TSTP Solution File: SWV411+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWV411+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n020.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 : Wed Aug 31 18:45:29 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   32 (   8 unt;   0 def)
%            Number of atoms       :  112 (  31 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  125 (  45   ~;  38   |;  29   &)
%                                         (   4 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  121 (  94   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f100,plain,
    $false,
    inference(subsumption_resolution,[],[f96,f92]) ).

fof(f92,plain,
    sK2 != sK3,
    inference(constrained_resolution,[],[f75,f88]) ).

fof(f88,plain,
    ! [X3,X0,X4] : pair_in_list(insert_slb(X0,pair(X4,X3)),X4,X3),
    inference(equality_resolution,[],[f87]) ).

fof(f87,plain,
    ! [X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X4,X3)
      | X1 != X4 ),
    inference(equality_resolution,[],[f78]) ).

fof(f78,plain,
    ! [X2,X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X4,X2)
      | X2 != X3
      | X1 != X4 ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( X2 = X3
          & X1 = X4 )
        | pair_in_list(X0,X4,X2)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X4,X2) )
      & ( pair_in_list(insert_slb(X0,pair(X1,X3)),X4,X2)
        | ( ( X2 != X3
            | X1 != X4 )
          & ~ pair_in_list(X0,X4,X2) ) ) ),
    inference(rectify,[],[f55]) ).

fof(f55,plain,
    ! [X1,X0,X2,X3,X4] :
      ( ( ( X2 = X3
          & X0 = X4 )
        | pair_in_list(X1,X4,X2)
        | ~ pair_in_list(insert_slb(X1,pair(X0,X3)),X4,X2) )
      & ( pair_in_list(insert_slb(X1,pair(X0,X3)),X4,X2)
        | ( ( X2 != X3
            | X0 != X4 )
          & ~ pair_in_list(X1,X4,X2) ) ) ),
    inference(flattening,[],[f54]) ).

fof(f54,plain,
    ! [X1,X0,X2,X3,X4] :
      ( ( ( X2 = X3
          & X0 = X4 )
        | pair_in_list(X1,X4,X2)
        | ~ pair_in_list(insert_slb(X1,pair(X0,X3)),X4,X2) )
      & ( pair_in_list(insert_slb(X1,pair(X0,X3)),X4,X2)
        | ( ( X2 != X3
            | X0 != X4 )
          & ~ pair_in_list(X1,X4,X2) ) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0,X2,X3,X4] :
      ( ( ( X2 = X3
          & X0 = X4 )
        | pair_in_list(X1,X4,X2) )
    <=> pair_in_list(insert_slb(X1,pair(X0,X3)),X4,X2) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X1,X0,X4,X3,X2] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
    <=> ( pair_in_list(X0,X2,X4)
        | ( X1 = X2
          & X3 = X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).

fof(f75,plain,
    ! [X4] : ~ pair_in_list(insert_slb(sK0,pair(sK3,sK1)),sK2,X4),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ( contains_slb(insert_slb(sK0,pair(sK3,sK1)),sK2)
    & ! [X4] : ~ pair_in_list(insert_slb(sK0,pair(sK3,sK1)),sK2,X4)
    & ! [X5] :
        ( pair_in_list(sK0,X5,sK4(X5))
        | ~ contains_slb(sK0,X5) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f49,f52,f51,f50]) ).

fof(f50,plain,
    ( ? [X0] :
        ( ? [X1,X2,X3] :
            ( contains_slb(insert_slb(X0,pair(X3,X1)),X2)
            & ! [X4] : ~ pair_in_list(insert_slb(X0,pair(X3,X1)),X2,X4) )
        & ! [X5] :
            ( ? [X6] : pair_in_list(X0,X5,X6)
            | ~ contains_slb(X0,X5) ) )
   => ( ? [X3,X2,X1] :
          ( contains_slb(insert_slb(sK0,pair(X3,X1)),X2)
          & ! [X4] : ~ pair_in_list(insert_slb(sK0,pair(X3,X1)),X2,X4) )
      & ! [X5] :
          ( ? [X6] : pair_in_list(sK0,X5,X6)
          | ~ contains_slb(sK0,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f51,plain,
    ( ? [X3,X2,X1] :
        ( contains_slb(insert_slb(sK0,pair(X3,X1)),X2)
        & ! [X4] : ~ pair_in_list(insert_slb(sK0,pair(X3,X1)),X2,X4) )
   => ( contains_slb(insert_slb(sK0,pair(sK3,sK1)),sK2)
      & ! [X4] : ~ pair_in_list(insert_slb(sK0,pair(sK3,sK1)),sK2,X4) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ! [X5] :
      ( ? [X6] : pair_in_list(sK0,X5,X6)
     => pair_in_list(sK0,X5,sK4(X5)) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ? [X0] :
      ( ? [X1,X2,X3] :
          ( contains_slb(insert_slb(X0,pair(X3,X1)),X2)
          & ! [X4] : ~ pair_in_list(insert_slb(X0,pair(X3,X1)),X2,X4) )
      & ! [X5] :
          ( ? [X6] : pair_in_list(X0,X5,X6)
          | ~ contains_slb(X0,X5) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ? [X0] :
      ( ? [X5,X3,X4] :
          ( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
          & ! [X6] : ~ pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) )
      & ! [X1] :
          ( ? [X2] : pair_in_list(X0,X1,X2)
          | ~ contains_slb(X0,X1) ) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X0] :
        ( ! [X1] :
            ( contains_slb(X0,X1)
           => ? [X2] : pair_in_list(X0,X1,X2) )
       => ! [X3,X5,X4] :
            ( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
           => ? [X6] : pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X0] :
      ( ! [X1] :
          ( contains_slb(X0,X1)
         => ? [X2] : pair_in_list(X0,X1,X2) )
     => ! [X3,X5,X4] :
          ( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
         => ? [X6] : pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l47_co) ).

fof(f96,plain,
    sK2 = sK3,
    inference(resolution,[],[f95,f76]) ).

fof(f76,plain,
    contains_slb(insert_slb(sK0,pair(sK3,sK1)),sK2),
    inference(cnf_transformation,[],[f53]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ~ contains_slb(insert_slb(sK0,pair(X0,X1)),sK2)
      | sK2 = X0 ),
    inference(resolution,[],[f94,f81]) ).

fof(f81,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(X0,X3)
      | ~ contains_slb(insert_slb(X0,pair(X1,X2)),X3)
      | X1 = X3 ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(insert_slb(X0,pair(X1,X2)),X3)
        | ( X1 != X3
          & ~ contains_slb(X0,X3) ) )
      & ( X1 = X3
        | contains_slb(X0,X3)
        | ~ contains_slb(insert_slb(X0,pair(X1,X2)),X3) ) ),
    inference(rectify,[],[f58]) ).

fof(f58,plain,
    ! [X3,X2,X1,X0] :
      ( ( contains_slb(insert_slb(X3,pair(X2,X1)),X0)
        | ( X0 != X2
          & ~ contains_slb(X3,X0) ) )
      & ( X0 = X2
        | contains_slb(X3,X0)
        | ~ contains_slb(insert_slb(X3,pair(X2,X1)),X0) ) ),
    inference(flattening,[],[f57]) ).

fof(f57,plain,
    ! [X3,X2,X1,X0] :
      ( ( contains_slb(insert_slb(X3,pair(X2,X1)),X0)
        | ( X0 != X2
          & ~ contains_slb(X3,X0) ) )
      & ( X0 = X2
        | contains_slb(X3,X0)
        | ~ contains_slb(insert_slb(X3,pair(X2,X1)),X0) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X3,X2,X1,X0] :
      ( contains_slb(insert_slb(X3,pair(X2,X1)),X0)
    <=> ( X0 = X2
        | contains_slb(X3,X0) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X2,X3,X1,X0] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
    <=> ( contains_slb(X0,X2)
        | X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).

fof(f94,plain,
    ~ contains_slb(sK0,sK2),
    inference(resolution,[],[f91,f74]) ).

fof(f74,plain,
    ! [X5] :
      ( pair_in_list(sK0,X5,sK4(X5))
      | ~ contains_slb(sK0,X5) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f91,plain,
    ! [X0] : ~ pair_in_list(sK0,sK2,X0),
    inference(resolution,[],[f75,f77]) ).

fof(f77,plain,
    ! [X2,X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X4,X2)
      | ~ pair_in_list(X0,X4,X2) ),
    inference(cnf_transformation,[],[f56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SWV411+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n020.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   : Tue Aug 30 19:25:15 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (22388)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50  % (22374)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (22387)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50  % (22376)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.50  % (22394)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50  % (22382)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.50  % (22374)Instruction limit reached!
% 0.19/0.50  % (22374)------------------------------
% 0.19/0.50  % (22374)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (22374)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (22374)Termination reason: Unknown
% 0.19/0.50  % (22374)Termination phase: Saturation
% 0.19/0.50  
% 0.19/0.50  % (22374)Memory used [KB]: 6012
% 0.19/0.50  % (22374)Time elapsed: 0.106 s
% 0.19/0.50  % (22374)Instructions burned: 3 (million)
% 0.19/0.50  % (22374)------------------------------
% 0.19/0.50  % (22374)------------------------------
% 0.19/0.50  % (22380)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.51  % (22386)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51  % (22386)Instruction limit reached!
% 0.19/0.51  % (22386)------------------------------
% 0.19/0.51  % (22386)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (22386)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (22386)Termination reason: Unknown
% 0.19/0.51  % (22386)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (22386)Memory used [KB]: 6012
% 0.19/0.51  % (22386)Time elapsed: 0.065 s
% 0.19/0.51  % (22386)Instructions burned: 4 (million)
% 0.19/0.51  % (22386)------------------------------
% 0.19/0.51  % (22386)------------------------------
% 0.19/0.51  % (22388)First to succeed.
% 0.19/0.51  % (22379)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (22388)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (22388)------------------------------
% 0.19/0.51  % (22388)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (22388)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (22388)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (22388)Memory used [KB]: 6140
% 0.19/0.51  % (22388)Time elapsed: 0.112 s
% 0.19/0.51  % (22388)Instructions burned: 3 (million)
% 0.19/0.51  % (22388)------------------------------
% 0.19/0.51  % (22388)------------------------------
% 0.19/0.51  % (22371)Success in time 0.164 s
%------------------------------------------------------------------------------