)
      | ~ coll(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f99]) ).

fof(f113,plain,
    ! [A,B,C,D] :
      ( perp(C,D,A,B)
      | ~ perp(A,B,C,D) ),
    inference(pre_NNF_transformation,[status(thm)],[f8]) ).

fof(f114,plain,
    ! [X0,X1,X2,X3] :
      ( perp(X2,X3,X0,X1)
      | ~ perp(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(thm)],[f113]) ).

fof(f115,plain,
    ! [A,B,C,D,E,F] :
      ( para(A,B,E,F)
      | ~ perp(C,D,E,F)
      | ~ perp(A,B,C,D) ),
    inference(pre_NNF_transformation,[status(thm)],[f9]) ).

fof(f116,plain,
    ! [A,B,E,F] :
      ( para(A,B,E,F)
      | ! [C,D] :
          ( ~ perp(C,D,E,F)
          | ~ perp(A,B,C,D) ) ),
    inference(miniscoping,[status(thm)],[f115]) ).

fof(f117,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( para(X0,X1,X4,X5)
      | ~ perp(X2,X3,X4,X5)
      | ~ perp(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(thm)],[f116]) ).

fof(f139,plain,
    ! [A,B,C,D,P,Q,U,V] :
      ( eqangle(C,D,A,B,U,V,P,Q)
      | ~ eqangle(A,B,C,D,P,Q,U,V) ),
    inference(pre_NNF_transformation,[status(thm)],[f19]) ).

fof(f140,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
      | ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(cnf_transformation,[status(thm)],[f139]) ).

fof(f143,plain,
    ! [A,B,C,D,P,Q,U,V] :
      ( eqangle(A,B,P,Q,C,D,U,V)
      | ~ eqangle(A,B,C,D,P,Q,U,V) ),
    inference(pre_NNF_transformation,[status(thm)],[f21]) ).

fof(f144,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
      | ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(cnf_transformation,[status(thm)],[f143]) ).

fof(f184,plain,
    ! [A,B,C,D,P,Q] :
      ( para(A,B,C,D)
      | ~ eqangle(A,B,P,Q,C,D,P,Q) ),
    inference(pre_NNF_transformation,[status(thm)],[f39]) ).

fof(f185,plain,
    ! [A,B,C,D] :
      ( para(A,B,C,D)
      | ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
    inference(miniscoping,[status(thm)],[f184]) ).

fof(f186,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( para(X0,X1,X4,X5)
      | ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
    inference(cnf_transformation,[status(thm)],[f185]) ).

fof(f187,plain,
    ! [A,B,C,D,P,Q] :
      ( eqangle(A,B,P,Q,C,D,P,Q)
      | ~ para(A,B,C,D) ),
    inference(pre_NNF_transformation,[status(thm)],[f40]) ).

fof(f188,plain,
    ! [A,B,C,D] :
      ( ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q)
      | ~ para(A,B,C,D) ),
    inference(miniscoping,[status(thm)],[f187]) ).

fof(f189,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
      | ~ para(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(thm)],[f188]) ).

fof(f192,plain,
    ! [A,B,P,Q] :
      ( cyclic(A,B,P,Q)
      | coll(P,Q,A)
      | ~ eqangle(P,A,P,B,Q,A,Q,B) ),
    inference(pre_NNF_transformation,[status(thm)],[f42]) ).

fof(f193,plain,
    ! [X0,X1,X2,X3] :
      ( cyclic(X1,X2,X0,X3)
      | coll(X0,X3,X1)
      | ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
    inference(cnf_transformation,[status(thm)],[f192]) ).

fof(f194,plain,
    ! [A,B,P,Q] :
      ( cyclic(A,B,P,Q)
      | ~ coll(P,Q,B)
      | ~ eqangle(P,A,P,B,Q,A,Q,B) ),
    inference(pre_NNF_transformation,[status(thm)],[f43]) ).

fof(f195,plain,
    ! [X0,X1,X2,X3] :
      ( cyclic(X1,X2,X0,X3)
      | ~ coll(X0,X3,X2)
      | ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
    inference(cnf_transformation,[status(thm)],[f194]) ).

fof(f196,plain,
    ! [A,B,C,P,Q,R] :
      ( cong(A,B,P,Q)
      | ~ eqangle(C,A,C,B,R,P,R,Q)
      | ~ cyclic(A,B,C,R)
      | ~ cyclic(A,B,C,Q)
      | ~ cyclic(A,B,C,P) ),
    inference(pre_NNF_transformation,[status(thm)],[f44]) ).

fof(f197,plain,
    ! [A,B,P,Q] :
      ( cong(A,B,P,Q)
      | ! [C,R] :
          ( ~ eqangle(C,A,C,B,R,P,R,Q)
          | ~ cyclic(A,B,C,R)
          | ~ cyclic(A,B,C,Q)
          | ~ cyclic(A,B,C,P) ) ),
    inference(miniscoping,[status(thm)],[f196]) ).

fof(f198,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( cong(X0,X1,X3,X4)
      | ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
      | ~ cyclic(X0,X1,X2,X5)
      | ~ cyclic(X0,X1,X2,X4)
      | ~ cyclic(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(thm)],[f197]) ).

fof(f202,plain,
    ! [A,B,C,E,F] :
      ( midp(F,A,C)
      | ~ coll(F,A,C)
      | ~ para(E,F,B,C)
      | ~ midp(E,A,B) ),
    inference(pre_NNF_transformation,[status(thm)],[f46]) ).

fof(f203,plain,
    ! [A,C,F] :
      ( midp(F,A,C)
      | ~ coll(F,A,C)
      | ! [B,E] :
          ( ~ para(E,F,B,C)
          | ~ midp(E,A,B) ) ),
    inference(miniscoping,[status(thm)],[f202]) ).

fof(f204,plain,
    ! [X0,X1,X2,X3,X4] :
      ( midp(X3,X1,X4)
      | ~ coll(X3,X1,X4)
      | ~ para(X0,X3,X2,X4)
      | ~ midp(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f203]) ).

fof(f231,plain,
    ! [A,B,P,Q] :
      ( perp(A,B,P,Q)
      | ~ cong(A,Q,B,Q)
      | ~ cong(A,P,B,P) ),
    inference(pre_NNF_transformation,[status(thm)],[f57]) ).

fof(f232,plain,
    ! [X0,X1,X2,X3] :
      ( perp(X0,X2,X1,X3)
      | ~ cong(X0,X3,X2,X3)
      | ~ cong(X0,X1,X2,X1) ),
    inference(cnf_transformation,[status(thm)],[f231]) ).

fof(f250,plain,
    ! [A,B,C,D,M] :
      ( midp(M,C,D)
      | ~ para(A,D,B,C)
      | ~ para(A,C,B,D)
      | ~ midp(M,A,B) ),
    inference(pre_NNF_transformation,[status(thm)],[f65]) ).

fof(f251,plain,
    ! [C,D,M] :
      ( midp(M,C,D)
      | ! [A,B] :
          ( ~ para(A,D,B,C)
          | ~ para(A,C,B,D)
          | ~ midp(M,A,B) ) ),
    inference(miniscoping,[status(thm)],[f250]) ).

fof(f252,plain,
    ! [X0,X1,X2,X3,X4] :
      ( midp(X0,X3,X4)
      | ~ para(X1,X4,X2,X3)
      | ~ para(X1,X3,X2,X4)
      | ~ midp(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f251]) ).

fof(f255,plain,
    ! [A,B,C] :
      ( coll(A,B,C)
      | ~ para(A,B,A,C) ),
    inference(pre_NNF_transformation,[status(thm)],[f67]) ).

fof(f256,plain,
    ! [X0,X1,X2] :
      ( coll(X0,X1,X2)
      | ~ para(X0,X1,X0,X2) ),
    inference(cnf_transformation,[status(thm)],[f255]) ).

fof(f257,plain,
    ! [A,B,C] :
      ( midp(A,B,C)
      | ~ coll(A,B,C)
      | ~ cong(A,B,A,C) ),
    inference(pre_NNF_transformation,[status(thm)],[f68]) ).

fof(f258,plain,
    ! [X0,X1,X2] :
      ( midp(X0,X1,X2)
      | ~ coll(X0,X1,X2)
      | ~ cong(X0,X1,X0,X2) ),
    inference(cnf_transformation,[status(thm)],[f257]) ).

fof(f259,plain,
    ! [A,B,C] :
      ( cong(A,B,A,C)
      | ~ midp(A,B,C) ),
    inference(pre_NNF_transformation,[status(thm)],[f69]) ).

fof(f260,plain,
    ! [X0,X1,X2] :
      ( cong(X0,X1,X0,X2)
      | ~ midp(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f259]) ).

fof(f331,plain,
    ! [A,B,C,O] :
    ? [P] :
      ( perp(P,A,A,O)
      | ~ circle(O,A,B,C) ),
    inference(pre_NNF_transformation,[status(thm)],[f87]) ).

fof(f332,plain,
    ! [A,O] :
      ( ? [P] : perp(P,A,A,O)
      | ! [B,C] : ~ circle(O,A,B,C) ),
    inference(miniscoping,[status(thm)],[f331]) ).

fof(f333,plain,
    ! [A,O] :
      ( perp(sK11_skl(O,A),A,A,O)
      | ! [B,C] : ~ circle(O,A,B,C) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(P,sK11_skl(O,A))],[f332]) ).

fof(f334,plain,
    ! [X0,X1,X2,X3] :
      ( perp(sK11_skl(X0,X1),X1,X1,X0)
      | ~ circle(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(thm)],[f333]) ).

fof(f369,plain,
    ? [A,B,C,D,E,F,G,H,I,J,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
      ( ~ para(E,F,I,J)
      & circle(C,B,J,NWPNT21)
      & coll(B,G,J)
      & circle(C,D,I,NWPNT11)
      & coll(D,H,I)
      & circle(A,B,H,NWPNT01)
      & coll(B,F,H)
      & circle(A,D,G,NWPNT9)
      & coll(D,E,G)
      & circle(C,B,F,NWPNT8)
      & circle(C,B,E,NWPNT7)
      & circle(C,B,D,NWPNT6)
      & circle(A,B,D,NWPNT5)
      & circle(C,B,NWPNT3,NWPNT4)
      & circle(A,B,NWPNT1,NWPNT2) ),
    inference(pre_NNF_transformation,[status(thm)],[f96]) ).

fof(f370,plain,
    ? [E,F,I,J] :
      ( ~ para(E,F,I,J)
      & ? [B,C] :
          ( ? [NWPNT21] : circle(C,B,J,NWPNT21)
          & ? [G] :
              ( coll(B,G,J)
              & ? [D] :
                  ( ? [NWPNT11] : circle(C,D,I,NWPNT11)
                  & ? [H] :
                      ( coll(D,H,I)
                      & ? [A] :
                          ( ? [NWPNT01] : circle(A,B,H,NWPNT01)
                          & coll(B,F,H)
                          & ? [NWPNT9] : circle(A,D,G,NWPNT9)
                          & coll(D,E,G)
                          & ? [NWPNT8] : circle(C,B,F,NWPNT8)
                          & ? [NWPNT7] : circle(C,B,E,NWPNT7)
                          & ? [NWPNT6] : circle(C,B,D,NWPNT6)
                          & ? [NWPNT5] : circle(A,B,D,NWPNT5)
                          & ? [NWPNT3,NWPNT4] : circle(C,B,NWPNT3,NWPNT4)
                          & ? [NWPNT1,NWPNT2] : circle(A,B,NWPNT1,NWPNT2) ) ) ) ) ) ),
    inference(miniscoping,[status(thm)],[f369]) ).

fof(f371,plain,
    ( ~ para(sK20_skl,sK21_skl,sK22_skl,sK23_skl)
    & circle(sK25_skl,sK24_skl,sK23_skl,sK41_skl)
    & coll(sK24_skl,sK26_skl,sK23_skl)
    & circle(sK25_skl,sK27_skl,sK22_skl,sK40_skl)
    & coll(sK27_skl,sK28_skl,sK22_skl)
    & circle(sK29_skl,sK24_skl,sK28_skl,sK39_skl)
    & coll(sK24_skl,sK21_skl,sK28_skl)
    & circle(sK29_skl,sK27_skl,sK26_skl,sK38_skl)
    & coll(sK27_skl,sK20_skl,sK26_skl)
    & circle(sK25_skl,sK24_skl,sK21_skl,sK37_skl)
    & circle(sK25_skl,sK24_skl,sK20_skl,sK36_skl)
    & circle(sK25_skl,sK24_skl,sK27_skl,sK35_skl)
    & circle(sK29_skl,sK24_skl,sK27_skl,sK34_skl)
    & circle(sK25_skl,sK24_skl,sK32_skl,sK33_skl)
    & circle(sK29_skl,sK24_skl,sK30_skl,sK31_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl,sK29_skl,sK30_skl,sK31_skl,sK32_skl,sK33_skl,sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl,sK39_skl,sK40_skl,sK41_skl]),skolemize(E,sK20_skl),skolemize(F,sK21_skl),skolemize(I,sK22_skl),skolemize(J,sK23_skl),skolemize(B,sK24_skl),skolemize(C,sK25_skl),skolemize(G,sK26_skl),skolemize(D,sK27_skl),skolemize(H,sK28_skl),skolemize(A,sK29_skl),skolemize(NWPNT1,sK30_skl),skolemize(NWPNT2,sK31_skl),skolemize(NWPNT3,sK32_skl),skolemize(NWPNT4,sK33_skl),skolemize(NWPNT5,sK34_skl),skolemize(NWPNT6,sK35_skl),skolemize(NWPNT7,sK36_skl),skolemize(NWPNT8,sK37_skl),skolemize(NWPNT9,sK38_skl),skolemize(NWPNT01,sK39_skl),skolemize(NWPNT11,sK40_skl),skolemize(NWPNT21,sK41_skl)],[f370]) ).

fof(f377,plain,
    circle(sK25_skl,sK24_skl,sK21_skl,sK37_skl),
    inference(cnf_transformation,[status(thm)],[f371]) ).

fof(f386,plain,
    ~ para(sK20_skl,sK21_skl,sK22_skl,sK23_skl),
    inference(cnf_transformation,[status(thm)],[f371]) ).

fof(f451,plain,
    perp(sK11_skl(sK25_skl,sK24_skl),sK24_skl,sK24_skl,sK25_skl),
    inference(resolution,[status(thm)],[f334,f377]) ).

fof(f528,plain,
    ! [X0,X1] :
      ( para(X0,X1,sK24_skl,sK25_skl)
      | ~ perp(X0,X1,sK11_skl(sK25_skl,sK24_skl),sK24_skl) ),
    inference(resolution,[status(thm)],[f451,f117]) ).

fof(f529,plain,
    perp(sK24_skl,sK25_skl,sK11_skl(sK25_skl,sK24_skl),sK24_skl),
    inference(resolution,[status(thm)],[f451,f114]) ).

fof(f1475,plain,
    para(sK24_skl,sK25_skl,sK24_skl,sK25_skl),
    inference(resolution,[status(thm)],[f529,f528]) ).

fof(f2264,plain,
    ! [X0,X1] : eqangle(sK24_skl,sK25_skl,X0,X1,sK24_skl,sK25_skl,X0,X1),
    inference(resolution,[status(thm)],[f1475,f189]) ).

fof(f2302,plain,
    ! [X0,X1] : eqangle(sK24_skl,sK25_skl,sK24_skl,sK25_skl,X0,X1,X0,X1),
    inference(resolution,[status(thm)],[f2264,f144]) ).

fof(f2306,plain,
    ! [X0,X1] : eqangle(X0,X1,sK24_skl,sK25_skl,X0,X1,sK24_skl,sK25_skl),
    inference(resolution,[status(thm)],[f2264,f140]) ).

fof(f2439,plain,
    ! [X0,X1] :
      ( cong(sK25_skl,sK25_skl,X0,X0)
      | ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X1)
      | ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
      | ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ),
    inference(resolution,[status(thm)],[f2302,f198]) ).

fof(f2440,plain,
    ! [X0] :
      ( cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
      | coll(sK24_skl,X0,sK25_skl) ),
    inference(resolution,[status(thm)],[f2302,f193]) ).

fof(f2441,plain,
    ! [X0] :
      ( cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
      | ~ coll(sK24_skl,X0,sK25_skl) ),
    inference(resolution,[status(thm)],[f2302,f195]) ).

fof(f2469,definition,
    ! [X0] :
      ( sQ333_spl
    <=> ( cong(sK25_skl,sK25_skl,X0,X0)
        | ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
        | ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ) ),
    introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).

fof(f2470,plain,
    ! [X0] :
      ( ~ sQ333_spl
      | cong(sK25_skl,sK25_skl,X0,X0)
      | ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
      | ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ),
    inference(component_clause,[status(thm)],[f2469]) ).

fof(f2472,definition,
    ! [X1] :
      ( sQ334_spl
    <=> ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X1) ),
    introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).

fof(f2473,plain,
    ! [X0] :
      ( ~ sQ334_spl
      | ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ),
    inference(component_clause,[status(thm)],[f2472]) ).

fof(f2475,plain,
    ( sQ334_spl
    | sQ333_spl ),
    inference(split_clause,[status(thm)],[f2439,f2469,f2472]) ).

fof(f2476,plain,
    ! [X0] : cyclic(sK25_skl,sK25_skl,sK24_skl,X0),
    inference(forward_subsumption_resolution,[status(thm)],[f2441,f2440]) ).

fof(f2485,definition,
    ( sQ337_spl
  <=> coll(sK25_skl,sK25_skl,sK25_skl) ),
    introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).

fof(f2487,plain,
    ( sQ337_spl
    | ~ coll(sK25_skl,sK25_skl,sK25_skl) ),
    inference(component_clause,[status(thm)],[f2485]) ).

fof(f2488,definition,
    ( sQ338_spl
  <=> midp(sK25_skl,sK25_skl,sK25_skl) ),
    introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).

fof(f2489,plain,
    ( ~ sQ338_spl
    | midp(sK25_skl,sK25_skl,sK25_skl) ),
    inference(component_clause,[status(thm)],[f2488]) ).

fof(f2497,plain,
    ! [X0] :
      ( ~ sQ333_spl
      | cong(sK25_skl,sK25_skl,X0,X0)
      | ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f2470]) ).

fof(f2498,plain,
    ! [X0] :
      ( ~ sQ333_spl
      | cong(sK25_skl,sK25_skl,X0,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2497,f2476]) ).

fof(f2519,plain,
    ( ~ sQ333_spl
    | midp(sK25_skl,sK25_skl,sK25_skl)
    | ~ coll(sK25_skl,sK25_skl,sK25_skl) ),
    inference(resolution,[status(thm)],[f2498,f258]) ).

fof(f2541,plain,
    ( ~ sQ333_spl
    | sQ338_spl
    | ~ sQ337_spl ),
    inference(split_clause,[status(thm)],[f2519,f2485,f2488,f2469]) ).

fof(f2736,plain,
    ! [X0,X1] : para(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[f2306,f186]) ).

fof(f2780,plain,
    ! [X0,X1,X2] :
      ( midp(X0,X2,X2)
      | ~ para(X1,X2,X1,X2)
      | ~ midp(X0,X1,X1) ),
    inference(resolution,[status(thm)],[f2736,f252]) ).

fof(f2781,plain,
    ! [X0,X1,X2] :
      ( midp(X2,X1,X2)
      | ~ coll(X2,X1,X2)
      | ~ midp(X0,X1,X0) ),
    inference(resolution,[status(thm)],[f2736,f204]) ).

fof(f2784,plain,
    ! [X0,X1] : coll(X0,X1,X1),
    inference(resolution,[status(thm)],[f2736,f256]) ).

fof(f2788,plain,
    ! [X0,X1,X2] :
      ( midp(X0,X2,X2)
      | ~ midp(X0,X1,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2780,f2736]) ).

fof(f2790,plain,
    ( sQ337_spl
    | $false ),
    inference(backward_subsumption_resolution,[status(thm)],[f2487,f2784]) ).

fof(f2794,plain,
    sQ337_spl,
    inference(contradiction_clause,[status(thm)],[f2790]) ).

fof(f2833,plain,
    ! [X0,X1] : coll(X0,X1,X0),
    inference(resolution,[status(thm)],[f2784,f100]) ).

fof(f2847,plain,
    ! [X0,X1,X2] :
      ( midp(X2,X1,X2)
      | ~ midp(X0,X1,X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f2781,f2833]) ).

fof(f3017,plain,
    ( ~ sQ334_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f2473,f2476]) ).

fof(f3018,plain,
    ~ sQ334_spl,
    inference(contradiction_clause,[status(thm)],[f3017]) ).

fof(f3328,plain,
    ! [X0] :
      ( ~ sQ338_spl
      | midp(X0,sK25_skl,X0) ),
    inference(resolution,[status(thm)],[f2847,f2489]) ).

fof(f3879,plain,
    ! [X0] :
      ( ~ sQ338_spl
      | midp(sK25_skl,X0,X0) ),
    inference(resolution,[status(thm)],[f2788,f3328]) ).

fof(f3910,plain,
    ! [X0] :
      ( ~ sQ338_spl
      | cong(sK25_skl,X0,sK25_skl,X0) ),
    inference(resolution,[status(thm)],[f3879,f260]) ).

fof(f3931,plain,
    ! [X0,X1] :
      ( ~ sQ338_spl
      | perp(sK25_skl,sK25_skl,X0,X1)
      | ~ cong(sK25_skl,X0,sK25_skl,X0) ),
    inference(resolution,[status(thm)],[f3910,f232]) ).

fof(f3942,plain,
    ! [X0,X1] :
      ( ~ sQ338_spl
      | perp(sK25_skl,sK25_skl,X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f3931,f3910]) ).

fof(f4022,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sQ338_spl
      | para(X0,X1,X2,X3)
      | ~ perp(X0,X1,sK25_skl,sK25_skl) ),
    inference(resolution,[status(thm)],[f3942,f117]) ).

fof(f4023,plain,
    ! [X0,X1] :
      ( ~ sQ338_spl
      | perp(X0,X1,sK25_skl,sK25_skl) ),
    inference(resolution,[status(thm)],[f3942,f114]) ).

fof(f4040,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sQ338_spl
      | para(X0,X1,X2,X3) ),
    inference(backward_subsumption_resolution,[status(thm)],[f4022,f4023]) ).

fof(f4044,plain,
    ( ~ sQ338_spl
    | $false ),
    inference(backward_subsumption_resolution,[status(thm)],[f386,f4040]) ).

fof(f4063,plain,
    ~ sQ338_spl,
    inference(contradiction_clause,[status(thm)],[f4044]) ).

fof(f4064,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f2475,f2541,f2794,f3018,f4063]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : GEO652+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03  % Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35  % Computer : n005.cluster.edu
% 0.07/0.35  % Model    : x86_64 x86_64
% 0.07/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35  % Memory   : 8046.5625MB
% 0.07/0.35  % OS       : Linux 6.8.0-71-generic
% 0.07/0.35  % CPULimit : 300
% 0.07/0.35  % WCLimit  : 300
% 0.07/0.35  % DateTime : Sun Sep 20 18:12:18 UTC 2026
% 0.07/0.36  % CPUTime  : 
% 0.13/0.37  % Drodi V4.1.1
% 7.22/1.48  % Refutation found
% 7.22/1.48  % SZS status Theorem for theBenchmark: Theorem is valid
% 7.22/1.48  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.22/1.50  % Elapsed time: 1.130615 seconds
% 7.22/1.50  % CPU time: 8.650425 seconds
% 7.22/1.50  % Total memory used: 154.557 MB
% 7.22/1.50  % Net memory used: 145.748 MB
%------------------------------------------------------------------------------