TSTP Solution File: ALG398-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ALG398-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n013.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 18:37:37 EDT 2024

% Result   : Unsatisfiable 8.80s 1.69s
% Output   : Refutation 8.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   25 (  18 unt;   0 def)
%            Number of atoms       :   36 (  25 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   26 (  15   ~;  11   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :   23 (  23   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f30722,plain,
    $false,
    inference(trivial_inequality_removal,[],[f30721]) ).

fof(f30721,plain,
    c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(superposition,[],[f559,f30715]) ).

fof(f30715,plain,
    c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(trivial_inequality_removal,[],[f30714]) ).

fof(f30714,plain,
    ( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex)
    | c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(superposition,[],[f30709,f27964]) ).

fof(f27964,plain,
    ! [X0,X1] :
      ( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1
      | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ),
    inference(resolution,[],[f25115,f878]) ).

fof(f878,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

fof(f25115,plain,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1
      | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ),
    inference(forward_demodulation,[],[f25114,f1348]) ).

fof(f1348,plain,
    ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),
    inference(resolution,[],[f830,f879]) ).

fof(f879,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

fof(f830,axiom,
    ! [X0,X9,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X5,X9,X0) = c_HOL_Otimes__class_Otimes(X9,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

fof(f25114,plain,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
      | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X1 ),
    inference(resolution,[],[f572,f900]) ).

fof(f900,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

fof(f572,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X3,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).

fof(f30709,plain,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(forward_demodulation,[],[f30708,f785]) ).

fof(f785,axiom,
    ! [X9,X5] : c_HOL_Oinverse__class_Odivide(X5,X9,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Oinverse(X9,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__divide__def_0) ).

fof(f30708,plain,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(forward_demodulation,[],[f30706,f1348]) ).

fof(f30706,plain,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(backward_demodulation,[],[f2564,f30704]) ).

fof(f30704,plain,
    ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(resolution,[],[f832,f880]) ).

fof(f880,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).

fof(f832,axiom,
    ! [X0,X1,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X13,X0),X5,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X13,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).

fof(f2564,plain,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(superposition,[],[f961,f1348]) ).

fof(f961,plain,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(backward_demodulation,[],[f835,f766]) ).

fof(f766,axiom,
    c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pqc0_0) ).

fof(f835,axiom,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f559,axiom,
    c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pc0_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : ALG398-1 : TPTP v8.2.0. Released v4.1.0.
% 0.11/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat May 18 23:35:53 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.18/0.34  % (13163)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.39  % (13166)WARNING: value z3 for option sas not known
% 0.18/0.39  % (13170)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)
% 0.18/0.39  % (13165)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.39  % (13168)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)
% 0.18/0.39  % (13167)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.39  % (13169)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)
% 0.18/0.39  % (13164)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.39  % (13166)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)
% 0.18/0.45  TRYING [1]
% 0.18/0.46  TRYING [2]
% 1.96/0.73  TRYING [3]
% 2.63/0.75  TRYING [1]
% 3.04/0.81  TRYING [2]
% 7.13/1.43  TRYING [1]
% 7.13/1.44  TRYING [2]
% 8.80/1.68  % (13169)First to succeed.
% 8.80/1.69  % (13169)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-13163"
% 8.80/1.69  % (13169)Refutation found. Thanks to Tanya!
% 8.80/1.69  % SZS status Unsatisfiable for theBenchmark
% 8.80/1.69  % SZS output start Proof for theBenchmark
% See solution above
% 8.80/1.69  % (13169)------------------------------
% 8.80/1.69  % (13169)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 8.80/1.69  % (13169)Termination reason: Refutation
% 8.80/1.69  
% 8.80/1.69  % (13169)Memory used [KB]: 10121
% 8.80/1.69  % (13169)Time elapsed: 1.293 s
% 8.80/1.69  % (13169)Instructions burned: 2305 (million)
% 8.80/1.69  % (13163)Success in time 1.33 s
%------------------------------------------------------------------------------