TSTP Solution File: LCL798-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL798-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n019.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 Aug 22 10:49:02 EDT 2023

% Result   : Unsatisfiable 5.35s 2.31s
% Output   : CNFRefutation 5.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   47 (   9 unt;  34 typ;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   21 (  12   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   37 (  21   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   23 (  23 usr;  13 con; 0-4 aty)
%            Number of variables   :    9 (;   9   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_Type_Otyping > c_HOL_Oord__class_Oless > c_Lambda_Obeta > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__idom > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Nat_Osemiring__char__0 > c_InductTermi_OIT > c_Type_Oshift > c_List_Olist_OCons > c_Lambda_Osubst > c_Nat_Osemiring__1__class_Oof__nat > c_Lambda_Osko__Lambda__Xbeta__cases__2__1 > c_Lambda_Olift > c_Lambda_OdB_OApp > #nlpp > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > v_ua______ > v_u____ > v_rs____ > v_n____ > v_i____ > v_e____ > v_as____ > v_a____ > v_T____ > v_T_H_H____ > tc_nat > tc_Type_Otype > tc_Lambda_OdB

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(c_Lambda_Olift,type,
    c_Lambda_Olift: ( $i * $i ) > $i ).

tff(class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

tff(c_HOL_Oord__class_Oless,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(tc_Type_Otype,type,
    tc_Type_Otype: $i ).

tff(c_InductTermi_OIT,type,
    c_InductTermi_OIT: $i > $o ).

tff(c_Nat_Osemiring__1__class_Oof__nat,type,
    c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).

tff(c_Lambda_Obeta,type,
    c_Lambda_Obeta: ( $i * $i ) > $o ).

tff(class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

tff(class_Orderings_Opreorder,type,
    class_Orderings_Opreorder: $i > $o ).

tff(c_Lambda_Osubst,type,
    c_Lambda_Osubst: ( $i * $i * $i ) > $i ).

tff(v_rs____,type,
    v_rs____: $i ).

tff(c_Lambda_OdB_OApp,type,
    c_Lambda_OdB_OApp: ( $i * $i ) > $i ).

tff(v_ua______,type,
    v_ua______: $i ).

tff(c_Lambda_OdB_OVar,type,
    c_Lambda_OdB_OVar: $i > $i ).

tff(c_Type_Oshift,type,
    c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).

tff(v_n____,type,
    v_n____: $i ).

tff(c_Type_Otyping,type,
    c_Type_Otyping: ( $i * $i * $i ) > $o ).

tff(v_e____,type,
    v_e____: $i ).

tff(class_Ring__and__Field_Oordered__idom,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(c_Lambda_OdB_OAbs,type,
    c_Lambda_OdB_OAbs: $i > $i ).

tff(tc_nat,type,
    tc_nat: $i ).

tff(class_Nat_Osemiring__char__0,type,
    class_Nat_Osemiring__char__0: $i > $o ).

tff(tc_Lambda_OdB,type,
    tc_Lambda_OdB: $i ).

tff(c_HOL_Ozero__class_Ozero,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(c_List_Olist_OCons,type,
    c_List_Olist_OCons: ( $i * $i * $i ) > $i ).

tff(c_Lambda_Osko__Lambda__Xbeta__cases__2__1,type,
    c_Lambda_Osko__Lambda__Xbeta__cases__2__1: ( $i * $i ) > $i ).

tff(v_T____,type,
    v_T____: $i ).

tff(v_i____,type,
    v_i____: $i ).

tff(v_as____,type,
    v_as____: $i ).

tff(v_a____,type,
    v_a____: $i ).

tff(v_u____,type,
    v_u____: $i ).

tff(v_T_H_H____,type,
    v_T_H_H____: $i ).

tff(class_Ring__and__Field_Osemiring__1,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

tff(class_Ring__and__Field_Oordered__semidom,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

tff(f_385,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    file(unknown,unknown) ).

tff(f_386,axiom,
    c_InductTermi_OIT(v_u____),
    file(unknown,unknown) ).

tff(f_387,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
    file(unknown,unknown) ).

tff(f_384,axiom,
    ! [V_u,V_i,V_e,V_T_H] :
      ( c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u,V_i))
      | ~ c_Type_Otyping(V_e,V_u,v_T____)
      | ~ c_InductTermi_OIT(V_u)
      | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H) ),
    file(unknown,unknown) ).

tff(f_389,axiom,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
    file(unknown,unknown) ).

tff(c_142,plain,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    inference(cnfTransformation,[status(thm)],[f_385]) ).

tff(c_144,plain,
    c_InductTermi_OIT(v_u____),
    inference(cnfTransformation,[status(thm)],[f_386]) ).

tff(c_146,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
    inference(cnfTransformation,[status(thm)],[f_387]) ).

tff(c_1641,plain,
    ! [V_e_420,V_i_421,V_T_H_422,V_u_423] :
      ( ~ c_Type_Otyping(c_Type_Oshift(V_e_420,V_i_421,v_T____,tc_Type_Otype),v_a____,V_T_H_422)
      | ~ c_InductTermi_OIT(V_u_423)
      | ~ c_Type_Otyping(V_e_420,V_u_423,v_T____)
      | c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u_423,V_i_421)) ),
    inference(cnfTransformation,[status(thm)],[f_384]) ).

tff(c_1670,plain,
    ! [V_u_442] :
      ( ~ c_InductTermi_OIT(V_u_442)
      | ~ c_Type_Otyping(v_e____,V_u_442,v_T____)
      | c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u_442,v_i____)) ),
    inference(resolution,[status(thm)],[c_146,c_1641]) ).

tff(c_148,plain,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
    inference(cnfTransformation,[status(thm)],[f_389]) ).

tff(c_1673,plain,
    ( ~ c_InductTermi_OIT(v_u____)
    | ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
    inference(resolution,[status(thm)],[c_1670,c_148]) ).

tff(c_1677,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_144,c_1673]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL798-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.20/0.36  % Computer : n019.cluster.edu
% 0.20/0.36  % Model    : x86_64 x86_64
% 0.20/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.36  % Memory   : 8042.1875MB
% 0.20/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.36  % CPULimit : 300
% 0.20/0.36  % WCLimit  : 300
% 0.20/0.36  % DateTime : Thu Aug  3 14:06:01 EDT 2023
% 0.20/0.36  % CPUTime  : 
% 5.35/2.31  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.35/2.31  
% 5.35/2.31  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.75/2.33  
% 5.75/2.33  Inference rules
% 5.75/2.33  ----------------------
% 5.75/2.33  #Ref     : 8
% 5.75/2.33  #Sup     : 324
% 5.75/2.33  #Fact    : 6
% 5.75/2.33  #Define  : 0
% 5.75/2.33  #Split   : 0
% 5.75/2.33  #Chain   : 0
% 5.75/2.33  #Close   : 0
% 5.75/2.33  
% 5.75/2.33  Ordering : KBO
% 5.75/2.33  
% 5.75/2.33  Simplification rules
% 5.75/2.33  ----------------------
% 5.75/2.33  #Subsume      : 101
% 5.75/2.33  #Demod        : 77
% 5.75/2.33  #Tautology    : 95
% 5.75/2.33  #SimpNegUnit  : 20
% 5.75/2.33  #BackRed      : 0
% 5.75/2.33  
% 5.75/2.33  #Partial instantiations: 0
% 5.75/2.33  #Strategies tried      : 1
% 5.75/2.33  
% 5.75/2.33  Timing (in seconds)
% 5.75/2.33  ----------------------
% 5.75/2.34  Preprocessing        : 0.63
% 5.75/2.34  Parsing              : 0.33
% 5.75/2.34  CNF conversion       : 0.04
% 5.75/2.34  Main loop            : 0.63
% 5.75/2.34  Inferencing          : 0.24
% 5.75/2.34  Reduction            : 0.18
% 5.75/2.34  Demodulation         : 0.12
% 5.75/2.34  BG Simplification    : 0.04
% 5.75/2.34  Subsumption          : 0.13
% 5.75/2.34  Abstraction          : 0.02
% 5.75/2.34  MUC search           : 0.00
% 5.75/2.34  Cooper               : 0.00
% 5.75/2.34  Total                : 1.30
% 5.75/2.34  Index Insertion      : 0.00
% 5.75/2.34  Index Deletion       : 0.00
% 5.75/2.34  Index Matching       : 0.00
% 5.75/2.34  BG Taut test         : 0.00
%------------------------------------------------------------------------------