%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : MSC012+1 : 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 : n011.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 17:51:47 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   33 (  10 unt;   0 def)
%            Number of atoms       :   80 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   86 (  39   ~;  34   |;   8   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-1 aty)
%            Number of variables   :   53 (  49   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f52,plain,
    $false,
    inference(subsumption_resolution,[],[f51,f48]) ).

fof(f48,plain,
    ! [X0] : ~ p(X0),
    inference(subsumption_resolution,[],[f45,f27]) ).

fof(f27,plain,
    ! [X4] :
      ( ~ p(sK1(X4))
      | ~ p(X4) ),
    inference(resolution,[],[f24,f22]) ).

fof(f22,plain,
    ! [X0] : less(X0,sK1(X0)),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0] : less(X0,sK1(X0)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f4,f15]) ).

fof(f15,plain,
    ! [X0] :
      ( ? [X1] : less(X0,X1)
     => less(X0,sK1(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f4,axiom,
    ! [X0] :
    ? [X1] : less(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',serial_less) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | ~ p(X0)
      | ~ p(X1) ),
    inference(resolution,[],[f20,f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ p(X0)
      | ~ p(X1)
      | goal
      | ~ less(X0,X1) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ~ p(X1)
      | ~ less(X0,X1)
      | goal
      | ~ p(X0) ),
    inference(flattening,[],[f9]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( goal
      | ~ less(X0,X1)
      | ~ p(X0)
      | ~ p(X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ( less(X0,X1)
        & p(X0)
        & p(X1) )
     => goal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_to_right) ).

fof(f20,plain,
    ~ goal,
    inference(cnf_transformation,[],[f8]) ).

fof(f8,plain,
    ~ goal,
    inference(flattening,[],[f6]) ).

fof(f6,negated_conjecture,
    ~ goal,
    inference(negated_conjecture,[],[f5]) ).

fof(f5,conjecture,
    goal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).

fof(f45,plain,
    ! [X0] :
      ( p(sK1(X0))
      | ~ p(X0) ),
    inference(resolution,[],[f39,f19]) ).

fof(f19,plain,
    ! [X0] :
      ( p(X0)
      | p(sK0(X0)) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0] :
      ( p(X0)
      | ( p(sK0(X0))
        & less(X0,sK0(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f2,f13]) ).

fof(f13,plain,
    ! [X0] :
      ( ? [X1] :
          ( p(X1)
          & less(X0,X1) )
     => ( p(sK0(X0))
        & less(X0,sK0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f2,axiom,
    ! [X0] :
      ( p(X0)
      | ? [X1] :
          ( p(X1)
          & less(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_to_left) ).

fof(f39,plain,
    ! [X4] :
      ( ~ p(sK0(sK1(X4)))
      | ~ p(X4) ),
    inference(resolution,[],[f33,f22]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | ~ p(X0)
      | ~ p(sK0(X1)) ),
    inference(subsumption_resolution,[],[f30,f24]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( p(X1)
      | ~ p(X0)
      | ~ p(sK0(X1))
      | ~ less(X0,X1) ),
    inference(resolution,[],[f26,f18]) ).

fof(f18,plain,
    ! [X0] :
      ( less(X0,sK0(X0))
      | p(X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f26,plain,
    ! [X2,X3,X1] :
      ( ~ less(X3,X2)
      | ~ less(X1,X3)
      | ~ p(X2)
      | ~ p(X1) ),
    inference(resolution,[],[f24,f23]) ).

fof(f23,plain,
    ! [X2,X0,X1] :
      ( ~ less(X2,X0)
      | less(X1,X0)
      | ~ less(X1,X2) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ~ less(X2,X0)
      | less(X1,X0)
      | ~ less(X1,X2) ),
    inference(rectify,[],[f12]) ).

fof(f12,plain,
    ! [X0,X2,X1] :
      ( ~ less(X1,X0)
      | less(X2,X0)
      | ~ less(X2,X1) ),
    inference(flattening,[],[f11]) ).

fof(f11,plain,
    ! [X2,X0,X1] :
      ( less(X2,X0)
      | ~ less(X2,X1)
      | ~ less(X1,X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ! [X2,X0,X1] :
      ( ( less(X2,X1)
        & less(X1,X0) )
     => less(X2,X0) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X2,X1,X0] :
      ( ( less(X0,X1)
        & less(X1,X2) )
     => less(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_less) ).

fof(f51,plain,
    ! [X2] : p(X2),
    inference(resolution,[],[f48,f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n011.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 03:24:55 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (25097)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)
% 0.20/0.50  % (25097)First to succeed.
% 0.20/0.50  % (25107)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.20/0.51  % (25097)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (25097)------------------------------
% 0.20/0.51  % (25097)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (25097)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (25097)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (25097)Memory used [KB]: 5884
% 0.20/0.51  % (25097)Time elapsed: 0.093 s
% 0.20/0.51  % (25097)Instructions burned: 2 (million)
% 0.20/0.51  % (25097)------------------------------
% 0.20/0.51  % (25097)------------------------------
% 0.20/0.51  % (25086)Success in time 0.148 s
%------------------------------------------------------------------------------