TSTP Solution File: GRP777+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP777+1 : TPTP v8.1.2. Released v4.1.0.
% 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 10:42:06 EDT 2023
% Result : Theorem 32.29s 18.93s
% Output : CNFRefutation 32.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 18
% Syntax : Number of formulae : 157 ( 149 unt; 8 typ; 0 def)
% Number of atoms : 149 ( 148 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 212 (; 212 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ bigC > quotient > product > difference > #nlpp > c > b > a > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(b,type,
b: $i ).
tff(product,type,
product: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(bigC,type,
bigC: ( $i * $i * $i ) > $i ).
tff(quotient,type,
quotient: ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_41,axiom,
! [C,B,A] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
tff(f_34,axiom,
! [D,C,B,A] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
tff(f_36,axiom,
! [A] : ( product(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
tff(f_30,axiom,
! [B,A] : ( quotient(product(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
tff(f_32,axiom,
! [B,A] : ( product(quotient(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
tff(f_28,axiom,
! [B,A] : ( product(A,difference(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
tff(f_26,axiom,
! [B,A] : ( difference(A,product(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
tff(f_42,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
tff(f_39,axiom,
! [B,A] : ( product(product(product(A,B),B),product(B,product(B,A))) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
tff(f_45,negated_conjecture,
~ ! [X0] : ( bigC(a,b,X0) = bigC(c,c,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(c_16,plain,
! [A_18,B_17,C_16] : ( product(product(A_18,B_17),product(C_16,A_18)) = bigC(A_18,B_17,C_16) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_365,plain,
! [A_40,C_41,B_42,D_43] : ( product(product(A_40,C_41),product(B_42,D_43)) = product(product(A_40,B_42),product(C_41,D_43)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_874,plain,
! [A_52,C_53,B_54] : ( product(product(A_52,C_53),product(B_54,A_52)) = bigC(A_52,B_54,C_53) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_365]) ).
tff(c_937,plain,
! [A_52,C_53,B_54] : ( bigC(A_52,C_53,B_54) = bigC(A_52,B_54,C_53) ),
inference(superposition,[status(thm),theory(equality)],[c_874,c_16]) ).
tff(c_12,plain,
! [A_13] : ( product(A_13,A_13) = A_13 ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_204,plain,
! [A_34,B_35,C_36] : ( product(product(A_34,B_35),product(C_36,A_34)) = bigC(A_34,B_35,C_36) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_256,plain,
! [A_13,B_35] : ( product(product(A_13,B_35),A_13) = bigC(A_13,B_35,A_13) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_204]) ).
tff(c_6,plain,
! [A_6,B_5] : ( quotient(product(A_6,B_5),B_5) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_8,plain,
! [A_8,B_7] : ( product(quotient(A_8,B_7),B_7) = A_8 ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_696,plain,
! [A_46,C_47] : ( product(A_46,product(C_47,A_46)) = bigC(A_46,A_46,C_47) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_204]) ).
tff(c_782,plain,
! [B_7,A_8] : ( bigC(B_7,B_7,quotient(A_8,B_7)) = product(B_7,A_8) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_696]) ).
tff(c_4,plain,
! [A_4,B_3] : ( product(A_4,difference(A_4,B_3)) = B_3 ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_3586,plain,
! [A_116,C_117,D_118] : ( product(product(A_116,C_117),product(A_116,D_118)) = product(A_116,product(C_117,D_118)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_365]) ).
tff(c_2,plain,
! [A_2,B_1] : ( difference(A_2,product(A_2,B_1)) = B_1 ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_30556,plain,
! [A_321,C_322,D_323] : ( difference(product(A_321,C_322),product(A_321,product(C_322,D_323))) = product(A_321,D_323) ),
inference(superposition,[status(thm),theory(equality)],[c_3586,c_2]) ).
tff(c_31093,plain,
! [A_321,A_4,B_3] : ( difference(product(A_321,A_4),product(A_321,B_3)) = product(A_321,difference(A_4,B_3)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_30556]) ).
tff(c_1135,plain,
! [A_60,C_61] : ( product(product(A_60,C_61),A_60) = bigC(A_60,A_60,C_61) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_874]) ).
tff(c_1676,plain,
! [A_74,C_75] : ( quotient(bigC(A_74,A_74,C_75),A_74) = product(A_74,C_75) ),
inference(superposition,[status(thm),theory(equality)],[c_1135,c_6]) ).
tff(c_1713,plain,
! [B_7,A_8] : ( quotient(product(B_7,A_8),B_7) = product(B_7,quotient(A_8,B_7)) ),
inference(superposition,[status(thm),theory(equality)],[c_782,c_1676]) ).
tff(c_18,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_4182,plain,
! [A_124,A_125,B_126] : ( product(product(A_124,A_125),product(B_126,A_125)) = product(product(A_124,B_126),A_125) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_365]) ).
tff(c_6022,plain,
! [A_147,A_148,B_149] : ( product(product(A_147,quotient(A_148,B_149)),B_149) = product(product(A_147,B_149),A_148) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_4182]) ).
tff(c_35619,plain,
! [A_340,A_341,B_342] : ( difference(product(A_340,quotient(A_341,B_342)),product(product(A_340,B_342),A_341)) = B_342 ),
inference(superposition,[status(thm),theory(equality)],[c_6022,c_2]) ).
tff(c_36162,plain,
difference(product(a,quotient(product(c,b),c)),product(a,b)) = c,
inference(superposition,[status(thm),theory(equality)],[c_18,c_35619]) ).
tff(c_36221,plain,
product(a,difference(product(c,quotient(b,c)),b)) = c,
inference(demodulation,[status(thm),theory(equality)],[c_31093,c_1713,c_36162]) ).
tff(c_37100,plain,
difference(product(c,quotient(b,c)),b) = difference(a,c),
inference(superposition,[status(thm),theory(equality)],[c_36221,c_2]) ).
tff(c_37218,plain,
product(product(c,quotient(b,c)),difference(a,c)) = b,
inference(superposition,[status(thm),theory(equality)],[c_37100,c_4]) ).
tff(c_29326,plain,
! [A_316,C_317,D_318] : ( quotient(product(A_316,product(C_317,D_318)),product(A_316,D_318)) = product(A_316,C_317) ),
inference(superposition,[status(thm),theory(equality)],[c_3586,c_6]) ).
tff(c_39619,plain,
! [A_357,B_358,A_359] : ( quotient(product(A_357,B_358),product(A_357,difference(A_359,B_358))) = product(A_357,A_359) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_29326]) ).
tff(c_39757,plain,
quotient(product(product(c,quotient(b,c)),c),b) = product(product(c,quotient(b,c)),a),
inference(superposition,[status(thm),theory(equality)],[c_37218,c_39619]) ).
tff(c_40178,plain,
product(product(c,quotient(b,c)),a) = c,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_782,c_937,c_256,c_39757]) ).
tff(c_40460,plain,
product(c,quotient(b,c)) = quotient(c,a),
inference(superposition,[status(thm),theory(equality)],[c_40178,c_6]) ).
tff(c_51,plain,
! [A_23,B_24] : ( product(A_23,difference(A_23,B_24)) = B_24 ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_57,plain,
! [B_24,A_23] : ( quotient(B_24,difference(A_23,B_24)) = A_23 ),
inference(superposition,[status(thm),theory(equality)],[c_51,c_6]) ).
tff(c_37215,plain,
quotient(b,difference(a,c)) = product(c,quotient(b,c)),
inference(superposition,[status(thm),theory(equality)],[c_37100,c_57]) ).
tff(c_40623,plain,
quotient(b,difference(a,c)) = quotient(c,a),
inference(demodulation,[status(thm),theory(equality)],[c_40460,c_37215]) ).
tff(c_265,plain,
! [A_37,B_38] : ( product(product(product(A_37,B_38),B_38),product(B_38,product(B_38,A_37))) = B_38 ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_5638,plain,
! [A_142,B_143] : ( difference(product(product(A_142,B_143),B_143),B_143) = product(B_143,product(B_143,A_142)) ),
inference(superposition,[status(thm),theory(equality)],[c_265,c_2]) ).
tff(c_5756,plain,
! [B_7,A_8] : ( product(B_7,product(B_7,quotient(A_8,B_7))) = difference(product(A_8,B_7),B_7) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_5638]) ).
tff(c_7358,plain,
! [B_161,A_162] : ( product(B_161,product(B_161,quotient(A_162,B_161))) = difference(product(A_162,B_161),B_161) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_5638]) ).
tff(c_1263,plain,
! [A_62,B_63] : ( product(A_62,product(B_63,A_62)) = bigC(A_62,B_63,A_62) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_874]) ).
tff(c_1379,plain,
! [B_7,A_8] : ( bigC(B_7,quotient(A_8,B_7),B_7) = product(B_7,A_8) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1263]) ).
tff(c_1946,plain,
! [A_82,B_83,C_84] : ( difference(product(A_82,B_83),bigC(A_82,B_83,C_84)) = product(C_84,A_82) ),
inference(superposition,[status(thm),theory(equality)],[c_204,c_2]) ).
tff(c_1975,plain,
! [B_7,A_8] : ( difference(product(B_7,quotient(A_8,B_7)),product(B_7,A_8)) = product(B_7,B_7) ),
inference(superposition,[status(thm),theory(equality)],[c_1379,c_1946]) ).
tff(c_2045,plain,
! [B_7,A_8] : ( difference(product(B_7,quotient(A_8,B_7)),product(B_7,A_8)) = B_7 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1975]) ).
tff(c_7437,plain,
! [B_161,A_162] : ( difference(product(B_161,quotient(product(B_161,quotient(A_162,B_161)),B_161)),difference(product(A_162,B_161),B_161)) = B_161 ),
inference(superposition,[status(thm),theory(equality)],[c_7358,c_2045]) ).
tff(c_7931,plain,
! [A_167,B_168] : ( difference(difference(A_167,B_168),difference(product(A_167,B_168),B_168)) = B_168 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_5756,c_1713,c_7437]) ).
tff(c_8357,plain,
! [A_173,B_174] : ( difference(difference(quotient(A_173,B_174),B_174),difference(A_173,B_174)) = B_174 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_7931]) ).
tff(c_8405,plain,
! [A_173,B_174] : ( product(difference(quotient(A_173,B_174),B_174),B_174) = difference(A_173,B_174) ),
inference(superposition,[status(thm),theory(equality)],[c_8357,c_4]) ).
tff(c_12565,plain,
! [A_213,B_214,D_215] : ( product(A_213,product(difference(A_213,B_214),D_215)) = product(B_214,product(A_213,D_215)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3586]) ).
tff(c_12796,plain,
! [A_173,B_174] : ( product(quotient(A_173,B_174),difference(A_173,B_174)) = product(B_174,product(quotient(A_173,B_174),B_174)) ),
inference(superposition,[status(thm),theory(equality)],[c_8405,c_12565]) ).
tff(c_12940,plain,
! [A_216,B_217] : ( product(quotient(A_216,B_217),difference(A_216,B_217)) = product(B_217,A_216) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_12796]) ).
tff(c_13096,plain,
! [B_217,A_216] : ( quotient(product(B_217,A_216),difference(A_216,B_217)) = quotient(A_216,B_217) ),
inference(superposition,[status(thm),theory(equality)],[c_12940,c_6]) ).
tff(c_1022,plain,
! [A_4,B_54,B_3] : ( bigC(A_4,B_54,difference(A_4,B_3)) = product(B_3,product(B_54,A_4)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_874]) ).
tff(c_253,plain,
! [A_13,C_36] : ( product(A_13,product(C_36,A_13)) = bigC(A_13,A_13,C_36) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_204]) ).
tff(c_3820,plain,
! [A_4,C_117,B_3] : ( product(A_4,product(C_117,difference(A_4,B_3))) = product(product(A_4,C_117),B_3) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3586]) ).
tff(c_12946,plain,
! [A_216,B_217] : ( product(product(A_216,quotient(A_216,B_217)),B_217) = product(A_216,product(B_217,A_216)) ),
inference(superposition,[status(thm),theory(equality)],[c_12940,c_3820]) ).
tff(c_14943,plain,
! [A_230,B_231] : ( product(product(A_230,quotient(A_230,B_231)),B_231) = bigC(A_230,A_230,B_231) ),
inference(demodulation,[status(thm),theory(equality)],[c_253,c_12946]) ).
tff(c_20017,plain,
! [A_264,B_265] : ( quotient(bigC(A_264,A_264,B_265),B_265) = product(A_264,quotient(A_264,B_265)) ),
inference(superposition,[status(thm),theory(equality)],[c_14943,c_6]) ).
tff(c_20133,plain,
! [B_3,B_54] : ( quotient(product(B_3,product(B_54,B_54)),difference(B_54,B_3)) = product(B_54,quotient(B_54,difference(B_54,B_3))) ),
inference(superposition,[status(thm),theory(equality)],[c_1022,c_20017]) ).
tff(c_20186,plain,
! [B_266,B_267] : ( product(B_266,quotient(B_266,difference(B_266,B_267))) = quotient(B_266,B_267) ),
inference(demodulation,[status(thm),theory(equality)],[c_13096,c_12,c_20133]) ).
tff(c_20505,plain,
! [A_2,B_1] : ( quotient(A_2,product(A_2,B_1)) = product(A_2,quotient(A_2,B_1)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_20186]) ).
tff(c_83,plain,
! [A_27,B_28] : ( product(quotient(A_27,B_28),B_28) = A_27 ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_89,plain,
! [A_27,B_28] : ( difference(quotient(A_27,B_28),A_27) = B_28 ),
inference(superposition,[status(thm),theory(equality)],[c_83,c_2]) ).
tff(c_8242,plain,
! [B_171,A_172] : ( difference(B_171,difference(product(quotient(A_172,B_171),A_172),A_172)) = A_172 ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_7931]) ).
tff(c_8287,plain,
! [A_172,B_171] : ( difference(product(quotient(A_172,B_171),A_172),A_172) = product(B_171,A_172) ),
inference(superposition,[status(thm),theory(equality)],[c_8242,c_4]) ).
tff(c_7434,plain,
! [B_161,A_162] : ( product(B_161,quotient(product(B_161,quotient(A_162,B_161)),B_161)) = quotient(difference(product(A_162,B_161),B_161),B_161) ),
inference(superposition,[status(thm),theory(equality)],[c_7358,c_1713]) ).
tff(c_7584,plain,
! [A_163,B_164] : ( quotient(difference(product(A_163,B_164),B_164),B_164) = difference(A_163,B_164) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_5756,c_1713,c_7434]) ).
tff(c_7632,plain,
! [A_163,B_164] : ( product(difference(A_163,B_164),B_164) = difference(product(A_163,B_164),B_164) ),
inference(superposition,[status(thm),theory(equality)],[c_7584,c_8]) ).
tff(c_12813,plain,
! [A_163,B_164] : ( product(A_163,difference(product(A_163,B_164),B_164)) = product(B_164,product(A_163,B_164)) ),
inference(superposition,[status(thm),theory(equality)],[c_7632,c_12565]) ).
tff(c_13758,plain,
! [A_222,B_223] : ( product(A_222,difference(product(A_222,B_223),B_223)) = bigC(B_223,B_223,A_222) ),
inference(demodulation,[status(thm),theory(equality)],[c_253,c_12813]) ).
tff(c_13938,plain,
! [A_222,B_223] : ( difference(product(A_222,B_223),B_223) = difference(A_222,bigC(B_223,B_223,A_222)) ),
inference(superposition,[status(thm),theory(equality)],[c_13758,c_2]) ).
tff(c_4439,plain,
! [A_124,A_8,B_7] : ( product(product(A_124,quotient(A_8,B_7)),B_7) = product(product(A_124,B_7),A_8) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_4182]) ).
tff(c_40796,plain,
product(quotient(c,a),c) = product(product(c,c),b),
inference(superposition,[status(thm),theory(equality)],[c_40460,c_4439]) ).
tff(c_40926,plain,
product(quotient(c,a),c) = product(c,b),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_40796]) ).
tff(c_14077,plain,
! [A_224,B_225] : ( difference(product(A_224,B_225),B_225) = difference(A_224,bigC(B_225,B_225,A_224)) ),
inference(superposition,[status(thm),theory(equality)],[c_13758,c_2]) ).
tff(c_14218,plain,
! [A_224,B_225] : ( product(product(A_224,B_225),difference(A_224,bigC(B_225,B_225,A_224))) = B_225 ),
inference(superposition,[status(thm),theory(equality)],[c_14077,c_4]) ).
tff(c_41952,plain,
product(product(c,b),difference(quotient(c,a),bigC(c,c,quotient(c,a)))) = c,
inference(superposition,[status(thm),theory(equality)],[c_40926,c_14218]) ).
tff(c_42135,plain,
bigC(c,a,b) = c,
inference(demodulation,[status(thm),theory(equality)],[c_937,c_16,c_8287,c_13938,c_41952]) ).
tff(c_536,plain,
! [C_41,D_43] : ( product(product(product(a,c),C_41),product(product(c,b),D_43)) = product(product(a,b),product(C_41,D_43)) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_365]) ).
tff(c_579,plain,
! [A_40,A_13,B_42] : ( product(product(A_40,A_13),product(B_42,A_13)) = product(product(A_40,B_42),A_13) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_365]) ).
tff(c_320,plain,
product(product(product(a,b),product(c,b)),product(product(c,b),product(product(c,b),product(a,c)))) = product(c,b),
inference(superposition,[status(thm),theory(equality)],[c_18,c_265]) ).
tff(c_350,plain,
product(product(product(a,b),product(c,b)),product(product(c,b),bigC(c,b,a))) = product(c,b),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_320]) ).
tff(c_48489,plain,
product(product(a,b),product(b,c)) = product(c,b),
inference(demodulation,[status(thm),theory(equality)],[c_42135,c_536,c_579,c_937,c_350]) ).
tff(c_6176,plain,
! [A_147,B_149,A_148] : ( quotient(product(product(A_147,B_149),A_148),B_149) = product(A_147,quotient(A_148,B_149)) ),
inference(superposition,[status(thm),theory(equality)],[c_6022,c_6]) ).
tff(c_48532,plain,
product(a,quotient(product(b,c),b)) = quotient(product(c,b),b),
inference(superposition,[status(thm),theory(equality)],[c_48489,c_6176]) ).
tff(c_48806,plain,
product(a,product(b,quotient(c,b))) = c,
inference(demodulation,[status(thm),theory(equality)],[c_1713,c_6,c_48532]) ).
tff(c_49120,plain,
product(b,quotient(c,b)) = difference(a,c),
inference(superposition,[status(thm),theory(equality)],[c_48806,c_2]) ).
tff(c_290,plain,
! [B_38,A_37] : ( quotient(B_38,product(B_38,product(B_38,A_37))) = product(product(A_37,B_38),B_38) ),
inference(superposition,[status(thm),theory(equality)],[c_265,c_6]) ).
tff(c_49501,plain,
quotient(b,product(b,difference(a,c))) = product(product(quotient(c,b),b),b),
inference(superposition,[status(thm),theory(equality)],[c_49120,c_290]) ).
tff(c_49635,plain,
product(b,quotient(c,a)) = product(c,b),
inference(demodulation,[status(thm),theory(equality)],[c_40623,c_20505,c_8,c_49501]) ).
tff(c_56940,plain,
difference(b,product(c,b)) = quotient(c,a),
inference(superposition,[status(thm),theory(equality)],[c_49635,c_2]) ).
tff(c_1248,plain,
! [A_4,B_3] : ( bigC(A_4,A_4,difference(A_4,B_3)) = product(B_3,A_4) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1135]) ).
tff(c_1982,plain,
! [A_4,B_3] : ( difference(product(A_4,A_4),product(B_3,A_4)) = product(difference(A_4,B_3),A_4) ),
inference(superposition,[status(thm),theory(equality)],[c_1248,c_1946]) ).
tff(c_2047,plain,
! [A_4,B_3] : ( product(difference(A_4,B_3),A_4) = difference(A_4,product(B_3,A_4)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1982]) ).
tff(c_10,plain,
! [A_12,C_10,B_11,D_9] : ( product(product(A_12,C_10),product(B_11,D_9)) = product(product(A_12,B_11),product(C_10,D_9)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_323,plain,
product(product(product(product(c,b),product(a,c)),product(a,c)),product(product(a,c),product(a,b))) = product(a,c),
inference(superposition,[status(thm),theory(equality)],[c_18,c_265]) ).
tff(c_351,plain,
product(product(bigC(c,b,a),product(a,c)),product(product(a,c),product(a,b))) = product(a,c),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_323]) ).
tff(c_54250,plain,
product(product(c,a),product(a,b)) = product(a,c),
inference(demodulation,[status(thm),theory(equality)],[c_42135,c_937,c_18,c_10,c_12,c_10,c_351]) ).
tff(c_12765,plain,
! [A_213,B_214,D_215] : ( difference(A_213,product(B_214,product(A_213,D_215))) = product(difference(A_213,B_214),D_215) ),
inference(superposition,[status(thm),theory(equality)],[c_12565,c_2]) ).
tff(c_54308,plain,
product(difference(a,product(c,a)),b) = difference(a,product(a,c)),
inference(superposition,[status(thm),theory(equality)],[c_54250,c_12765]) ).
tff(c_54592,plain,
product(difference(a,product(c,a)),b) = c,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_54308]) ).
tff(c_54921,plain,
difference(a,product(c,a)) = quotient(c,b),
inference(superposition,[status(thm),theory(equality)],[c_54592,c_6]) ).
tff(c_40624,plain,
product(quotient(c,a),difference(a,c)) = b,
inference(demodulation,[status(thm),theory(equality)],[c_40460,c_37218]) ).
tff(c_31159,plain,
! [A_324,A_325,B_326] : ( difference(product(A_324,A_325),product(A_324,B_326)) = product(A_324,difference(A_325,B_326)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_30556]) ).
tff(c_173,plain,
difference(product(a,c),product(a,b)) = product(c,b),
inference(superposition,[status(thm),theory(equality)],[c_18,c_2]) ).
tff(c_31303,plain,
product(a,difference(c,b)) = product(c,b),
inference(superposition,[status(thm),theory(equality)],[c_31159,c_173]) ).
tff(c_31907,plain,
difference(a,product(c,b)) = difference(c,b),
inference(superposition,[status(thm),theory(equality)],[c_31303,c_2]) ).
tff(c_40457,plain,
difference(product(c,quotient(b,c)),c) = a,
inference(superposition,[status(thm),theory(equality)],[c_40178,c_2]) ).
tff(c_40560,plain,
difference(product(product(c,quotient(b,c)),c),c) = product(a,c),
inference(superposition,[status(thm),theory(equality)],[c_40457,c_7632]) ).
tff(c_40611,plain,
difference(product(c,b),c) = product(a,c),
inference(demodulation,[status(thm),theory(equality)],[c_782,c_937,c_256,c_40560]) ).
tff(c_41575,plain,
product(product(c,b),product(a,c)) = c,
inference(superposition,[status(thm),theory(equality)],[c_40611,c_4]) ).
tff(c_43821,plain,
product(difference(a,product(c,b)),c) = difference(a,c),
inference(superposition,[status(thm),theory(equality)],[c_41575,c_12765]) ).
tff(c_44136,plain,
difference(c,product(b,c)) = difference(a,c),
inference(demodulation,[status(thm),theory(equality)],[c_2047,c_31907,c_43821]) ).
tff(c_45941,plain,
quotient(product(b,c),difference(a,c)) = c,
inference(superposition,[status(thm),theory(equality)],[c_44136,c_57]) ).
tff(c_49579,plain,
bigC(b,quotient(c,b),b) = product(difference(a,c),b),
inference(superposition,[status(thm),theory(equality)],[c_49120,c_256]) ).
tff(c_49645,plain,
product(difference(a,c),b) = product(b,c),
inference(demodulation,[status(thm),theory(equality)],[c_1379,c_49579]) ).
tff(c_56177,plain,
product(difference(a,c),quotient(b,difference(a,c))) = quotient(product(b,c),difference(a,c)),
inference(superposition,[status(thm),theory(equality)],[c_49645,c_1713]) ).
tff(c_56276,plain,
product(difference(a,c),quotient(c,a)) = c,
inference(demodulation,[status(thm),theory(equality)],[c_45941,c_40623,c_56177]) ).
tff(c_241,plain,
! [A_8,C_36,B_7] : ( product(A_8,product(C_36,quotient(A_8,B_7))) = bigC(quotient(A_8,B_7),B_7,C_36) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_204]) ).
tff(c_59029,plain,
bigC(quotient(c,a),a,difference(a,c)) = product(c,c),
inference(superposition,[status(thm),theory(equality)],[c_56276,c_241]) ).
tff(c_59191,plain,
bigC(quotient(c,a),a,difference(a,c)) = c,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_59029]) ).
tff(c_940,plain,
! [A_52,C_53,B_54] : ( difference(product(A_52,C_53),bigC(A_52,B_54,C_53)) = product(B_54,A_52) ),
inference(superposition,[status(thm),theory(equality)],[c_874,c_2]) ).
tff(c_79148,plain,
difference(product(quotient(c,a),difference(a,c)),c) = product(a,quotient(c,a)),
inference(superposition,[status(thm),theory(equality)],[c_59191,c_940]) ).
tff(c_79160,plain,
product(a,quotient(c,a)) = difference(b,c),
inference(demodulation,[status(thm),theory(equality)],[c_40624,c_79148]) ).
tff(c_335,plain,
! [A_4,B_3] : ( product(product(product(difference(A_4,B_3),A_4),A_4),product(A_4,B_3)) = A_4 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_265]) ).
tff(c_5181,plain,
! [A_4,B_3] : ( product(difference(A_4,product(product(B_3,A_4),A_4)),product(A_4,B_3)) = A_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_2047,c_2047,c_335]) ).
tff(c_79614,plain,
product(difference(a,product(product(quotient(c,a),a),a)),difference(b,c)) = a,
inference(superposition,[status(thm),theory(equality)],[c_79160,c_5181]) ).
tff(c_79762,plain,
product(quotient(c,b),difference(b,c)) = a,
inference(demodulation,[status(thm),theory(equality)],[c_54921,c_8,c_79614]) ).
tff(c_4436,plain,
! [A_8,B_7,B_126] : ( product(product(quotient(A_8,B_7),B_126),B_7) = product(A_8,product(B_126,B_7)) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_4182]) ).
tff(c_80952,plain,
product(c,product(difference(b,c),b)) = product(a,b),
inference(superposition,[status(thm),theory(equality)],[c_79762,c_4436]) ).
tff(c_81092,plain,
product(c,quotient(c,a)) = product(a,b),
inference(demodulation,[status(thm),theory(equality)],[c_56940,c_2047,c_80952]) ).
tff(c_545,plain,
! [A_40,A_8,B_7,C_41] : ( product(product(A_40,quotient(A_8,B_7)),product(C_41,B_7)) = product(product(A_40,C_41),A_8) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_365]) ).
tff(c_81631,plain,
! [C_41] : ( product(product(a,b),product(C_41,a)) = product(product(c,C_41),c) ),
inference(superposition,[status(thm),theory(equality)],[c_81092,c_545]) ).
tff(c_81820,plain,
! [C_41] : ( bigC(c,C_41,c) = bigC(a,b,C_41) ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_16,c_81631]) ).
tff(c_20,plain,
bigC(c,c,'#skF_1') != bigC(a,b,'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_1048,plain,
bigC(c,'#skF_1',c) != bigC(a,'#skF_1',b),
inference(demodulation,[status(thm),theory(equality)],[c_937,c_937,c_20]) ).
tff(c_82639,plain,
bigC(a,b,'#skF_1') != bigC(a,'#skF_1',b),
inference(demodulation,[status(thm),theory(equality)],[c_81820,c_1048]) ).
tff(c_82642,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_937,c_82639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP777+1 : TPTP v8.1.2. Released v4.1.0.
% 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
% 0.14/0.36 % Computer : n016.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 22:26:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 32.29/18.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.29/18.96
% 32.29/18.96 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.45/19.01
% 32.45/19.01 Inference rules
% 32.45/19.01 ----------------------
% 32.45/19.01 #Ref : 0
% 32.45/19.01 #Sup : 23654
% 32.45/19.01 #Fact : 0
% 32.45/19.01 #Define : 0
% 32.45/19.01 #Split : 0
% 32.45/19.01 #Chain : 0
% 32.45/19.01 #Close : 0
% 32.45/19.01
% 32.45/19.01 Ordering : KBO
% 32.45/19.01
% 32.45/19.01 Simplification rules
% 32.45/19.01 ----------------------
% 32.45/19.01 #Subsume : 136
% 32.45/19.01 #Demod : 17955
% 32.45/19.01 #Tautology : 3049
% 32.45/19.01 #SimpNegUnit : 0
% 32.45/19.01 #BackRed : 33
% 32.45/19.01
% 32.45/19.01 #Partial instantiations: 0
% 32.45/19.01 #Strategies tried : 1
% 32.45/19.01
% 32.45/19.01 Timing (in seconds)
% 32.45/19.01 ----------------------
% 32.45/19.01 Preprocessing : 0.45
% 32.45/19.01 Parsing : 0.24
% 32.45/19.01 CNF conversion : 0.02
% 32.45/19.01 Main loop : 17.48
% 32.45/19.01 Inferencing : 2.32
% 32.45/19.01 Reduction : 11.08
% 32.45/19.01 Demodulation : 10.39
% 32.45/19.01 BG Simplification : 0.40
% 32.45/19.01 Subsumption : 2.71
% 32.45/19.01 Abstraction : 0.68
% 32.45/19.01 MUC search : 0.00
% 32.45/19.01 Cooper : 0.00
% 32.45/19.01 Total : 18.02
% 32.45/19.01 Index Insertion : 0.00
% 32.45/19.01 Index Deletion : 0.00
% 32.45/19.01 Index Matching : 0.00
% 32.45/19.01 BG Taut test : 0.00
%------------------------------------------------------------------------------