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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---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_sat --cores 0 -t %d %s

% Computer : n010.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 18:11:57 EDT 2022

% Result   : Unsatisfiable 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   38 (  18 unt;   0 def)
%            Number of atoms       :   64 (  14 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   55 (  29   ~;  25   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   2 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;  11 con; 0-4 aty)
%            Number of variables   :   32 (  32   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f64,plain,
    $false,
    inference(avatar_sat_refutation,[],[f31,f63]) ).

fof(f63,plain,
    ~ spl0_1,
    inference(avatar_contradiction_clause,[],[f62]) ).

fof(f62,plain,
    ( $false
    | ~ spl0_1 ),
    inference(trivial_inequality_removal,[],[f61]) ).

fof(f61,plain,
    ( 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)))
    | ~ spl0_1 ),
    inference(forward_demodulation,[],[f60,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(f60,plain,
    ( 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_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | ~ spl0_1 ),
    inference(superposition,[],[f57,f56]) ).

fof(f56,plain,
    ( ! [X1] : c_Suc(c_Finite__Set_Ocard(c_inter(X1,v_t,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(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_1 ),
    inference(resolution,[],[f50,f43]) ).

fof(f43,plain,
    ~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[],[f39,f27]) ).

fof(f27,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,[],[f26,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(f26,plain,
    ! [X0] :
      ( ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
      | ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
      | c_in(X0,c_emptyset,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(f39,plain,
    c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[],[f32,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(f32,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(f50,plain,
    ( ! [X0,X1] :
        ( c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
        | c_Suc(c_Finite__Set_Ocard(c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) )
    | ~ spl0_1 ),
    inference(resolution,[],[f42,f4]) ).

fof(f42,plain,
    ( ! [X8,X7] :
        ( c_in(X7,c_inter(X8,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
        | c_Finite__Set_Ocard(c_insert(X7,c_inter(X8,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(X8,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) )
    | ~ spl0_1 ),
    inference(resolution,[],[f34,f18]) ).

fof(f18,plain,
    ( c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f17]) ).

fof(f17,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(f34,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(X0,c_inter(X1,X2,X3),X3)
      | c_Suc(c_Finite__Set_Ocard(c_inter(X1,X2,X3),X3)) = c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,X2,X3),X3),X3) ),
    inference(resolution,[],[f1,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(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(X2,X0,X1)
      | c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).

fof(f57,plain,
    ( 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)) != 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_1 ),
    inference(backward_demodulation,[],[f13,f55]) ).

fof(f55,plain,
    ( ! [X0] : c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(X0,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(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | ~ spl0_1 ),
    inference(resolution,[],[f50,f38]) ).

fof(f38,plain,
    ~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[],[f33,f27]) ).

fof(f33,plain,
    c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[],[f28,f4]) ).

fof(f28,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(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(f31,plain,
    spl0_1,
    inference(avatar_contradiction_clause,[],[f30]) ).

fof(f30,plain,
    ( $false
    | spl0_1 ),
    inference(subsumption_resolution,[],[f29,f19]) ).

fof(f19,plain,
    ( ~ c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f17]) ).

fof(f29,plain,
    c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(resolution,[],[f3,f8]) ).

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) ).

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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n010.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 10:38:29 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.52  % (19140)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.52  % (19124)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.52  % (19140)First to succeed.
% 0.19/0.52  % (19128)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (19132)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.52  % (19127)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.52  % (19127)Instruction limit reached!
% 0.19/0.52  % (19127)------------------------------
% 0.19/0.52  % (19127)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (19127)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (19127)Termination reason: Unknown
% 0.19/0.52  % (19127)Termination phase: Saturation
% 0.19/0.52  
% 0.19/0.52  % (19127)Memory used [KB]: 5373
% 0.19/0.52  % (19127)Time elapsed: 0.113 s
% 0.19/0.52  % (19127)Instructions burned: 2 (million)
% 0.19/0.52  % (19127)------------------------------
% 0.19/0.52  % (19127)------------------------------
% 0.19/0.53  % (19141)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.53  % (19131)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.53  % (19130)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53  % (19129)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53  % (19140)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53  % (19140)------------------------------
% 0.19/0.53  % (19140)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (19140)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (19140)Termination reason: Refutation
% 0.19/0.53  
% 0.19/0.53  % (19140)Memory used [KB]: 5500
% 0.19/0.53  % (19140)Time elapsed: 0.110 s
% 0.19/0.53  % (19140)Instructions burned: 6 (million)
% 0.19/0.53  % (19140)------------------------------
% 0.19/0.53  % (19140)------------------------------
% 0.19/0.53  % (19118)Success in time 0.176 s
%------------------------------------------------------------------------------