TSTP Solution File: ALG030-10 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG030-10 : TPTP v8.1.2. Released v7.3.0.
% 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 : n001.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 10:30:56 EDT 2023

% Result   : Unsatisfiable 4.81s 2.24s
% Output   : CNFRefutation 4.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   54 (  43 unt;  11 typ;   0 def)
%            Number of atoms       :   43 (  42 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  :   16 (   8   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-4 aty)
%            Number of variables   :   30 (;  30   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ ifeq2 > ifeq > op2 > op1 > #nlpp > sorti2 > sorti1 > j > h > true > sK2_ax3_U > sK1_ax3_V

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(sK1_ax3_V,type,
    sK1_ax3_V: $i ).

tff(sorti1,type,
    sorti1: $i > $i ).

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

tff(op2,type,
    op2: ( $i * $i ) > $i ).

tff(sorti2,type,
    sorti2: $i > $i ).

tff(op1,type,
    op1: ( $i * $i ) > $i ).

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

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

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

tff(sK2_ax3_U,type,
    sK2_ax3_U: $i ).

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

tff(f_32,axiom,
    op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
    file(unknown,unknown) ).

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

tff(f_33,axiom,
    sorti1(sK1_ax3_V) = true,
    file(unknown,unknown) ).

tff(f_34,axiom,
    sorti1(sK2_ax3_U) = true,
    file(unknown,unknown) ).

tff(f_40,axiom,
    ! [X,W] : ( ifeq2(sorti1(X),true,ifeq2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ),
    file(unknown,unknown) ).

tff(f_42,axiom,
    ! [X2] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 ),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ! [U] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
    file(unknown,unknown) ).

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

tff(f_46,axiom,
    ! [Z,Y] : ( ifeq2(sorti2(Z),true,ifeq2(sorti2(Y),true,op1(j(Y),j(Z)),j(op2(Y,Z))),j(op2(Y,Z))) = j(op2(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ! [V,U] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) ),
    file(unknown,unknown) ).

tff(c_10,plain,
    op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

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_12,plain,
    sorti1(sK1_ax3_V) = true,
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_14,plain,
    sorti1(sK2_ax3_U) = true,
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_412,plain,
    ! [X_39,W_40] : ( ifeq2(sorti1(X_39),true,ifeq2(sorti1(W_40),true,op2(h(W_40),h(X_39)),h(op1(W_40,X_39))),h(op1(W_40,X_39))) = h(op1(W_40,X_39)) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_2441,plain,
    ! [W_52] : ( ifeq2(true,true,ifeq2(sorti1(W_52),true,op2(h(W_52),h(sK2_ax3_U)),h(op1(W_52,sK2_ax3_U))),h(op1(W_52,sK2_ax3_U))) = h(op1(W_52,sK2_ax3_U)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_412]) ).

tff(c_2529,plain,
    ifeq2(true,true,ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))) = h(op1(sK1_ax3_V,sK2_ax3_U)),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_2441]) ).

tff(c_2559,plain,
    op2(h(sK1_ax3_V),h(sK2_ax3_U)) = h(op1(sK1_ax3_V,sK2_ax3_U)),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_2529]) ).

tff(c_125,plain,
    ! [X2_29] : ( ifeq2(sorti1(X2_29),true,j(h(X2_29)),X2_29) = X2_29 ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_137,plain,
    ifeq2(true,true,j(h(sK2_ax3_U)),sK2_ax3_U) = sK2_ax3_U,
    inference(superposition,[status(thm),theory(equality)],[c_14,c_125]) ).

tff(c_185,plain,
    j(h(sK2_ax3_U)) = sK2_ax3_U,
    inference(superposition,[status(thm),theory(equality)],[c_137,c_2]) ).

tff(c_134,plain,
    ifeq2(true,true,j(h(sK1_ax3_V)),sK1_ax3_V) = sK1_ax3_V,
    inference(superposition,[status(thm),theory(equality)],[c_12,c_125]) ).

tff(c_143,plain,
    j(h(sK1_ax3_V)) = sK1_ax3_V,
    inference(superposition,[status(thm),theory(equality)],[c_134,c_2]) ).

tff(c_55,plain,
    ! [U_27] : ( ifeq(sorti1(U_27),true,sorti2(h(U_27)),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_65,plain,
    ifeq(true,true,sorti2(h(sK2_ax3_U)),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_14,c_55]) ).

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_104,plain,
    sorti2(h(sK2_ax3_U)) = true,
    inference(superposition,[status(thm),theory(equality)],[c_65,c_4]) ).

tff(c_62,plain,
    ifeq(true,true,sorti2(h(sK1_ax3_V)),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_12,c_55]) ).

tff(c_71,plain,
    sorti2(h(sK1_ax3_V)) = true,
    inference(superposition,[status(thm),theory(equality)],[c_62,c_4]) ).

tff(c_26,plain,
    ! [Z_18,Y_19] : ( ifeq2(sorti2(Z_18),true,ifeq2(sorti2(Y_19),true,op1(j(Y_19),j(Z_18)),j(op2(Y_19,Z_18))),j(op2(Y_19,Z_18))) = j(op2(Y_19,Z_18)) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_2598,plain,
    ifeq2(sorti2(h(sK2_ax3_U)),true,ifeq2(sorti2(h(sK1_ax3_V)),true,op1(j(h(sK1_ax3_V)),j(h(sK2_ax3_U))),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),j(op2(h(sK1_ax3_V),h(sK2_ax3_U)))) = j(op2(h(sK1_ax3_V),h(sK2_ax3_U))),
    inference(superposition,[status(thm),theory(equality)],[c_2559,c_26]) ).

tff(c_2622,plain,
    j(h(op1(sK1_ax3_V,sK2_ax3_U))) = op1(sK1_ax3_V,sK2_ax3_U),
    inference(demodulation,[status(thm),theory(equality)],[c_2559,c_185,c_143,c_2,c_104,c_2,c_71,c_2598]) ).

tff(c_2090,plain,
    ! [W_51] : ( ifeq2(true,true,ifeq2(sorti1(W_51),true,op2(h(W_51),h(sK1_ax3_V)),h(op1(W_51,sK1_ax3_V))),h(op1(W_51,sK1_ax3_V))) = h(op1(W_51,sK1_ax3_V)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_412]) ).

tff(c_2178,plain,
    ifeq2(true,true,ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = h(op1(sK2_ax3_U,sK1_ax3_V)),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_2090]) ).

tff(c_2205,plain,
    op2(h(sK2_ax3_U),h(sK1_ax3_V)) = h(op1(sK2_ax3_U,sK1_ax3_V)),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_2178]) ).

tff(c_16,plain,
    ! [V_11,U_12] : ( ifeq2(sorti2(V_11),true,ifeq2(sorti2(U_12),true,op2(U_12,V_11),op2(V_11,U_12)),op2(V_11,U_12)) = op2(V_11,U_12) ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_2613,plain,
    ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(sorti2(h(sK2_ax3_U)),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),op2(h(sK1_ax3_V),h(sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
    inference(superposition,[status(thm),theory(equality)],[c_2559,c_16]) ).

tff(c_2627,plain,
    h(op1(sK2_ax3_U,sK1_ax3_V)) = h(op1(sK1_ax3_V,sK2_ax3_U)),
    inference(demodulation,[status(thm),theory(equality)],[c_2559,c_2205,c_2,c_104,c_2,c_71,c_2613]) ).

tff(c_2412,plain,
    ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(sorti2(h(sK2_ax3_U)),true,op1(j(h(sK2_ax3_U)),j(h(sK1_ax3_V))),j(op2(h(sK2_ax3_U),h(sK1_ax3_V)))),j(h(op1(sK2_ax3_U,sK1_ax3_V)))) = j(op2(h(sK2_ax3_U),h(sK1_ax3_V))),
    inference(superposition,[status(thm),theory(equality)],[c_2205,c_26]) ).

tff(c_2434,plain,
    j(h(op1(sK2_ax3_U,sK1_ax3_V))) = op1(sK2_ax3_U,sK1_ax3_V),
    inference(demodulation,[status(thm),theory(equality)],[c_2205,c_185,c_143,c_2,c_104,c_2,c_71,c_2412]) ).

tff(c_2655,plain,
    j(h(op1(sK1_ax3_V,sK2_ax3_U))) = op1(sK2_ax3_U,sK1_ax3_V),
    inference(demodulation,[status(thm),theory(equality)],[c_2627,c_2434]) ).

tff(c_2658,plain,
    op1(sK2_ax3_U,sK1_ax3_V) = op1(sK1_ax3_V,sK2_ax3_U),
    inference(demodulation,[status(thm),theory(equality)],[c_2622,c_2655]) ).

tff(c_2660,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_2658]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ALG030-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.15  % 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
% 0.15/0.36  % Computer : n001.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 20:57:55 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 4.81/2.24  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.81/2.25  
% 4.81/2.25  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.81/2.28  
% 4.81/2.28  Inference rules
% 4.81/2.28  ----------------------
% 4.81/2.28  #Ref     : 0
% 4.81/2.28  #Sup     : 776
% 4.81/2.28  #Fact    : 0
% 4.81/2.28  #Define  : 0
% 4.81/2.28  #Split   : 0
% 4.81/2.28  #Chain   : 0
% 4.81/2.28  #Close   : 0
% 4.81/2.28  
% 4.81/2.28  Ordering : KBO
% 4.81/2.28  
% 4.81/2.28  Simplification rules
% 4.81/2.28  ----------------------
% 4.81/2.28  #Subsume      : 0
% 4.81/2.28  #Demod        : 723
% 4.81/2.28  #Tautology    : 324
% 4.81/2.28  #SimpNegUnit  : 1
% 4.81/2.28  #BackRed      : 20
% 4.81/2.28  
% 4.81/2.28  #Partial instantiations: 0
% 4.81/2.28  #Strategies tried      : 1
% 4.81/2.28  
% 4.81/2.28  Timing (in seconds)
% 4.81/2.28  ----------------------
% 4.81/2.28  Preprocessing        : 0.46
% 4.81/2.28  Parsing              : 0.24
% 4.81/2.28  CNF conversion       : 0.02
% 4.81/2.28  Main loop            : 0.75
% 4.81/2.28  Inferencing          : 0.23
% 4.81/2.28  Reduction            : 0.31
% 4.81/2.28  Demodulation         : 0.24
% 4.81/2.28  BG Simplification    : 0.03
% 4.81/2.28  Subsumption          : 0.12
% 4.81/2.28  Abstraction          : 0.03
% 4.81/2.28  MUC search           : 0.00
% 4.81/2.28  Cooper               : 0.00
% 4.81/2.28  Total                : 1.27
% 4.81/2.28  Index Insertion      : 0.00
% 4.81/2.28  Index Deletion       : 0.00
% 4.81/2.28  Index Matching       : 0.00
% 4.81/2.28  BG Taut test         : 0.00
%------------------------------------------------------------------------------