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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : GEO641+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 : n026.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 12:25:26 PM UTC 2026

% Result   : Theorem 0.09s 0.49s
% Output   : CNFRefutation 0.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   92 (  23 unt;   0 def)
%            Number of atoms       :  229 (   0 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  215 (  78   ~;  73   |;  46   &)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-8 aty)
%            Number of functors    :    8 (   8 usr;   8 con; 0-0 aty)
%            Number of variables   :  388 ( 372   !;  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,D)
        & coll(A,B,C) )
     => coll(C,D,A) ),
    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(f17,axiom,
    ! [A,B,C,D,E] :
      ( ( cyclic(A,B,C,E)
        & cyclic(A,B,C,D) )
     => cyclic(B,C,D,E) ),
    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(f23,axiom,
    ! [A,B,C,D] :
      ( cong(A,B,C,D)
     => cong(A,B,D,C) ),
    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(f41,axiom,
    ! [A,B,P,Q] :
      ( cyclic(A,B,P,Q)
     => eqangle(P,A,P,B,Q,A,Q,B) ),
    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(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(f67,axiom,
    ! [A,B,C] :
      ( para(A,B,A,C)
     => coll(A,B,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

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

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

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

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

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

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(f134,plain,
    ! [A,B,C,D,E] :
      ( cyclic(B,C,D,E)
      | ~ cyclic(A,B,C,E)
      | ~ cyclic(A,B,C,D) ),
    inference(pre_NNF_transformation,[status(thm)],[f17]) ).

fof(f135,plain,
    ! [B,C,D,E] :
      ( cyclic(B,C,D,E)
      | ! [A] :
          ( ~ cyclic(A,B,C,E)
          | ~ cyclic(A,B,C,D) ) ),
    inference(miniscoping,[status(thm)],[f134]) ).

fof(f136,plain,
    ! [X0,X1,X2,X3,X4] :
      ( cyclic(X1,X2,X3,X4)
      | ~ cyclic(X0,X1,X2,X4)
      | ~ cyclic(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(thm)],[f135]) ).

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(f148,plain,
    ! [A,B,C,D] :
      ( cong(A,B,D,C)
      | ~ cong(A,B,C,D) ),
    inference(pre_NNF_transformation,[status(thm)],[f23]) ).

fof(f149,plain,
    ! [X0,X1,X2,X3] :
      ( cong(X0,X1,X3,X2)
      | ~ cong(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(thm)],[f148]) ).

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(f190,plain,
    ! [A,B,P,Q] :
      ( eqangle(P,A,P,B,Q,A,Q,B)
      | ~ cyclic(A,B,P,Q) ),
    inference(pre_NNF_transformation,[status(thm)],[f41]) ).

fof(f191,plain,
    ! [X0,X1,X2,X3] :
      ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
      | ~ cyclic(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(thm)],[f190]) ).

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

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

fof(f371,plain,
    ( ~ para(sK22_skl,sK23_skl,sK20_skl,sK21_skl)
    & perp(sK21_skl,sK25_skl,sK24_skl,sK23_skl)
    & perp(sK24_skl,sK25_skl,sK21_skl,sK23_skl)
    & perp(sK24_skl,sK21_skl,sK25_skl,sK23_skl)
    & perp(sK20_skl,sK25_skl,sK24_skl,sK22_skl)
    & perp(sK24_skl,sK25_skl,sK20_skl,sK22_skl)
    & perp(sK24_skl,sK20_skl,sK25_skl,sK22_skl)
    & circle(sK26_skl,sK24_skl,sK25_skl,sK27_skl)
    & circle(sK26_skl,sK24_skl,sK20_skl,sK21_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl]),skolemize(B,sK20_skl),skolemize(C,sK21_skl),skolemize(U,sK22_skl),skolemize(V,sK23_skl),skolemize(A,sK24_skl),skolemize(D,sK25_skl),skolemize(O,sK26_skl),skolemize(NWPNT1,sK27_skl)],[f370]) ).

fof(f376,plain,
    perp(sK20_skl,sK25_skl,sK24_skl,sK22_skl),
    inference(cnf_transformation,[status(thm)],[f371]) ).

fof(f380,plain,
    ~ para(sK22_skl,sK23_skl,sK20_skl,sK21_skl),
    inference(cnf_transformation,[status(thm)],[f371]) ).

fof(f396,plain,
    perp(sK24_skl,sK22_skl,sK20_skl,sK25_skl),
    inference(resolution,[status(thm)],[f114,f376]) ).

fof(f447,plain,
    ! [X0,X1] :
      ( para(sK20_skl,sK25_skl,X0,X1)
      | ~ perp(sK24_skl,sK22_skl,X0,X1) ),
    inference(resolution,[status(thm)],[f117,f376]) ).

fof(f571,plain,
    para(sK20_skl,sK25_skl,sK20_skl,sK25_skl),
    inference(resolution,[status(thm)],[f447,f396]) ).

fof(f611,plain,
    ! [X0,X1] : eqangle(sK20_skl,sK25_skl,X0,X1,sK20_skl,sK25_skl,X0,X1),
    inference(resolution,[status(thm)],[f189,f571]) ).

fof(f836,plain,
    ! [X0,X1] : eqangle(X0,X1,sK20_skl,sK25_skl,X0,X1,sK20_skl,sK25_skl),
    inference(resolution,[status(thm)],[f611,f140]) ).

fof(f1169,plain,
    ! [X0,X1] : para(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[f836,f186]) ).

fof(f1170,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
    inference(resolution,[status(thm)],[f1169,f189]) ).

fof(f1175,plain,
    ! [X0,X1] : coll(X0,X1,X1),
    inference(resolution,[status(thm)],[f1169,f256]) ).

fof(f1228,plain,
    ! [X0,X1] : coll(X0,X1,X0),
    inference(resolution,[status(thm)],[f1175,f100]) ).

fof(f1272,plain,
    ! [X0,X1] : coll(X0,X0,X1),
    inference(resolution,[status(thm)],[f1228,f98]) ).

fof(f1284,plain,
    ! [X0,X1,X2] :
      ( coll(X2,X1,X0)
      | ~ coll(X0,X0,X1) ),
    inference(resolution,[status(thm)],[f1272,f103]) ).

fof(f1287,plain,
    ! [X0,X1,X2] : coll(X0,X1,X2),
    inference(forward_subsumption_resolution,[status(thm)],[f1284,f1272]) ).

fof(f1297,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X1,X2,X3,X2,X3),
    inference(resolution,[status(thm)],[f1170,f144]) ).

fof(f1512,plain,
    ! [X0,X1,X2,X3] :
      ( cyclic(X1,X2,X0,X3)
      | ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f195,f1287]) ).

fof(f1518,plain,
    ! [X0,X1,X2] : cyclic(X0,X0,X1,X2),
    inference(resolution,[status(thm)],[f1512,f1297]) ).

fof(f1558,plain,
    ! [X0,X1,X2,X3] :
      ( cyclic(X0,X1,X3,X2)
      | ~ cyclic(X0,X0,X1,X2) ),
    inference(resolution,[status(thm)],[f1518,f136]) ).

fof(f1562,plain,
    ! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
    inference(forward_subsumption_resolution,[status(thm)],[f1558,f1518]) ).

fof(f1573,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,X4)
      | ~ cyclic(X0,X1,X2,X3) ),
    inference(backward_subsumption_resolution,[status(thm)],[f198,f1562]) ).

fof(f1574,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
    inference(backward_subsumption_resolution,[status(thm)],[f191,f1562]) ).

fof(f1575,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( cong(X0,X1,X5,X3)
      | ~ eqangle(X2,X0,X2,X1,X4,X5,X4,X3)
      | ~ cyclic(X0,X1,X2,X3) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1573,f1562]) ).

fof(f1593,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( cong(X1,X2,X4,X5)
      | ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1575,f1562]) ).

fof(f1594,plain,
    ! [X0,X1] : cong(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[f1593,f1574]) ).

fof(f1605,plain,
    ! [X0,X1] : cong(X0,X1,X1,X0),
    inference(resolution,[status(thm)],[f1594,f149]) ).

fof(f1946,plain,
    ! [X0,X1] :
      ( perp(X0,X0,X0,X1)
      | ~ cong(X0,X1,X0,X1) ),
    inference(resolution,[status(thm)],[f232,f1605]) ).

fof(f1948,plain,
    ! [X0,X1,X2] :
      ( perp(X0,X0,X2,X1)
      | ~ cong(X0,X1,X0,X1) ),
    inference(resolution,[status(thm)],[f232,f1594]) ).

fof(f1949,plain,
    ! [X0,X1] : perp(X0,X0,X0,X1),
    inference(forward_subsumption_resolution,[status(thm)],[f1946,f1594]) ).

fof(f1951,plain,
    ! [X0,X1,X2] : perp(X0,X0,X1,X2),
    inference(forward_subsumption_resolution,[status(thm)],[f1948,f1594]) ).

fof(f1956,plain,
    ! [X0,X1] : perp(X0,X1,X0,X0),
    inference(resolution,[status(thm)],[f1949,f114]) ).

fof(f1973,plain,
    ! [X0,X1,X2,X3] :
      ( para(X0,X3,X1,X2)
      | ~ perp(X0,X0,X1,X2) ),
    inference(resolution,[status(thm)],[f1956,f117]) ).

fof(f1976,plain,
    ! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
    inference(forward_subsumption_resolution,[status(thm)],[f1973,f1951]) ).

fof(f1997,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f380,f1976]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GEO641+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36  % Computer : n026.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Sun Sep 20 18:13:52 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.38  % Drodi V4.1.1
% 0.09/0.49  % Refutation found
% 0.09/0.49  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.49  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.51  % Elapsed time: 0.131702 seconds
% 0.09/0.51  % CPU time: 0.747467 seconds
% 0.09/0.51  % Total memory used: 94.796 MB
% 0.09/0.51  % Net memory used: 93.735 MB
%------------------------------------------------------------------------------