TSTP Solution File: BOO004-10 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : BOO004-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n018.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 10:34:21 EDT 2023

% Result   : Unsatisfiable 177.06s 133.84s
% Output   : CNFRefutation 177.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   61 (  50 unt;  11 typ;   0 def)
%            Number of atoms       :   50 (  49 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   19 (   7   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-4 aty)
%            Number of variables   :  120 (; 120   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ ifeq2 > ifeq > sum > product > multiply > add > #nlpp > inverse > x > true > multiplicative_identity > additive_identity

%Foreground sorts:

%Background operators:

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

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

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

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

tff(ifeq2,type,
    ifeq2: ( $i * $i * $i * $i ) > $i ).

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

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

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

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

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

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

tff(f_26,axiom,
    ! [A,B,C] : ( ifeq(A,A,B,C) = B ),
    file(unknown,unknown) ).

tff(f_24,axiom,
    ! [A,B,C] : ( ifeq2(A,A,B,C) = B ),
    file(unknown,unknown) ).

tff(f_28,axiom,
    ! [X,Y] : ( sum(X,Y,add(X,Y)) = true ),
    file(unknown,unknown) ).

tff(f_32,axiom,
    ! [X,Y,Z] : ( ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true ),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ! [X] : ( sum(X,additive_identity,X) = true ),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ! [X,Y,V,U] : ( ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V ),
    file(unknown,unknown) ).

tff(f_40,axiom,
    ! [X] : ( product(multiplicative_identity,X,X) = true ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ! [X] : ( sum(additive_identity,X,X) = true ),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ! [V3,Z,V1,X,Y,V2,V4] : ( ifeq(product(Y,Z,V3),true,ifeq(sum(V3,X,V4),true,ifeq(sum(Z,X,V2),true,ifeq(sum(Y,X,V1),true,product(V1,V2,V4),true),true),true),true) = true ),
    file(unknown,unknown) ).

tff(f_42,axiom,
    ! [X] : ( product(X,multiplicative_identity,X) = true ),
    file(unknown,unknown) ).

tff(f_70,axiom,
    ! [X,Y,V,U] : ( ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V ),
    file(unknown,unknown) ).

tff(f_48,axiom,
    ! [V3,Z,V1,X,Y,V2,V4] : ( ifeq(product(V3,X,V4),true,ifeq(product(Z,X,V2),true,ifeq(product(Y,X,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true ),
    file(unknown,unknown) ).

tff(f_72,axiom,
    sum(x,x,x) != true,
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [A_4,B_5,C_6] : ( ifeq(A_4,A_4,B_5,C_6) = B_5 ),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_2,plain,
    ! [A_1,B_2,C_3] : ( ifeq2(A_1,A_1,B_2,C_3) = B_2 ),
    inference(cnfTransformation,[status(thm)],[f_24]) ).

tff(c_6,plain,
    ! [X_7,Y_8] : ( sum(X_7,Y_8,add(X_7,Y_8)) = true ),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_217,plain,
    ! [X_112,Y_113,Z_114] : ( ifeq(sum(X_112,Y_113,Z_114),true,sum(Y_113,X_112,Z_114),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_1424,plain,
    ! [Y_179,X_180] : ( ifeq(true,true,sum(Y_179,X_180,add(X_180,Y_179)),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_217]) ).

tff(c_1429,plain,
    ! [Y_179,X_180] : ( sum(Y_179,X_180,add(X_180,Y_179)) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_1424,c_4]) ).

tff(c_16,plain,
    ! [X_18] : ( sum(X_18,additive_identity,X_18) = true ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_289,plain,
    ! [X_117,Y_118,V_119,U_120] : ( ifeq2(sum(X_117,Y_118,V_119),true,ifeq2(sum(X_117,Y_118,U_120),true,U_120,V_119),V_119) = V_119 ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_325,plain,
    ! [X_18,V_119] : ( ifeq2(sum(X_18,additive_identity,V_119),true,ifeq2(true,true,X_18,V_119),V_119) = V_119 ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_289]) ).

tff(c_462,plain,
    ! [X_128,V_129] : ( ifeq2(sum(X_128,additive_identity,V_129),true,X_128,V_129) = V_129 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_325]) ).

tff(c_484,plain,
    ! [X_7] : ( ifeq2(true,true,X_7,add(X_7,additive_identity)) = add(X_7,additive_identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_462]) ).

tff(c_501,plain,
    ! [X_7] : ( add(X_7,additive_identity) = X_7 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_484]) ).

tff(c_18,plain,
    ! [X_19] : ( product(multiplicative_identity,X_19,X_19) = true ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_14,plain,
    ! [X_17] : ( sum(additive_identity,X_17,X_17) = true ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_2535,plain,
    ! [V1_226,Y_228,V3_230,X_224,V4_229,Z_225,V2_227] : ( ifeq(product(Y_228,Z_225,V3_230),true,ifeq(sum(V3_230,X_224,V4_229),true,ifeq(sum(Z_225,X_224,V2_227),true,ifeq(sum(Y_228,X_224,V1_226),true,product(V1_226,V2_227,V4_229),true),true),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_2611,plain,
    ! [V1_226,Y_228,V3_230,V4_229,X_17] : ( ifeq(product(Y_228,additive_identity,V3_230),true,ifeq(sum(V3_230,X_17,V4_229),true,ifeq(true,true,ifeq(sum(Y_228,X_17,V1_226),true,product(V1_226,X_17,V4_229),true),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_2535]) ).

tff(c_6481,plain,
    ! [V4_380,V1_376,X_378,Y_379,V3_377] : ( ifeq(product(Y_379,additive_identity,V3_377),true,ifeq(sum(V3_377,X_378,V4_380),true,ifeq(sum(Y_379,X_378,V1_376),true,product(V1_376,X_378,V4_380),true),true),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2611]) ).

tff(c_48299,plain,
    ! [X_1194,V4_1195,V1_1196] : ( ifeq(true,true,ifeq(sum(additive_identity,X_1194,V4_1195),true,ifeq(sum(multiplicative_identity,X_1194,V1_1196),true,product(V1_1196,X_1194,V4_1195),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_6481]) ).

tff(c_48348,plain,
    ! [X_180,V1_1196] : ( ifeq(true,true,ifeq(true,true,ifeq(sum(multiplicative_identity,X_180,V1_1196),true,product(V1_1196,X_180,add(X_180,additive_identity)),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_1429,c_48299]) ).

tff(c_48423,plain,
    ! [X_1197,V1_1198] : ( ifeq(sum(multiplicative_identity,X_1197,V1_1198),true,product(V1_1198,X_1197,X_1197),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_501,c_4,c_4,c_48348]) ).

tff(c_48676,plain,
    ! [X_1199] : ( ifeq(true,true,product(add(X_1199,multiplicative_identity),X_1199,X_1199),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_1429,c_48423]) ).

tff(c_48709,plain,
    ! [X_1200] : ( product(add(X_1200,multiplicative_identity),X_1200,X_1200) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_48676,c_4]) ).

tff(c_20,plain,
    ! [X_20] : ( product(X_20,multiplicative_identity,X_20) = true ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_411,plain,
    ! [X_124,Y_125,V_126,U_127] : ( ifeq2(product(X_124,Y_125,V_126),true,ifeq2(product(X_124,Y_125,U_127),true,U_127,V_126),V_126) = V_126 ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_2913,plain,
    ! [X_239,U_240] : ( ifeq2(true,true,ifeq2(product(X_239,multiplicative_identity,U_240),true,U_240,X_239),X_239) = X_239 ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_411]) ).

tff(c_2919,plain,
    ! [X_239,U_240] : ( ifeq2(product(X_239,multiplicative_identity,U_240),true,U_240,X_239) = X_239 ),
    inference(superposition,[status(thm),theory(equality)],[c_2913,c_2]) ).

tff(c_49331,plain,
    ifeq2(true,true,multiplicative_identity,add(multiplicative_identity,multiplicative_identity)) = add(multiplicative_identity,multiplicative_identity),
    inference(superposition,[status(thm),theory(equality)],[c_48709,c_2919]) ).

tff(c_49522,plain,
    add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_49331]) ).

tff(c_49567,plain,
    sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) = true,
    inference(superposition,[status(thm),theory(equality)],[c_49522,c_1429]) ).

tff(c_750,plain,
    ! [X_144,Y_147,V4_143,Z_148,V1_146,V3_142,V2_145] : ( ifeq(product(V3_142,X_144,V4_143),true,ifeq(product(Z_148,X_144,V2_145),true,ifeq(product(Y_147,X_144,V1_146),true,ifeq(sum(Y_147,Z_148,V3_142),true,sum(V1_146,V2_145,V4_143),true),true),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_131405,plain,
    ! [Y_1987,V2_1989,V1_1990,Z_1991,X_1988] : ( ifeq(true,true,ifeq(product(Z_1991,X_1988,V2_1989),true,ifeq(product(Y_1987,X_1988,V1_1990),true,ifeq(sum(Y_1987,Z_1991,multiplicative_identity),true,sum(V1_1990,V2_1989,X_1988),true),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_750]) ).

tff(c_131690,plain,
    ! [Z_1991,X_19,V2_1989] : ( ifeq(true,true,ifeq(product(Z_1991,X_19,V2_1989),true,ifeq(true,true,ifeq(sum(multiplicative_identity,Z_1991,multiplicative_identity),true,sum(X_19,V2_1989,X_19),true),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_131405]) ).

tff(c_308826,plain,
    ! [Z_2696,X_2697,V2_2698] : ( ifeq(product(Z_2696,X_2697,V2_2698),true,ifeq(sum(multiplicative_identity,Z_2696,multiplicative_identity),true,sum(X_2697,V2_2698,X_2697),true),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_131690]) ).

tff(c_309148,plain,
    ! [X_19] : ( ifeq(true,true,ifeq(sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),true,sum(X_19,X_19,X_19),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_308826]) ).

tff(c_309201,plain,
    ! [X_19] : ( sum(X_19,X_19,X_19) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_49567,c_309148]) ).

tff(c_50,plain,
    sum(x,x,x) != true,
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_309206,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_309201,c_50]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : BOO004-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.15  % 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
% 0.18/0.37  % Computer : n018.cluster.edu
% 0.18/0.37  % Model    : x86_64 x86_64
% 0.18/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.37  % Memory   : 8042.1875MB
% 0.18/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.37  % CPULimit : 300
% 0.18/0.37  % WCLimit  : 300
% 0.18/0.37  % DateTime : Thu Aug  3 18:45:20 EDT 2023
% 0.18/0.37  % CPUTime  : 
% 177.06/133.84  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 177.06/133.85  
% 177.06/133.85  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 177.38/133.88  
% 177.38/133.88  Inference rules
% 177.38/133.88  ----------------------
% 177.38/133.88  #Ref     : 0
% 177.38/133.88  #Sup     : 78114
% 177.38/133.88  #Fact    : 0
% 177.38/133.88  #Define  : 0
% 177.38/133.88  #Split   : 0
% 177.38/133.88  #Chain   : 0
% 177.38/133.88  #Close   : 0
% 177.38/133.88  
% 177.38/133.88  Ordering : KBO
% 177.38/133.88  
% 177.38/133.88  Simplification rules
% 177.38/133.88  ----------------------
% 177.38/133.88  #Subsume      : 444
% 177.38/133.88  #Demod        : 94434
% 177.38/133.88  #Tautology    : 35585
% 177.38/133.88  #SimpNegUnit  : 0
% 177.38/133.88  #BackRed      : 231
% 177.38/133.88  
% 177.38/133.88  #Partial instantiations: 0
% 177.38/133.88  #Strategies tried      : 1
% 177.38/133.88  
% 177.38/133.88  Timing (in seconds)
% 177.38/133.88  ----------------------
% 177.38/133.89  Preprocessing        : 0.62
% 177.38/133.89  Parsing              : 0.32
% 177.38/133.89  CNF conversion       : 0.05
% 177.38/133.89  Main loop            : 132.06
% 177.38/133.89  Inferencing          : 11.11
% 177.38/133.89  Reduction            : 92.13
% 177.38/133.89  Demodulation         : 88.13
% 177.38/133.89  BG Simplification    : 0.43
% 177.38/133.89  Subsumption          : 24.07
% 177.38/133.89  Abstraction          : 0.45
% 177.38/133.89  MUC search           : 0.00
% 177.38/133.89  Cooper               : 0.00
% 177.38/133.89  Total                : 132.73
% 177.38/133.89  Index Insertion      : 0.00
% 177.38/133.89  Index Deletion       : 0.00
% 177.38/133.89  Index Matching       : 0.00
% 177.38/133.89  BG Taut test         : 0.00
%------------------------------------------------------------------------------