TSTP Solution File: SWV409+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n032.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 : Tue Apr 30 16:46:43 EDT 2024

% Result   : Theorem 0.11s 0.33s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   49 (   7 unt;   0 def)
%            Number of atoms       :  161 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  203 (  91   ~;  69   |;  34   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :  102 (  84   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1586,plain,
    $false,
    inference(resolution,[],[f1583,f1549]) ).

fof(f1549,plain,
    less_than(sK3(sK0,sK1),sK2),
    inference(resolution,[],[f1547,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).

fof(f1547,plain,
    ~ less_than(sK2,sK3(sK0,sK1)),
    inference(resolution,[],[f1546,f51]) ).

fof(f51,plain,
    contains_slb(sK0,sK1),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ( ! [X3] :
        ( ~ less_than(sK2,X3)
        | ~ pair_in_list(update_slb(sK0,sK2),sK1,X3) )
    & ~ pair_in_list(update_slb(sK0,sK2),sK1,sK2)
    & strictly_less_than(sK1,sK2)
    & contains_slb(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f25,f39]) ).

fof(f39,plain,
    ( ? [X0,X1,X2] :
        ( ! [X3] :
            ( ~ less_than(X2,X3)
            | ~ pair_in_list(update_slb(X0,X2),X1,X3) )
        & ~ pair_in_list(update_slb(X0,X2),X1,X2)
        & strictly_less_than(X1,X2)
        & contains_slb(X0,X1) )
   => ( ! [X3] :
          ( ~ less_than(sK2,X3)
          | ~ pair_in_list(update_slb(sK0,sK2),sK1,X3) )
      & ~ pair_in_list(update_slb(sK0,sK2),sK1,sK2)
      & strictly_less_than(sK1,sK2)
      & contains_slb(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ? [X0,X1,X2] :
      ( ! [X3] :
          ( ~ less_than(X2,X3)
          | ~ pair_in_list(update_slb(X0,X2),X1,X3) )
      & ~ pair_in_list(update_slb(X0,X2),X1,X2)
      & strictly_less_than(X1,X2)
      & contains_slb(X0,X1) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ? [X0,X1,X2] :
      ( ! [X3] :
          ( ~ less_than(X2,X3)
          | ~ pair_in_list(update_slb(X0,X2),X1,X3) )
      & ~ pair_in_list(update_slb(X0,X2),X1,X2)
      & strictly_less_than(X1,X2)
      & contains_slb(X0,X1) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( strictly_less_than(X1,X2)
          & contains_slb(X0,X1) )
       => ( ? [X3] :
              ( less_than(X2,X3)
              & pair_in_list(update_slb(X0,X2),X1,X3) )
          | pair_in_list(update_slb(X0,X2),X1,X2) ) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f22,conjecture,
    ! [X0,X1,X2] :
      ( ( strictly_less_than(X1,X2)
        & contains_slb(X0,X1) )
     => ( ? [X3] :
            ( less_than(X2,X3)
            & pair_in_list(update_slb(X0,X2),X1,X3) )
        | pair_in_list(update_slb(X0,X2),X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_co) ).

fof(f1546,plain,
    ( ~ contains_slb(sK0,sK1)
    | ~ less_than(sK2,sK3(sK0,sK1)) ),
    inference(duplicate_literal_removal,[],[f1545]) ).

fof(f1545,plain,
    ( ~ less_than(sK2,sK3(sK0,sK1))
    | ~ less_than(sK2,sK3(sK0,sK1))
    | ~ contains_slb(sK0,sK1) ),
    inference(resolution,[],[f1543,f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( pair_in_list(X0,X1,sK3(X0,X1))
      | ~ contains_slb(X0,X1) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( pair_in_list(X0,X1,sK3(X0,X1))
      | ~ contains_slb(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f26,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ? [X2] : pair_in_list(X0,X1,X2)
     => pair_in_list(X0,X1,sK3(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ? [X2] : pair_in_list(X0,X1,X2)
      | ~ contains_slb(X0,X1) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( contains_slb(X0,X1)
     => ? [X2] : pair_in_list(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).

fof(f1543,plain,
    ! [X0] :
      ( ~ pair_in_list(sK0,sK1,X0)
      | ~ less_than(sK2,sK3(sK0,sK1))
      | ~ less_than(sK2,X0) ),
    inference(resolution,[],[f1448,f52]) ).

fof(f52,plain,
    strictly_less_than(sK1,sK2),
    inference(cnf_transformation,[],[f40]) ).

fof(f1448,plain,
    ! [X0] :
      ( ~ strictly_less_than(sK1,sK2)
      | ~ less_than(sK2,X0)
      | ~ less_than(sK2,sK3(sK0,sK1))
      | ~ pair_in_list(sK0,sK1,X0) ),
    inference(resolution,[],[f1447,f58]) ).

fof(f58,plain,
    ! [X2,X3,X0,X1] :
      ( less_than(X3,sK4(X0,X1,X3))
      | ~ less_than(X3,X2)
      | ~ strictly_less_than(X1,X3)
      | ~ pair_in_list(X0,X1,X2) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1,X2,X3] :
      ( ( less_than(X3,sK4(X0,X1,X3))
        & pair_in_list(update_slb(X0,X3),X1,sK4(X0,X1,X3)) )
      | ~ less_than(X3,X2)
      | ~ strictly_less_than(X1,X3)
      | ~ pair_in_list(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f30,f43]) ).

fof(f43,plain,
    ! [X0,X1,X3] :
      ( ? [X4] :
          ( less_than(X3,X4)
          & pair_in_list(update_slb(X0,X3),X1,X4) )
     => ( less_than(X3,sK4(X0,X1,X3))
        & pair_in_list(update_slb(X0,X3),X1,sK4(X0,X1,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( less_than(X3,X4)
          & pair_in_list(update_slb(X0,X3),X1,X4) )
      | ~ less_than(X3,X2)
      | ~ strictly_less_than(X1,X3)
      | ~ pair_in_list(X0,X1,X2) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( less_than(X3,X4)
          & pair_in_list(update_slb(X0,X3),X1,X4) )
      | ~ less_than(X3,X2)
      | ~ strictly_less_than(X1,X3)
      | ~ pair_in_list(X0,X1,X2) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1,X2,X3] :
      ( ( less_than(X3,X2)
        & strictly_less_than(X1,X3)
        & pair_in_list(X0,X1,X2) )
     => ? [X4] :
          ( less_than(X3,X4)
          & pair_in_list(update_slb(X0,X3),X1,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l49) ).

fof(f1447,plain,
    ( ~ less_than(sK2,sK4(sK0,sK1,sK2))
    | ~ less_than(sK2,sK3(sK0,sK1)) ),
    inference(resolution,[],[f1446,f51]) ).

fof(f1446,plain,
    ( ~ contains_slb(sK0,sK1)
    | ~ less_than(sK2,sK4(sK0,sK1,sK2))
    | ~ less_than(sK2,sK3(sK0,sK1)) ),
    inference(resolution,[],[f1444,f55]) ).

fof(f1444,plain,
    ! [X0] :
      ( ~ pair_in_list(sK0,sK1,X0)
      | ~ less_than(sK2,X0)
      | ~ less_than(sK2,sK4(sK0,sK1,sK2)) ),
    inference(resolution,[],[f1440,f52]) ).

fof(f1440,plain,
    ! [X0] :
      ( ~ strictly_less_than(sK1,sK2)
      | ~ less_than(sK2,X0)
      | ~ pair_in_list(sK0,sK1,X0)
      | ~ less_than(sK2,sK4(sK0,sK1,sK2)) ),
    inference(resolution,[],[f57,f54]) ).

fof(f54,plain,
    ! [X3] :
      ( ~ pair_in_list(update_slb(sK0,sK2),sK1,X3)
      | ~ less_than(sK2,X3) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f57,plain,
    ! [X2,X3,X0,X1] :
      ( pair_in_list(update_slb(X0,X3),X1,sK4(X0,X1,X3))
      | ~ less_than(X3,X2)
      | ~ strictly_less_than(X1,X3)
      | ~ pair_in_list(X0,X1,X2) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f1583,plain,
    ~ less_than(sK3(sK0,sK1),sK2),
    inference(resolution,[],[f1548,f51]) ).

fof(f1548,plain,
    ( ~ contains_slb(sK0,sK1)
    | ~ less_than(sK3(sK0,sK1),sK2) ),
    inference(resolution,[],[f1547,f610]) ).

fof(f610,plain,
    ( less_than(sK2,sK3(sK0,sK1))
    | ~ less_than(sK3(sK0,sK1),sK2)
    | ~ contains_slb(sK0,sK1) ),
    inference(resolution,[],[f609,f55]) ).

fof(f609,plain,
    ! [X0] :
      ( ~ pair_in_list(sK0,sK1,X0)
      | less_than(sK2,X0)
      | ~ less_than(X0,sK2) ),
    inference(resolution,[],[f603,f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( strictly_less_than(X0,X1)
        | less_than(X1,X0)
        | ~ less_than(X0,X1) )
      & ( ( ~ less_than(X1,X0)
          & less_than(X0,X1) )
        | ~ strictly_less_than(X0,X1) ) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( strictly_less_than(X0,X1)
        | less_than(X1,X0)
        | ~ less_than(X0,X1) )
      & ( ( ~ less_than(X1,X0)
          & less_than(X0,X1) )
        | ~ strictly_less_than(X0,X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
    <=> ( ~ less_than(X1,X0)
        & less_than(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).

fof(f603,plain,
    ! [X0] :
      ( ~ strictly_less_than(X0,sK2)
      | ~ pair_in_list(sK0,sK1,X0) ),
    inference(resolution,[],[f600,f52]) ).

fof(f600,plain,
    ! [X0] :
      ( ~ strictly_less_than(sK1,sK2)
      | ~ strictly_less_than(X0,sK2)
      | ~ pair_in_list(sK0,sK1,X0) ),
    inference(resolution,[],[f56,f53]) ).

fof(f53,plain,
    ~ pair_in_list(update_slb(sK0,sK2),sK1,sK2),
    inference(cnf_transformation,[],[f40]) ).

fof(f56,plain,
    ! [X2,X3,X0,X1] :
      ( pair_in_list(update_slb(X0,X3),X1,X3)
      | ~ strictly_less_than(X2,X3)
      | ~ strictly_less_than(X1,X3)
      | ~ pair_in_list(X0,X1,X2) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] :
      ( pair_in_list(update_slb(X0,X3),X1,X3)
      | ~ strictly_less_than(X2,X3)
      | ~ strictly_less_than(X1,X3)
      | ~ pair_in_list(X0,X1,X2) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2,X3] :
      ( pair_in_list(update_slb(X0,X3),X1,X3)
      | ~ strictly_less_than(X2,X3)
      | ~ strictly_less_than(X1,X3)
      | ~ pair_in_list(X0,X1,X2) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0,X1,X2,X3] :
      ( ( strictly_less_than(X2,X3)
        & strictly_less_than(X1,X3)
        & pair_in_list(X0,X1,X2) )
     => pair_in_list(update_slb(X0,X3),X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l48) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem    : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.09  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.27  % Computer : n032.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit   : 300
% 0.07/0.27  % WCLimit    : 300
% 0.07/0.27  % DateTime   : Tue Apr 30 04:45:06 EDT 2024
% 0.07/0.27  % CPUTime    : 
% 0.07/0.28  % (8544)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.29  % (8549)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.07/0.29  % (8545)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.29  % (8550)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.07/0.29  % (8547)WARNING: value z3 for option sas not known
% 0.07/0.29  % (8548)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.29  % (8546)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.29  % (8547)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.07/0.29  % (8551)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.07/0.29  TRYING [1]
% 0.07/0.29  TRYING [2]
% 0.07/0.30  TRYING [3]
% 0.07/0.30  TRYING [1]
% 0.07/0.30  TRYING [2]
% 0.11/0.31  TRYING [4]
% 0.11/0.32  TRYING [3]
% 0.11/0.32  TRYING [1]
% 0.11/0.32  TRYING [2]
% 0.11/0.32  TRYING [3]
% 0.11/0.33  % (8550)First to succeed.
% 0.11/0.33  % (8550)Refutation found. Thanks to Tanya!
% 0.11/0.33  % SZS status Theorem for theBenchmark
% 0.11/0.33  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.33  % (8550)------------------------------
% 0.11/0.33  % (8550)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.33  % (8550)Termination reason: Refutation
% 0.11/0.33  
% 0.11/0.33  % (8550)Memory used [KB]: 1082
% 0.11/0.33  % (8550)Time elapsed: 0.039 s
% 0.11/0.33  % (8550)Instructions burned: 112 (million)
% 0.11/0.33  % (8550)------------------------------
% 0.11/0.33  % (8550)------------------------------
% 0.11/0.33  % (8544)Success in time 0.053 s
%------------------------------------------------------------------------------