TSTP Solution File: GEO627+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO627+1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 : Wed May 31 12:09:22 EDT 2023

% Result   : Theorem 2.15s 0.70s
% Output   : CNFRefutation 2.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   69 (   7 unt;   0 def)
%            Number of atoms       :  226 (   0 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  243 (  86   ~;  76   |;  67   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   9 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-8 aty)
%            Number of functors    :   13 (  13 usr;  13 con; 0-0 aty)
%            Number of variables   :  350 (; 324   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
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(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(f14,axiom,
    ! [A,B,C,D] :
      ( cyclic(A,B,C,D)
     => cyclic(A,B,D,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [A,B,C,D] :
      ( cyclic(A,B,C,D)
     => cyclic(A,C,B,D) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [A,B,C,D] :
      ( cyclic(A,B,C,D)
     => cyclic(B,A,C,D) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [A,B,C,D,E] :
      ( ( cyclic(A,B,C,D)
        & cyclic(A,B,C,E) )
     => 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(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(f95,conjecture,
    ! [A,B,C,O,P1,F,G,P,G1,F1,K,NWPNT1,NWPNT2] :
      ( ( circle(O,A,B,C)
        & circle(O,A,P1,NWPNT1)
        & perp(F,P1,A,C)
        & coll(F,A,C)
        & perp(G,P1,A,B)
        & coll(G,A,B)
        & circle(O,A,P,NWPNT2)
        & perp(G1,P,A,B)
        & coll(G1,A,B)
        & perp(F1,P,A,C)
        & coll(F1,A,C)
        & perp(F,G,P,K)
        & perp(G1,F1,P1,K) )
     => cyclic(A,P1,P,K) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f96,negated_conjecture,
    ~ ! [A,B,C,O,P1,F,G,P,G1,F1,K,NWPNT1,NWPNT2] :
        ( ( circle(O,A,B,C)
          & circle(O,A,P1,NWPNT1)
          & perp(F,P1,A,C)
          & coll(F,A,C)
          & perp(G,P1,A,B)
          & coll(G,A,B)
          & circle(O,A,P,NWPNT2)
          & perp(G1,P,A,B)
          & coll(G1,A,B)
          & perp(F1,P,A,C)
          & coll(F1,A,C)
          & perp(F,G,P,K)
          & perp(G1,F1,P1,K) )
       => cyclic(A,P1,P,K) ),
    inference(negated_conjecture,[status(cth)],[f95]) ).

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(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(f128,plain,
    ! [A,B,C,D] :
      ( ~ cyclic(A,B,C,D)
      | cyclic(A,B,D,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f129,plain,
    ! [X0,X1,X2,X3] :
      ( ~ cyclic(X0,X1,X2,X3)
      | cyclic(X0,X1,X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f130,plain,
    ! [A,B,C,D] :
      ( ~ cyclic(A,B,C,D)
      | cyclic(A,C,B,D) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f131,plain,
    ! [X0,X1,X2,X3] :
      ( ~ cyclic(X0,X1,X2,X3)
      | cyclic(X0,X2,X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f130]) ).

fof(f132,plain,
    ! [A,B,C,D] :
      ( ~ cyclic(A,B,C,D)
      | cyclic(B,A,C,D) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f133,plain,
    ! [X0,X1,X2,X3] :
      ( ~ cyclic(X0,X1,X2,X3)
      | cyclic(X1,X0,X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f132]) ).

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

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

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

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(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(f369,plain,
    ? [A,B,C,O,P1,F,G,P,G1,F1,K,NWPNT1,NWPNT2] :
      ( circle(O,A,B,C)
      & circle(O,A,P1,NWPNT1)
      & perp(F,P1,A,C)
      & coll(F,A,C)
      & perp(G,P1,A,B)
      & coll(G,A,B)
      & circle(O,A,P,NWPNT2)
      & perp(G1,P,A,B)
      & coll(G1,A,B)
      & perp(F1,P,A,C)
      & coll(F1,A,C)
      & perp(F,G,P,K)
      & perp(G1,F1,P1,K)
      & ~ cyclic(A,P1,P,K) ),
    inference(pre_NNF_transformation,[status(esa)],[f96]) ).

fof(f370,plain,
    ? [A,P1,P,K] :
      ( ? [G1,F1] :
          ( ? [F,G] :
              ( ? [C] :
                  ( ? [B] :
                      ( ? [O] :
                          ( circle(O,A,B,C)
                          & ? [NWPNT1] : circle(O,A,P1,NWPNT1)
                          & perp(F,P1,A,C)
                          & coll(F,A,C)
                          & perp(G,P1,A,B)
                          & coll(G,A,B)
                          & ? [NWPNT2] : circle(O,A,P,NWPNT2) )
                      & perp(G1,P,A,B)
                      & coll(G1,A,B) )
                  & perp(F1,P,A,C)
                  & coll(F1,A,C) )
              & perp(F,G,P,K) )
          & perp(G1,F1,P1,K) )
      & ~ cyclic(A,P1,P,K) ),
    inference(miniscoping,[status(esa)],[f369]) ).

fof(f371,plain,
    ( circle(sk0_30,sk0_20,sk0_29,sk0_28)
    & circle(sk0_30,sk0_20,sk0_21,sk0_31)
    & perp(sk0_26,sk0_21,sk0_20,sk0_28)
    & coll(sk0_26,sk0_20,sk0_28)
    & perp(sk0_27,sk0_21,sk0_20,sk0_29)
    & coll(sk0_27,sk0_20,sk0_29)
    & circle(sk0_30,sk0_20,sk0_22,sk0_32)
    & perp(sk0_24,sk0_22,sk0_20,sk0_29)
    & coll(sk0_24,sk0_20,sk0_29)
    & perp(sk0_25,sk0_22,sk0_20,sk0_28)
    & coll(sk0_25,sk0_20,sk0_28)
    & perp(sk0_26,sk0_27,sk0_22,sk0_23)
    & perp(sk0_24,sk0_25,sk0_21,sk0_23)
    & ~ cyclic(sk0_20,sk0_21,sk0_22,sk0_23) ),
    inference(skolemization,[status(esa)],[f370]) ).

fof(f381,plain,
    perp(sk0_25,sk0_22,sk0_20,sk0_28),
    inference(cnf_transformation,[status(esa)],[f371]) ).

fof(f382,plain,
    coll(sk0_25,sk0_20,sk0_28),
    inference(cnf_transformation,[status(esa)],[f371]) ).

fof(f385,plain,
    ~ cyclic(sk0_20,sk0_21,sk0_22,sk0_23),
    inference(cnf_transformation,[status(esa)],[f371]) ).

fof(f570,plain,
    ! [X0,X1,X2,X3] :
      ( ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
      | ~ coll(X0,X3,X1)
      | cyclic(X2,X1,X0,X3) ),
    inference(resolution,[status(thm)],[f140,f195]) ).

fof(f1648,plain,
    ! [X0,X1,X2] :
      ( ~ coll(X0,X0,X1)
      | cyclic(X2,X1,X0,X0)
      | ~ para(X0,X1,X0,X1) ),
    inference(resolution,[status(thm)],[f570,f189]) ).

fof(f1654,plain,
    ! [X0,X1,X2,X3] :
      ( cyclic(X0,X1,X2,X2)
      | ~ para(X2,X1,X2,X1)
      | ~ coll(X1,X3,X2)
      | ~ coll(X1,X3,X2) ),
    inference(resolution,[status(thm)],[f1648,f103]) ).

fof(f1655,plain,
    ! [X0,X1,X2,X3] :
      ( cyclic(X0,X1,X2,X2)
      | ~ para(X2,X1,X2,X1)
      | ~ coll(X1,X3,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f1654]) ).

fof(f1661,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( cyclic(X0,X1,X2,X2)
      | ~ coll(X1,X3,X2)
      | ~ perp(X2,X1,X4,X5)
      | ~ perp(X4,X5,X2,X1) ),
    inference(resolution,[status(thm)],[f1655,f117]) ).

fof(f1662,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( cyclic(X0,X1,X2,X2)
      | ~ coll(X1,X3,X2)
      | ~ perp(X2,X1,X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1661,f114]) ).

fof(f1696,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4)
      | cyclic(X0,X5,X2,X2) ),
    inference(resolution,[status(thm)],[f1662,f133]) ).

fof(f1715,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4)
      | cyclic(X0,X2,X5,X2) ),
    inference(resolution,[status(thm)],[f1696,f131]) ).

fof(f1745,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4)
      | cyclic(X0,X2,X2,X5) ),
    inference(resolution,[status(thm)],[f1715,f129]) ).

fof(f1795,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4)
      | ~ cyclic(X0,X2,X2,X5)
      | cyclic(X2,X2,X5,X6) ),
    inference(resolution,[status(thm)],[f1745,f136]) ).

fof(f1796,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4)
      | cyclic(X2,X2,X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1795,f1745]) ).

fof(f2063,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4)
      | ~ cyclic(X2,X2,X5,X6)
      | cyclic(X2,X5,X6,X7) ),
    inference(resolution,[status(thm)],[f1796,f136]) ).

fof(f2064,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4)
      | cyclic(X2,X5,X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2063,f1796]) ).

fof(f2129,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4)
      | ~ cyclic(X2,X5,X6,X7)
      | cyclic(X5,X6,X7,X8) ),
    inference(resolution,[status(thm)],[f2064,f136]) ).

fof(f2130,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4)
      | cyclic(X5,X6,X7,X8) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2129,f2064]) ).

fof(f2154,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ coll(X0,X1,X2)
      | ~ perp(X2,X0,X3,X4) ),
    inference(resolution,[status(thm)],[f2130,f385]) ).

fof(f2251,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ perp(X0,X1,X2,X3)
      | ~ coll(X4,X1,X0) ),
    inference(resolution,[status(thm)],[f2154,f100]) ).

fof(f2541,plain,
    ! [X0,X1] : ~ perp(sk0_28,sk0_20,X0,X1),
    inference(resolution,[status(thm)],[f2251,f382]) ).

fof(f2563,plain,
    ! [X0,X1] : ~ perp(X0,X1,sk0_28,sk0_20),
    inference(resolution,[status(thm)],[f2541,f114]) ).

fof(f2585,plain,
    ! [X0,X1] : ~ perp(X0,X1,sk0_20,sk0_28),
    inference(resolution,[status(thm)],[f2563,f112]) ).

fof(f2586,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f381,f2585]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO627+1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue May 30 11:57:57 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 2.15/0.70  % Refutation found
% 2.15/0.70  % SZS status Theorem for theBenchmark: Theorem is valid
% 2.15/0.70  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.75/0.72  % Elapsed time: 0.377676 seconds
% 2.75/0.72  % CPU time: 2.840305 seconds
% 2.75/0.72  % Memory used: 82.598 MB
%------------------------------------------------------------------------------