TSTP Solution File: NUM325+1 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM325+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 : Thu Aug 31 11:29:25 EDT 2023

% Result   : Theorem 69.84s 10.26s
% Output   : CNFRefutation 69.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   59 (  34 unt;   0 def)
%            Number of atoms       :  127 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  125 (  57   ~;  52   |;  11   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-1 aty)
%            Number of variables   :  103 (   2 sgn;  69   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn3) ).

fof(f6,axiom,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn5) ).

fof(f130,axiom,
    rdn_translate(nn2,rdn_neg(rdnn(n2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn2) ).

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

fof(f269,axiom,
    rdn_positive_less(rdnn(n3),rdnn(n4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less34) ).

fof(f270,axiom,
    rdn_positive_less(rdnn(n4),rdnn(n5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less45) ).

fof(f275,axiom,
    ! [X0,X1,X2] :
      ( ( rdn_positive_less(rdnn(X1),rdnn(X2))
        & rdn_positive_less(rdnn(X0),rdnn(X1)) )
     => rdn_positive_less(rdnn(X0),rdnn(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less_transitivity) ).

fof(f290,axiom,
    ! [X0,X1,X2,X9,X10,X11] :
      ( ( rdn_translate(X2,rdn_pos(X11))
        & rdn_add_with_carry(rdnn(n0),X10,X11,X9)
        & rdn_positive_less(X10,X9)
        & rdn_translate(X1,rdn_neg(X10))
        & rdn_translate(X0,rdn_pos(X9)) )
     => sum(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_neg_2) ).

fof(f297,axiom,
    ! [X20,X21,X22,X23,X24] :
      ( ( rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(n0))
        & rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(n0)) )
     => rdn_add_with_carry(rdnn(X20),rdnn(X21),rdnn(X22),rdnn(X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_digit) ).

fof(f325,axiom,
    rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n2_n3_n5_n0) ).

fof(f352,axiom,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n5_n0_n5_n0) ).

fof(f402,conjecture,
    ? [X0] : sum(X0,nn2,n3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_what_nn2_n3) ).

fof(f403,negated_conjecture,
    ~ ? [X0] : sum(X0,nn2,n3),
    inference(negated_conjecture,[],[f402]) ).

fof(f414,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( rdn_translate(X2,rdn_pos(X5))
        & rdn_add_with_carry(rdnn(n0),X4,X5,X3)
        & rdn_positive_less(X4,X3)
        & rdn_translate(X1,rdn_neg(X4))
        & rdn_translate(X0,rdn_pos(X3)) )
     => sum(X0,X1,X2) ),
    inference(rectify,[],[f290]) ).

fof(f420,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
        & rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) )
     => rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
    inference(rectify,[],[f297]) ).

fof(f426,plain,
    ! [X0,X1,X2] :
      ( rdn_positive_less(rdnn(X0),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X1),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
    inference(ennf_transformation,[],[f275]) ).

fof(f427,plain,
    ! [X0,X1,X2] :
      ( rdn_positive_less(rdnn(X0),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X1),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
    inference(flattening,[],[f426]) ).

fof(f450,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_pos(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
      | ~ rdn_positive_less(X4,X3)
      | ~ rdn_translate(X1,rdn_neg(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(ennf_transformation,[],[f414]) ).

fof(f451,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_pos(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
      | ~ rdn_positive_less(X4,X3)
      | ~ rdn_translate(X1,rdn_neg(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(flattening,[],[f450]) ).

fof(f462,plain,
    ! [X0,X1,X2,X3,X4] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
      | ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
    inference(ennf_transformation,[],[f420]) ).

fof(f463,plain,
    ! [X0,X1,X2,X3,X4] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
      | ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
    inference(flattening,[],[f462]) ).

fof(f471,plain,
    ! [X0] : ~ sum(X0,nn2,n3),
    inference(ennf_transformation,[],[f403]) ).

fof(f478,plain,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    inference(cnf_transformation,[],[f4]) ).

fof(f480,plain,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    inference(cnf_transformation,[],[f6]) ).

fof(f604,plain,
    rdn_translate(nn2,rdn_neg(rdnn(n2))),
    inference(cnf_transformation,[],[f130]) ).

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

fof(f743,plain,
    rdn_positive_less(rdnn(n3),rdnn(n4)),
    inference(cnf_transformation,[],[f269]) ).

fof(f744,plain,
    rdn_positive_less(rdnn(n4),rdnn(n5)),
    inference(cnf_transformation,[],[f270]) ).

fof(f749,plain,
    ! [X2,X0,X1] :
      ( rdn_positive_less(rdnn(X0),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X1),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
    inference(cnf_transformation,[],[f427]) ).

fof(f766,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_pos(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
      | ~ rdn_positive_less(X4,X3)
      | ~ rdn_translate(X1,rdn_neg(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(cnf_transformation,[],[f451]) ).

fof(f774,plain,
    ! [X2,X3,X0,X1,X4] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
      | ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
    inference(cnf_transformation,[],[f463]) ).

fof(f802,plain,
    rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f325]) ).

fof(f829,plain,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f352]) ).

fof(f879,plain,
    ! [X0] : ~ sum(X0,nn2,n3),
    inference(cnf_transformation,[],[f471]) ).

cnf(c_52,plain,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    inference(cnf_transformation,[],[f478]) ).

cnf(c_54,plain,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    inference(cnf_transformation,[],[f480]) ).

cnf(c_178,plain,
    rdn_translate(nn2,rdn_neg(rdnn(n2))),
    inference(cnf_transformation,[],[f604]) ).

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

cnf(c_317,plain,
    rdn_positive_less(rdnn(n3),rdnn(n4)),
    inference(cnf_transformation,[],[f743]) ).

cnf(c_318,plain,
    rdn_positive_less(rdnn(n4),rdnn(n5)),
    inference(cnf_transformation,[],[f744]) ).

cnf(c_323,plain,
    ( ~ rdn_positive_less(rdnn(X0),rdnn(X1))
    | ~ rdn_positive_less(rdnn(X1),rdnn(X2))
    | rdn_positive_less(rdnn(X0),rdnn(X2)) ),
    inference(cnf_transformation,[],[f749]) ).

cnf(c_340,plain,
    ( ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2)
    | ~ rdn_translate(X3,rdn_pos(X2))
    | ~ rdn_translate(X4,rdn_pos(X1))
    | ~ rdn_translate(X5,rdn_neg(X0))
    | ~ rdn_positive_less(X0,X2)
    | sum(X3,X5,X4) ),
    inference(cnf_transformation,[],[f766]) ).

cnf(c_348,plain,
    ( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
    | ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
    | rdn_add_with_carry(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4)) ),
    inference(cnf_transformation,[],[f774]) ).

cnf(c_376,plain,
    rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f802]) ).

cnf(c_403,plain,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f829]) ).

cnf(c_453,negated_conjecture,
    ~ sum(X0,nn2,n3),
    inference(cnf_transformation,[],[f879]) ).

cnf(c_10799,plain,
    ( ~ rdn_positive_less(rdnn(n3),rdnn(X0))
    | rdn_positive_less(rdnn(n2),rdnn(X0)) ),
    inference(superposition,[status(thm)],[c_316,c_323]) ).

cnf(c_10800,plain,
    ( ~ rdn_positive_less(rdnn(n4),rdnn(X0))
    | rdn_positive_less(rdnn(n3),rdnn(X0)) ),
    inference(superposition,[status(thm)],[c_317,c_323]) ).

cnf(c_10833,plain,
    rdn_positive_less(rdnn(n3),rdnn(n5)),
    inference(superposition,[status(thm)],[c_318,c_10800]) ).

cnf(c_10835,plain,
    rdn_positive_less(rdnn(n2),rdnn(n5)),
    inference(superposition,[status(thm)],[c_10833,c_10799]) ).

cnf(c_35293,plain,
    ( ~ rdn_digit_add(rdnn(n5),rdnn(X0),rdnn(X1),rdnn(n0))
    | rdn_add_with_carry(rdnn(X0),rdnn(n2),rdnn(n3),rdnn(X1)) ),
    inference(superposition,[status(thm)],[c_376,c_348]) ).

cnf(c_35534,plain,
    rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
    inference(superposition,[status(thm)],[c_403,c_35293]) ).

cnf(c_35711,plain,
    ( ~ rdn_translate(X0,rdn_pos(rdnn(n5)))
    | ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
    | ~ rdn_translate(X2,rdn_neg(rdnn(n2)))
    | ~ rdn_positive_less(rdnn(n2),rdnn(n5))
    | sum(X0,X2,X1) ),
    inference(superposition,[status(thm)],[c_35534,c_340]) ).

cnf(c_35722,plain,
    ( ~ rdn_translate(X2,rdn_neg(rdnn(n2)))
    | ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
    | ~ rdn_translate(X0,rdn_pos(rdnn(n5)))
    | sum(X0,X2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_35711,c_10835,c_35711]) ).

cnf(c_35723,plain,
    ( ~ rdn_translate(X0,rdn_pos(rdnn(n5)))
    | ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
    | ~ rdn_translate(X2,rdn_neg(rdnn(n2)))
    | sum(X0,X2,X1) ),
    inference(renaming,[status(thm)],[c_35722]) ).

cnf(c_36157,plain,
    ( ~ rdn_translate(X0,rdn_pos(rdnn(n5)))
    | ~ rdn_translate(X1,rdn_neg(rdnn(n2)))
    | sum(X0,X1,n3) ),
    inference(superposition,[status(thm)],[c_52,c_35723]) ).

cnf(c_36450,plain,
    ( ~ rdn_translate(X0,rdn_pos(rdnn(n5)))
    | sum(X0,nn2,n3) ),
    inference(superposition,[status(thm)],[c_178,c_36157]) ).

cnf(c_36452,plain,
    ~ rdn_translate(X0,rdn_pos(rdnn(n5))),
    inference(global_subsumption_just,[status(thm)],[c_36450,c_453,c_36450]) ).

cnf(c_36455,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_54,c_36452]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUM325+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n023.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 : Fri Aug 25 14:00:57 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 69.84/10.26  % SZS status Started for theBenchmark.p
% 69.84/10.26  % SZS status Theorem for theBenchmark.p
% 69.84/10.26  
% 69.84/10.26  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 69.84/10.26  
% 69.84/10.26  ------  iProver source info
% 69.84/10.26  
% 69.84/10.26  git: date: 2023-05-31 18:12:56 +0000
% 69.84/10.26  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 69.84/10.26  git: non_committed_changes: false
% 69.84/10.26  git: last_make_outside_of_git: false
% 69.84/10.26  
% 69.84/10.26  ------ Parsing...
% 69.84/10.26  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 69.84/10.26  
% 69.84/10.26  ------ 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 
% 69.84/10.26  
% 69.84/10.26  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 69.84/10.26  
% 69.84/10.26  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 69.84/10.26  ------ Proving...
% 69.84/10.26  ------ Problem Properties 
% 69.84/10.26  
% 69.84/10.26  
% 69.84/10.26  clauses                                 402
% 69.84/10.26  conjectures                             1
% 69.84/10.26  EPR                                     8
% 69.84/10.26  Horn                                    400
% 69.84/10.26  unary                                   376
% 69.84/10.26  binary                                  6
% 69.84/10.26  lits                                    472
% 69.84/10.26  lits eq                                 5
% 69.84/10.26  fd_pure                                 0
% 69.84/10.26  fd_pseudo                               0
% 69.84/10.26  fd_cond                                 0
% 69.84/10.26  fd_pseudo_cond                          5
% 69.84/10.26  AC symbols                              0
% 69.84/10.26  
% 69.84/10.26  ------ Input Options Time Limit: Unbounded
% 69.84/10.26  
% 69.84/10.26  
% 69.84/10.26  ------ 
% 69.84/10.26  Current options:
% 69.84/10.26  ------ 
% 69.84/10.26  
% 69.84/10.26  
% 69.84/10.26  
% 69.84/10.26  
% 69.84/10.26  ------ Proving...
% 69.84/10.26  
% 69.84/10.26  
% 69.84/10.26  % SZS status Theorem for theBenchmark.p
% 69.84/10.26  
% 69.84/10.26  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 69.84/10.26  
% 69.88/10.27  
%------------------------------------------------------------------------------