TSTP Solution File: SWC277+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC277+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : Thu Aug 31 20:42:13 EDT 2023

% Result   : Theorem 0.46s 1.16s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   70 (  24 unt;   0 def)
%            Number of atoms       :  271 (  70 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  295 (  94   ~;  87   |;  90   &)
%                                         (   6 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   72 (   0 sgn;  34   !;  29   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).

fof(f65,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).

fof(f66,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( neq(X3,nil)
                      & ~ singletonP(X2) )
                    | totalorderedP(X0)
                    | ~ segmentP(X3,X2)
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( neq(X3,nil)
                        & ~ singletonP(X2) )
                      | totalorderedP(X0)
                      | ~ segmentP(X3,X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f100,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f118,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f176,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f180,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | singletonP(X2) )
                  & ~ totalorderedP(X0)
                  & segmentP(X3,X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | singletonP(X2) )
                  & ~ totalorderedP(X0)
                  & segmentP(X3,X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f241,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f100]) ).

fof(f242,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f241]) ).

fof(f243,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK10(X0),nil) = X0
        & ssItem(sK10(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f244,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK10(X0),nil) = X0
            & ssItem(sK10(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f242,f243]) ).

fof(f316,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f330,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ neq(X3,nil)
                      | singletonP(X2) )
                    & ~ totalorderedP(X0)
                    & segmentP(X3,X2)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | singletonP(X2) )
                  & ~ totalorderedP(sK53)
                  & segmentP(X3,X2)
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ neq(X3,nil)
                  | singletonP(X2) )
                & ~ totalorderedP(sK53)
                & segmentP(X3,X2)
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ neq(X3,nil)
                | singletonP(X2) )
              & ~ totalorderedP(sK53)
              & segmentP(X3,X2)
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ neq(X3,nil)
              | singletonP(X2) )
            & ~ totalorderedP(sK53)
            & segmentP(X3,X2)
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ neq(X3,nil)
            | singletonP(sK55) )
          & ~ totalorderedP(sK53)
          & segmentP(X3,sK55)
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( ~ neq(X3,nil)
          | singletonP(sK55) )
        & ~ totalorderedP(sK53)
        & segmentP(X3,sK55)
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ~ neq(sK56,nil)
        | singletonP(sK55) )
      & ~ totalorderedP(sK53)
      & segmentP(sK56,sK55)
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ( ~ neq(sK56,nil)
      | singletonP(sK55) )
    & ~ totalorderedP(sK53)
    & segmentP(sK56,sK55)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f222,f346,f345,f344,f343]) ).

fof(f357,plain,
    ! [X0] :
      ( ssItem(sK10(X0))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f244]) ).

fof(f358,plain,
    ! [X0] :
      ( cons(sK10(X0),nil) = X0
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f244]) ).

fof(f438,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f316]) ).

fof(f440,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f494,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f502,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f503,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f66]) ).

fof(f547,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f347]) ).

fof(f548,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f347]) ).

fof(f551,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f347]) ).

fof(f552,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f347]) ).

fof(f553,plain,
    segmentP(sK56,sK55),
    inference(cnf_transformation,[],[f347]) ).

fof(f554,plain,
    ~ totalorderedP(sK53),
    inference(cnf_transformation,[],[f347]) ).

fof(f555,plain,
    ( ~ neq(sK56,nil)
    | singletonP(sK55) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f556,plain,
    ~ totalorderedP(sK55),
    inference(definition_unfolding,[],[f554,f552]) ).

fof(f557,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f548,f551]) ).

fof(f558,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f547,f552]) ).

cnf(c_59,plain,
    ( ~ ssList(X0)
    | ~ singletonP(X0)
    | cons(sK10(X0),nil) = X0 ),
    inference(cnf_transformation,[],[f358]) ).

cnf(c_60,plain,
    ( ~ ssList(X0)
    | ~ singletonP(X0)
    | ssItem(sK10(X0)) ),
    inference(cnf_transformation,[],[f357]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f438]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f440]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f494]) ).

cnf(c_203,plain,
    ( ~ ssItem(X0)
    | totalorderedP(cons(X0,nil)) ),
    inference(cnf_transformation,[],[f502]) ).

cnf(c_204,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f503]) ).

cnf(c_246,negated_conjecture,
    ( ~ neq(sK56,nil)
    | singletonP(sK55) ),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_247,negated_conjecture,
    ~ totalorderedP(sK55),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_248,negated_conjecture,
    segmentP(sK56,sK55),
    inference(cnf_transformation,[],[f553]) ).

cnf(c_251,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_252,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_3237,plain,
    ( X0 != sK56
    | X1 != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | singletonP(sK55) ),
    inference(resolution_lifted,[status(thm)],[c_138,c_246]) ).

cnf(c_3238,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK56)
    | sK56 = nil
    | singletonP(sK55) ),
    inference(unflattening,[status(thm)],[c_3237]) ).

cnf(c_3239,plain,
    ( sK56 = nil
    | singletonP(sK55) ),
    inference(global_subsumption_just,[status(thm)],[c_3238,c_251,c_141,c_3238]) ).

cnf(c_3283,plain,
    ( X0 != sK55
    | ~ ssList(X0)
    | nil = sK56
    | ssItem(sK10(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_60,c_3239]) ).

cnf(c_3284,plain,
    ( ~ ssList(sK55)
    | nil = sK56
    | ssItem(sK10(sK55)) ),
    inference(unflattening,[status(thm)],[c_3283]) ).

cnf(c_3285,plain,
    ( nil = sK56
    | ssItem(sK10(sK55)) ),
    inference(global_subsumption_just,[status(thm)],[c_3284,c_252,c_3284]) ).

cnf(c_12669,plain,
    ( ~ ssList(sK55)
    | cons(sK10(sK55),nil) = sK55
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_3239,c_59]) ).

cnf(c_12670,plain,
    ( cons(sK10(sK55),nil) = sK55
    | nil = sK56 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12669,c_252]) ).

cnf(c_12691,plain,
    ( ~ ssItem(sK10(sK55))
    | nil = sK56
    | totalorderedP(sK55) ),
    inference(superposition,[status(thm)],[c_12670,c_203]) ).

cnf(c_12695,plain,
    ( ~ ssItem(sK10(sK55))
    | nil = sK56 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12691,c_247]) ).

cnf(c_12706,plain,
    nil = sK56,
    inference(global_subsumption_just,[status(thm)],[c_12695,c_3285,c_12695]) ).

cnf(c_12717,plain,
    segmentP(nil,sK55),
    inference(demodulation,[status(thm)],[c_248,c_12706]) ).

cnf(c_12719,plain,
    ( ~ ssList(sK55)
    | nil = sK55 ),
    inference(superposition,[status(thm)],[c_12717,c_196]) ).

cnf(c_12720,plain,
    nil = sK55,
    inference(forward_subsumption_resolution,[status(thm)],[c_12719,c_252]) ).

cnf(c_12729,plain,
    ~ totalorderedP(nil),
    inference(demodulation,[status(thm)],[c_247,c_12720]) ).

cnf(c_12731,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_12729,c_204]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWC277+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Aug 28 18:04:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  Running first-order theorem proving
% 0.20/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.46/1.16  % SZS status Started for theBenchmark.p
% 0.46/1.16  % SZS status Theorem for theBenchmark.p
% 0.46/1.16  
% 0.46/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.46/1.16  
% 0.46/1.16  ------  iProver source info
% 0.46/1.16  
% 0.46/1.16  git: date: 2023-05-31 18:12:56 +0000
% 0.46/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.46/1.16  git: non_committed_changes: false
% 0.46/1.16  git: last_make_outside_of_git: false
% 0.46/1.16  
% 0.46/1.16  ------ Parsing...
% 0.46/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.46/1.16  
% 0.46/1.16  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e 
% 0.46/1.16  
% 0.46/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.46/1.16  
% 0.46/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.46/1.16  ------ Proving...
% 0.46/1.16  ------ Problem Properties 
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  clauses                                 185
% 0.46/1.16  conjectures                             4
% 0.46/1.16  EPR                                     54
% 0.46/1.16  Horn                                    116
% 0.46/1.16  unary                                   20
% 0.46/1.16  binary                                  41
% 0.46/1.16  lits                                    624
% 0.46/1.16  lits eq                                 79
% 0.46/1.16  fd_pure                                 0
% 0.46/1.16  fd_pseudo                               0
% 0.46/1.16  fd_cond                                 21
% 0.46/1.16  fd_pseudo_cond                          14
% 0.46/1.16  AC symbols                              0
% 0.46/1.16  
% 0.46/1.16  ------ Schedule dynamic 5 is on 
% 0.46/1.16  
% 0.46/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  ------ 
% 0.46/1.16  Current options:
% 0.46/1.16  ------ 
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  ------ Proving...
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  % SZS status Theorem for theBenchmark.p
% 0.46/1.16  
% 0.46/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.16  
% 0.81/1.16  
%------------------------------------------------------------------------------