TSTP Solution File: NUM727^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM727^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n032.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 : Tue May 21 02:13:03 EDT 2024

% Result   : Theorem 5.50s 1.10s
% Output   : Refutation 5.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   50 (  26 unt;  18 typ;   0 def)
%            Number of atoms       :  294 (  37 equ;   0 cnn)
%            Maximal formula atoms :    2 (   9 avg)
%            Number of connectives :   18 (  12   ~;   5   |;   0   &;   0   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   22 (  21   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   4 con; 0-6 aty)
%            Number of variables   :   53 (   0   ^  47   !;   0   ?;  53   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    frac: $tType ).

thf(type_def_6,type,
    nat: $tType ).

thf(type_def_7,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(func_def_0,type,
    frac: $tType ).

thf(func_def_1,type,
    x: frac ).

thf(func_def_2,type,
    y: frac ).

thf(func_def_3,type,
    z: frac ).

thf(func_def_4,type,
    nat: $tType ).

thf(func_def_5,type,
    ts: nat > nat > nat ).

thf(func_def_6,type,
    num: frac > nat ).

thf(func_def_7,type,
    den: frac > nat ).

thf(func_def_11,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_12,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_13,type,
    vAND: $o > $o > $o ).

thf(func_def_14,type,
    vOR: $o > $o > $o ).

thf(func_def_15,type,
    vIMP: $o > $o > $o ).

thf(func_def_16,type,
    vNOT: $o > $o ).

thf(func_def_17,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f7738,plain,
    $false,
    inference(subsumption_resolution,[],[f7737,f261]) ).

thf(f261,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X2),X0)) ),
    inference(superposition,[],[f146,f104]) ).

thf(f104,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1)) ),
    inference(superposition,[],[f16,f15]) ).

thf(f15,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X0) ),
    inference(cnf_transformation,[],[f4]) ).

thf(f4,axiom,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).

thf(f16,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X2)) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f5,axiom,
    ! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz31) ).

thf(f146,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X2)) ),
    inference(superposition,[],[f99,f16]) ).

thf(f99,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X0)),X2) ),
    inference(superposition,[],[f16,f15]) ).

thf(f7737,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,z)),vAPP(frac,nat,num,y))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,den,z))),
    inference(forward_demodulation,[],[f7511,f257]) ).

thf(f257,plain,
    ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),vAPP(frac,nat,den,y))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,den,z))) ),
    inference(superposition,[],[f146,f13]) ).

thf(f13,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,den,z)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(frac,nat,den,y)),
    inference(cnf_transformation,[],[f2]) ).

thf(f2,axiom,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,den,z)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(frac,nat,den,y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f) ).

thf(f7511,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,z)),vAPP(frac,nat,num,y))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,y))),
    inference(superposition,[],[f372,f3502]) ).

thf(f3502,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,y)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,num,y)),
    inference(forward_demodulation,[],[f3396,f15]) ).

thf(f3396,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,num,y)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),vAPP(frac,nat,num,x)),
    inference(unit_resulting_resolution,[],[f117,f155]) ).

thf(f155,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X2),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X2)) )
      | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1) = X3 ) ),
    inference(superposition,[],[f50,f99]) ).

thf(f50,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X0) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X2),X1) )
      | ( X0 = X2 ) ),
    inference(superposition,[],[f17,f15]) ).

thf(f17,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X2) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( X0 = X1 )
      | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X2) ) ),
    inference(ennf_transformation,[],[f3]) ).

thf(f3,axiom,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X2) )
     => ( X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz33b) ).

thf(f117,plain,
    ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),X0)) ),
    inference(forward_demodulation,[],[f102,f16]) ).

thf(f102,plain,
    ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,y))),X0) ),
    inference(superposition,[],[f16,f14]) ).

thf(f14,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,y)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,den,x)),
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,y)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,den,x)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).

thf(f372,plain,
    ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,z)),X0)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),X0)) ),
    inference(forward_demodulation,[],[f340,f16]) ).

thf(f340,plain,
    ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,z))),X0) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),X0)) ),
    inference(unit_resulting_resolution,[],[f12,f108]) ).

thf(f108,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X2)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X3),X2) )
      | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1) = X3 ) ),
    inference(superposition,[],[f17,f16]) ).

thf(f12,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,z)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(frac,nat,den,x)),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,z)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(frac,nat,den,x)),
    inference(flattening,[],[f7]) ).

thf(f7,negated_conjecture,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,z)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(frac,nat,den,x)),
    inference(negated_conjecture,[],[f6]) ).

thf(f6,conjecture,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,den,z)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,z)),vAPP(frac,nat,den,x)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : NUM727^1 : TPTP v8.2.0. Released v3.7.0.
% 0.00/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.29  % Computer : n032.cluster.edu
% 0.11/0.29  % Model    : x86_64 x86_64
% 0.11/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29  % Memory   : 8042.1875MB
% 0.11/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29  % CPULimit   : 300
% 0.11/0.29  % WCLimit    : 300
% 0.11/0.29  % DateTime   : Mon May 20 05:17:22 EDT 2024
% 0.11/0.29  % CPUTime    : 
% 0.11/0.30  % (21364)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.31  % (21367)WARNING: value z3 for option sas not known
% 0.11/0.31  % (21367)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.31  % (21365)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.31  % Exception at run slice level
% 0.11/0.31  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.31  % (21371)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.31  % (21371)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.32  % (21368)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.32  % Exception at run slice level
% 0.15/0.32  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.32  % (21372)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.32  % (21372)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.32  % Exception at run slice level
% 0.15/0.32  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.32  % (21366)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.32  % Exception at run slice level
% 0.15/0.32  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.32  % (21369)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.32  % (21370)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.33  % (21374)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.33  % (21373)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.33  % (21373)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.34  % (21375)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 5.50/1.10  % (21373)First to succeed.
% 5.50/1.10  % (21373)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21364"
% 5.50/1.10  % (21373)Refutation found. Thanks to Tanya!
% 5.50/1.10  % SZS status Theorem for theBenchmark
% 5.50/1.10  % SZS output start Proof for theBenchmark
% See solution above
% 5.50/1.10  % (21373)------------------------------
% 5.50/1.10  % (21373)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.50/1.10  % (21373)Termination reason: Refutation
% 5.50/1.10  
% 5.50/1.10  % (21373)Memory used [KB]: 2749
% 5.50/1.10  % (21373)Time elapsed: 0.765 s
% 5.50/1.10  % (21373)Instructions burned: 3045 (million)
% 5.50/1.10  % (21364)Success in time 0.788 s
%------------------------------------------------------------------------------