TSTP Solution File: GRP659+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP659+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/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 : 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 10:41:51 EDT 2023

% Result   : Theorem 12.35s 4.09s
% Output   : CNFRefutation 12.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   56 (  49 unt;   5 typ;   0 def)
%            Number of atoms       :   53 (  52 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    6 (   4   ~;   1   |;   1   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 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    :    5 (   5 usr;   0 con; 1-2 aty)
%            Number of variables   :  111 (; 110   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ rd > mult > ld > #nlpp > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(ld,type,
    ld: ( $i * $i ) > $i ).

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

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

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

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

tff(f_30,axiom,
    ! [B,A] : ( ld(A,mult(A,B)) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).

tff(f_32,axiom,
    ! [B,A] : ( mult(rd(A,B),B) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).

tff(f_28,axiom,
    ! [B,A] : ( mult(A,ld(A,B)) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).

tff(f_36,axiom,
    ! [C,B,A] : ( mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).

tff(f_34,axiom,
    ! [B,A] : ( rd(mult(A,B),B) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).

tff(f_42,negated_conjecture,
    ~ ? [X0] :
      ! [X1] :
        ( ( mult(X1,X0) = X1 )
        & ( mult(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

tff(c_4,plain,
    ! [A_4,B_3] : ( ld(A_4,mult(A_4,B_3)) = B_3 ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_6,plain,
    ! [A_6,B_5] : ( mult(rd(A_6,B_5),B_5) = A_6 ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_39,plain,
    ! [A_18,B_19] : ( ld(A_18,mult(A_18,B_19)) = B_19 ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_48,plain,
    ! [A_6,B_5] : ( ld(rd(A_6,B_5),A_6) = B_5 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_39]) ).

tff(c_2,plain,
    ! [A_2,B_1] : ( mult(A_2,ld(A_2,B_1)) = B_1 ),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_114,plain,
    ! [A_27,B_28,C_29] : ( mult(mult(A_27,mult(B_28,C_29)),B_28) = mult(mult(A_27,B_28),mult(C_29,B_28)) ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_239,plain,
    ! [A_36,A_37,B_38] : ( mult(mult(A_36,A_37),mult(ld(A_37,B_38),A_37)) = mult(mult(A_36,B_38),A_37) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_114]) ).

tff(c_420,plain,
    ! [A_42,A_43,B_44] : ( ld(mult(A_42,A_43),mult(mult(A_42,B_44),A_43)) = mult(ld(A_43,B_44),A_43) ),
    inference(superposition,[status(thm),theory(equality)],[c_239,c_4]) ).

tff(c_608,plain,
    ! [B_48] : ( mult(ld(B_48,B_48),B_48) = B_48 ),
    inference(superposition,[status(thm),theory(equality)],[c_420,c_4]) ).

tff(c_8,plain,
    ! [A_8,B_7] : ( rd(mult(A_8,B_7),B_7) = A_8 ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_665,plain,
    ! [B_48] : ( rd(B_48,B_48) = ld(B_48,B_48) ),
    inference(superposition,[status(thm),theory(equality)],[c_608,c_8]) ).

tff(c_51,plain,
    ! [A_20,B_21] : ( mult(A_20,ld(A_20,B_21)) = B_21 ),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_60,plain,
    ! [B_21,A_20] : ( rd(B_21,ld(A_20,B_21)) = A_20 ),
    inference(superposition,[status(thm),theory(equality)],[c_51,c_8]) ).

tff(c_278,plain,
    ! [A_36,A_37,B_38] : ( ld(mult(A_36,A_37),mult(mult(A_36,B_38),A_37)) = mult(ld(A_37,B_38),A_37) ),
    inference(superposition,[status(thm),theory(equality)],[c_239,c_4]) ).

tff(c_127,plain,
    ! [A_27,B_28,C_29] : ( ld(mult(A_27,mult(B_28,C_29)),mult(mult(A_27,B_28),mult(C_29,B_28))) = B_28 ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_4]) ).

tff(c_642,plain,
    ! [A_27,B_48] : ( ld(mult(A_27,B_48),mult(mult(A_27,ld(B_48,B_48)),mult(B_48,ld(B_48,B_48)))) = ld(B_48,B_48) ),
    inference(superposition,[status(thm),theory(equality)],[c_608,c_127]) ).

tff(c_814,plain,
    ! [B_52] : ( mult(ld(B_52,ld(B_52,B_52)),B_52) = ld(B_52,B_52) ),
    inference(demodulation,[status(thm),theory(equality)],[c_278,c_2,c_642]) ).

tff(c_868,plain,
    ! [B_52] : ( ld(ld(B_52,ld(B_52,B_52)),ld(B_52,B_52)) = B_52 ),
    inference(superposition,[status(thm),theory(equality)],[c_814,c_4]) ).

tff(c_313,plain,
    ! [A_39,B_40,C_41] : ( mult(mult(rd(A_39,mult(B_40,C_41)),B_40),mult(C_41,B_40)) = mult(A_39,B_40) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_114]) ).

tff(c_2002,plain,
    ! [A_76,B_77,A_78] : ( mult(mult(rd(A_76,B_77),A_78),mult(ld(A_78,B_77),A_78)) = mult(A_76,A_78) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_313]) ).

tff(c_4559,plain,
    ! [A_116,A_117,B_118] : ( mult(mult(A_116,A_117),mult(ld(A_117,ld(A_116,B_118)),A_117)) = mult(B_118,A_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_60,c_2002]) ).

tff(c_4759,plain,
    ! [B_52] : ( mult(mult(B_52,ld(B_52,ld(B_52,B_52))),mult(B_52,ld(B_52,ld(B_52,B_52)))) = mult(B_52,ld(B_52,ld(B_52,B_52))) ),
    inference(superposition,[status(thm),theory(equality)],[c_868,c_4559]) ).

tff(c_4855,plain,
    ! [B_52] : ( mult(ld(B_52,B_52),ld(B_52,B_52)) = ld(B_52,B_52) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_2,c_4759]) ).

tff(c_204,plain,
    ! [A_33,B_34,C_35] : ( rd(mult(mult(A_33,B_34),mult(C_35,B_34)),B_34) = mult(A_33,mult(B_34,C_35)) ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_8]) ).

tff(c_5895,plain,
    ! [A_128,A_129,B_130] : ( rd(mult(mult(A_128,ld(A_129,B_130)),B_130),ld(A_129,B_130)) = mult(A_128,mult(ld(A_129,B_130),A_129)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_204]) ).

tff(c_10462,plain,
    ! [B_171,A_172] : ( rd(mult(B_171,B_171),ld(A_172,B_171)) = mult(A_172,mult(ld(A_172,B_171),A_172)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_5895]) ).

tff(c_10748,plain,
    ! [B_52,A_172] : ( rd(ld(B_52,B_52),ld(A_172,ld(B_52,B_52))) = mult(A_172,mult(ld(A_172,ld(B_52,B_52)),A_172)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4855,c_10462]) ).

tff(c_10826,plain,
    ! [A_173,B_174] : ( mult(A_173,mult(ld(A_173,ld(B_174,B_174)),A_173)) = A_173 ),
    inference(demodulation,[status(thm),theory(equality)],[c_60,c_10748]) ).

tff(c_1413,plain,
    ! [A_64,B_65,B_66] : ( mult(mult(rd(A_64,B_65),B_66),B_65) = mult(A_64,mult(ld(B_65,B_66),B_65)) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_239]) ).

tff(c_1512,plain,
    ! [A_64,B_65,B_66] : ( rd(mult(A_64,mult(ld(B_65,B_66),B_65)),B_65) = mult(rd(A_64,B_65),B_66) ),
    inference(superposition,[status(thm),theory(equality)],[c_1413,c_8]) ).

tff(c_10835,plain,
    ! [A_173,B_174] : ( mult(rd(A_173,A_173),ld(B_174,B_174)) = rd(A_173,A_173) ),
    inference(superposition,[status(thm),theory(equality)],[c_10826,c_1512]) ).

tff(c_11052,plain,
    ! [A_173,B_174] : ( mult(ld(A_173,A_173),ld(B_174,B_174)) = ld(A_173,A_173) ),
    inference(demodulation,[status(thm),theory(equality)],[c_665,c_665,c_10835]) ).

tff(c_11376,plain,
    ! [A_177,B_178] : ( mult(ld(A_177,A_177),ld(B_178,B_178)) = ld(A_177,A_177) ),
    inference(demodulation,[status(thm),theory(equality)],[c_665,c_665,c_10835]) ).

tff(c_153,plain,
    ! [A_30,B_31,C_32] : ( ld(mult(A_30,mult(B_31,C_32)),mult(mult(A_30,B_31),mult(C_32,B_31))) = B_31 ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_4]) ).

tff(c_1834,plain,
    ! [A_73,B_74,C_75] : ( ld(mult(rd(A_73,B_74),mult(B_74,C_75)),mult(A_73,mult(C_75,B_74))) = B_74 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_153]) ).

tff(c_1985,plain,
    ! [A_6,C_75,B_74] : ( ld(mult(rd(rd(A_6,mult(C_75,B_74)),B_74),mult(B_74,C_75)),A_6) = B_74 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_1834]) ).

tff(c_11411,plain,
    ! [A_6,A_177,B_178] : ( ld(mult(rd(rd(A_6,ld(A_177,A_177)),ld(B_178,B_178)),mult(ld(B_178,B_178),ld(A_177,A_177))),A_6) = ld(B_178,B_178) ),
    inference(superposition,[status(thm),theory(equality)],[c_11376,c_1985]) ).

tff(c_11699,plain,
    ! [B_179,A_180] : ( ld(B_179,B_179) = ld(A_180,A_180) ),
    inference(demodulation,[status(thm),theory(equality)],[c_48,c_6,c_11052,c_11411]) ).

tff(c_1509,plain,
    ! [A_64,B_65,B_66] : ( ld(mult(rd(A_64,B_65),B_66),mult(A_64,mult(ld(B_65,B_66),B_65))) = B_65 ),
    inference(superposition,[status(thm),theory(equality)],[c_1413,c_4]) ).

tff(c_11770,plain,
    ! [A_64,A_180,B_179] : ( ld(mult(rd(A_64,A_180),A_180),mult(A_64,mult(ld(B_179,B_179),A_180))) = A_180 ),
    inference(superposition,[status(thm),theory(equality)],[c_11699,c_1509]) ).

tff(c_11968,plain,
    ! [B_179,A_180] : ( mult(ld(B_179,B_179),A_180) = A_180 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_11770]) ).

tff(c_12544,plain,
    ! [B_184,A_185] : ( mult(B_184,ld(A_185,A_185)) = B_184 ),
    inference(superposition,[status(thm),theory(equality)],[c_11699,c_2]) ).

tff(c_12,plain,
    ! [X0_12] :
      ( ( mult('#skF_2'(X0_12),X0_12) != '#skF_2'(X0_12) )
      | ( mult(X0_12,'#skF_1'(X0_12)) != '#skF_1'(X0_12) ) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_13016,plain,
    ! [A_185] : ( mult(ld(A_185,A_185),'#skF_1'(ld(A_185,A_185))) != '#skF_1'(ld(A_185,A_185)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12544,c_12]) ).

tff(c_14238,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_11968,c_13016]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP659+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/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
% 0.12/0.35  % Computer : n005.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Thu Aug  3 21:57:26 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 12.35/4.09  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.35/4.10  
% 12.35/4.10  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.35/4.13  
% 12.35/4.13  Inference rules
% 12.35/4.13  ----------------------
% 12.35/4.13  #Ref     : 0
% 12.35/4.13  #Sup     : 3840
% 12.35/4.13  #Fact    : 0
% 12.35/4.13  #Define  : 0
% 12.35/4.13  #Split   : 0
% 12.35/4.13  #Chain   : 0
% 12.35/4.13  #Close   : 0
% 12.35/4.13  
% 12.35/4.13  Ordering : KBO
% 12.35/4.13  
% 12.35/4.13  Simplification rules
% 12.35/4.13  ----------------------
% 12.35/4.13  #Subsume      : 41
% 12.35/4.13  #Demod        : 3626
% 12.35/4.13  #Tautology    : 1066
% 12.35/4.13  #SimpNegUnit  : 0
% 12.35/4.13  #BackRed      : 8
% 12.35/4.13  
% 12.35/4.13  #Partial instantiations: 0
% 12.35/4.13  #Strategies tried      : 1
% 12.35/4.13  
% 12.35/4.13  Timing (in seconds)
% 12.35/4.13  ----------------------
% 12.35/4.14  Preprocessing        : 0.43
% 12.35/4.14  Parsing              : 0.24
% 12.35/4.14  CNF conversion       : 0.03
% 12.35/4.14  Main loop            : 2.65
% 12.35/4.14  Inferencing          : 0.89
% 12.35/4.14  Reduction            : 1.15
% 12.35/4.14  Demodulation         : 1.04
% 12.35/4.14  BG Simplification    : 0.14
% 12.35/4.14  Subsumption          : 0.34
% 12.35/4.14  Abstraction          : 0.24
% 12.35/4.14  MUC search           : 0.00
% 12.35/4.14  Cooper               : 0.00
% 12.35/4.14  Total                : 3.13
% 12.35/4.14  Index Insertion      : 0.00
% 12.35/4.14  Index Deletion       : 0.00
% 12.35/4.14  Index Matching       : 0.00
% 12.35/4.14  BG Taut test         : 0.00
%------------------------------------------------------------------------------