TSTP Solution File: NUM303+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM303+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n028.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 : Mon Jun 24 12:51:05 EDT 2024

% Result   : Theorem 7.93s 1.58s
% Output   : CNFRefutation 7.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   37 (  19 unt;   0 def)
%            Number of atoms       :   78 (  10 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   81 (  40   ~;  27   |;   9   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   66 (   7 sgn  45   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f22,axiom,
    rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn21) ).

fof(f32,axiom,
    rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn31) ).

fof(f268,axiom,
    rdn_positive_less(rdnn(n2),rdnn(n3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less23) ).

fof(f276,axiom,
    ! [X3,X4,X5,X6] :
      ( rdn_positive_less(X4,X6)
     => rdn_positive_less(rdn(rdnn(X3),X4),rdn(rdnn(X5),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less_multi_digit_high) ).

fof(f281,axiom,
    ! [X0,X1,X9,X10] :
      ( ( rdn_positive_less(X9,X10)
        & rdn_translate(X1,rdn_pos(X10))
        & rdn_translate(X0,rdn_pos(X9)) )
     => less(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_entry_point_pos_pos) ).

fof(f284,axiom,
    ! [X0,X1] :
      ( less(X0,X1)
    <=> ( X0 != X1
        & ~ less(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).

fof(f402,conjecture,
    n21 != n31,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',n31_not_n12) ).

fof(f403,negated_conjecture,
    ~ ( n21 != n31 ),
    inference(negated_conjecture,[],[f402]) ).

fof(f404,plain,
    ! [X0,X1,X2,X3] :
      ( rdn_positive_less(X1,X3)
     => rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3)) ),
    inference(rectify,[],[f276]) ).

fof(f408,plain,
    ! [X0,X1,X2,X3] :
      ( ( rdn_positive_less(X2,X3)
        & rdn_translate(X1,rdn_pos(X3))
        & rdn_translate(X0,rdn_pos(X2)) )
     => less(X0,X1) ),
    inference(rectify,[],[f281]) ).

fof(f425,plain,
    n21 = n31,
    inference(flattening,[],[f403]) ).

fof(f429,plain,
    ! [X0,X1,X2,X3] :
      ( rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3))
      | ~ rdn_positive_less(X1,X3) ),
    inference(ennf_transformation,[],[f404]) ).

fof(f435,plain,
    ! [X0,X1,X2,X3] :
      ( less(X0,X1)
      | ~ rdn_positive_less(X2,X3)
      | ~ rdn_translate(X1,rdn_pos(X3))
      | ~ rdn_translate(X0,rdn_pos(X2)) ),
    inference(ennf_transformation,[],[f408]) ).

fof(f436,plain,
    ! [X0,X1,X2,X3] :
      ( less(X0,X1)
      | ~ rdn_positive_less(X2,X3)
      | ~ rdn_translate(X1,rdn_pos(X3))
      | ~ rdn_translate(X0,rdn_pos(X2)) ),
    inference(flattening,[],[f435]) ).

fof(f472,plain,
    ! [X0,X1] :
      ( ( less(X0,X1)
        | X0 = X1
        | less(X1,X0) )
      & ( ( X0 != X1
          & ~ less(X1,X0) )
        | ~ less(X0,X1) ) ),
    inference(nnf_transformation,[],[f284]) ).

fof(f473,plain,
    ! [X0,X1] :
      ( ( less(X0,X1)
        | X0 = X1
        | less(X1,X0) )
      & ( ( X0 != X1
          & ~ less(X1,X0) )
        | ~ less(X0,X1) ) ),
    inference(flattening,[],[f472]) ).

fof(f496,plain,
    rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
    inference(cnf_transformation,[],[f22]) ).

fof(f506,plain,
    rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
    inference(cnf_transformation,[],[f32]) ).

fof(f742,plain,
    rdn_positive_less(rdnn(n2),rdnn(n3)),
    inference(cnf_transformation,[],[f268]) ).

fof(f750,plain,
    ! [X2,X3,X0,X1] :
      ( rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3))
      | ~ rdn_positive_less(X1,X3) ),
    inference(cnf_transformation,[],[f429]) ).

fof(f755,plain,
    ! [X2,X3,X0,X1] :
      ( less(X0,X1)
      | ~ rdn_positive_less(X2,X3)
      | ~ rdn_translate(X1,rdn_pos(X3))
      | ~ rdn_translate(X0,rdn_pos(X2)) ),
    inference(cnf_transformation,[],[f436]) ).

fof(f759,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ less(X0,X1) ),
    inference(cnf_transformation,[],[f473]) ).

fof(f879,plain,
    n21 = n31,
    inference(cnf_transformation,[],[f425]) ).

fof(f880,plain,
    rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
    inference(definition_unfolding,[],[f496,f879]) ).

fof(f881,plain,
    ! [X1] : ~ less(X1,X1),
    inference(equality_resolution,[],[f759]) ).

cnf(c_70,negated_conjecture,
    rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
    inference(cnf_transformation,[],[f880]) ).

cnf(c_80,plain,
    rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
    inference(cnf_transformation,[],[f506]) ).

cnf(c_316,plain,
    rdn_positive_less(rdnn(n2),rdnn(n3)),
    inference(cnf_transformation,[],[f742]) ).

cnf(c_324,plain,
    ( ~ rdn_positive_less(X0,X1)
    | rdn_positive_less(rdn(rdnn(X2),X0),rdn(rdnn(X3),X1)) ),
    inference(cnf_transformation,[],[f750]) ).

cnf(c_329,plain,
    ( ~ rdn_translate(X0,rdn_pos(X1))
    | ~ rdn_translate(X2,rdn_pos(X3))
    | ~ rdn_positive_less(X1,X3)
    | less(X0,X2) ),
    inference(cnf_transformation,[],[f755]) ).

cnf(c_333,plain,
    ~ less(X0,X0),
    inference(cnf_transformation,[],[f881]) ).

cnf(c_5060,plain,
    ( ~ rdn_translate(X0,rdn_pos(X1))
    | ~ rdn_translate(X0,rdn_pos(X2))
    | ~ rdn_positive_less(X1,X2) ),
    inference(resolution,[status(thm)],[c_329,c_333]) ).

cnf(c_5088,plain,
    ( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2)))
    | ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X3),X4)))
    | ~ rdn_positive_less(X2,X4) ),
    inference(resolution,[status(thm)],[c_5060,c_324]) ).

cnf(c_5138,plain,
    ( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n3))))
    | ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X2),rdnn(n2)))) ),
    inference(resolution,[status(thm)],[c_5088,c_316]) ).

cnf(c_5274,plain,
    ~ rdn_translate(n31,rdn_pos(rdn(rdnn(X0),rdnn(n2)))),
    inference(resolution,[status(thm)],[c_5138,c_80]) ).

cnf(c_5275,plain,
    ~ rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
    inference(instantiation,[status(thm)],[c_5274]) ).

cnf(c_5276,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_5275,c_70]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : NUM303+1 : TPTP v8.2.0. Released v3.1.0.
% 0.05/0.09  % Command  : run_iprover %s %d THM
% 0.09/0.29  % Computer : n028.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Sun Jun 23 00:57:54 EDT 2024
% 0.09/0.29  % CPUTime  : 
% 0.15/0.40  Running first-order theorem proving
% 0.15/0.40  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.93/1.58  % SZS status Started for theBenchmark.p
% 7.93/1.58  % SZS status Theorem for theBenchmark.p
% 7.93/1.58  
% 7.93/1.58  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.93/1.58  
% 7.93/1.58  ------  iProver source info
% 7.93/1.58  
% 7.93/1.58  git: date: 2024-06-12 09:56:46 +0000
% 7.93/1.58  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 7.93/1.58  git: non_committed_changes: false
% 7.93/1.58  
% 7.93/1.58  ------ Parsing...
% 7.93/1.58  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.93/1.58  
% 7.93/1.58  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 7.93/1.58  
% 7.93/1.58  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.93/1.58  
% 7.93/1.58  ------ Preprocessing... sf_s  rm: 1 0s  sf_e 
% 7.93/1.58  ------ Proving...
% 7.93/1.58  ------ Problem Properties 
% 7.93/1.58  
% 7.93/1.58  
% 7.93/1.58  clauses                                 405
% 7.93/1.58  conjectures                             1
% 7.93/1.58  EPR                                     8
% 7.93/1.58  Horn                                    403
% 7.93/1.58  unary                                   379
% 7.93/1.58  binary                                  6
% 7.93/1.58  lits                                    475
% 7.93/1.58  lits eq                                 9
% 7.93/1.58  fd_pure                                 0
% 7.93/1.58  fd_pseudo                               0
% 7.93/1.58  fd_cond                                 0
% 7.93/1.58  fd_pseudo_cond                          5
% 7.93/1.58  AC symbols                              0
% 7.93/1.58  
% 7.93/1.58  ------ Input Options Time Limit: Unbounded
% 7.93/1.58  
% 7.93/1.58  
% 7.93/1.58  ------ 
% 7.93/1.58  Current options:
% 7.93/1.58  ------ 
% 7.93/1.58  
% 7.93/1.58  
% 7.93/1.58  
% 7.93/1.58  
% 7.93/1.58  ------ Proving...
% 7.93/1.58  
% 7.93/1.58  
% 7.93/1.58  % SZS status Theorem for theBenchmark.p
% 7.93/1.58  
% 7.93/1.58  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.93/1.58  
% 7.93/1.58  
%------------------------------------------------------------------------------