TSTP Solution File: NUM934_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM934_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 : Sun May  5 08:43:56 EDT 2024

% Result   : Theorem 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   90 (  42 unt;  24 typ;   0 def)
%            Number of atoms       :  106 (  35 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   74 (  34   ~;  21   |;   9   &)
%                                         (   8 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   13 (   9   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   86 (  73   !;   0   ?;  86   :)
%                                         (  13  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    bool: $tType ).

tff(type_def_6,type,
    int: $tType ).

tff(type_def_7,type,
    nat: $tType ).

tff(func_def_0,type,
    one_one: 
      !>[X0: $tType] : X0 ).

tff(func_def_1,type,
    plus_plus: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

tff(func_def_2,type,
    times_times: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

tff(func_def_3,type,
    bit0: int > int ).

tff(func_def_4,type,
    bit1: int > int ).

tff(func_def_5,type,
    pls: int ).

tff(func_def_6,type,
    number_number_of: 
      !>[X0: $tType] : ( int > X0 ) ).

tff(func_def_7,type,
    fFalse: bool ).

tff(func_def_8,type,
    fTrue: bool ).

tff(func_def_9,type,
    m: int ).

tff(pred_def_1,type,
    number: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    semiring: 
      !>[X0: $tType] : $o ).

tff(pred_def_3,type,
    number_ring: 
      !>[X0: $tType] : $o ).

tff(pred_def_4,type,
    ring_char_0: 
      !>[X0: $tType] : $o ).

tff(pred_def_5,type,
    linorder: 
      !>[X0: $tType] : $o ).

tff(pred_def_6,type,
    number_semiring: 
      !>[X0: $tType] : $o ).

tff(pred_def_7,type,
    linordered_idom: 
      !>[X0: $tType] : $o ).

tff(pred_def_8,type,
    zprime: int > $o ).

tff(pred_def_9,type,
    ord_less: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_10,type,
    ord_less_eq: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_11,type,
    pp: bool > $o ).

tff(f2118,plain,
    $false,
    inference(subsumption_resolution,[],[f2109,f771]) ).

tff(f771,plain,
    ~ ord_less(int,pls,m),
    inference(resolution,[],[f770,f590]) ).

tff(f590,plain,
    ! [X0: int] :
      ( ord_less(int,one_one(int),bit0(X0))
      | ~ ord_less(int,pls,X0) ),
    inference(superposition,[],[f413,f483]) ).

tff(f483,plain,
    one_one(int) = bit1(pls),
    inference(superposition,[],[f310,f315]) ).

tff(f315,plain,
    ! [X0: int] : ( number_number_of(int,X0) = X0 ),
    inference(cnf_transformation,[],[f118]) ).

tff(f118,plain,
    ! [X0: int] : ( number_number_of(int,X0) = X0 ),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X6: int] : ( number_number_of(int,X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_number__of__is__id) ).

tff(f310,plain,
    one_one(int) = number_number_of(int,bit1(pls)),
    inference(cnf_transformation,[],[f87]) ).

tff(f87,axiom,
    one_one(int) = number_number_of(int,bit1(pls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_one__is__num__one) ).

tff(f413,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit0(X0))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f270,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,bit1(X1),bit0(X0))
        | ~ ord_less(int,X1,X0) )
      & ( ord_less(int,X1,X0)
        | ~ ord_less(int,bit1(X1),bit0(X0)) ) ),
    inference(nnf_transformation,[],[f175]) ).

tff(f175,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit0(X0))
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f80]) ).

tff(f80,axiom,
    ! [X16: int,X17: int] :
      ( ord_less(int,bit1(X17),bit0(X16))
    <=> ord_less(int,X17,X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_less__int__code_I15_J) ).

tff(f770,plain,
    ~ ord_less(int,one_one(int),bit0(m)),
    inference(resolution,[],[f768,f397]) ).

tff(f397,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,X0)
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f263]) ).

tff(f263,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(int,X1,X0) )
      & ( ( ( X0 != X1 )
          & ord_less_eq(int,X1,X0) )
        | ~ ord_less(int,X1,X0) ) ),
    inference(flattening,[],[f262]) ).

tff(f262,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(int,X1,X0) )
      & ( ( ( X0 != X1 )
          & ord_less_eq(int,X1,X0) )
        | ~ ord_less(int,X1,X0) ) ),
    inference(nnf_transformation,[],[f168]) ).

tff(f168,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
    <=> ( ( X0 != X1 )
        & ord_less_eq(int,X1,X0) ) ),
    inference(rectify,[],[f56]) ).

tff(f56,axiom,
    ! [X15: int,X14: int] :
      ( ord_less(int,X14,X15)
    <=> ( ( X14 != X15 )
        & ord_less_eq(int,X14,X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__int__def) ).

tff(f768,plain,
    ~ ord_less_eq(int,one_one(int),bit0(m)),
    inference(resolution,[],[f766,f409]) ).

tff(f409,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit0(X1),bit1(X0))
      | ~ ord_less_eq(int,X1,X0) ),
    inference(cnf_transformation,[],[f268]) ).

tff(f268,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,bit0(X1),bit1(X0))
        | ~ ord_less_eq(int,X1,X0) )
      & ( ord_less_eq(int,X1,X0)
        | ~ ord_less(int,bit0(X1),bit1(X0)) ) ),
    inference(nnf_transformation,[],[f173]) ).

tff(f173,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit0(X1),bit1(X0))
    <=> ord_less_eq(int,X1,X0) ),
    inference(rectify,[],[f63]) ).

tff(f63,axiom,
    ! [X16: int,X17: int] :
      ( ord_less(int,bit0(X17),bit1(X16))
    <=> ord_less_eq(int,X17,X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__int__code_I14_J) ).

tff(f766,plain,
    ~ ord_less(int,bit0(one_one(int)),bit1(bit0(m))),
    inference(backward_demodulation,[],[f725,f764]) ).

tff(f764,plain,
    ! [X0: int] : ( bit1(X0) = plus_plus(int,bit0(X0),one_one(int)) ),
    inference(forward_demodulation,[],[f762,f317]) ).

tff(f317,plain,
    ! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
    inference(cnf_transformation,[],[f120]) ).

tff(f120,plain,
    ! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
    inference(rectify,[],[f68]) ).

tff(f68,axiom,
    ! [X6: int] : ( plus_plus(int,X6,pls) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_add__Pls__right) ).

tff(f762,plain,
    ! [X0: int] : ( bit1(plus_plus(int,X0,pls)) = plus_plus(int,bit0(X0),one_one(int)) ),
    inference(superposition,[],[f389,f483]) ).

tff(f389,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
    inference(cnf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X5: int,X6: int] : ( plus_plus(int,bit0(X6),bit1(X5)) = bit1(plus_plus(int,X6,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add__Bit0__Bit1) ).

tff(f725,plain,
    ~ ord_less(int,bit0(one_one(int)),plus_plus(int,bit0(bit0(m)),one_one(int))),
    inference(backward_demodulation,[],[f509,f723]) ).

tff(f723,plain,
    ! [X0: int] : ( times_times(int,bit0(bit0(one_one(int))),X0) = bit0(bit0(X0)) ),
    inference(superposition,[],[f386,f720]) ).

tff(f720,plain,
    ! [X0: int] : ( bit0(X0) = times_times(int,bit0(one_one(int)),X0) ),
    inference(superposition,[],[f386,f719]) ).

tff(f719,plain,
    ! [X0: int] : ( times_times(int,one_one(int),X0) = X0 ),
    inference(forward_demodulation,[],[f718,f315]) ).

tff(f718,plain,
    ! [X0: int] : ( times_times(int,number_number_of(int,one_one(int)),X0) = X0 ),
    inference(resolution,[],[f490,f295]) ).

tff(f295,plain,
    number_ring(int),
    inference(cnf_transformation,[],[f103]) ).

tff(f103,axiom,
    number_ring(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).

tff(f490,plain,
    ! [X0: $tType,X1: X0] :
      ( ~ number_ring(X0)
      | ( times_times(X0,number_number_of(X0,one_one(int)),X1) = X1 ) ),
    inference(backward_demodulation,[],[f326,f483]) ).

tff(f326,plain,
    ! [X0: $tType,X1: X0] :
      ( ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f200]) ).

tff(f200,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f127]) ).

tff(f127,plain,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
    inference(rectify,[],[f84]) ).

tff(f84,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X11: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X11) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_mult__numeral__1) ).

tff(f386,plain,
    ! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
    inference(cnf_transformation,[],[f159]) ).

tff(f159,plain,
    ! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
    inference(rectify,[],[f32]) ).

tff(f32,axiom,
    ! [X5: int,X6: int] : ( bit0(times_times(int,X6,X5)) = times_times(int,bit0(X6),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_mult__Bit0) ).

tff(f509,plain,
    ~ ord_less(int,bit0(one_one(int)),plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int))),
    inference(backward_demodulation,[],[f465,f483]) ).

tff(f465,plain,
    ~ ord_less(int,bit0(bit1(pls)),plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))),
    inference(forward_demodulation,[],[f463,f315]) ).

tff(f463,plain,
    ~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))),
    inference(backward_demodulation,[],[f290,f315]) ).

tff(f290,plain,
    ~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
    inference(cnf_transformation,[],[f115]) ).

tff(f115,plain,
    ~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
    inference(flattening,[],[f114]) ).

tff(f114,negated_conjecture,
    ~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
    inference(negated_conjecture,[],[f113]) ).

tff(f113,conjecture,
    ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f2109,plain,
    ord_less(int,pls,m),
    inference(resolution,[],[f873,f308]) ).

tff(f308,plain,
    ord_less_eq(int,one_one(int),m),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ord_less_eq(int,one_one(int),m),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__0961_A_060_061_Am_096) ).

tff(f873,plain,
    ! [X0: int] :
      ( ~ ord_less_eq(int,one_one(int),X0)
      | ord_less(int,pls,X0) ),
    inference(superposition,[],[f449,f318]) ).

tff(f318,plain,
    ! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
    inference(cnf_transformation,[],[f121]) ).

tff(f121,plain,
    ! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
    inference(rectify,[],[f69]) ).

tff(f69,axiom,
    ! [X6: int] : ( plus_plus(int,pls,X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__Pls) ).

tff(f449,plain,
    ! [X0: int,X1: int] :
      ( ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0)
      | ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f289]) ).

tff(f289,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0)
        | ~ ord_less(int,X1,X0) )
      & ( ord_less(int,X1,X0)
        | ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0) ) ),
    inference(nnf_transformation,[],[f192]) ).

tff(f192,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0)
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f65]) ).

tff(f65,axiom,
    ! [X14: int,X15: int] :
      ( ord_less_eq(int,plus_plus(int,X15,one_one(int)),X14)
    <=> ord_less(int,X15,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_add1__zle__eq) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM934_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n020.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   : Fri May  3 14:44:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (32596)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (32599)WARNING: value z3 for option sas not known
% 0.13/0.37  % (32603)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)
% 0.13/0.37  % (32600)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (32602)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)
% 0.13/0.37  % (32601)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)
% 0.13/0.37  % (32597)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (32598)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (32599)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)
% 0.13/0.38  % (32603)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.38  % Exception at run slice level
% 0.13/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.38  % Exception at run slice level
% 0.13/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.38  % Exception at run slice level
% 0.13/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.39  % (32604)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.39  % (32605)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)
% 0.13/0.39  % (32606)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)
% 0.13/0.40  % (32604)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.40  % (32605)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.40  % Exception at run slice level
% 0.13/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.41  % (32607)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)
% 0.20/0.45  % (32606)First to succeed.
% 0.20/0.45  % (32606)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-32596"
% 0.20/0.45  % (32606)Refutation found. Thanks to Tanya!
% 0.20/0.45  % SZS status Theorem for theBenchmark
% 0.20/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.45  % (32606)------------------------------
% 0.20/0.45  % (32606)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.45  % (32606)Termination reason: Refutation
% 0.20/0.45  
% 0.20/0.45  % (32606)Memory used [KB]: 1711
% 0.20/0.45  % (32606)Time elapsed: 0.059 s
% 0.20/0.45  % (32606)Instructions burned: 101 (million)
% 0.20/0.45  % (32596)Success in time 0.093 s
%------------------------------------------------------------------------------