%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : HEN010-6 : TPTP v8.1.0. Released v1.0.0.
% 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 : n027.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 16:24:40 EDT 2022

% Result   : Unsatisfiable 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   29 (  23 unt;   0 def)
%            Number of atoms       :   36 (  16 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   18 (  11   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   24 (  24   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f356,plain,
    $false,
    inference(subsumption_resolution,[],[f351,f52]) ).

fof(f52,plain,
    zero != divide(sF0,sF2),
    inference(resolution,[],[f51,f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( less_equal(X0,X1)
      | divide(X0,X1) != zero ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).

fof(f51,plain,
    ~ less_equal(sF0,sF2),
    inference(subsumption_resolution,[],[f50,f20]) ).

fof(f20,plain,
    sF0 != sF2,
    inference(definition_folding,[],[f16,f19,f18,f17,f17,f17]) ).

fof(f17,plain,
    divide(identity,a) = sF0,
    introduced(function_definition,[]) ).

fof(f18,plain,
    sF1 = divide(identity,sF0),
    introduced(function_definition,[]) ).

fof(f19,plain,
    divide(sF0,sF1) = sF2,
    introduced(function_definition,[]) ).

fof(f16,axiom,
    divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_inversion) ).

fof(f50,plain,
    ( sF0 = sF2
    | ~ less_equal(sF0,sF2) ),
    inference(resolution,[],[f6,f27]) ).

fof(f27,plain,
    less_equal(sF2,sF0),
    inference(superposition,[],[f3,f19]) ).

fof(f3,axiom,
    ! [X0,X1] : less_equal(divide(X0,X1),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | X0 = X1
      | ~ less_equal(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).

fof(f351,plain,
    zero = divide(sF0,sF2),
    inference(resolution,[],[f336,f48]) ).

fof(f48,plain,
    ! [X5] :
      ( ~ less_equal(X5,zero)
      | zero = X5 ),
    inference(resolution,[],[f6,f5]) ).

fof(f5,axiom,
    ! [X0] : less_equal(zero,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).

fof(f336,plain,
    less_equal(divide(sF0,sF2),zero),
    inference(superposition,[],[f300,f130]) ).

fof(f130,plain,
    divide(identity,sF1) = sF0,
    inference(forward_demodulation,[],[f121,f18]) ).

fof(f121,plain,
    sF0 = divide(identity,divide(identity,sF0)),
    inference(superposition,[],[f15,f17]) ).

fof(f15,axiom,
    ! [X0] : divide(identity,X0) = divide(identity,divide(identity,divide(identity,X0))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_inversion_equals_three) ).

fof(f300,plain,
    ! [X15] : less_equal(divide(divide(X15,sF1),sF2),zero),
    inference(backward_demodulation,[],[f163,f294]) ).

fof(f294,plain,
    ! [X6] : zero = divide(divide(X6,sF0),sF1),
    inference(resolution,[],[f231,f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | divide(X0,X1) = zero ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal1) ).

fof(f231,plain,
    ! [X3] : less_equal(divide(X3,sF0),sF1),
    inference(superposition,[],[f80,f18]) ).

fof(f80,plain,
    ! [X0,X1] : less_equal(divide(X0,X1),divide(identity,X1)),
    inference(resolution,[],[f14,f7]) ).

fof(f7,axiom,
    ! [X0] : less_equal(X0,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).

fof(f14,axiom,
    ! [X2,X0,X1] :
      ( ~ less_equal(X0,X1)
      | less_equal(divide(X0,X2),divide(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide3) ).

fof(f163,plain,
    ! [X15] : less_equal(divide(divide(X15,sF1),sF2),divide(divide(X15,sF0),sF1)),
    inference(superposition,[],[f4,f19]) ).

fof(f4,axiom,
    ! [X2,X0,X1] : less_equal(divide(divide(X0,X2),divide(X1,X2)),divide(divide(X0,X1),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : HEN010-6 : TPTP v8.1.0. Released v1.0.0.
% 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 : n027.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   : Mon Aug 29 23:10:00 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.49  % (12370)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.49  % (12378)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.51  % (12370)First to succeed.
% 0.20/0.51  % (12370)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (12370)------------------------------
% 0.20/0.51  % (12370)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (12370)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (12370)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (12370)Memory used [KB]: 1151
% 0.20/0.51  % (12370)Time elapsed: 0.073 s
% 0.20/0.51  % (12370)Instructions burned: 14 (million)
% 0.20/0.51  % (12370)------------------------------
% 0.20/0.51  % (12370)------------------------------
% 0.20/0.51  % (12354)Success in time 0.153 s
%------------------------------------------------------------------------------