TSTP Solution File: RNG007-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG007-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n025.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 10:54:41 EDT 2023

% Result   : Unsatisfiable 22.88s 12.12s
% Output   : CNFRefutation 23.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   99 (  33 unt;   7 typ;   0 def)
%            Number of atoms       :  197 (  29 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  212 ( 107   ~; 105   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   5   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  252 (; 252   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sum > product > multiply > add > #nlpp > additive_inverse > additive_identity > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

tff(f_51,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file(unknown,unknown) ).

tff(f_183,axiom,
    ! [X] : product(X,X,X),
    file(unknown,unknown) ).

tff(f_179,axiom,
    ! [X,Y,U,V] :
      ( ~ product(X,Y,U)
      | ~ product(X,Y,V)
      | ( U = V ) ),
    file(unknown,unknown) ).

tff(f_55,axiom,
    ! [X] : sum(additive_inverse(X),X,additive_identity),
    file(unknown,unknown) ).

tff(f_47,axiom,
    ! [X] : sum(additive_identity,X,X),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ! [W,U,Z,X,Y,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(Y,Z,V)
      | ~ sum(U,Z,W)
      | sum(X,V,W) ),
    file(unknown,unknown) ).

tff(f_49,axiom,
    ! [X] : sum(X,additive_identity,X),
    file(unknown,unknown) ).

tff(f_171,axiom,
    ! [X,Y,U,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(X,Y,V)
      | ( U = V ) ),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [X,Y] : sum(X,Y,add(X,Y)),
    file(unknown,unknown) ).

tff(f_148,axiom,
    ! [V3,Z,V1,X,Y,V2,V4] :
      ( ~ product(Y,X,V1)
      | ~ product(Z,X,V2)
      | ~ sum(Y,Z,V3)
      | ~ product(V3,X,V4)
      | sum(V1,V2,V4) ),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [X] : sum(X,additive_inverse(X),additive_identity),
    file(unknown,unknown) ).

tff(f_79,axiom,
    ! [W,U,Z,X,Y,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(Y,Z,V)
      | ~ sum(X,V,W)
      | sum(U,Z,W) ),
    file(unknown,unknown) ).

tff(f_84,axiom,
    ! [X,Y,Z] :
      ( ~ sum(X,Y,Z)
      | sum(Y,X,Z) ),
    file(unknown,unknown) ).

tff(f_106,axiom,
    ! [W,U,Z,X,Y,V] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(X,V,W)
      | product(U,Z,W) ),
    file(unknown,unknown) ).

tff(f_120,axiom,
    ! [V3,Z,V1,X,Y,V2,V4] :
      ( ~ product(X,Y,V1)
      | ~ product(X,Z,V2)
      | ~ sum(Y,Z,V3)
      | ~ product(X,V3,V4)
      | sum(V1,V2,V4) ),
    file(unknown,unknown) ).

tff(f_185,axiom,
    ~ sum(a,a,additive_identity),
    file(unknown,unknown) ).

tff(c_6,plain,
    ! [X_3,Y_4] : product(X_3,Y_4,multiply(X_3,Y_4)),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_36,plain,
    ! [X_72] : product(X_72,X_72,X_72),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_66,plain,
    ! [V_85,U_86,X_87,Y_88] :
      ( ( V_85 = U_86 )
      | ~ product(X_87,Y_88,V_85)
      | ~ product(X_87,Y_88,U_86) ),
    inference(cnfTransformation,[status(thm)],[f_179]) ).

tff(c_78,plain,
    ! [X_91,U_92] :
      ( ( X_91 = U_92 )
      | ~ product(X_91,X_91,U_92) ),
    inference(resolution,[status(thm)],[c_36,c_66]) ).

tff(c_86,plain,
    ! [Y_4] : ( multiply(Y_4,Y_4) = Y_4 ),
    inference(resolution,[status(thm)],[c_6,c_78]) ).

tff(c_10,plain,
    ! [X_7] : sum(additive_inverse(X_7),X_7,additive_identity),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_2,plain,
    ! [X_1] : sum(additive_identity,X_1,X_1),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_132,plain,
    ! [U_105,V_104,Y_103,X_102,W_101,Z_106] :
      ( sum(X_102,V_104,W_101)
      | ~ sum(U_105,Z_106,W_101)
      | ~ sum(Y_103,Z_106,V_104)
      | ~ sum(X_102,Y_103,U_105) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_1866,plain,
    ! [X_228,V_229,X_230,Y_231] :
      ( sum(X_228,V_229,X_230)
      | ~ sum(Y_231,X_230,V_229)
      | ~ sum(X_228,Y_231,additive_identity) ),
    inference(resolution,[status(thm)],[c_2,c_132]) ).

tff(c_1971,plain,
    ! [X_235,X_236] :
      ( sum(X_235,additive_identity,X_236)
      | ~ sum(X_235,additive_inverse(X_236),additive_identity) ),
    inference(resolution,[status(thm)],[c_10,c_1866]) ).

tff(c_2002,plain,
    ! [X_237] : sum(additive_inverse(additive_inverse(X_237)),additive_identity,X_237),
    inference(resolution,[status(thm)],[c_10,c_1971]) ).

tff(c_4,plain,
    ! [X_2] : sum(X_2,additive_identity,X_2),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_113,plain,
    ! [V_97,U_98,X_99,Y_100] :
      ( ( V_97 = U_98 )
      | ~ sum(X_99,Y_100,V_97)
      | ~ sum(X_99,Y_100,U_98) ),
    inference(cnfTransformation,[status(thm)],[f_171]) ).

tff(c_131,plain,
    ! [X_2,U_98] :
      ( ( X_2 = U_98 )
      | ~ sum(X_2,additive_identity,U_98) ),
    inference(resolution,[status(thm)],[c_4,c_113]) ).

tff(c_2052,plain,
    ! [X_237] : ( additive_inverse(additive_inverse(X_237)) = X_237 ),
    inference(resolution,[status(thm)],[c_2002,c_131]) ).

tff(c_8,plain,
    ! [X_5,Y_6] : sum(X_5,Y_6,add(X_5,Y_6)),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_151,plain,
    ! [X_107,U_108] :
      ( ( X_107 = U_108 )
      | ~ sum(additive_identity,X_107,U_108) ),
    inference(resolution,[status(thm)],[c_2,c_113]) ).

tff(c_172,plain,
    ! [Y_6] : ( add(additive_identity,Y_6) = Y_6 ),
    inference(resolution,[status(thm)],[c_8,c_151]) ).

tff(c_795,plain,
    ! [V2_166,Z_167,Y_170,V4_171,V1_168,V3_169,X_172] :
      ( sum(V1_168,V2_166,V4_171)
      | ~ product(V3_169,X_172,V4_171)
      | ~ sum(Y_170,Z_167,V3_169)
      | ~ product(Z_167,X_172,V2_166)
      | ~ product(Y_170,X_172,V1_168) ),
    inference(cnfTransformation,[status(thm)],[f_148]) ).

tff(c_7366,plain,
    ! [Z_385,Y_387,X_383,V1_384,V2_386] :
      ( sum(V1_384,V2_386,X_383)
      | ~ sum(Y_387,Z_385,X_383)
      | ~ product(Z_385,X_383,V2_386)
      | ~ product(Y_387,X_383,V1_384) ),
    inference(resolution,[status(thm)],[c_36,c_795]) ).

tff(c_35619,plain,
    ! [V1_723,V2_724,X_725] :
      ( sum(V1_723,V2_724,X_725)
      | ~ product(additive_identity,X_725,V2_724)
      | ~ product(X_725,X_725,V1_723) ),
    inference(resolution,[status(thm)],[c_4,c_7366]) ).

tff(c_35631,plain,
    ! [Y_4,V2_724] :
      ( sum(multiply(Y_4,Y_4),V2_724,Y_4)
      | ~ product(additive_identity,Y_4,V2_724) ),
    inference(resolution,[status(thm)],[c_6,c_35619]) ).

tff(c_35640,plain,
    ! [Y_726,V2_727] :
      ( sum(Y_726,V2_727,Y_726)
      | ~ product(additive_identity,Y_726,V2_727) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86,c_35631]) ).

tff(c_12,plain,
    ! [X_8] : sum(X_8,additive_inverse(X_8),additive_identity),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_521,plain,
    ! [Y_141,W_136,U_139,Z_137,X_138,V_140] :
      ( sum(U_139,Z_137,W_136)
      | ~ sum(X_138,V_140,W_136)
      | ~ sum(Y_141,Z_137,V_140)
      | ~ sum(X_138,Y_141,U_139) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_2371,plain,
    ! [U_251,Z_252,X_253,Y_254] :
      ( sum(U_251,Z_252,X_253)
      | ~ sum(Y_254,Z_252,additive_identity)
      | ~ sum(X_253,Y_254,U_251) ),
    inference(resolution,[status(thm)],[c_4,c_521]) ).

tff(c_2397,plain,
    ! [U_251,X_8,X_253] :
      ( sum(U_251,additive_inverse(X_8),X_253)
      | ~ sum(X_253,X_8,U_251) ),
    inference(resolution,[status(thm)],[c_12,c_2371]) ).

tff(c_5688,plain,
    ! [U_342,X_343,X_344] :
      ( sum(U_342,additive_inverse(X_343),X_344)
      | ~ sum(X_344,X_343,U_342) ),
    inference(resolution,[status(thm)],[c_12,c_2371]) ).

tff(c_18,plain,
    ! [Y_22,X_21,Z_23] :
      ( sum(Y_22,X_21,Z_23)
      | ~ sum(X_21,Y_22,Z_23) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_12813,plain,
    ! [X_483,U_484,X_485] :
      ( sum(additive_inverse(X_483),U_484,X_485)
      | ~ sum(X_485,X_483,U_484) ),
    inference(resolution,[status(thm)],[c_5688,c_18]) ).

tff(c_129,plain,
    ! [U_98,X_8] :
      ( ( additive_identity = U_98 )
      | ~ sum(X_8,additive_inverse(X_8),U_98) ),
    inference(resolution,[status(thm)],[c_12,c_113]) ).

tff(c_5825,plain,
    ! [X_344,X_343] :
      ( ( additive_identity = X_344 )
      | ~ sum(X_344,X_343,X_343) ),
    inference(resolution,[status(thm)],[c_5688,c_129]) ).

tff(c_13020,plain,
    ! [X_486,X_487] :
      ( ( additive_inverse(X_486) = additive_identity )
      | ~ sum(X_487,X_486,X_487) ),
    inference(resolution,[status(thm)],[c_12813,c_5825]) ).

tff(c_13052,plain,
    ! [X_8,X_253] :
      ( ( additive_inverse(additive_inverse(X_8)) = additive_identity )
      | ~ sum(X_253,X_8,X_253) ),
    inference(resolution,[status(thm)],[c_2397,c_13020]) ).

tff(c_13113,plain,
    ! [X_8,X_253] :
      ( ( additive_identity = X_8 )
      | ~ sum(X_253,X_8,X_253) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2052,c_13052]) ).

tff(c_36112,plain,
    ! [V2_729,Y_730] :
      ( ( additive_identity = V2_729 )
      | ~ product(additive_identity,Y_730,V2_729) ),
    inference(resolution,[status(thm)],[c_35640,c_13113]) ).

tff(c_36136,plain,
    ! [Y_4] : ( multiply(additive_identity,Y_4) = additive_identity ),
    inference(resolution,[status(thm)],[c_6,c_36112]) ).

tff(c_12105,plain,
    ! [X_463,Z_462,V2_464,Y_465,V1_461,Y_466] :
      ( sum(V1_461,V2_464,multiply(X_463,Y_465))
      | ~ sum(Y_466,Z_462,X_463)
      | ~ product(Z_462,Y_465,V2_464)
      | ~ product(Y_466,Y_465,V1_461) ),
    inference(resolution,[status(thm)],[c_6,c_795]) ).

tff(c_12198,plain,
    ! [V1_461,V2_464,Y_465,X_7] :
      ( sum(V1_461,V2_464,multiply(additive_identity,Y_465))
      | ~ product(X_7,Y_465,V2_464)
      | ~ product(additive_inverse(X_7),Y_465,V1_461) ),
    inference(resolution,[status(thm)],[c_10,c_12105]) ).

tff(c_97837,plain,
    ! [V1_1356,V2_1357,X_1358,Y_1359] :
      ( sum(V1_1356,V2_1357,additive_identity)
      | ~ product(X_1358,Y_1359,V2_1357)
      | ~ product(additive_inverse(X_1358),Y_1359,V1_1356) ),
    inference(demodulation,[status(thm),theory(equality)],[c_36136,c_12198]) ).

tff(c_98586,plain,
    ! [V1_1364,X_1365] :
      ( sum(V1_1364,X_1365,additive_identity)
      | ~ product(additive_inverse(X_1365),X_1365,V1_1364) ),
    inference(resolution,[status(thm)],[c_36,c_97837]) ).

tff(c_98687,plain,
    ! [Y_1366] : sum(multiply(additive_inverse(Y_1366),Y_1366),Y_1366,additive_identity),
    inference(resolution,[status(thm)],[c_6,c_98586]) ).

tff(c_2450,plain,
    ! [U_257,X_258,X_259] :
      ( sum(U_257,X_258,X_259)
      | ~ sum(X_259,additive_inverse(X_258),U_257) ),
    inference(resolution,[status(thm)],[c_10,c_2371]) ).

tff(c_2640,plain,
    ! [X_262,X_263] : sum(add(X_262,additive_inverse(X_263)),X_263,X_262),
    inference(resolution,[status(thm)],[c_8,c_2450]) ).

tff(c_127,plain,
    ! [X_5,Y_6,U_98] :
      ( ( add(X_5,Y_6) = U_98 )
      | ~ sum(X_5,Y_6,U_98) ),
    inference(resolution,[status(thm)],[c_8,c_113]) ).

tff(c_2754,plain,
    ! [X_262,X_263] : ( add(add(X_262,additive_inverse(X_263)),X_263) = X_262 ),
    inference(resolution,[status(thm)],[c_2640,c_127]) ).

tff(c_46,plain,
    ! [Y_82,X_83,Z_84] :
      ( sum(Y_82,X_83,Z_84)
      | ~ sum(X_83,Y_82,Z_84) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_57,plain,
    ! [Y_6,X_5] : sum(Y_6,X_5,add(X_5,Y_6)),
    inference(resolution,[status(thm)],[c_8,c_46]) ).

tff(c_2517,plain,
    ! [X_260,Y_261] : sum(add(additive_inverse(X_260),Y_261),X_260,Y_261),
    inference(resolution,[status(thm)],[c_57,c_2450]) ).

tff(c_32,plain,
    ! [V_67,U_66,X_64,Y_65] :
      ( ( V_67 = U_66 )
      | ~ sum(X_64,Y_65,V_67)
      | ~ sum(X_64,Y_65,U_66) ),
    inference(cnfTransformation,[status(thm)],[f_171]) ).

tff(c_13654,plain,
    ! [Y_502,U_503,X_504] :
      ( ( Y_502 = U_503 )
      | ~ sum(add(additive_inverse(X_504),Y_502),X_504,U_503) ),
    inference(resolution,[status(thm)],[c_2517,c_32]) ).

tff(c_13694,plain,
    ! [Y_502,X_253,X_8] :
      ( ( Y_502 = X_253 )
      | ~ sum(X_253,X_8,add(additive_inverse(additive_inverse(X_8)),Y_502)) ),
    inference(resolution,[status(thm)],[c_2397,c_13654]) ).

tff(c_14051,plain,
    ! [Y_509,X_510,X_511] :
      ( ( Y_509 = X_510 )
      | ~ sum(X_510,X_511,add(X_511,Y_509)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2052,c_13694]) ).

tff(c_14117,plain,
    ! [X_510,X_263,X_262] :
      ( ( X_510 = X_263 )
      | ~ sum(X_510,add(X_262,additive_inverse(X_263)),X_262) ),
    inference(superposition,[status(thm),theory(equality)],[c_2754,c_14051]) ).

tff(c_98691,plain,
    ! [X_263] : ( multiply(additive_inverse(add(additive_identity,additive_inverse(X_263))),add(additive_identity,additive_inverse(X_263))) = X_263 ),
    inference(resolution,[status(thm)],[c_98687,c_14117]) ).

tff(c_99020,plain,
    ! [X_1367] : ( multiply(X_1367,additive_inverse(X_1367)) = X_1367 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2052,c_172,c_172,c_98691]) ).

tff(c_99077,plain,
    ! [X_1367] : product(X_1367,additive_inverse(X_1367),X_1367),
    inference(superposition,[status(thm),theory(equality)],[c_99020,c_6]) ).

tff(c_354,plain,
    ! [X_126,U_123,Y_128,Z_125,V_124,W_127] :
      ( product(U_123,Z_125,W_127)
      | ~ product(X_126,V_124,W_127)
      | ~ product(Y_128,Z_125,V_124)
      | ~ product(X_126,Y_128,U_123) ),
    inference(cnfTransformation,[status(thm)],[f_106]) ).

tff(c_5027,plain,
    ! [Z_308,Y_311,U_310,X_309,Y_312] :
      ( product(U_310,Z_308,multiply(X_309,Y_312))
      | ~ product(Y_311,Z_308,Y_312)
      | ~ product(X_309,Y_311,U_310) ),
    inference(resolution,[status(thm)],[c_6,c_354]) ).

tff(c_5036,plain,
    ! [U_310,X_72,X_309] :
      ( product(U_310,X_72,multiply(X_309,X_72))
      | ~ product(X_309,X_72,U_310) ),
    inference(resolution,[status(thm)],[c_36,c_5027]) ).

tff(c_685,plain,
    ! [V2_160,V3_155,Y_157,V1_159,X_161,V4_156,Z_158] :
      ( sum(V1_159,V2_160,V4_156)
      | ~ product(X_161,V3_155,V4_156)
      | ~ sum(Y_157,Z_158,V3_155)
      | ~ product(X_161,Z_158,V2_160)
      | ~ product(X_161,Y_157,V1_159) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_9219,plain,
    ! [V1_413,V2_410,Y_409,X_411,Z_412] :
      ( sum(V1_413,V2_410,X_411)
      | ~ sum(Y_409,Z_412,X_411)
      | ~ product(X_411,Z_412,V2_410)
      | ~ product(X_411,Y_409,V1_413) ),
    inference(resolution,[status(thm)],[c_36,c_685]) ).

tff(c_38454,plain,
    ! [V1_763,V2_764,X_765] :
      ( sum(V1_763,V2_764,X_765)
      | ~ product(X_765,additive_identity,V2_764)
      | ~ product(X_765,X_765,V1_763) ),
    inference(resolution,[status(thm)],[c_4,c_9219]) ).

tff(c_38472,plain,
    ! [Y_4,V2_764] :
      ( sum(multiply(Y_4,Y_4),V2_764,Y_4)
      | ~ product(Y_4,additive_identity,V2_764) ),
    inference(resolution,[status(thm)],[c_6,c_38454]) ).

tff(c_38483,plain,
    ! [Y_766,V2_767] :
      ( sum(Y_766,V2_767,Y_766)
      | ~ product(Y_766,additive_identity,V2_767) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86,c_38472]) ).

tff(c_38948,plain,
    ! [Y_768] :
      ( ( additive_identity = Y_768 )
      | ~ product(Y_768,additive_identity,Y_768) ),
    inference(resolution,[status(thm)],[c_38483,c_5825]) ).

tff(c_38956,plain,
    ! [X_309] :
      ( ( multiply(X_309,additive_identity) = additive_identity )
      | ~ product(X_309,additive_identity,multiply(X_309,additive_identity)) ),
    inference(resolution,[status(thm)],[c_5036,c_38948]) ).

tff(c_38969,plain,
    ! [X_309] : ( multiply(X_309,additive_identity) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_38956]) ).

tff(c_12707,plain,
    ! [Z_479,Y_477,V2_478,Y_482,X_480,V1_481] :
      ( sum(V1_481,V2_478,multiply(X_480,Y_482))
      | ~ sum(Y_477,Z_479,Y_482)
      | ~ product(X_480,Z_479,V2_478)
      | ~ product(X_480,Y_477,V1_481) ),
    inference(resolution,[status(thm)],[c_6,c_685]) ).

tff(c_12807,plain,
    ! [V1_481,V2_478,X_480,X_8] :
      ( sum(V1_481,V2_478,multiply(X_480,additive_identity))
      | ~ product(X_480,additive_inverse(X_8),V2_478)
      | ~ product(X_480,X_8,V1_481) ),
    inference(resolution,[status(thm)],[c_12,c_12707]) ).

tff(c_100365,plain,
    ! [V1_1384,V2_1385,X_1386,X_1387] :
      ( sum(V1_1384,V2_1385,additive_identity)
      | ~ product(X_1386,additive_inverse(X_1387),V2_1385)
      | ~ product(X_1386,X_1387,V1_1384) ),
    inference(demodulation,[status(thm),theory(equality)],[c_38969,c_12807]) ).

tff(c_101144,plain,
    ! [V1_1396,X_1397] :
      ( sum(V1_1396,X_1397,additive_identity)
      | ~ product(X_1397,X_1397,V1_1396) ),
    inference(resolution,[status(thm)],[c_99077,c_100365]) ).

tff(c_101194,plain,
    ! [Y_4] : sum(multiply(Y_4,Y_4),Y_4,additive_identity),
    inference(resolution,[status(thm)],[c_6,c_101144]) ).

tff(c_101216,plain,
    ! [Y_4] : sum(Y_4,Y_4,additive_identity),
    inference(demodulation,[status(thm),theory(equality)],[c_86,c_101194]) ).

tff(c_38,plain,
    ~ sum(a,a,additive_identity),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_101220,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_101216,c_38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : RNG007-1 : TPTP v8.1.2. Released v1.0.0.
% 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
% 0.14/0.36  % Computer : n025.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 18:09:04 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 22.88/12.12  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.88/12.14  
% 22.88/12.14  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.03/12.18  
% 23.03/12.18  Inference rules
% 23.03/12.18  ----------------------
% 23.03/12.18  #Ref     : 0
% 23.03/12.18  #Sup     : 24910
% 23.03/12.18  #Fact    : 0
% 23.03/12.18  #Define  : 0
% 23.03/12.18  #Split   : 0
% 23.03/12.18  #Chain   : 0
% 23.03/12.18  #Close   : 0
% 23.03/12.18  
% 23.03/12.18  Ordering : KBO
% 23.03/12.18  
% 23.03/12.18  Simplification rules
% 23.03/12.18  ----------------------
% 23.03/12.18  #Subsume      : 6328
% 23.03/12.18  #Demod        : 12493
% 23.03/12.18  #Tautology    : 4732
% 23.03/12.18  #SimpNegUnit  : 0
% 23.03/12.18  #BackRed      : 14
% 23.03/12.18  
% 23.03/12.18  #Partial instantiations: 0
% 23.03/12.18  #Strategies tried      : 1
% 23.03/12.18  
% 23.03/12.18  Timing (in seconds)
% 23.03/12.18  ----------------------
% 23.03/12.18  Preprocessing        : 0.49
% 23.03/12.18  Parsing              : 0.27
% 23.03/12.18  CNF conversion       : 0.03
% 23.03/12.18  Main loop            : 10.55
% 23.03/12.18  Inferencing          : 1.49
% 23.03/12.18  Reduction            : 3.21
% 23.03/12.18  Demodulation         : 2.64
% 23.03/12.18  BG Simplification    : 0.13
% 23.03/12.18  Subsumption          : 4.77
% 23.03/12.18  Abstraction          : 0.18
% 23.03/12.18  MUC search           : 0.00
% 23.03/12.18  Cooper               : 0.00
% 23.03/12.19  Total                : 11.12
% 23.03/12.19  Index Insertion      : 0.00
% 23.03/12.19  Index Deletion       : 0.00
% 23.03/12.19  Index Matching       : 0.00
% 23.03/12.19  BG Taut test         : 0.00
%------------------------------------------------------------------------------