TSTP Solution File: COL121-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : COL121-2 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n003.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 10:35:10 EDT 2023

% Result   : Unsatisfiable 15.19s 6.29s
% Output   : CNFRefutation 15.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   44 (   7 unt;  13 typ;   0 def)
%            Number of atoms       :   75 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   93 (  49   ~;  44   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (   7   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-4 aty)
%            Number of variables   :   58 (;  58   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_in > c_Comb_Odiamond > c_Pair > c_Comb_Odiamond__strip__lemmaE__1 > tc_prod > c_Transitive__Closure_Ortrancl > #nlpp > v_x > v_z > v_ya > v_y > v_xaa > v_r > t_a

%Foreground sorts:

%Background operators:

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

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

tff(t_a,type,
    t_a: $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_xaa,type,
    v_xaa: $i ).

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

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

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

tff(c_Comb_Odiamond__strip__lemmaE__1,type,
    c_Comb_Odiamond__strip__lemmaE__1: ( $i * $i * $i * $i ) > $i ).

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

tff(f_63,axiom,
    c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
    file(unknown,unknown) ).

tff(f_62,axiom,
    c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    file(unknown,unknown) ).

tff(f_61,axiom,
    c_Comb_Odiamond(v_r,t_a),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ! [V_U] :
      ( c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    file(unknown,unknown) ).

tff(f_47,axiom,
    ! [V_r,T_a,V_y,V_x,V_y_H] :
      ( ~ c_Comb_Odiamond(V_r,T_a)
      | ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
      | c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ! [V_p,V_r,T_a] :
      ( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
      | c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
    file(unknown,unknown) ).

tff(f_73,axiom,
    ! [V_U] :
      ( c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    file(unknown,unknown) ).

tff(f_60,axiom,
    ! [V_r,V_a,T_a,V_c,V_b] :
      ( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
      | ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
      | c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ! [V_r,T_a,V_y,V_x,V_y_H] :
      ( ~ c_Comb_Odiamond(V_r,T_a)
      | ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
      | c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
    file(unknown,unknown) ).

tff(f_79,axiom,
    ! [V_U] :
      ( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    file(unknown,unknown) ).

tff(c_14,plain,
    c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_12,plain,
    c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_10,plain,
    c_Comb_Odiamond(v_r,t_a),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_16,plain,
    ! [V_U_19] :
      ( ~ c_in(c_Pair(v_y,V_U_19,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | c_in(c_Pair(v_ya,v_x(V_U_19),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_74,plain,
    ! [V_x_38,V_y_H_40,V_y_37,V_r_39,T_a_36] :
      ( c_in(c_Pair(V_y_37,c_Comb_Odiamond__strip__lemmaE__1(V_r_39,V_y_37,V_y_H_40,T_a_36),T_a_36,T_a_36),V_r_39,tc_prod(T_a_36,T_a_36))
      | ~ c_in(c_Pair(V_x_38,V_y_37,T_a_36,T_a_36),c_Transitive__Closure_Ortrancl(V_r_39,T_a_36),tc_prod(T_a_36,T_a_36))
      | ~ c_in(c_Pair(V_x_38,V_y_H_40,T_a_36,T_a_36),V_r_39,tc_prod(T_a_36,T_a_36))
      | ~ c_Comb_Odiamond(V_r_39,T_a_36) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_80,plain,
    ! [V_U_19,V_y_H_40] :
      ( c_in(c_Pair(v_x(V_U_19),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_19),V_y_H_40,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_ya,V_y_H_40,t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_Comb_Odiamond(v_r,t_a)
      | ~ c_in(c_Pair(v_y,V_U_19,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(resolution,[status(thm)],[c_16,c_74]) ).

tff(c_94,plain,
    ! [V_U_19,V_y_H_40] :
      ( c_in(c_Pair(v_x(V_U_19),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_19),V_y_H_40,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_ya,V_y_H_40,t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_y,V_U_19,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_80]) ).

tff(c_6,plain,
    ! [V_p_11,V_r_12,T_a_13] :
      ( c_in(V_p_11,c_Transitive__Closure_Ortrancl(V_r_12,T_a_13),tc_prod(T_a_13,T_a_13))
      | ~ c_in(V_p_11,V_r_12,tc_prod(T_a_13,T_a_13)) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_18,plain,
    ! [V_U_20] :
      ( ~ c_in(c_Pair(v_y,V_U_20,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | c_in(c_Pair(V_U_20,v_x(V_U_20),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_47,plain,
    ! [V_r_34,V_a_30,T_a_33,V_b_31,V_c_32] :
      ( c_in(c_Pair(V_a_30,V_c_32,T_a_33,T_a_33),c_Transitive__Closure_Ortrancl(V_r_34,T_a_33),tc_prod(T_a_33,T_a_33))
      | ~ c_in(c_Pair(V_a_30,V_b_31,T_a_33,T_a_33),c_Transitive__Closure_Ortrancl(V_r_34,T_a_33),tc_prod(T_a_33,T_a_33))
      | ~ c_in(c_Pair(V_b_31,V_c_32,T_a_33,T_a_33),c_Transitive__Closure_Ortrancl(V_r_34,T_a_33),tc_prod(T_a_33,T_a_33)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_466,plain,
    ! [V_U_76,V_c_77] :
      ( c_in(c_Pair(V_U_76,V_c_77,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_x(V_U_76),V_c_77,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_y,V_U_76,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(resolution,[status(thm)],[c_18,c_47]) ).

tff(c_770,plain,
    ! [V_U_100,V_c_101] :
      ( c_in(c_Pair(V_U_100,V_c_101,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_y,V_U_100,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_x(V_U_100),V_c_101,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
    inference(resolution,[status(thm)],[c_6,c_466]) ).

tff(c_25189,plain,
    ! [V_U_500,V_y_H_501] :
      ( c_in(c_Pair(V_U_500,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_500),V_y_H_501,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_ya,V_y_H_501,t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_y,V_U_500,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(resolution,[status(thm)],[c_94,c_770]) ).

tff(c_104,plain,
    ! [V_y_H_44,T_a_42,V_r_43,V_x_46,V_y_45] :
      ( c_in(c_Pair(V_y_H_44,c_Comb_Odiamond__strip__lemmaE__1(V_r_43,V_y_45,V_y_H_44,T_a_42),T_a_42,T_a_42),c_Transitive__Closure_Ortrancl(V_r_43,T_a_42),tc_prod(T_a_42,T_a_42))
      | ~ c_in(c_Pair(V_x_46,V_y_45,T_a_42,T_a_42),c_Transitive__Closure_Ortrancl(V_r_43,T_a_42),tc_prod(T_a_42,T_a_42))
      | ~ c_in(c_Pair(V_x_46,V_y_H_44,T_a_42,T_a_42),V_r_43,tc_prod(T_a_42,T_a_42))
      | ~ c_Comb_Odiamond(V_r_43,T_a_42) ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_110,plain,
    ! [V_y_H_44,V_U_19] :
      ( c_in(c_Pair(V_y_H_44,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_19),V_y_H_44,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_ya,V_y_H_44,t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_Comb_Odiamond(v_r,t_a)
      | ~ c_in(c_Pair(v_y,V_U_19,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(resolution,[status(thm)],[c_16,c_104]) ).

tff(c_1317,plain,
    ! [V_y_H_129,V_U_130] :
      ( c_in(c_Pair(V_y_H_129,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_130),V_y_H_129,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_ya,V_y_H_129,t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_y,V_U_130,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_110]) ).

tff(c_20,plain,
    ! [V_U_21] :
      ( ~ c_in(c_Pair(v_z,V_U_21,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_xaa,V_U_21,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_1360,plain,
    ! [V_U_130] :
      ( ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_130),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_y,V_U_130,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(resolution,[status(thm)],[c_1317,c_20]) ).

tff(c_1382,plain,
    ! [V_U_130] :
      ( ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_130),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_y,V_U_130,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_1360]) ).

tff(c_25355,plain,
    ( ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(resolution,[status(thm)],[c_25189,c_1382]) ).

tff(c_25519,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_12,c_25355]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : COL121-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.09  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.30  % Computer : n003.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Thu Aug  3 18:18:38 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 15.19/6.29  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.19/6.30  
% 15.19/6.30  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.30/6.33  
% 15.30/6.33  Inference rules
% 15.30/6.33  ----------------------
% 15.30/6.33  #Ref     : 0
% 15.30/6.33  #Sup     : 6007
% 15.30/6.33  #Fact    : 0
% 15.30/6.33  #Define  : 0
% 15.30/6.33  #Split   : 43
% 15.30/6.33  #Chain   : 0
% 15.30/6.33  #Close   : 0
% 15.30/6.33  
% 15.30/6.33  Ordering : KBO
% 15.30/6.33  
% 15.30/6.33  Simplification rules
% 15.30/6.33  ----------------------
% 15.30/6.33  #Subsume      : 2171
% 15.30/6.33  #Demod        : 1165
% 15.30/6.33  #Tautology    : 225
% 15.30/6.33  #SimpNegUnit  : 1
% 15.30/6.33  #BackRed      : 0
% 15.30/6.33  
% 15.30/6.33  #Partial instantiations: 0
% 15.30/6.33  #Strategies tried      : 1
% 15.30/6.33  
% 15.30/6.33  Timing (in seconds)
% 15.30/6.33  ----------------------
% 15.30/6.33  Preprocessing        : 0.46
% 15.30/6.33  Parsing              : 0.26
% 15.30/6.33  CNF conversion       : 0.02
% 15.30/6.33  Main loop            : 4.96
% 15.30/6.33  Inferencing          : 1.21
% 15.30/6.33  Reduction            : 1.27
% 15.30/6.33  Demodulation         : 0.87
% 15.30/6.33  BG Simplification    : 0.07
% 15.30/6.33  Subsumption          : 2.13
% 15.30/6.33  Abstraction          : 0.10
% 15.30/6.33  MUC search           : 0.00
% 15.30/6.33  Cooper               : 0.00
% 15.30/6.33  Total                : 5.47
% 15.30/6.33  Index Insertion      : 0.00
% 15.30/6.33  Index Deletion       : 0.00
% 15.30/6.33  Index Matching       : 0.00
% 15.30/6.33  BG Taut test         : 0.00
%------------------------------------------------------------------------------