TSTP Solution File: GEO641+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO641+1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n020.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  : 300s
% DateTime : Tue Apr 30 20:18:29 EDT 2024

% Result   : Theorem 3.18s 0.86s
% Output   : CNFRefutation 3.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   21
% Syntax   : Number of formulae    :  110 (  29 unt;   0 def)
%            Number of atoms       :  266 (   0 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  247 (  91   ~;  86   |;  48   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-8 aty)
%            Number of functors    :    8 (   8 usr;   8 con; 0-0 aty)
%            Number of variables   :  456 ( 440   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B,C] :
      ( coll(A,B,C)
     => coll(A,C,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f3,axiom,
    ! [A,B,C,D] :
      ( ( coll(A,B,C)
        & coll(A,B,D) )
     => coll(C,D,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A,B,C,D] :
      ( para(A,B,C,D)
     => para(A,B,D,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B,C,D] :
      ( perp(A,B,C,D)
     => perp(A,B,D,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(A,B,C,D)
        & perp(C,D,E,F) )
     => para(A,B,E,F) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [A,B,C,D,P,Q,U,V] :
      ( eqangle(A,B,C,D,P,Q,U,V)
     => eqangle(B,A,C,D,P,Q,U,V) ),
    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(f20,axiom,
    ! [A,B,C,D,P,Q,U,V] :
      ( eqangle(A,B,C,D,P,Q,U,V)
     => eqangle(P,Q,U,V,A,B,C,D) ),
    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(f43,axiom,
    ! [A,B,P,Q] :
      ( ( eqangle(P,A,P,B,Q,A,Q,B)
        & coll(P,Q,B) )
     => cyclic(A,B,P,Q) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

fof(f65,axiom,
    ! [A,B,C,D,M] :
      ( ( midp(M,A,B)
        & para(A,C,B,D)
        & para(A,D,B,C) )
     => 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] :
      ( ( cong(A,B,A,C)
        & coll(A,B,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(f95,conjecture,
    ! [A,B,C,O,D,U,V,NWPNT1] :
      ( ( circle(O,A,B,C)
        & circle(O,A,D,NWPNT1)
        & perp(A,B,D,U)
        & perp(A,D,B,U)
        & perp(B,D,A,U)
        & perp(A,C,D,V)
        & perp(A,D,C,V)
        & perp(C,D,A,V) )
     => para(U,V,B,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f96,negated_conjecture,
    ~ ! [A,B,C,O,D,U,V,NWPNT1] :
        ( ( circle(O,A,B,C)
          & circle(O,A,D,NWPNT1)
          & perp(A,B,D,U)
          & perp(A,D,B,U)
          & perp(B,D,A,U)
          & perp(A,C,D,V)
          & perp(A,D,C,V)
          & perp(C,D,A,V) )
       => para(U,V,B,C) ),
    inference(negated_conjecture,[status(cth)],[f95]) ).

fof(f97,plain,
    ! [A,B,C] :
      ( ~ coll(A,B,C)
      | coll(A,C,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ~ coll(X0,X1,X2)
      | coll(X0,X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f97]) ).

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

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

fof(f101,plain,
    ! [A,B,C,D] :
      ( ~ coll(A,B,C)
      | ~ coll(A,B,D)
      | coll(C,D,A) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f102,plain,
    ! [A,C,D] :
      ( ! [B] :
          ( ~ coll(A,B,C)
          | ~ coll(A,B,D) )
      | coll(C,D,A) ),
    inference(miniscoping,[status(esa)],[f101]) ).

fof(f103,plain,
    ! [X0,X1,X2,X3] :
      ( ~ coll(X0,X1,X2)
      | ~ coll(X0,X1,X3)
      | coll(X2,X3,X0) ),
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f104,plain,
    ! [A,B,C,D] :
      ( ~ para(A,B,C,D)
      | para(A,B,D,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f105,plain,
    ! [X0,X1,X2,X3] :
      ( ~ para(X0,X1,X2,X3)
      | para(X0,X1,X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f111,plain,
    ! [A,B,C,D] :
      ( ~ perp(A,B,C,D)
      | perp(A,B,D,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f112,plain,
    ! [X0,X1,X2,X3] :
      ( ~ perp(X0,X1,X2,X3)
      | perp(X0,X1,X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f111]) ).

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

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

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

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

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

fof(f137,plain,
    ! [A,B,C,D,P,Q,U,V] :
      ( ~ eqangle(A,B,C,D,P,Q,U,V)
      | eqangle(B,A,C,D,P,Q,U,V) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f138,plain,
    ! [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) ),
    inference(cnf_transformation,[status(esa)],[f137]) ).

fof(f139,plain,
    ! [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) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f140,plain,
    ! [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) ),
    inference(cnf_transformation,[status(esa)],[f139]) ).

fof(f141,plain,
    ! [A,B,C,D,P,Q,U,V] :
      ( ~ eqangle(A,B,C,D,P,Q,U,V)
      | eqangle(P,Q,U,V,A,B,C,D) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f142,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
      | eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f141]) ).

fof(f143,plain,
    ! [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) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f144,plain,
    ! [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) ),
    inference(cnf_transformation,[status(esa)],[f143]) ).

fof(f184,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(esa)],[f39]) ).

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

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

fof(f187,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(esa)],[f40]) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(f369,plain,
    ? [A,B,C,O,D,U,V,NWPNT1] :
      ( circle(O,A,B,C)
      & circle(O,A,D,NWPNT1)
      & perp(A,B,D,U)
      & perp(A,D,B,U)
      & perp(B,D,A,U)
      & perp(A,C,D,V)
      & perp(A,D,C,V)
      & perp(C,D,A,V)
      & ~ para(U,V,B,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f96]) ).

fof(f370,plain,
    ? [B,C,U,V] :
      ( ? [A,D] :
          ( ? [O] :
              ( circle(O,A,B,C)
              & ? [NWPNT1] : circle(O,A,D,NWPNT1) )
          & perp(A,B,D,U)
          & perp(A,D,B,U)
          & perp(B,D,A,U)
          & perp(A,C,D,V)
          & perp(A,D,C,V)
          & perp(C,D,A,V) )
      & ~ para(U,V,B,C) ),
    inference(miniscoping,[status(esa)],[f369]) ).

fof(f371,plain,
    ( circle(sk0_26,sk0_24,sk0_20,sk0_21)
    & circle(sk0_26,sk0_24,sk0_25,sk0_27)
    & perp(sk0_24,sk0_20,sk0_25,sk0_22)
    & perp(sk0_24,sk0_25,sk0_20,sk0_22)
    & perp(sk0_20,sk0_25,sk0_24,sk0_22)
    & perp(sk0_24,sk0_21,sk0_25,sk0_23)
    & perp(sk0_24,sk0_25,sk0_21,sk0_23)
    & perp(sk0_21,sk0_25,sk0_24,sk0_23)
    & ~ para(sk0_22,sk0_23,sk0_20,sk0_21) ),
    inference(skolemization,[status(esa)],[f370]) ).

fof(f375,plain,
    perp(sk0_24,sk0_25,sk0_20,sk0_22),
    inference(cnf_transformation,[status(esa)],[f371]) ).

fof(f380,plain,
    ~ para(sk0_22,sk0_23,sk0_20,sk0_21),
    inference(cnf_transformation,[status(esa)],[f371]) ).

fof(f402,plain,
    perp(sk0_20,sk0_22,sk0_24,sk0_25),
    inference(resolution,[status(thm)],[f114,f375]) ).

fof(f424,plain,
    perp(sk0_20,sk0_22,sk0_25,sk0_24),
    inference(resolution,[status(thm)],[f402,f112]) ).

fof(f447,plain,
    perp(sk0_25,sk0_24,sk0_20,sk0_22),
    inference(resolution,[status(thm)],[f424,f114]) ).

fof(f477,plain,
    ! [X0,X1] :
      ( ~ perp(X0,X1,sk0_25,sk0_24)
      | para(X0,X1,sk0_20,sk0_22) ),
    inference(resolution,[status(thm)],[f117,f447]) ).

fof(f572,plain,
    para(sk0_20,sk0_22,sk0_20,sk0_22),
    inference(resolution,[status(thm)],[f477,f424]) ).

fof(f585,plain,
    ! [X0,X1] : eqangle(sk0_20,sk0_22,X0,X1,sk0_20,sk0_22,X0,X1),
    inference(resolution,[status(thm)],[f572,f189]) ).

fof(f891,plain,
    ! [X0,X1] : eqangle(X0,X1,sk0_20,sk0_22,X0,X1,sk0_20,sk0_22),
    inference(resolution,[status(thm)],[f140,f585]) ).

fof(f2273,plain,
    ! [X0,X1] : para(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[f891,f186]) ).

fof(f2280,plain,
    ! [X0,X1,X2] :
      ( ~ midp(X0,X1,X1)
      | ~ para(X1,X2,X1,X2)
      | midp(X0,X2,X2) ),
    inference(resolution,[status(thm)],[f2273,f252]) ).

fof(f2281,plain,
    ! [X0,X1,X2] :
      ( ~ midp(X0,X1,X1)
      | midp(X0,X2,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2280,f2273]) ).

fof(f2283,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
    inference(resolution,[status(thm)],[f2273,f189]) ).

fof(f2285,plain,
    ! [X0,X1] : para(X0,X1,X1,X0),
    inference(resolution,[status(thm)],[f2273,f105]) ).

fof(f2286,plain,
    ! [X0,X1] : coll(X0,X1,X1),
    inference(resolution,[status(thm)],[f2273,f256]) ).

fof(f2312,plain,
    ! [X0,X1] : coll(X0,X1,X0),
    inference(resolution,[status(thm)],[f2286,f100]) ).

fof(f2341,plain,
    ! [X0,X1] : coll(X0,X0,X1),
    inference(resolution,[status(thm)],[f2312,f98]) ).

fof(f2372,plain,
    ! [X0,X1,X2] :
      ( ~ coll(X0,X0,X1)
      | coll(X1,X2,X0) ),
    inference(resolution,[status(thm)],[f2341,f103]) ).

fof(f2373,plain,
    ! [X0,X1,X2] : coll(X0,X1,X2),
    inference(forward_subsumption_resolution,[status(thm)],[f2372,f2341]) ).

fof(f2414,plain,
    ! [X0,X1,X2] :
      ( ~ cong(X0,X1,X0,X2)
      | midp(X0,X1,X2) ),
    inference(backward_subsumption_resolution,[status(thm)],[f258,f2373]) ).

fof(f2417,plain,
    ! [X0,X1,X2,X3] :
      ( ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
      | cyclic(X1,X2,X0,X3) ),
    inference(backward_subsumption_resolution,[status(thm)],[f195,f2373]) ).

fof(f2424,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X1,X0,X2,X3),
    inference(resolution,[status(thm)],[f2285,f189]) ).

fof(f2429,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X1,X2,X3,X2,X3),
    inference(resolution,[status(thm)],[f2283,f144]) ).

fof(f2446,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X1,X0,X2,X3,X2,X3),
    inference(resolution,[status(thm)],[f2424,f144]) ).

fof(f2503,plain,
    ! [X0,X1,X2] : cyclic(X0,X0,X1,X2),
    inference(resolution,[status(thm)],[f2417,f2429]) ).

fof(f2526,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X1,X2,X3,X3,X2),
    inference(resolution,[status(thm)],[f2446,f142]) ).

fof(f2616,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X1,X0,X2,X3,X3,X2),
    inference(resolution,[status(thm)],[f2526,f138]) ).

fof(f2963,plain,
    ! [X0,X1] :
      ( ~ cyclic(X0,X0,X0,X1)
      | ~ cyclic(X0,X0,X0,X1)
      | ~ cyclic(X0,X0,X0,X1)
      | cong(X0,X0,X1,X1) ),
    inference(resolution,[status(thm)],[f198,f2616]) ).

fof(f2964,plain,
    ! [X0,X1] :
      ( ~ cyclic(X0,X0,X0,X1)
      | cong(X0,X0,X1,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f2963]) ).

fof(f2965,plain,
    ! [X0,X1] : cong(X0,X0,X1,X1),
    inference(forward_subsumption_resolution,[status(thm)],[f2964,f2503]) ).

fof(f3502,plain,
    ! [X0] : midp(X0,X0,X0),
    inference(resolution,[status(thm)],[f2965,f2414]) ).

fof(f3514,plain,
    ! [X0,X1] : midp(X0,X1,X1),
    inference(resolution,[status(thm)],[f3502,f2281]) ).

fof(f3543,plain,
    ! [X0,X1] : cong(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[f3514,f260]) ).

fof(f3575,plain,
    ! [X0,X1,X2] :
      ( ~ cong(X0,X1,X0,X1)
      | perp(X0,X0,X1,X2) ),
    inference(resolution,[status(thm)],[f3543,f232]) ).

fof(f3576,plain,
    ! [X0,X1,X2] : perp(X0,X0,X1,X2),
    inference(forward_subsumption_resolution,[status(thm)],[f3575,f3543]) ).

fof(f3629,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ perp(X0,X1,X2,X2)
      | para(X0,X1,X3,X4) ),
    inference(resolution,[status(thm)],[f3576,f117]) ).

fof(f3630,plain,
    ! [X0,X1,X2] : perp(X0,X1,X2,X2),
    inference(resolution,[status(thm)],[f3576,f114]) ).

fof(f3632,plain,
    ! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
    inference(backward_subsumption_resolution,[status(thm)],[f3629,f3630]) ).

fof(f3633,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f380,f3632]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : GEO641+1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Apr 30 01:29:32 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 3.18/0.86  % Refutation found
% 3.18/0.86  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.18/0.86  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.98/0.88  % Elapsed time: 0.525789 seconds
% 3.98/0.88  % CPU time: 4.040255 seconds
% 3.98/0.88  % Total memory used: 102.332 MB
% 3.98/0.88  % Net memory used: 95.905 MB
%------------------------------------------------------------------------------