TSTP Solution File: SWC127+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC127+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.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 : Fri May  3 03:11:19 EDT 2024

% Result   : Theorem 3.19s 1.19s
% Output   : CNFRefutation 3.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   42 (  21 unt;   0 def)
%            Number of atoms       :  205 (  39 equ)
%            Maximal formula atoms :   24 (   4 avg)
%            Number of connectives :  237 (  74   ~;  55   |;  92   &)
%                                         (   2 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   44 (   0 sgn  16   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
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(f39,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).

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

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

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

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

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

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

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

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

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

fof(f347,plain,
    ( ( ~ segmentP(sK54,sK53)
      | ~ neq(sK53,nil) )
    & ( ~ neq(sK56,nil)
      | singletonP(sK55) )
    & segmentP(sK56,sK55)
    & neq(sK54,nil)
    & 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(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(f471,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f39]) ).

fof(f547,plain,
    ssList(sK53),
    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,
    neq(sK54,nil),
    inference(cnf_transformation,[],[f347]) ).

fof(f554,plain,
    segmentP(sK56,sK55),
    inference(cnf_transformation,[],[f347]) ).

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

fof(f556,plain,
    ( ~ segmentP(sK54,sK53)
    | ~ neq(sK53,nil) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f557,plain,
    ( ~ segmentP(sK56,sK55)
    | ~ neq(sK55,nil) ),
    inference(definition_unfolding,[],[f556,f551,f552,f552]) ).

fof(f558,plain,
    neq(sK56,nil),
    inference(definition_unfolding,[],[f553,f551]) ).

fof(f560,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f547,f552]) ).

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_172,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f471]) ).

cnf(c_246,negated_conjecture,
    ( ~ neq(sK55,nil)
    | ~ segmentP(sK56,sK55) ),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_247,negated_conjecture,
    ( ~ neq(sK56,nil)
    | singletonP(sK55) ),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_248,negated_conjecture,
    segmentP(sK56,sK55),
    inference(cnf_transformation,[],[f554]) ).

cnf(c_249,negated_conjecture,
    neq(sK56,nil),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_253,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_360,negated_conjecture,
    singletonP(sK55),
    inference(global_subsumption_just,[status(thm)],[c_247,c_249,c_247]) ).

cnf(c_368,negated_conjecture,
    ~ neq(sK55,nil),
    inference(global_subsumption_just,[status(thm)],[c_246,c_248,c_246]) ).

cnf(c_3226,plain,
    ( X0 != sK55
    | X1 != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_368]) ).

cnf(c_3227,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK55)
    | sK55 = nil ),
    inference(unflattening,[status(thm)],[c_3226]) ).

cnf(c_3228,plain,
    sK55 = nil,
    inference(global_subsumption_just,[status(thm)],[c_3227,c_253,c_141,c_3227]) ).

cnf(c_6058,plain,
    singletonP(nil),
    inference(demodulation,[status(thm)],[c_360,c_3228]) ).

cnf(c_6059,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_6058,c_172]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SWC127+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May  2 23:52:51 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 3.19/1.19  % SZS status Started for theBenchmark.p
% 3.19/1.19  % SZS status Theorem for theBenchmark.p
% 3.19/1.19  
% 3.19/1.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.19/1.19  
% 3.19/1.19  ------  iProver source info
% 3.19/1.19  
% 3.19/1.19  git: date: 2024-05-02 19:28:25 +0000
% 3.19/1.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.19/1.19  git: non_committed_changes: false
% 3.19/1.19  
% 3.19/1.19  ------ Parsing...
% 3.19/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.19/1.19  
% 3.19/1.19  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e 
% 3.19/1.19  
% 3.19/1.19  % SZS status Theorem for theBenchmark.p
% 3.19/1.19  
% 3.19/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.19/1.20  
% 3.19/1.20  
%------------------------------------------------------------------------------