TSTP Solution File: ARI601_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ARI601_1 : TPTP v8.2.0. Released v5.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 : Mon May 20 18:50:46 EDT 2024

% Result   : Theorem 0.13s 0.40s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   40 (  15 unt;   2 typ;   0 def)
%            Number of atoms       :   69 (   5 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   61 (  30   ~;  19   |;   4   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  155 (  50 atm;  26 fun;  48 num;  31 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   2 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   2 usr;   4 con; 0-2 aty)
%            Number of variables   :   31 (  31   !;   0   ?;  31   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_0,type,
    a: $int ).

tff(func_def_1,type,
    f: $int > $int ).

tff(f862,plain,
    $false,
    inference(avatar_sat_refutation,[],[f259,f843,f861]) ).

tff(f861,plain,
    ~ spl0_1,
    inference(avatar_contradiction_clause,[],[f854]) ).

tff(f854,plain,
    ( $false
    | ~ spl0_1 ),
    inference(resolution,[],[f852,f630]) ).

tff(f630,plain,
    ~ $less($sum(1,a),4),
    inference(resolution,[],[f611,f45]) ).

tff(f45,plain,
    ! [X0: $int] : $less(X0,$sum(1,X0)),
    inference(superposition,[],[f34,f4]) ).

tff(f4,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f34,plain,
    ! [X0: $int] : $less(X0,$sum(X0,1)),
    inference(resolution,[],[f13,f9]) ).

tff(f9,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f13,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_147,[]) ).

tff(f611,plain,
    ! [X0: $int] :
      ( ~ $less(X0,4)
      | ~ $less(a,X0) ),
    inference(evaluation,[],[f590]) ).

tff(f590,plain,
    ! [X0: $int] :
      ( ~ $less(X0,$sum(3,1))
      | ~ $less(a,X0) ),
    inference(resolution,[],[f49,f19]) ).

tff(f19,plain,
    $less(3,a),
    inference(cnf_transformation,[],[f17]) ).

tff(f17,plain,
    ( ~ $less(4,f($sum(a,1)))
    & $less(3,a)
    & ! [X0: $int] : $less(X0,f(X0)) ),
    inference(flattening,[],[f16]) ).

tff(f16,plain,
    ( ~ $less(4,f($sum(a,1)))
    & $less(3,a)
    & ! [X0: $int] : $less(X0,f(X0)) ),
    inference(ennf_transformation,[],[f3]) ).

tff(f3,plain,
    ~ ( ! [X0: $int] : $less(X0,f(X0))
     => ( $less(3,a)
       => $less(4,f($sum(a,1))) ) ),
    inference(theory_normalization,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ( ! [X0: $int] : $greater(f(X0),X0)
     => ( $less(3,a)
       => $less(4,f($sum(a,1))) ) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ( ! [X0: $int] : $greater(f(X0),X0)
   => ( $less(3,a)
     => $less(4,f($sum(a,1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fX_gt_X_implies_ineq) ).

tff(f49,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,$sum(X1,1))
      | ~ $less(X2,X0)
      | ~ $less(X1,X2) ),
    inference(resolution,[],[f10,f15]) ).

tff(f15,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(X0,1))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_161,[]) ).

tff(f10,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X0,X2)
      | ~ $less(X1,X2)
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_143,[]) ).

tff(f852,plain,
    ( $less($sum(1,a),4)
    | ~ spl0_1 ),
    inference(superposition,[],[f18,f254]) ).

tff(f254,plain,
    ( ( 4 = f($sum(1,a)) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f252]) ).

tff(f252,plain,
    ( spl0_1
  <=> ( 4 = f($sum(1,a)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

tff(f18,plain,
    ! [X0: $int] : $less(X0,f(X0)),
    inference(cnf_transformation,[],[f17]) ).

tff(f843,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f840]) ).

tff(f840,plain,
    ( $false
    | ~ spl0_2 ),
    inference(resolution,[],[f627,f258]) ).

tff(f258,plain,
    ( $less(f($sum(1,a)),4)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f256]) ).

tff(f256,plain,
    ( spl0_2
  <=> $less(f($sum(1,a)),4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

tff(f627,plain,
    ~ $less(f($sum(1,a)),4),
    inference(resolution,[],[f611,f155]) ).

tff(f155,plain,
    ! [X0: $int] : $less(X0,f($sum(1,X0))),
    inference(resolution,[],[f35,f60]) ).

tff(f60,plain,
    ! [X0: $int] : ~ $less(f(X0),X0),
    inference(resolution,[],[f48,f18]) ).

tff(f48,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X0) ),
    inference(resolution,[],[f10,f9]) ).

tff(f35,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(1,X0))
      | $less(X0,X1) ),
    inference(superposition,[],[f13,f4]) ).

tff(f259,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f58,f256,f252]) ).

tff(f58,plain,
    ( $less(f($sum(1,a)),4)
    | ( 4 = f($sum(1,a)) ) ),
    inference(resolution,[],[f11,f25]) ).

tff(f25,plain,
    ~ $less(4,f($sum(1,a))),
    inference(backward_demodulation,[],[f20,f4]) ).

tff(f20,plain,
    ~ $less(4,f($sum(a,1))),
    inference(cnf_transformation,[],[f17]) ).

tff(f11,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : ARI601_1 : TPTP v8.2.0. Released v5.1.0.
% 0.12/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n005.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   : Sun May 19 13:29:23 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (22335)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (22340)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.36  % (22342)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.36  % (22336)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.36  % (22341)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.36  % (22336)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36  % (22336)Terminated due to inappropriate strategy.
% 0.13/0.36  % (22336)------------------------------
% 0.13/0.36  % (22336)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.36  % (22342)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36  % (22336)Termination reason: Inappropriate
% 0.13/0.36  % (22342)Terminated due to inappropriate strategy.
% 0.13/0.36  % (22342)------------------------------
% 0.13/0.36  % (22342)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.36  % (22342)Termination reason: Inappropriate
% 0.13/0.36  
% 0.13/0.36  % (22342)Memory used [KB]: 718
% 0.13/0.36  % (22342)Time elapsed: 0.002 s
% 0.13/0.36  % (22342)Instructions burned: 2 (million)
% 0.13/0.36  % (22339)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.36  
% 0.13/0.36  % (22336)Memory used [KB]: 717
% 0.13/0.36  % (22336)Time elapsed: 0.002 s
% 0.13/0.36  % (22336)Instructions burned: 2 (million)
% 0.13/0.36  % (22336)------------------------------
% 0.13/0.36  % (22336)------------------------------
% 0.13/0.36  % (22342)------------------------------
% 0.13/0.36  % (22342)------------------------------
% 0.13/0.36  % (22339)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36  % (22339)Terminated due to inappropriate strategy.
% 0.13/0.36  % (22339)------------------------------
% 0.13/0.36  % (22339)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.36  % (22339)Termination reason: Inappropriate
% 0.13/0.36  
% 0.13/0.36  % (22339)Memory used [KB]: 717
% 0.13/0.36  % (22339)Time elapsed: 0.002 s
% 0.13/0.36  % (22339)Instructions burned: 2 (million)
% 0.13/0.37  % (22339)------------------------------
% 0.13/0.37  % (22339)------------------------------
% 0.13/0.37  % (22337)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37  % (22337)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (22337)Terminated due to inappropriate strategy.
% 0.13/0.37  % (22337)------------------------------
% 0.13/0.37  % (22337)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37  % (22337)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (22337)Memory used [KB]: 717
% 0.13/0.37  % (22337)Time elapsed: 0.002 s
% 0.13/0.37  % (22337)Instructions burned: 2 (million)
% 0.13/0.37  % (22337)------------------------------
% 0.13/0.37  % (22337)------------------------------
% 0.13/0.38  % (22338)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.38  % (22343)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.38  % (22343)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.38  % (22343)Terminated due to inappropriate strategy.
% 0.13/0.38  % (22343)------------------------------
% 0.13/0.38  % (22343)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38  % (22343)Termination reason: Inappropriate
% 0.13/0.38  
% 0.13/0.38  % (22343)Memory used [KB]: 718
% 0.13/0.38  % (22343)Time elapsed: 0.002 s
% 0.13/0.38  % (22343)Instructions burned: 2 (million)
% 0.13/0.38  % (22343)------------------------------
% 0.13/0.38  % (22343)------------------------------
% 0.13/0.38  WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.13/0.38  % (22344)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.40  % (22345)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.40  % (22345)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.40  % (22345)Terminated due to inappropriate strategy.
% 0.13/0.40  % (22345)------------------------------
% 0.13/0.40  % (22345)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.40  % (22345)Termination reason: Inappropriate
% 0.13/0.40  
% 0.13/0.40  % (22345)Memory used [KB]: 718
% 0.13/0.40  % (22345)Time elapsed: 0.002 s
% 0.13/0.40  % (22345)Instructions burned: 2 (million)
% 0.13/0.40  % (22345)------------------------------
% 0.13/0.40  % (22345)------------------------------
% 0.13/0.40  WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.13/0.40  % (22347)dis+11_4:5_nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.40  WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.13/0.40  % (22338)First to succeed.
% 0.13/0.40  % (22346)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.40  % (22338)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22335"
% 0.13/0.40  % (22338)Refutation found. Thanks to Tanya!
% 0.13/0.40  % SZS status Theorem for theBenchmark
% 0.13/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.40  % (22338)------------------------------
% 0.13/0.40  % (22338)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.40  % (22338)Termination reason: Refutation
% 0.13/0.40  
% 0.13/0.40  % (22338)Memory used [KB]: 1017
% 0.13/0.40  % (22338)Time elapsed: 0.026 s
% 0.13/0.40  % (22338)Instructions burned: 43 (million)
% 0.13/0.40  % (22335)Success in time 0.052 s
%------------------------------------------------------------------------------