TSTP Solution File: SEU025+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU025+1 : 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 : n005.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 10:57:30 EDT 2023

% Result   : Theorem 22.42s 10.78s
% Output   : CNFRefutation 22.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   60 (  13 unt;  26 typ;   0 def)
%            Number of atoms       :   98 (  21 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  124 (  60   ~;  47   |;   6   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  16   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  10 con; 0-2 aty)
%            Number of variables   :   23 (;  23   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > relation_composition > #nlpp > relation_rng > relation_dom > powerset > function_inverse > empty_set > #skF_4 > #skF_11 > #skF_1 > #skF_8 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_9 > #skF_12

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(relation,type,
    relation: $i > $o ).

tff('#skF_4',type,
    '#skF_4': $i > $i ).

tff('#skF_11',type,
    '#skF_11': $i ).

tff('#skF_1',type,
    '#skF_1': $i > $i ).

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

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

tff('#skF_8',type,
    '#skF_8': $i > $i ).

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

tff('#skF_7',type,
    '#skF_7': $i ).

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

tff('#skF_10',type,
    '#skF_10': $i ).

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

tff('#skF_5',type,
    '#skF_5': $i ).

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

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

tff('#skF_6',type,
    '#skF_6': $i ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff('#skF_3',type,
    '#skF_3': $i ).

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

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

tff('#skF_9',type,
    '#skF_9': $i ).

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

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

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

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

tff('#skF_12',type,
    '#skF_12': $i ).

tff(f_245,negated_conjecture,
    ~ ! [A] :
        ( ( relation(A)
          & function(A) )
       => ( one_to_one(A)
         => ( ( relation_dom(relation_composition(A,function_inverse(A))) = relation_dom(A) )
            & ( relation_rng(relation_composition(A,function_inverse(A))) = relation_dom(A) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).

tff(f_234,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( one_to_one(A)
       => ( ( relation_rng(A) = relation_dom(function_inverse(A)) )
          & ( relation_dom(A) = relation_rng(function_inverse(A)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).

tff(f_59,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( relation(function_inverse(A))
        & function(function_inverse(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).

tff(f_186,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

tff(f_218,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( relation(B)
         => ( subset(relation_dom(A),relation_rng(B))
           => ( relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).

tff(f_209,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( relation(B)
         => ( subset(relation_rng(A),relation_dom(B))
           => ( relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).

tff(c_126,plain,
    relation('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_124,plain,
    function('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_122,plain,
    one_to_one('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_116,plain,
    ! [A_43] :
      ( ( relation_rng(function_inverse(A_43)) = relation_dom(A_43) )
      | ~ one_to_one(A_43)
      | ~ function(A_43)
      | ~ relation(A_43) ),
    inference(cnfTransformation,[status(thm)],[f_234]) ).

tff(c_16,plain,
    ! [A_6] :
      ( relation(function_inverse(A_6))
      | ~ function(A_6)
      | ~ relation(A_6) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_100,plain,
    ! [A_26] : subset(A_26,A_26),
    inference(cnfTransformation,[status(thm)],[f_186]) ).

tff(c_118,plain,
    ! [A_43] :
      ( ( relation_dom(function_inverse(A_43)) = relation_rng(A_43) )
      | ~ one_to_one(A_43)
      | ~ function(A_43)
      | ~ relation(A_43) ),
    inference(cnfTransformation,[status(thm)],[f_234]) ).

tff(c_46213,plain,
    ! [B_797,A_798] :
      ( ( relation_rng(relation_composition(B_797,A_798)) = relation_rng(A_798) )
      | ~ subset(relation_dom(A_798),relation_rng(B_797))
      | ~ relation(B_797)
      | ~ relation(A_798) ),
    inference(cnfTransformation,[status(thm)],[f_218]) ).

tff(c_72698,plain,
    ! [B_1006,A_1007] :
      ( ( relation_rng(relation_composition(B_1006,function_inverse(A_1007))) = relation_rng(function_inverse(A_1007)) )
      | ~ subset(relation_rng(A_1007),relation_rng(B_1006))
      | ~ relation(B_1006)
      | ~ relation(function_inverse(A_1007))
      | ~ one_to_one(A_1007)
      | ~ function(A_1007)
      | ~ relation(A_1007) ),
    inference(superposition,[status(thm),theory(equality)],[c_118,c_46213]) ).

tff(c_106478,plain,
    ! [A_1381] :
      ( ( relation_rng(relation_composition(A_1381,function_inverse(A_1381))) = relation_rng(function_inverse(A_1381)) )
      | ~ relation(function_inverse(A_1381))
      | ~ one_to_one(A_1381)
      | ~ function(A_1381)
      | ~ relation(A_1381) ),
    inference(resolution,[status(thm)],[c_100,c_72698]) ).

tff(c_2311,plain,
    ! [A_169,B_170] :
      ( ( relation_dom(relation_composition(A_169,B_170)) = relation_dom(A_169) )
      | ~ subset(relation_rng(A_169),relation_dom(B_170))
      | ~ relation(B_170)
      | ~ relation(A_169) ),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_27955,plain,
    ! [A_387,A_388] :
      ( ( relation_dom(relation_composition(A_387,function_inverse(A_388))) = relation_dom(A_387) )
      | ~ subset(relation_rng(A_387),relation_rng(A_388))
      | ~ relation(function_inverse(A_388))
      | ~ relation(A_387)
      | ~ one_to_one(A_388)
      | ~ function(A_388)
      | ~ relation(A_388) ),
    inference(superposition,[status(thm),theory(equality)],[c_118,c_2311]) ).

tff(c_43644,plain,
    ! [A_676] :
      ( ( relation_dom(relation_composition(A_676,function_inverse(A_676))) = relation_dom(A_676) )
      | ~ relation(function_inverse(A_676))
      | ~ one_to_one(A_676)
      | ~ function(A_676)
      | ~ relation(A_676) ),
    inference(resolution,[status(thm)],[c_100,c_27955]) ).

tff(c_120,plain,
    ( ( relation_rng(relation_composition('#skF_12',function_inverse('#skF_12'))) != relation_dom('#skF_12') )
    | ( relation_dom(relation_composition('#skF_12',function_inverse('#skF_12'))) != relation_dom('#skF_12') ) ),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_138,plain,
    relation_dom(relation_composition('#skF_12',function_inverse('#skF_12'))) != relation_dom('#skF_12'),
    inference(splitLeft,[status(thm)],[c_120]) ).

tff(c_43831,plain,
    ( ~ relation(function_inverse('#skF_12'))
    | ~ one_to_one('#skF_12')
    | ~ function('#skF_12')
    | ~ relation('#skF_12') ),
    inference(superposition,[status(thm),theory(equality)],[c_43644,c_138]) ).

tff(c_43879,plain,
    ~ relation(function_inverse('#skF_12')),
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_124,c_122,c_43831]) ).

tff(c_43894,plain,
    ( ~ function('#skF_12')
    | ~ relation('#skF_12') ),
    inference(resolution,[status(thm)],[c_16,c_43879]) ).

tff(c_43901,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_124,c_43894]) ).

tff(c_43902,plain,
    relation_rng(relation_composition('#skF_12',function_inverse('#skF_12'))) != relation_dom('#skF_12'),
    inference(splitRight,[status(thm)],[c_120]) ).

tff(c_106725,plain,
    ( ( relation_rng(function_inverse('#skF_12')) != relation_dom('#skF_12') )
    | ~ relation(function_inverse('#skF_12'))
    | ~ one_to_one('#skF_12')
    | ~ function('#skF_12')
    | ~ relation('#skF_12') ),
    inference(superposition,[status(thm),theory(equality)],[c_106478,c_43902]) ).

tff(c_106788,plain,
    ( ( relation_rng(function_inverse('#skF_12')) != relation_dom('#skF_12') )
    | ~ relation(function_inverse('#skF_12')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_124,c_122,c_106725]) ).

tff(c_106806,plain,
    ~ relation(function_inverse('#skF_12')),
    inference(splitLeft,[status(thm)],[c_106788]) ).

tff(c_106809,plain,
    ( ~ function('#skF_12')
    | ~ relation('#skF_12') ),
    inference(resolution,[status(thm)],[c_16,c_106806]) ).

tff(c_106816,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_124,c_106809]) ).

tff(c_106817,plain,
    relation_rng(function_inverse('#skF_12')) != relation_dom('#skF_12'),
    inference(splitRight,[status(thm)],[c_106788]) ).

tff(c_107411,plain,
    ( ~ one_to_one('#skF_12')
    | ~ function('#skF_12')
    | ~ relation('#skF_12') ),
    inference(superposition,[status(thm),theory(equality)],[c_116,c_106817]) ).

tff(c_107415,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_124,c_122,c_107411]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU025+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 11:47:27 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 22.42/10.78  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.42/10.79  
% 22.42/10.79  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.48/10.82  
% 22.48/10.82  Inference rules
% 22.48/10.82  ----------------------
% 22.48/10.82  #Ref     : 0
% 22.48/10.82  #Sup     : 26535
% 22.48/10.82  #Fact    : 0
% 22.48/10.82  #Define  : 0
% 22.48/10.82  #Split   : 36
% 22.48/10.82  #Chain   : 0
% 22.48/10.82  #Close   : 0
% 22.48/10.82  
% 22.48/10.82  Ordering : KBO
% 22.48/10.82  
% 22.48/10.82  Simplification rules
% 22.48/10.82  ----------------------
% 22.48/10.82  #Subsume      : 5600
% 22.48/10.82  #Demod        : 25001
% 22.48/10.82  #Tautology    : 12766
% 22.48/10.82  #SimpNegUnit  : 38
% 22.48/10.82  #BackRed      : 26
% 22.48/10.82  
% 22.48/10.82  #Partial instantiations: 0
% 22.48/10.82  #Strategies tried      : 1
% 22.48/10.82  
% 22.48/10.82  Timing (in seconds)
% 22.48/10.82  ----------------------
% 22.48/10.82  Preprocessing        : 0.58
% 22.48/10.82  Parsing              : 0.32
% 22.48/10.82  CNF conversion       : 0.05
% 22.48/10.82  Main loop            : 9.18
% 22.48/10.82  Inferencing          : 1.75
% 22.48/10.82  Reduction            : 2.99
% 22.48/10.82  Demodulation         : 2.25
% 22.48/10.82  BG Simplification    : 0.14
% 22.48/10.82  Subsumption          : 3.79
% 22.48/10.82  Abstraction          : 0.18
% 22.48/10.82  MUC search           : 0.00
% 22.48/10.82  Cooper               : 0.00
% 22.48/10.82  Total                : 9.80
% 22.48/10.82  Index Insertion      : 0.00
% 22.48/10.82  Index Deletion       : 0.00
% 22.48/10.82  Index Matching       : 0.00
% 22.48/10.82  BG Taut test         : 0.00
%------------------------------------------------------------------------------