TSTP Solution File: COL110-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : COL110-2 : TPTP v8.1.2. Released v3.2.0.
% 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 : n027.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 10:35:07 EDT 2023

% Result   : Unsatisfiable 2.98s 1.81s
% Output   : CNFRefutation 2.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   43 (  10 unt;  14 typ;   0 def)
%            Number of atoms       :   54 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   62 (  37   ~;  25   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   6   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-4 aty)
%            Number of variables   :   28 (;  28   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_in > c_Pair > tc_prod > c_Comb_Ocomb_Oop_A_D_D > #nlpp > v_xb > v_xaa > v_z > v_yb > v_ya > v_x > v_wa > v_w > tc_Comb_Ocomb > c_Comb_Oparcontract

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(v_x,type,
    v_x: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_26,axiom,
    c_in(c_Pair(v_x,v_yb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ! [V_U] :
      ( c_in(c_Pair(v_ya,v_xb(V_U),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_x,V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    file(unknown,unknown) ).

tff(f_43,axiom,
    ! [V_U] :
      ( c_in(c_Pair(V_U,v_xb(V_U),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_x,V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    file(unknown,unknown) ).

tff(f_27,axiom,
    c_in(c_Pair(v_z,v_wa,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
    file(unknown,unknown) ).

tff(f_48,axiom,
    ! [V_U] :
      ( c_in(c_Pair(v_w,v_xaa(V_U),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_z,V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [V_U] :
      ( c_in(c_Pair(V_U,v_xaa(V_U),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_z,V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [V_z,V_w,V_x,V_y] :
      ( ~ c_in(c_Pair(V_z,V_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(V_x,V_y,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x,V_z),c_Comb_Ocomb_Oop_A_D_D(V_y,V_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    file(unknown,unknown) ).

tff(f_33,axiom,
    ! [V_U] :
      ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_yb,v_wa),V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    file(unknown,unknown) ).

tff(c_2,plain,
    c_in(c_Pair(v_x,v_yb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_8,plain,
    ! [V_U_2] :
      ( ~ c_in(c_Pair(v_x,V_U_2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | c_in(c_Pair(v_ya,v_xb(V_U_2),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_10,plain,
    ! [V_U_3] :
      ( ~ c_in(c_Pair(v_x,V_U_3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | c_in(c_Pair(V_U_3,v_xb(V_U_3),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_4,plain,
    c_in(c_Pair(v_z,v_wa,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_12,plain,
    ! [V_U_4] :
      ( ~ c_in(c_Pair(v_z,V_U_4,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | c_in(c_Pair(v_w,v_xaa(V_U_4),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_14,plain,
    ! [V_U_5] :
      ( ~ c_in(c_Pair(v_z,V_U_5,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | c_in(c_Pair(V_U_5,v_xaa(V_U_5),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_16,plain,
    ! [V_x_8,V_z_6,V_y_9,V_w_7] :
      ( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x_8,V_z_6),c_Comb_Ocomb_Oop_A_D_D(V_y_9,V_w_7),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(V_x_8,V_y_9,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(V_z_6,V_w_7,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_33,plain,
    ! [V_x_15,V_z_16,V_y_17,V_w_18] :
      ( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x_15,V_z_16),c_Comb_Ocomb_Oop_A_D_D(V_y_17,V_w_18),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(V_x_15,V_y_17,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(V_z_16,V_w_18,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_6,plain,
    ! [V_U_1] :
      ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),V_U_1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_yb,v_wa),V_U_1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_40,plain,
    ! [V_y_19,V_w_20] :
      ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),c_Comb_Ocomb_Oop_A_D_D(V_y_19,V_w_20),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_yb,V_y_19,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_wa,V_w_20,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(resolution,[status(thm)],[c_33,c_6]) ).

tff(c_45,plain,
    ! [V_y_9,V_w_7] :
      ( ~ c_in(c_Pair(v_yb,V_y_9,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_wa,V_w_7,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_ya,V_y_9,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_w,V_w_7,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(resolution,[status(thm)],[c_16,c_40]) ).

tff(c_47,plain,
    ! [V_w_21] :
      ( ~ c_in(c_Pair(v_wa,V_w_21,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_w,V_w_21,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(splitLeft,[status(thm)],[c_45]) ).

tff(c_51,plain,
    ( ~ c_in(c_Pair(v_w,v_xaa(v_wa),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | ~ c_in(c_Pair(v_z,v_wa,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(resolution,[status(thm)],[c_14,c_47]) ).

tff(c_58,plain,
    ~ c_in(c_Pair(v_w,v_xaa(v_wa),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_51]) ).

tff(c_62,plain,
    ~ c_in(c_Pair(v_z,v_wa,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
    inference(resolution,[status(thm)],[c_12,c_58]) ).

tff(c_66,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_62]) ).

tff(c_68,plain,
    ! [V_y_22] :
      ( ~ c_in(c_Pair(v_yb,V_y_22,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
      | ~ c_in(c_Pair(v_ya,V_y_22,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(splitRight,[status(thm)],[c_45]) ).

tff(c_76,plain,
    ( ~ c_in(c_Pair(v_ya,v_xb(v_yb),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | ~ c_in(c_Pair(v_x,v_yb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
    inference(resolution,[status(thm)],[c_10,c_68]) ).

tff(c_80,plain,
    ~ c_in(c_Pair(v_ya,v_xb(v_yb),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_76]) ).

tff(c_83,plain,
    ~ c_in(c_Pair(v_x,v_yb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
    inference(resolution,[status(thm)],[c_8,c_80]) ).

tff(c_87,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : COL110-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % 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
% 0.18/0.35  % Computer : n027.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit : 300
% 0.18/0.35  % WCLimit  : 300
% 0.18/0.35  % DateTime : Thu Aug  3 18:33:54 EDT 2023
% 0.18/0.35  % CPUTime  : 
% 2.98/1.81  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.98/1.82  
% 2.98/1.82  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.98/1.84  
% 2.98/1.85  Inference rules
% 2.98/1.85  ----------------------
% 2.98/1.85  #Ref     : 0
% 2.98/1.85  #Sup     : 10
% 2.98/1.85  #Fact    : 0
% 2.98/1.85  #Define  : 0
% 2.98/1.85  #Split   : 3
% 2.98/1.85  #Chain   : 0
% 2.98/1.85  #Close   : 0
% 2.98/1.85  
% 2.98/1.85  Ordering : KBO
% 2.98/1.85  
% 2.98/1.85  Simplification rules
% 2.98/1.85  ----------------------
% 2.98/1.85  #Subsume      : 0
% 2.98/1.85  #Demod        : 4
% 2.98/1.85  #Tautology    : 0
% 2.98/1.85  #SimpNegUnit  : 0
% 2.98/1.85  #BackRed      : 0
% 2.98/1.85  
% 2.98/1.85  #Partial instantiations: 0
% 2.98/1.85  #Strategies tried      : 1
% 2.98/1.85  
% 2.98/1.85  Timing (in seconds)
% 2.98/1.85  ----------------------
% 2.98/1.85  Preprocessing        : 0.48
% 2.98/1.85  Parsing              : 0.27
% 2.98/1.85  CNF conversion       : 0.02
% 2.98/1.85  Main loop            : 0.22
% 2.98/1.85  Inferencing          : 0.10
% 2.98/1.85  Reduction            : 0.05
% 2.98/1.85  Demodulation         : 0.04
% 2.98/1.85  BG Simplification    : 0.01
% 2.98/1.85  Subsumption          : 0.05
% 2.98/1.85  Abstraction          : 0.01
% 2.98/1.85  MUC search           : 0.00
% 2.98/1.85  Cooper               : 0.00
% 2.98/1.85  Total                : 0.75
% 2.98/1.85  Index Insertion      : 0.00
% 2.98/1.85  Index Deletion       : 0.00
% 2.98/1.85  Index Matching       : 0.00
% 2.98/1.85  BG Taut test         : 0.00
%------------------------------------------------------------------------------