TSTP Solution File: REL002+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : REL002+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n014.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 10:54:23 EDT 2023

% Result   : Theorem 5.47s 2.36s
% Output   : CNFRefutation 5.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   90 (  81 unt;   9 typ;   0 def)
%            Number of atoms       :   81 (  80 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   84 (;  84   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ meet > join > composition > #nlpp > converse > complement > zero > top > one > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

tff(f_53,axiom,
    ! [X0,X1] : ( join(X0,X1) = join(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).

tff(f_80,axiom,
    ! [X0] : ( zero = meet(X0,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).

tff(f_78,axiom,
    ! [X0] : ( top = join(X0,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).

tff(f_59,axiom,
    ! [X0,X1] : ( meet(X0,X1) = complement(join(complement(X0),complement(X1))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).

tff(f_57,axiom,
    ! [X0,X1] : ( X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).

tff(f_55,axiom,
    ! [X0,X1,X2] : ( join(X0,join(X1,X2)) = join(join(X0,X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).

tff(f_85,negated_conjecture,
    ~ ! [X0] : ( join(X0,top) = top ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

tff(c_2,plain,
    ! [X1_2,X0_1] : ( join(X1_2,X0_1) = join(X0_1,X1_2) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_26,plain,
    ! [X0_25] : ( meet(X0_25,complement(X0_25)) = zero ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_24,plain,
    ! [X0_24] : ( join(X0_24,complement(X0_24)) = top ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_145,plain,
    ! [X0_36,X1_37] : ( complement(join(complement(X0_36),complement(X1_37))) = meet(X0_36,X1_37) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_179,plain,
    ! [X0_36] : ( meet(X0_36,complement(X0_36)) = complement(top) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_145]) ).

tff(c_182,plain,
    complement(top) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_179]) ).

tff(c_8,plain,
    ! [X0_8,X1_9] : ( complement(join(complement(X0_8),complement(X1_9))) = meet(X0_8,X1_9) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_6,plain,
    ! [X0_6,X1_7] : ( join(complement(join(complement(X0_6),complement(X1_7))),complement(join(complement(X0_6),X1_7))) = X0_6 ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_560,plain,
    ! [X0_53,X1_54] : ( join(meet(X0_53,X1_54),complement(join(complement(X0_53),X1_54))) = X0_53 ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).

tff(c_614,plain,
    ! [X0_53] : ( join(meet(X0_53,complement(complement(X0_53))),complement(top)) = X0_53 ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_560]) ).

tff(c_625,plain,
    ! [X0_53] : ( join(zero,meet(X0_53,complement(complement(X0_53)))) = X0_53 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_182,c_614]) ).

tff(c_225,plain,
    join(top,zero) = top,
    inference(superposition,[status(thm),theory(equality)],[c_182,c_24]) ).

tff(c_317,plain,
    ! [X0_44,X1_45,X2_46] : ( join(join(X0_44,X1_45),X2_46) = join(X0_44,join(X1_45,X2_46)) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_525,plain,
    ! [X2_52] : ( join(top,join(zero,X2_52)) = join(top,X2_52) ),
    inference(superposition,[status(thm),theory(equality)],[c_225,c_317]) ).

tff(c_546,plain,
    join(top,complement(zero)) = join(top,top),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_525]) ).

tff(c_222,plain,
    ! [X0_8] : ( complement(join(complement(X0_8),zero)) = meet(X0_8,top) ),
    inference(superposition,[status(thm),theory(equality)],[c_182,c_8]) ).

tff(c_390,plain,
    ! [X0_47] : ( complement(join(zero,complement(X0_47))) = meet(X0_47,top) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_222]) ).

tff(c_439,plain,
    meet(zero,top) = complement(top),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_390]) ).

tff(c_443,plain,
    meet(zero,top) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_439]) ).

tff(c_581,plain,
    join(zero,complement(join(complement(zero),top))) = zero,
    inference(superposition,[status(thm),theory(equality)],[c_443,c_560]) ).

tff(c_623,plain,
    join(zero,complement(join(top,top))) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_546,c_2,c_581]) ).

tff(c_342,plain,
    ! [X2_46] : ( join(top,join(zero,X2_46)) = join(top,X2_46) ),
    inference(superposition,[status(thm),theory(equality)],[c_225,c_317]) ).

tff(c_646,plain,
    join(top,complement(join(top,top))) = join(top,zero),
    inference(superposition,[status(thm),theory(equality)],[c_623,c_342]) ).

tff(c_658,plain,
    join(top,complement(join(top,top))) = top,
    inference(demodulation,[status(thm),theory(equality)],[c_225,c_646]) ).

tff(c_231,plain,
    ! [X0_8] : ( complement(join(zero,complement(X0_8))) = meet(X0_8,top) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_222]) ).

tff(c_649,plain,
    meet(join(top,top),top) = complement(zero),
    inference(superposition,[status(thm),theory(equality)],[c_623,c_231]) ).

tff(c_29,plain,
    ! [X0_6,X1_7] : ( join(meet(X0_6,X1_7),complement(join(complement(X0_6),X1_7))) = X0_6 ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).

tff(c_738,plain,
    join(complement(zero),complement(join(complement(join(top,top)),top))) = join(top,top),
    inference(superposition,[status(thm),theory(equality)],[c_649,c_29]) ).

tff(c_747,plain,
    join(top,top) = top,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_182,c_2,c_658,c_2,c_738]) ).

tff(c_754,plain,
    join(zero,complement(top)) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_747,c_623]) ).

tff(c_757,plain,
    join(zero,zero) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_754]) ).

tff(c_4,plain,
    ! [X0_3,X1_4,X2_5] : ( join(join(X0_3,X1_4),X2_5) = join(X0_3,join(X1_4,X2_5)) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_1188,plain,
    ! [X2_67] : ( join(zero,join(zero,X2_67)) = join(zero,X2_67) ),
    inference(superposition,[status(thm),theory(equality)],[c_757,c_4]) ).

tff(c_1212,plain,
    ! [X0_53] : ( join(zero,meet(X0_53,complement(complement(X0_53)))) = join(zero,X0_53) ),
    inference(superposition,[status(thm),theory(equality)],[c_625,c_1188]) ).

tff(c_1247,plain,
    ! [X0_68] : ( join(zero,X0_68) = X0_68 ),
    inference(demodulation,[status(thm),theory(equality)],[c_625,c_1212]) ).

tff(c_1276,plain,
    complement(zero) = top,
    inference(superposition,[status(thm),theory(equality)],[c_1247,c_24]) ).

tff(c_1238,plain,
    ! [X0_53] : ( join(zero,X0_53) = X0_53 ),
    inference(demodulation,[status(thm),theory(equality)],[c_625,c_1212]) ).

tff(c_1332,plain,
    ! [X1_9] : ( complement(join(top,complement(X1_9))) = meet(zero,X1_9) ),
    inference(superposition,[status(thm),theory(equality)],[c_1276,c_8]) ).

tff(c_761,plain,
    ! [X2_5] : ( join(top,join(top,X2_5)) = join(top,X2_5) ),
    inference(superposition,[status(thm),theory(equality)],[c_747,c_4]) ).

tff(c_891,plain,
    ! [X1_60,X0_61] : ( complement(join(complement(X1_60),complement(X0_61))) = meet(X0_61,X1_60) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_145]) ).

tff(c_927,plain,
    ! [X1_60,X0_61] : ( meet(X1_60,X0_61) = meet(X0_61,X1_60) ),
    inference(superposition,[status(thm),theory(equality)],[c_891,c_8]) ).

tff(c_362,plain,
    ! [X0_24,X2_46] : ( join(X0_24,join(complement(X0_24),X2_46)) = join(top,X2_46) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_317]) ).

tff(c_219,plain,
    ! [X1_9] : ( complement(join(zero,complement(X1_9))) = meet(top,X1_9) ),
    inference(superposition,[status(thm),theory(equality)],[c_182,c_8]) ).

tff(c_1246,plain,
    ! [X1_9] : ( complement(complement(X1_9)) = meet(top,X1_9) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1238,c_219]) ).

tff(c_1260,plain,
    ! [X0_53] : ( meet(X0_53,complement(complement(X0_53))) = X0_53 ),
    inference(superposition,[status(thm),theory(equality)],[c_1247,c_625]) ).

tff(c_1883,plain,
    ! [X0_53] : ( meet(X0_53,meet(top,X0_53)) = X0_53 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1246,c_1260]) ).

tff(c_1688,plain,
    ! [X1_75] : ( complement(complement(X1_75)) = meet(top,X1_75) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1238,c_219]) ).

tff(c_979,plain,
    ! [X1_60] : ( meet(complement(X1_60),X1_60) = complement(top) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_891]) ).

tff(c_987,plain,
    ! [X1_60] : ( meet(complement(X1_60),X1_60) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_979]) ).

tff(c_2127,plain,
    ! [X1_82] : ( meet(meet(top,X1_82),complement(X1_82)) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_1688,c_987]) ).

tff(c_2138,plain,
    ! [X1_82] : ( join(zero,complement(join(complement(meet(top,X1_82)),complement(X1_82)))) = meet(top,X1_82) ),
    inference(superposition,[status(thm),theory(equality)],[c_2127,c_29]) ).

tff(c_2195,plain,
    ! [X1_82] : ( meet(top,X1_82) = X1_82 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1883,c_1238,c_8,c_2,c_2138]) ).

tff(c_2210,plain,
    ! [X1_9] : ( complement(complement(X1_9)) = X1_9 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2195,c_1246]) ).

tff(c_1245,plain,
    ! [X0_8] : ( complement(complement(X0_8)) = meet(X0_8,top) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1238,c_231]) ).

tff(c_2282,plain,
    ! [X0_8] : ( meet(X0_8,top) = X0_8 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2210,c_1245]) ).

tff(c_2713,plain,
    ! [X0_91,X1_92] : ( join(meet(X0_91,complement(X1_92)),meet(X0_91,X1_92)) = X0_91 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_560]) ).

tff(c_2760,plain,
    ! [X0_91] : ( join(meet(X0_91,top),meet(X0_91,zero)) = X0_91 ),
    inference(superposition,[status(thm),theory(equality)],[c_1276,c_2713]) ).

tff(c_2817,plain,
    ! [X0_93] : ( join(X0_93,meet(X0_93,zero)) = X0_93 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2282,c_2760]) ).

tff(c_366,plain,
    ! [X0_44,X1_45] : ( join(X0_44,join(X1_45,complement(join(X0_44,X1_45)))) = top ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_317]) ).

tff(c_2827,plain,
    ! [X0_93] : ( join(X0_93,join(meet(X0_93,zero),complement(X0_93))) = top ),
    inference(superposition,[status(thm),theory(equality)],[c_2817,c_366]) ).

tff(c_2892,plain,
    ! [X0_94] : ( join(top,meet(X0_94,zero)) = top ),
    inference(demodulation,[status(thm),theory(equality)],[c_362,c_2,c_2827]) ).

tff(c_2925,plain,
    ! [X0_61] : ( join(top,meet(zero,X0_61)) = top ),
    inference(superposition,[status(thm),theory(equality)],[c_927,c_2892]) ).

tff(c_3721,plain,
    ! [X1_106] : ( complement(join(top,complement(X1_106))) = meet(zero,X1_106) ),
    inference(superposition,[status(thm),theory(equality)],[c_1276,c_8]) ).

tff(c_3724,plain,
    ! [X1_106] : ( meet(zero,join(top,complement(X1_106))) = complement(join(top,meet(zero,X1_106))) ),
    inference(superposition,[status(thm),theory(equality)],[c_3721,c_1332]) ).

tff(c_3803,plain,
    ! [X1_107] : ( meet(zero,join(top,complement(X1_107))) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_2925,c_3724]) ).

tff(c_3821,plain,
    ! [X1_107] : ( join(zero,complement(join(complement(zero),join(top,complement(X1_107))))) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_3803,c_29]) ).

tff(c_3861,plain,
    ! [X1_108] : ( meet(zero,X1_108) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_1332,c_1238,c_761,c_1276,c_3821]) ).

tff(c_3901,plain,
    ! [X1_108] : ( join(zero,complement(join(complement(zero),X1_108))) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_3861,c_29]) ).

tff(c_4022,plain,
    ! [X1_110] : ( complement(join(top,X1_110)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_1238,c_1276,c_3901]) ).

tff(c_4033,plain,
    ! [X1_110] : ( join(top,X1_110) = complement(zero) ),
    inference(superposition,[status(thm),theory(equality)],[c_4022,c_2210]) ).

tff(c_4123,plain,
    ! [X1_111] : ( join(top,X1_111) = top ),
    inference(demodulation,[status(thm),theory(equality)],[c_1276,c_4033]) ).

tff(c_4153,plain,
    ! [X1_111] : ( join(X1_111,top) = top ),
    inference(superposition,[status(thm),theory(equality)],[c_4123,c_2]) ).

tff(c_28,plain,
    join('#skF_1',top) != top,
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_4193,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4153,c_28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : REL002+1 : TPTP v8.1.2. Released v4.0.0.
% 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
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 15:27:18 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 5.47/2.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/2.37  
% 5.67/2.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.67/2.41  
% 5.67/2.41  Inference rules
% 5.67/2.41  ----------------------
% 5.67/2.41  #Ref     : 0
% 5.67/2.41  #Sup     : 1050
% 5.67/2.41  #Fact    : 0
% 5.67/2.41  #Define  : 0
% 5.67/2.41  #Split   : 0
% 5.67/2.41  #Chain   : 0
% 5.67/2.41  #Close   : 0
% 5.67/2.41  
% 5.67/2.41  Ordering : KBO
% 5.67/2.41  
% 5.67/2.41  Simplification rules
% 5.67/2.41  ----------------------
% 5.67/2.41  #Subsume      : 16
% 5.67/2.41  #Demod        : 933
% 5.67/2.41  #Tautology    : 682
% 5.67/2.41  #SimpNegUnit  : 0
% 5.67/2.41  #BackRed      : 35
% 5.67/2.41  
% 5.67/2.41  #Partial instantiations: 0
% 5.67/2.41  #Strategies tried      : 1
% 5.67/2.41  
% 5.67/2.41  Timing (in seconds)
% 5.67/2.41  ----------------------
% 5.67/2.41  Preprocessing        : 0.46
% 5.67/2.41  Parsing              : 0.25
% 5.67/2.41  CNF conversion       : 0.03
% 5.67/2.41  Main loop            : 0.89
% 5.67/2.41  Inferencing          : 0.28
% 5.67/2.41  Reduction            : 0.38
% 5.67/2.41  Demodulation         : 0.32
% 5.67/2.41  BG Simplification    : 0.04
% 5.67/2.41  Subsumption          : 0.14
% 5.67/2.41  Abstraction          : 0.04
% 5.67/2.41  MUC search           : 0.00
% 5.67/2.41  Cooper               : 0.00
% 5.67/2.41  Total                : 1.42
% 5.67/2.41  Index Insertion      : 0.00
% 5.67/2.41  Index Deletion       : 0.00
% 5.67/2.41  Index Matching       : 0.00
% 5.67/2.41  BG Taut test         : 0.00
%------------------------------------------------------------------------------