TSTP Solution File: GEO083+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GEO083+1 : TPTP v8.2.0. Released v2.4.0.
% 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 : Mon Jun 24 06:13:01 EDT 2024

% Result   : Theorem 27.82s 4.72s
% Output   : CNFRefutation 27.82s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( incident_c(X2,X1)
         => incident_c(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn) ).

fof(f2,axiom,
    ! [X0,X1,X3] :
      ( sum(X1,X3) = X0
    <=> ! [X4] :
          ( incident_c(X4,X0)
        <=> ( incident_c(X4,X3)
            | incident_c(X4,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn) ).

fof(f17,conjecture,
    ! [X1,X3,X5,X2] :
      ( ( meet(X2,X1,X5)
        & meet(X2,X1,X3)
        & part_of(X3,X5) )
     => part_of(sum(X1,X3),sum(X1,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_1) ).

fof(f18,negated_conjecture,
    ~ ! [X1,X3,X5,X2] :
        ( ( meet(X2,X1,X5)
          & meet(X2,X1,X3)
          & part_of(X3,X5) )
       => part_of(sum(X1,X3),sum(X1,X5)) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( sum(X1,X2) = X0
    <=> ! [X3] :
          ( incident_c(X3,X0)
        <=> ( incident_c(X3,X2)
            | incident_c(X3,X1) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f32,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( meet(X3,X0,X2)
          & meet(X3,X0,X1)
          & part_of(X1,X2) )
       => part_of(sum(X0,X1),sum(X0,X2)) ),
    inference(rectify,[],[f18]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( incident_c(X2,X0)
          | ~ incident_c(X2,X1) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f54,plain,
    ? [X0,X1,X2,X3] :
      ( ~ part_of(sum(X0,X1),sum(X0,X2))
      & meet(X3,X0,X2)
      & meet(X3,X0,X1)
      & part_of(X1,X2) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f55,plain,
    ? [X0,X1,X2,X3] :
      ( ~ part_of(sum(X0,X1),sum(X0,X2))
      & meet(X3,X0,X2)
      & meet(X3,X0,X1)
      & part_of(X1,X2) ),
    inference(flattening,[],[f54]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ? [X2] :
            ( ~ incident_c(X2,X0)
            & incident_c(X2,X1) ) )
      & ( ! [X2] :
            ( incident_c(X2,X0)
            | ~ incident_c(X2,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(nnf_transformation,[],[f35]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ? [X2] :
            ( ~ incident_c(X2,X0)
            & incident_c(X2,X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(rectify,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ incident_c(X2,X0)
          & incident_c(X2,X1) )
     => ( ~ incident_c(sK0(X0,X1),X0)
        & incident_c(sK0(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ( ~ incident_c(sK0(X0,X1),X0)
          & incident_c(sK0(X0,X1),X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f57,f58]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) ) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | ~ incident_c(X3,X0) ) )
        | sum(X1,X2) != X0 ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) ) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | ~ incident_c(X3,X0) ) )
        | sum(X1,X2) != X0 ) ),
    inference(flattening,[],[f60]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X4] :
            ( ( incident_c(X4,X0)
              | ( ~ incident_c(X4,X2)
                & ~ incident_c(X4,X1) ) )
            & ( incident_c(X4,X2)
              | incident_c(X4,X1)
              | ~ incident_c(X4,X0) ) )
        | sum(X1,X2) != X0 ) ),
    inference(rectify,[],[f61]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ incident_c(X3,X2)
              & ~ incident_c(X3,X1) )
            | ~ incident_c(X3,X0) )
          & ( incident_c(X3,X2)
            | incident_c(X3,X1)
            | incident_c(X3,X0) ) )
     => ( ( ( ~ incident_c(sK1(X0,X1,X2),X2)
            & ~ incident_c(sK1(X0,X1,X2),X1) )
          | ~ incident_c(sK1(X0,X1,X2),X0) )
        & ( incident_c(sK1(X0,X1,X2),X2)
          | incident_c(sK1(X0,X1,X2),X1)
          | incident_c(sK1(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0
        | ( ( ( ~ incident_c(sK1(X0,X1,X2),X2)
              & ~ incident_c(sK1(X0,X1,X2),X1) )
            | ~ incident_c(sK1(X0,X1,X2),X0) )
          & ( incident_c(sK1(X0,X1,X2),X2)
            | incident_c(sK1(X0,X1,X2),X1)
            | incident_c(sK1(X0,X1,X2),X0) ) ) )
      & ( ! [X4] :
            ( ( incident_c(X4,X0)
              | ( ~ incident_c(X4,X2)
                & ~ incident_c(X4,X1) ) )
            & ( incident_c(X4,X2)
              | incident_c(X4,X1)
              | ~ incident_c(X4,X0) ) )
        | sum(X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f62,f63]) ).

fof(f93,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ part_of(sum(X0,X1),sum(X0,X2))
        & meet(X3,X0,X2)
        & meet(X3,X0,X1)
        & part_of(X1,X2) )
   => ( ~ part_of(sum(sK13,sK14),sum(sK13,sK15))
      & meet(sK16,sK13,sK15)
      & meet(sK16,sK13,sK14)
      & part_of(sK14,sK15) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ( ~ part_of(sum(sK13,sK14),sum(sK13,sK15))
    & meet(sK16,sK13,sK15)
    & meet(sK16,sK13,sK14)
    & part_of(sK14,sK15) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f55,f93]) ).

fof(f95,plain,
    ! [X3,X0,X1] :
      ( incident_c(X3,X0)
      | ~ incident_c(X3,X1)
      | ~ part_of(X1,X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
      | incident_c(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
      | ~ incident_c(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f98,plain,
    ! [X2,X0,X1,X4] :
      ( incident_c(X4,X2)
      | incident_c(X4,X1)
      | ~ incident_c(X4,X0)
      | sum(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f99,plain,
    ! [X2,X0,X1,X4] :
      ( incident_c(X4,X0)
      | ~ incident_c(X4,X1)
      | sum(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f100,plain,
    ! [X2,X0,X1,X4] :
      ( incident_c(X4,X0)
      | ~ incident_c(X4,X2)
      | sum(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f136,plain,
    part_of(sK14,sK15),
    inference(cnf_transformation,[],[f94]) ).

fof(f139,plain,
    ~ part_of(sum(sK13,sK14),sum(sK13,sK15)),
    inference(cnf_transformation,[],[f94]) ).

fof(f140,plain,
    ! [X2,X1,X4] :
      ( incident_c(X4,sum(X1,X2))
      | ~ incident_c(X4,X2) ),
    inference(equality_resolution,[],[f100]) ).

fof(f141,plain,
    ! [X2,X1,X4] :
      ( incident_c(X4,sum(X1,X2))
      | ~ incident_c(X4,X1) ),
    inference(equality_resolution,[],[f99]) ).

fof(f142,plain,
    ! [X2,X1,X4] :
      ( incident_c(X4,X2)
      | incident_c(X4,X1)
      | ~ incident_c(X4,sum(X1,X2)) ),
    inference(equality_resolution,[],[f98]) ).

cnf(c_49,plain,
    ( ~ incident_c(sK0(X0,X1),X0)
    | part_of(X1,X0) ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_50,plain,
    ( incident_c(sK0(X0,X1),X1)
    | part_of(X1,X0) ),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_51,plain,
    ( ~ part_of(X0,X1)
    | ~ incident_c(X2,X0)
    | incident_c(X2,X1) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_55,plain,
    ( ~ incident_c(X0,X1)
    | incident_c(X0,sum(X2,X1)) ),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_56,plain,
    ( ~ incident_c(X0,X1)
    | incident_c(X0,sum(X1,X2)) ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_57,plain,
    ( ~ incident_c(X0,sum(X1,X2))
    | incident_c(X0,X1)
    | incident_c(X0,X2) ),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_90,negated_conjecture,
    ~ part_of(sum(sK13,sK14),sum(sK13,sK15)),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_93,negated_conjecture,
    part_of(sK14,sK15),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_150,plain,
    sum(sK13,sK14) = sP0_iProver_def,
    definition ).

cnf(c_151,plain,
    sum(sK13,sK15) = sP1_iProver_def,
    definition ).

cnf(c_152,negated_conjecture,
    part_of(sK14,sK15),
    inference(demodulation,[status(thm)],[c_93]) ).

cnf(c_155,negated_conjecture,
    ~ part_of(sP0_iProver_def,sP1_iProver_def),
    inference(demodulation,[status(thm)],[c_90,c_151,c_150]) ).

cnf(c_206,plain,
    ( ~ incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
    | part_of(sP0_iProver_def,sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_264,plain,
    ( ~ incident_c(X0,sK13)
    | incident_c(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_151,c_56]) ).

cnf(c_388,plain,
    ( ~ part_of(X0,X1)
    | incident_c(sK0(X2,X0),X1)
    | part_of(X0,X2) ),
    inference(superposition,[status(thm)],[c_50,c_51]) ).

cnf(c_467,plain,
    ( incident_c(sK0(X0,sK13),sP1_iProver_def)
    | part_of(sK13,X0) ),
    inference(superposition,[status(thm)],[c_50,c_264]) ).

cnf(c_722,plain,
    ( ~ incident_c(X0,sP0_iProver_def)
    | incident_c(X0,sK13)
    | incident_c(X0,sK14) ),
    inference(superposition,[status(thm)],[c_150,c_57]) ).

cnf(c_814,plain,
    ( ~ incident_c(sK0(X0,X1),X2)
    | ~ part_of(X2,X3)
    | incident_c(sK0(X0,X1),X3) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_981,plain,
    part_of(sK13,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_467,c_49]) ).

cnf(c_3642,plain,
    ( ~ incident_c(sK0(sP1_iProver_def,sP0_iProver_def),X0)
    | ~ part_of(X0,sP1_iProver_def)
    | incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_814]) ).

cnf(c_3643,plain,
    ( ~ incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sK13)
    | ~ part_of(sK13,sP1_iProver_def)
    | incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_3642]) ).

cnf(c_15001,plain,
    ( ~ incident_c(X0,sK15)
    | incident_c(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_151,c_55]) ).

cnf(c_16929,plain,
    ( ~ part_of(X0,sK15)
    | incident_c(sK0(X1,X0),sP1_iProver_def)
    | part_of(X0,X1) ),
    inference(superposition,[status(thm)],[c_388,c_15001]) ).

cnf(c_16970,plain,
    ( ~ part_of(X0,sK15)
    | part_of(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_16929,c_49]) ).

cnf(c_17029,plain,
    part_of(sK14,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_152,c_16970]) ).

cnf(c_19786,plain,
    ( incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
    | part_of(sP0_iProver_def,sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_43646,plain,
    ( ~ incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sK14)
    | ~ part_of(sK14,sP1_iProver_def)
    | incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_3642]) ).

cnf(c_63448,plain,
    ( ~ incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
    | incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sK13)
    | incident_c(sK0(sP1_iProver_def,sP0_iProver_def),sK14) ),
    inference(instantiation,[status(thm)],[c_722]) ).

cnf(c_63449,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_63448,c_43646,c_19786,c_17029,c_3643,c_981,c_206,c_155]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GEO083+1 : TPTP v8.2.0. Released v2.4.0.
% 0.04/0.13  % 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 Jun 21 10:45:09 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  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
% 27.82/4.72  % SZS status Started for theBenchmark.p
% 27.82/4.72  % SZS status Theorem for theBenchmark.p
% 27.82/4.72  
% 27.82/4.72  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 27.82/4.72  
% 27.82/4.72  ------  iProver source info
% 27.82/4.72  
% 27.82/4.72  git: date: 2024-06-12 09:56:46 +0000
% 27.82/4.72  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 27.82/4.72  git: non_committed_changes: false
% 27.82/4.72  
% 27.82/4.72  ------ Parsing...
% 27.82/4.72  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 27.82/4.72  
% 27.82/4.72  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e 
% 27.82/4.72  
% 27.82/4.72  ------ Preprocessing...
% 27.82/4.72  
% 27.82/4.72  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 27.82/4.72  ------ Proving...
% 27.82/4.72  ------ Problem Properties 
% 27.82/4.72  
% 27.82/4.72  
% 27.82/4.72  clauses                                 47
% 27.82/4.72  conjectures                             6
% 27.82/4.72  EPR                                     17
% 27.82/4.72  Horn                                    31
% 27.82/4.72  unary                                   7
% 27.82/4.72  binary                                  16
% 27.82/4.72  lits                                    135
% 27.82/4.72  lits eq                                 14
% 27.82/4.72  fd_pure                                 0
% 27.82/4.72  fd_pseudo                               0
% 27.82/4.72  fd_cond                                 0
% 27.82/4.73  fd_pseudo_cond                          7
% 27.82/4.73  AC symbols                              0
% 27.82/4.73  
% 27.82/4.73  ------ Input Options Time Limit: Unbounded
% 27.82/4.73  
% 27.82/4.73  
% 27.82/4.73  ------ 
% 27.82/4.73  Current options:
% 27.82/4.73  ------ 
% 27.82/4.73  
% 27.82/4.73  
% 27.82/4.73  
% 27.82/4.73  
% 27.82/4.73  ------ Proving...
% 27.82/4.73  
% 27.82/4.73  
% 27.82/4.73  % SZS status Theorem for theBenchmark.p
% 27.82/4.73  
% 27.82/4.73  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.82/4.73  
% 27.82/4.73  
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