TSTP Solution File: REL023+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : REL023+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 : n016.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 10:54:30 EDT 2023

% Result   : Theorem 7.97s 3.18s
% Output   : CNFRefutation 8.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   82 (  71 unt;  11 typ;   0 def)
%            Number of atoms       :   71 (  70 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    5 (   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    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   99 (;  99   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ meet > join > composition > #nlpp > converse > complement > zero > top > one > #skF_2 > #skF_3 > #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_2',type,
    '#skF_2': $i ).

tff('#skF_3',type,
    '#skF_3': $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_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_80,axiom,
    ! [X0] : ( zero = meet(X0,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).

tff(f_69,axiom,
    ! [X0] : ( converse(converse(X0)) = X0 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).

tff(f_64,axiom,
    ! [X0] : ( composition(X0,one) = X0 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).

tff(f_73,axiom,
    ! [X0,X1] : ( converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).

tff(f_75,axiom,
    ! [X0,X1] : ( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).

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

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_66,axiom,
    ! [X0,X1,X2] : ( composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).

tff(f_85,negated_conjecture,
    ~ ! [X0,X1,X2] : ( join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)) ),
    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_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_702,plain,
    ! [X0_54,X1_55] : ( join(meet(X0_54,X1_55),complement(join(complement(X0_54),X1_55))) = X0_54 ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).

tff(c_752,plain,
    ! [X0_54,X0_1] : ( join(meet(X0_54,X0_1),complement(join(X0_1,complement(X0_54)))) = X0_54 ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_702]) ).

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

tff(c_16,plain,
    ! [X0_17] : ( converse(converse(X0_17)) = X0_17 ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_12,plain,
    ! [X0_13] : ( composition(X0_13,one) = X0_13 ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_308,plain,
    ! [X1_37,X0_38] : ( composition(converse(X1_37),converse(X0_38)) = converse(composition(X0_38,X1_37)) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_358,plain,
    ! [X0_41,X1_42] : ( converse(composition(converse(X0_41),X1_42)) = composition(converse(X1_42),X0_41) ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_308]) ).

tff(c_392,plain,
    ! [X0_41] : ( composition(converse(one),X0_41) = converse(converse(X0_41)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_358]) ).

tff(c_402,plain,
    ! [X0_43] : ( composition(converse(one),X0_43) = X0_43 ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_392]) ).

tff(c_416,plain,
    converse(one) = one,
    inference(superposition,[status(thm),theory(equality)],[c_402,c_12]) ).

tff(c_400,plain,
    ! [X0_41] : ( composition(converse(one),X0_41) = X0_41 ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_392]) ).

tff(c_433,plain,
    ! [X0_41] : ( composition(one,X0_41) = X0_41 ),
    inference(demodulation,[status(thm),theory(equality)],[c_416,c_400]) ).

tff(c_912,plain,
    ! [X0_60,X1_61] : ( join(composition(converse(X0_60),complement(composition(X0_60,X1_61))),complement(X1_61)) = complement(X1_61) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_939,plain,
    ! [X1_61] : ( join(composition(one,complement(composition(one,X1_61))),complement(X1_61)) = complement(X1_61) ),
    inference(superposition,[status(thm),theory(equality)],[c_416,c_912]) ).

tff(c_1047,plain,
    ! [X1_63] : ( join(complement(X1_63),complement(X1_63)) = complement(X1_63) ),
    inference(demodulation,[status(thm),theory(equality)],[c_433,c_2,c_433,c_939]) ).

tff(c_30,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_1053,plain,
    ! [X1_63] : ( join(meet(X1_63,complement(X1_63)),complement(complement(X1_63))) = X1_63 ),
    inference(superposition,[status(thm),theory(equality)],[c_1047,c_30]) ).

tff(c_1098,plain,
    ! [X1_64] : ( join(zero,complement(complement(X1_64))) = X1_64 ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_1053]) ).

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

tff(c_105,plain,
    ! [X0_32,X1_33] : ( complement(join(complement(X0_32),complement(X1_33))) = meet(X0_32,X1_33) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_139,plain,
    ! [X0_32] : ( meet(X0_32,complement(X0_32)) = complement(top) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_105]) ).

tff(c_142,plain,
    complement(top) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_139]) ).

tff(c_149,plain,
    ! [X0_8] : ( complement(join(complement(X0_8),zero)) = meet(X0_8,top) ),
    inference(superposition,[status(thm),theory(equality)],[c_142,c_8]) ).

tff(c_158,plain,
    ! [X0_8] : ( complement(join(zero,complement(X0_8))) = meet(X0_8,top) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_149]) ).

tff(c_1110,plain,
    ! [X1_64] : ( meet(complement(X1_64),top) = complement(X1_64) ),
    inference(superposition,[status(thm),theory(equality)],[c_1098,c_158]) ).

tff(c_973,plain,
    ! [X1_61] : ( join(complement(X1_61),complement(X1_61)) = complement(X1_61) ),
    inference(demodulation,[status(thm),theory(equality)],[c_433,c_2,c_433,c_939]) ).

tff(c_521,plain,
    ! [X0_48,X1_49,X2_50] : ( join(join(X0_48,X1_49),X2_50) = join(X0_48,join(X1_49,X2_50)) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_1362,plain,
    ! [X0_70,X2_71] : ( join(X0_70,join(complement(X0_70),X2_71)) = join(top,X2_71) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_521]) ).

tff(c_1401,plain,
    ! [X1_61] : ( join(top,complement(X1_61)) = join(X1_61,complement(X1_61)) ),
    inference(superposition,[status(thm),theory(equality)],[c_973,c_1362]) ).

tff(c_1442,plain,
    ! [X1_72] : ( join(top,complement(X1_72)) = top ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_1401]) ).

tff(c_1462,plain,
    ! [X0_8,X1_9] : ( join(top,meet(X0_8,X1_9)) = top ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1442]) ).

tff(c_1132,plain,
    ! [X1_65] : ( meet(X1_65,X1_65) = complement(complement(X1_65)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1047,c_8]) ).

tff(c_1560,plain,
    ! [X1_77] : ( join(complement(X1_77),meet(X1_77,X1_77)) = top ),
    inference(superposition,[status(thm),theory(equality)],[c_1132,c_24]) ).

tff(c_575,plain,
    ! [X0_24,X2_50] : ( join(X0_24,join(complement(X0_24),X2_50)) = join(top,X2_50) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_521]) ).

tff(c_1565,plain,
    ! [X1_77] : ( join(top,meet(X1_77,X1_77)) = join(X1_77,top) ),
    inference(superposition,[status(thm),theory(equality)],[c_1560,c_575]) ).

tff(c_1607,plain,
    ! [X1_78] : ( join(X1_78,top) = top ),
    inference(demodulation,[status(thm),theory(equality)],[c_1462,c_1565]) ).

tff(c_1617,plain,
    ! [X0_6] : ( join(meet(X0_6,top),complement(top)) = X0_6 ),
    inference(superposition,[status(thm),theory(equality)],[c_1607,c_30]) ).

tff(c_1795,plain,
    ! [X0_82] : ( join(zero,meet(X0_82,top)) = X0_82 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_142,c_1617]) ).

tff(c_1833,plain,
    ! [X1_83] : ( join(zero,complement(X1_83)) = complement(X1_83) ),
    inference(superposition,[status(thm),theory(equality)],[c_1110,c_1795]) ).

tff(c_1088,plain,
    ! [X1_63] : ( join(zero,complement(complement(X1_63))) = X1_63 ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_1053]) ).

tff(c_1839,plain,
    ! [X1_63] : ( complement(complement(X1_63)) = X1_63 ),
    inference(superposition,[status(thm),theory(equality)],[c_1833,c_1088]) ).

tff(c_1944,plain,
    ! [X1_84] : ( complement(complement(X1_84)) = X1_84 ),
    inference(superposition,[status(thm),theory(equality)],[c_1833,c_1088]) ).

tff(c_1971,plain,
    ! [X1_84] : ( join(complement(complement(X1_84)),X1_84) = complement(complement(X1_84)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1944,c_973]) ).

tff(c_2348,plain,
    ! [X1_91] : ( join(X1_91,X1_91) = X1_91 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1839,c_1839,c_1971]) ).

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_13238,plain,
    ! [X1_198,X2_199] : ( join(X1_198,join(X1_198,X2_199)) = join(X1_198,X2_199) ),
    inference(superposition,[status(thm),theory(equality)],[c_2348,c_4]) ).

tff(c_13395,plain,
    ! [X0_54,X0_1] : ( join(meet(X0_54,X0_1),complement(join(X0_1,complement(X0_54)))) = join(meet(X0_54,X0_1),X0_54) ),
    inference(superposition,[status(thm),theory(equality)],[c_752,c_13238]) ).

tff(c_13580,plain,
    ! [X0_54,X0_1] : ( join(X0_54,meet(X0_54,X0_1)) = X0_54 ),
    inference(demodulation,[status(thm),theory(equality)],[c_752,c_2,c_13395]) ).

tff(c_2766,plain,
    ! [X1_99,X0_100] : ( complement(join(complement(X1_99),complement(X0_100))) = meet(X0_100,X1_99) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_105]) ).

tff(c_2855,plain,
    ! [X1_9,X0_8] : ( meet(X1_9,X0_8) = meet(X0_8,X1_9) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_2766]) ).

tff(c_14,plain,
    ! [X0_14,X2_16,X1_15] : ( join(composition(X0_14,X2_16),composition(X1_15,X2_16)) = composition(join(X0_14,X1_15),X2_16) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_28,plain,
    join(composition(meet('#skF_1',converse('#skF_2')),meet('#skF_2','#skF_3')),composition('#skF_1',meet('#skF_2','#skF_3'))) != composition('#skF_1',meet('#skF_2','#skF_3')),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_29,plain,
    composition(join(meet('#skF_1',converse('#skF_2')),'#skF_1'),meet('#skF_2','#skF_3')) != composition('#skF_1',meet('#skF_2','#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_28]) ).

tff(c_31,plain,
    composition(join('#skF_1',meet('#skF_1',converse('#skF_2'))),meet('#skF_2','#skF_3')) != composition('#skF_1',meet('#skF_2','#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_29]) ).

tff(c_2880,plain,
    composition(join('#skF_1',meet('#skF_1',converse('#skF_2'))),meet('#skF_3','#skF_2')) != composition('#skF_1',meet('#skF_3','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_2855,c_2855,c_31]) ).

tff(c_13622,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_13580,c_2880]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : REL023+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n016.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 16:04:23 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 7.97/3.18  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.60/3.19  
% 8.60/3.19  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.60/3.23  
% 8.60/3.23  Inference rules
% 8.60/3.23  ----------------------
% 8.60/3.23  #Ref     : 0
% 8.60/3.23  #Sup     : 3494
% 8.60/3.23  #Fact    : 0
% 8.60/3.23  #Define  : 0
% 8.60/3.23  #Split   : 0
% 8.60/3.23  #Chain   : 0
% 8.60/3.23  #Close   : 0
% 8.60/3.23  
% 8.60/3.23  Ordering : KBO
% 8.60/3.23  
% 8.60/3.23  Simplification rules
% 8.60/3.23  ----------------------
% 8.60/3.23  #Subsume      : 46
% 8.60/3.23  #Demod        : 3862
% 8.60/3.23  #Tautology    : 2214
% 8.60/3.23  #SimpNegUnit  : 0
% 8.60/3.23  #BackRed      : 26
% 8.60/3.23  
% 8.60/3.23  #Partial instantiations: 0
% 8.60/3.23  #Strategies tried      : 1
% 8.60/3.23  
% 8.60/3.23  Timing (in seconds)
% 8.60/3.23  ----------------------
% 8.60/3.23  Preprocessing        : 0.49
% 8.60/3.23  Parsing              : 0.27
% 8.60/3.23  CNF conversion       : 0.03
% 8.60/3.23  Main loop            : 1.61
% 8.60/3.23  Inferencing          : 0.45
% 8.60/3.23  Reduction            : 0.77
% 8.60/3.23  Demodulation         : 0.65
% 8.60/3.23  BG Simplification    : 0.05
% 8.60/3.23  Subsumption          : 0.23
% 8.60/3.23  Abstraction          : 0.06
% 8.60/3.23  MUC search           : 0.00
% 8.60/3.23  Cooper               : 0.00
% 8.60/3.23  Total                : 2.16
% 8.60/3.23  Index Insertion      : 0.00
% 8.60/3.23  Index Deletion       : 0.00
% 8.60/3.23  Index Matching       : 0.00
% 8.60/3.23  BG Taut test         : 0.00
%------------------------------------------------------------------------------