TSTP Solution File: GEO567+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO567+1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n016.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 12:09:11 EDT 2023

% Result   : Theorem 0.14s 0.39s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   67 (  16 unt;   0 def)
%            Number of atoms       :  155 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  136 (  48   ~;  43   |;  31   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-8 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :  279 (; 267   !;  12   ?)

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

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

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

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

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

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

fof(f95,conjecture,
    ! [A,B,C,D,Q,P] :
      ( ( perp(D,A,B,C)
        & coll(D,B,C)
        & perp(Q,D,A,B)
        & coll(Q,A,B)
        & perp(P,D,A,C)
        & coll(P,A,C) )
     => cyclic(B,Q,P,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f96,negated_conjecture,
    ~ ! [A,B,C,D,Q,P] :
        ( ( perp(D,A,B,C)
          & coll(D,B,C)
          & perp(Q,D,A,B)
          & coll(Q,A,B)
          & perp(P,D,A,C)
          & coll(P,A,C) )
       => cyclic(B,Q,P,C) ),
    inference(negated_conjecture,[status(cth)],[f95]) ).

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(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(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(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(f369,plain,
    ? [A,B,C,D,Q,P] :
      ( perp(D,A,B,C)
      & coll(D,B,C)
      & perp(Q,D,A,B)
      & coll(Q,A,B)
      & perp(P,D,A,C)
      & coll(P,A,C)
      & ~ cyclic(B,Q,P,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f96]) ).

fof(f370,plain,
    ? [B,C,Q,P] :
      ( ? [A] :
          ( ? [D] :
              ( perp(D,A,B,C)
              & coll(D,B,C)
              & perp(Q,D,A,B)
              & coll(Q,A,B)
              & perp(P,D,A,C) )
          & coll(P,A,C) )
      & ~ cyclic(B,Q,P,C) ),
    inference(miniscoping,[status(esa)],[f369]) ).

fof(f371,plain,
    ( perp(sk0_25,sk0_24,sk0_20,sk0_21)
    & coll(sk0_25,sk0_20,sk0_21)
    & perp(sk0_22,sk0_25,sk0_24,sk0_20)
    & coll(sk0_22,sk0_24,sk0_20)
    & perp(sk0_23,sk0_25,sk0_24,sk0_21)
    & coll(sk0_23,sk0_24,sk0_21)
    & ~ cyclic(sk0_20,sk0_22,sk0_23,sk0_21) ),
    inference(skolemization,[status(esa)],[f370]) ).

fof(f376,plain,
    perp(sk0_23,sk0_25,sk0_24,sk0_21),
    inference(cnf_transformation,[status(esa)],[f371]) ).

fof(f378,plain,
    ~ cyclic(sk0_20,sk0_22,sk0_23,sk0_21),
    inference(cnf_transformation,[status(esa)],[f371]) ).

fof(f389,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
      | ~ perp(X0,X1,X6,X7)
      | ~ perp(X6,X7,X4,X5) ),
    inference(resolution,[status(thm)],[f189,f117]) ).

fof(f478,plain,
    ! [X0,X1,X2,X3] :
      ( eqangle(X0,X1,X2,X3,sk0_24,sk0_21,X2,X3)
      | ~ perp(X0,X1,sk0_23,sk0_25) ),
    inference(resolution,[status(thm)],[f389,f376]) ).

fof(f502,plain,
    ! [X0,X1,X2,X3] :
      ( eqangle(X0,X1,X2,X3,sk0_24,sk0_21,X2,X3)
      | ~ perp(sk0_23,sk0_25,X0,X1) ),
    inference(resolution,[status(thm)],[f478,f114]) ).

fof(f567,plain,
    ! [X0,X1] : eqangle(sk0_24,sk0_21,X0,X1,sk0_24,sk0_21,X0,X1),
    inference(resolution,[status(thm)],[f502,f376]) ).

fof(f583,plain,
    ! [X0,X1] : eqangle(X0,X1,sk0_24,sk0_21,X0,X1,sk0_24,sk0_21),
    inference(resolution,[status(thm)],[f567,f140]) ).

fof(f644,plain,
    ! [X0,X1] : para(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[f583,f186]) ).

fof(f653,plain,
    ! [X0,X1] : para(X0,X1,X1,X0),
    inference(resolution,[status(thm)],[f644,f105]) ).

fof(f654,plain,
    ! [X0,X1] : coll(X0,X1,X1),
    inference(resolution,[status(thm)],[f644,f256]) ).

fof(f655,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X1,X0,X2,X3),
    inference(resolution,[status(thm)],[f653,f189]) ).

fof(f700,plain,
    ! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X0,X1,X3,X2),
    inference(resolution,[status(thm)],[f655,f140]) ).

fof(f757,plain,
    ! [X0,X1] :
      ( ~ coll(X0,X0,X0)
      | cyclic(X1,X0,X0,X0) ),
    inference(resolution,[status(thm)],[f700,f195]) ).

fof(f758,plain,
    ! [X0,X1] : cyclic(X0,X1,X1,X1),
    inference(forward_subsumption_resolution,[status(thm)],[f757,f654]) ).

fof(f769,plain,
    ! [X0,X1] : cyclic(X0,X1,X0,X0),
    inference(resolution,[status(thm)],[f758,f133]) ).

fof(f782,plain,
    ! [X0,X1] : cyclic(X0,X0,X1,X0),
    inference(resolution,[status(thm)],[f769,f131]) ).

fof(f795,plain,
    ! [X0,X1] : cyclic(X0,X0,X0,X1),
    inference(resolution,[status(thm)],[f782,f129]) ).

fof(f808,plain,
    ! [X0,X1,X2] :
      ( ~ cyclic(X0,X0,X0,X1)
      | cyclic(X0,X0,X1,X2) ),
    inference(resolution,[status(thm)],[f795,f136]) ).

fof(f809,plain,
    ! [X0,X1,X2] : cyclic(X0,X0,X1,X2),
    inference(forward_subsumption_resolution,[status(thm)],[f808,f795]) ).

fof(f826,plain,
    ! [X0,X1,X2,X3] :
      ( ~ cyclic(X0,X0,X1,X2)
      | cyclic(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[f809,f136]) ).

fof(f827,plain,
    ! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
    inference(forward_subsumption_resolution,[status(thm)],[f826,f809]) ).

fof(f832,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f378,f827]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO567+1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n016.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue May 30 12:28:29 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  % Drodi V3.5.1
% 0.14/0.39  % Refutation found
% 0.14/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41  % Elapsed time: 0.059413 seconds
% 0.14/0.41  % CPU time: 0.305525 seconds
% 0.14/0.41  % Memory used: 25.653 MB
%------------------------------------------------------------------------------