TSTP Solution File: PUZ062-2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% 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 : n002.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 18:10:59 EDT 2022

% Result   : Unsatisfiable 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   54 (  19 unt;   0 def)
%            Number of atoms       :  101 (  11 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   89 (  42   ~;  41   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   7 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;  11 con; 0-4 aty)
%            Number of variables   :   22 (  22   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f84,plain,
    $false,
    inference(avatar_sat_refutation,[],[f30,f57,f60,f72,f75,f78,f83]) ).

fof(f83,plain,
    ~ spl0_5,
    inference(avatar_contradiction_clause,[],[f82]) ).

fof(f82,plain,
    ( $false
    | ~ spl0_5 ),
    inference(subsumption_resolution,[],[f81,f42]) ).

fof(f42,plain,
    ~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[],[f41,f17]) ).

fof(f17,plain,
    ! [X0] :
      ( ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
      | ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) ),
    inference(subsumption_resolution,[],[f14,f7]) ).

fof(f7,axiom,
    ! [X1,X6] : ~ c_in(X6,c_emptyset,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).

fof(f14,plain,
    ! [X0] :
      ( ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
      | c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
      | ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat)) ),
    inference(superposition,[],[f5,f10]) ).

fof(f10,axiom,
    c_emptyset = c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f5,axiom,
    ! [X0,X1,X6,X7] :
      ( c_in(X6,c_inter(X0,X7,X1),X1)
      | ~ c_in(X6,X7,X1)
      | ~ c_in(X6,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).

fof(f41,plain,
    c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[],[f37,f4]) ).

fof(f4,axiom,
    ! [X0,X1,X6,X7] :
      ( ~ c_in(X6,c_inter(X0,X7,X1),X1)
      | c_in(X6,X7,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).

fof(f37,plain,
    c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    inference(superposition,[],[f6,f12]) ).

fof(f12,axiom,
    c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f6,axiom,
    ! [X2,X0,X1] : c_in(X2,c_insert(X2,X0,X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).

fof(f81,plain,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat))
    | ~ spl0_5 ),
    inference(resolution,[],[f56,f4]) ).

fof(f56,plain,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f54]) ).

fof(f54,plain,
    ( spl0_5
  <=> c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f78,plain,
    ~ spl0_6,
    inference(avatar_contradiction_clause,[],[f77]) ).

fof(f77,plain,
    ( $false
    | ~ spl0_6 ),
    inference(subsumption_resolution,[],[f76,f36]) ).

fof(f36,plain,
    ~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[],[f35,f17]) ).

fof(f35,plain,
    c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[],[f31,f4]) ).

fof(f31,plain,
    c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    inference(superposition,[],[f6,f11]) ).

fof(f11,axiom,
    c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f76,plain,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat))
    | ~ spl0_6 ),
    inference(resolution,[],[f67,f4]) ).

fof(f67,plain,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f65,plain,
    ( spl0_6
  <=> c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f75,plain,
    ( ~ spl0_1
    | spl0_7 ),
    inference(avatar_contradiction_clause,[],[f74]) ).

fof(f74,plain,
    ( $false
    | ~ spl0_1
    | spl0_7 ),
    inference(subsumption_resolution,[],[f73,f20]) ).

fof(f20,plain,
    ( c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f19]) ).

fof(f19,plain,
    ( spl0_1
  <=> c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f73,plain,
    ( ~ c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | spl0_7 ),
    inference(resolution,[],[f71,f2]) ).

fof(f2,axiom,
    ! [X3,X1,X4] :
      ( c_in(c_inter(X4,X3,X1),c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

fof(f71,plain,
    ( ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | spl0_7 ),
    inference(avatar_component_clause,[],[f69]) ).

fof(f69,plain,
    ( spl0_7
  <=> c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f72,plain,
    ( spl0_6
    | ~ spl0_7
    | spl0_3 ),
    inference(avatar_split_clause,[],[f63,f46,f69,f65]) ).

fof(f46,plain,
    ( spl0_3
  <=> c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f63,plain,
    ( ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | spl0_3 ),
    inference(trivial_inequality_removal,[],[f62]) ).

fof(f62,plain,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | spl0_3 ),
    inference(superposition,[],[f48,f1]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1))
      | c_in(X2,X0,X1)
      | ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).

fof(f48,plain,
    ( c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | spl0_3 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f60,plain,
    ( ~ spl0_1
    | spl0_4 ),
    inference(avatar_contradiction_clause,[],[f59]) ).

fof(f59,plain,
    ( $false
    | ~ spl0_1
    | spl0_4 ),
    inference(subsumption_resolution,[],[f58,f20]) ).

fof(f58,plain,
    ( ~ c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | spl0_4 ),
    inference(resolution,[],[f52,f2]) ).

fof(f52,plain,
    ( ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | spl0_4 ),
    inference(avatar_component_clause,[],[f50]) ).

fof(f50,plain,
    ( spl0_4
  <=> c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f57,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | spl0_5 ),
    inference(avatar_split_clause,[],[f44,f54,f50,f46]) ).

fof(f44,plain,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
    inference(forward_demodulation,[],[f43,f9]) ).

fof(f9,axiom,
    c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f43,plain,
    ( ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
    inference(superposition,[],[f13,f1]) ).

fof(f13,axiom,
    c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

fof(f30,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f27,f19]) ).

fof(f27,plain,
    c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(resolution,[],[f8,f3]) ).

fof(f3,axiom,
    ! [X5] :
      ( ~ c_in(X5,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
      | c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).

fof(f8,axiom,
    c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n002.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   : Tue Aug 30 10:58:14 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.20/0.43  % (20378)lrs+1011_1:1_aac=none:bsr=unit_only:ep=R:sac=on:sos=all:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.43  % (20370)fmb+10_1:1_fmbes=contour:fmbsr=2.0:fmbsso=input_usage:i=6:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.44  TRYING [1]
% 0.20/0.44  TRYING [2]
% 0.20/0.44  TRYING [2]
% 0.20/0.44  % (20370)Instruction limit reached!
% 0.20/0.44  % (20370)------------------------------
% 0.20/0.44  % (20370)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.44  % (20370)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.44  % (20370)Termination reason: Unknown
% 0.20/0.44  % (20370)Termination phase: Finite model building constraint generation
% 0.20/0.44  
% 0.20/0.44  % (20370)Memory used [KB]: 6012
% 0.20/0.44  % (20370)Time elapsed: 0.040 s
% 0.20/0.44  % (20370)Instructions burned: 6 (million)
% 0.20/0.44  % (20370)------------------------------
% 0.20/0.44  % (20370)------------------------------
% 0.20/0.44  % (20362)lrs+1010_1:4_amm=off:bce=on:sd=1:sos=on:ss=included:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.45  % (20362)First to succeed.
% 0.20/0.45  % (20362)Refutation found. Thanks to Tanya!
% 0.20/0.45  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.45  % (20362)------------------------------
% 0.20/0.45  % (20362)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.45  % (20362)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.45  % (20362)Termination reason: Refutation
% 0.20/0.45  
% 0.20/0.45  % (20362)Memory used [KB]: 5884
% 0.20/0.45  % (20362)Time elapsed: 0.057 s
% 0.20/0.45  % (20362)Instructions burned: 5 (million)
% 0.20/0.45  % (20362)------------------------------
% 0.20/0.45  % (20362)------------------------------
% 0.20/0.45  % (20352)Success in time 0.11 s
%------------------------------------------------------------------------------