%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP498-1 : TPTP v9.0.0. Released v2.6.0.
% 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 : n002.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 : Wed Apr 9 06:26:22 PM UTC 2025
% Result : Unsatisfiable 8.09s 3.00s
% Output : CNFRefutation 8.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 69 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 112 ( 112 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > identity > c3 > b3 > a3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a3,type,
a3: $i ).
tff(c3,type,
c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(double_divide,type,
double_divide: ( $i * $i ) > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b3,type,
b3: $i ).
tff(identity,type,
identity: $i ).
tff(f_25,axiom,
! [A,B] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file(unknown,unknown) ).
tff(f_27,axiom,
! [A] : ( inverse(A) = double_divide(A,identity) ),
file(unknown,unknown) ).
tff(f_29,axiom,
! [A] : ( identity = double_divide(A,inverse(A)) ),
file(unknown,unknown) ).
tff(f_23,axiom,
! [A,B,C] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ),
file(unknown,unknown) ).
tff(f_31,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file(unknown,unknown) ).
tff(c_4,plain,
! [B_5,A_4] : ( double_divide(double_divide(B_5,A_4),identity) = multiply(A_4,B_5) ),
inference(cnfTransformation,[status(thm)],[f_25]) ).
tff(c_6,plain,
! [A_6] : ( double_divide(A_6,identity) = inverse(A_6) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_28,plain,
! [B_10,A_11] : ( double_divide(double_divide(B_10,A_11),identity) = multiply(A_11,B_10) ),
inference(cnfTransformation,[status(thm)],[f_25]) ).
tff(c_115,plain,
! [A_16] : ( double_divide(inverse(A_16),identity) = multiply(identity,A_16) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).
tff(c_124,plain,
! [A_16] : ( multiply(identity,inverse(A_16)) = double_divide(multiply(identity,A_16),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_4]) ).
tff(c_141,plain,
! [A_16] : ( multiply(identity,inverse(A_16)) = inverse(multiply(identity,A_16)) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_124]) ).
tff(c_8,plain,
! [A_7] : ( double_divide(A_7,inverse(A_7)) = identity ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( double_divide(double_divide(identity,double_divide(A_1,double_divide(B_2,identity))),double_divide(double_divide(B_2,double_divide(C_3,A_1)),identity)) = C_3 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_236,plain,
! [A_21,B_22,C_23] : ( double_divide(double_divide(identity,double_divide(A_21,inverse(B_22))),multiply(double_divide(C_23,A_21),B_22)) = C_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2]) ).
tff(c_65,plain,
! [B_13,A_14] : ( inverse(double_divide(B_13,A_14)) = multiply(A_14,B_13) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_6]) ).
tff(c_74,plain,
! [B_13,A_14] : ( double_divide(double_divide(B_13,A_14),multiply(A_14,B_13)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_65,c_8]) ).
tff(c_249,plain,
inverse(identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_236,c_74]) ).
tff(c_289,plain,
! [C_23,A_7] : ( double_divide(double_divide(identity,identity),multiply(double_divide(C_23,A_7),A_7)) = C_23 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_236]) ).
tff(c_296,plain,
! [C_23,A_7] : ( double_divide(inverse(identity),multiply(double_divide(C_23,A_7),A_7)) = C_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_289]) ).
tff(c_545,plain,
! [C_30,A_31] : ( double_divide(identity,multiply(double_divide(C_30,A_31),A_31)) = C_30 ),
inference(demodulation,[status(thm),theory(equality)],[c_249,c_296]) ).
tff(c_599,plain,
! [A_7] : ( double_divide(identity,multiply(identity,inverse(A_7))) = A_7 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_545]) ).
tff(c_651,plain,
! [A_33] : ( double_divide(identity,inverse(multiply(identity,A_33))) = A_33 ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_599]) ).
tff(c_678,plain,
! [A_33] : ( multiply(inverse(multiply(identity,A_33)),identity) = double_divide(A_33,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_651,c_4]) ).
tff(c_733,plain,
! [A_35] : ( multiply(inverse(multiply(identity,A_35)),identity) = inverse(A_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_678]) ).
tff(c_596,plain,
! [A_6] : ( double_divide(identity,multiply(inverse(A_6),identity)) = A_6 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_545]) ).
tff(c_768,plain,
! [A_36] : ( double_divide(identity,inverse(A_36)) = multiply(identity,A_36) ),
inference(superposition,[status(thm),theory(equality)],[c_733,c_596]) ).
tff(c_604,plain,
! [A_7] : ( double_divide(identity,inverse(multiply(identity,A_7))) = A_7 ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_599]) ).
tff(c_774,plain,
! [A_7] : ( multiply(identity,multiply(identity,A_7)) = A_7 ),
inference(superposition,[status(thm),theory(equality)],[c_768,c_604]) ).
tff(c_37,plain,
! [B_10,A_11] : ( inverse(double_divide(B_10,A_11)) = multiply(A_11,B_10) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_6]) ).
tff(c_46,plain,
! [A_6] : ( double_divide(inverse(A_6),identity) = multiply(identity,A_6) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).
tff(c_310,plain,
multiply(identity,identity) = double_divide(identity,identity),
inference(superposition,[status(thm),theory(equality)],[c_249,c_46]) ).
tff(c_320,plain,
multiply(identity,identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_249,c_6,c_310]) ).
tff(c_83,plain,
! [A_6] : ( inverse(inverse(A_6)) = multiply(identity,A_6) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_65]) ).
tff(c_1041,plain,
! [A_40,B_41] : ( double_divide(double_divide(identity,double_divide(inverse(A_40),inverse(B_41))),multiply(identity,B_41)) = A_40 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_236]) ).
tff(c_1091,plain,
! [A_40] : ( double_divide(double_divide(identity,double_divide(inverse(A_40),identity)),multiply(identity,identity)) = A_40 ),
inference(superposition,[status(thm),theory(equality)],[c_249,c_1041]) ).
tff(c_1124,plain,
! [A_42] : ( multiply(multiply(identity,A_42),identity) = A_42 ),
inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_320,c_83,c_6,c_1091]) ).
tff(c_1143,plain,
! [A_7] : ( multiply(identity,A_7) = multiply(A_7,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_774,c_1124]) ).
tff(c_593,plain,
! [A_4,B_5] : ( double_divide(identity,multiply(multiply(A_4,B_5),identity)) = double_divide(B_5,A_4) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_545]) ).
tff(c_1256,plain,
! [A_44,B_45] : ( double_divide(identity,multiply(identity,multiply(A_44,B_45))) = double_divide(B_45,A_44) ),
inference(demodulation,[status(thm),theory(equality)],[c_1143,c_593]) ).
tff(c_1301,plain,
! [A_7] : ( double_divide(identity,A_7) = double_divide(A_7,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_774,c_1256]) ).
tff(c_1335,plain,
! [A_7] : ( double_divide(identity,A_7) = inverse(A_7) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_1301]) ).
tff(c_11,plain,
! [A_1,B_2,C_3] : ( double_divide(double_divide(identity,double_divide(A_1,inverse(B_2))),multiply(double_divide(C_3,A_1),B_2)) = C_3 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2]) ).
tff(c_258,plain,
! [C_3,A_1,B_2,B_22] : ( double_divide(double_divide(identity,double_divide(multiply(double_divide(C_3,A_1),B_2),inverse(B_22))),multiply(C_3,B_22)) = double_divide(identity,double_divide(A_1,inverse(B_2))) ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_236]) ).
tff(c_3159,plain,
! [B_70,C_71,A_72,B_73] : ( double_divide(multiply(inverse(B_70),multiply(double_divide(C_71,A_72),B_73)),multiply(C_71,B_70)) = multiply(inverse(B_73),A_72) ),
inference(demodulation,[status(thm),theory(equality)],[c_37,c_1335,c_37,c_1335,c_258]) ).
tff(c_4069,plain,
! [B_81,B_82,A_83] : ( double_divide(multiply(inverse(B_81),multiply(identity,B_82)),multiply(A_83,B_81)) = multiply(inverse(B_82),inverse(A_83)) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_3159]) ).
tff(c_4204,plain,
! [B_82] : ( double_divide(multiply(inverse(identity),multiply(identity,B_82)),identity) = multiply(inverse(B_82),inverse(identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_320,c_4069]) ).
tff(c_4245,plain,
! [B_82] : ( inverse(multiply(identity,B_82)) = inverse(B_82) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_1143,c_774,c_249,c_6,c_249,c_4204]) ).
tff(c_1347,plain,
! [A_46] : ( double_divide(identity,A_46) = inverse(A_46) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_1301]) ).
tff(c_1403,plain,
! [A_7] : ( inverse(inverse(multiply(identity,A_7))) = A_7 ),
inference(superposition,[status(thm),theory(equality)],[c_604,c_1347]) ).
tff(c_4253,plain,
! [A_7] : ( inverse(inverse(A_7)) = A_7 ),
inference(demodulation,[status(thm),theory(equality)],[c_4245,c_1403]) ).
tff(c_4381,plain,
! [A_6] : ( multiply(identity,A_6) = A_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_4253,c_83]) ).
tff(c_136,plain,
! [B_10,A_11] : ( multiply(identity,double_divide(B_10,A_11)) = double_divide(multiply(A_11,B_10),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_37,c_115]) ).
tff(c_145,plain,
! [B_10,A_11] : ( multiply(identity,double_divide(B_10,A_11)) = inverse(multiply(A_11,B_10)) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_136]) ).
tff(c_4642,plain,
! [A_11,B_10] : ( inverse(multiply(A_11,B_10)) = double_divide(B_10,A_11) ),
inference(demodulation,[status(thm),theory(equality)],[c_4381,c_145]) ).
tff(c_4643,plain,
! [A_88,B_89] : ( inverse(multiply(A_88,B_89)) = double_divide(B_89,A_88) ),
inference(demodulation,[status(thm),theory(equality)],[c_4381,c_145]) ).
tff(c_544,plain,
! [C_23,A_7] : ( double_divide(identity,multiply(double_divide(C_23,A_7),A_7)) = C_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_249,c_296]) ).
tff(c_1365,plain,
! [C_23,A_7] : ( inverse(multiply(double_divide(C_23,A_7),A_7)) = C_23 ),
inference(superposition,[status(thm),theory(equality)],[c_1347,c_544]) ).
tff(c_4656,plain,
! [B_89,C_23] : ( double_divide(B_89,double_divide(C_23,B_89)) = C_23 ),
inference(superposition,[status(thm),theory(equality)],[c_4643,c_1365]) ).
tff(c_693,plain,
! [A_33] : ( multiply(inverse(multiply(identity,A_33)),identity) = inverse(A_33) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_678]) ).
tff(c_4179,plain,
! [B_82,A_33] : ( multiply(inverse(B_82),inverse(inverse(multiply(identity,A_33)))) = double_divide(multiply(inverse(identity),multiply(identity,B_82)),inverse(A_33)) ),
inference(superposition,[status(thm),theory(equality)],[c_693,c_4069]) ).
tff(c_4237,plain,
! [B_82,A_33] : ( multiply(inverse(B_82),A_33) = double_divide(B_82,inverse(A_33)) ),
inference(demodulation,[status(thm),theory(equality)],[c_774,c_774,c_249,c_83,c_4179]) ).
tff(c_581,plain,
! [C_3,A_1,B_2] : ( double_divide(identity,multiply(C_3,multiply(double_divide(C_3,A_1),B_2))) = double_divide(identity,double_divide(A_1,inverse(B_2))) ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_545]) ).
tff(c_10190,plain,
! [C_171,A_172,B_173] : ( double_divide(identity,multiply(C_171,multiply(double_divide(C_171,A_172),B_173))) = double_divide(B_173,inverse(A_172)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4237,c_37,c_1335,c_581]) ).
tff(c_10312,plain,
! [B_89,C_23,B_173] : ( double_divide(identity,multiply(B_89,multiply(C_23,B_173))) = double_divide(B_173,inverse(double_divide(C_23,B_89))) ),
inference(superposition,[status(thm),theory(equality)],[c_4656,c_10190]) ).
tff(c_10984,plain,
! [C_180,B_181,B_182] : ( double_divide(multiply(C_180,B_181),B_182) = double_divide(B_181,multiply(B_182,C_180)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4642,c_1335,c_37,c_10312]) ).
tff(c_12108,plain,
! [B_194,B_195,C_196] : ( double_divide(double_divide(B_194,multiply(B_195,C_196)),identity) = multiply(B_195,multiply(C_196,B_194)) ),
inference(superposition,[status(thm),theory(equality)],[c_10984,c_4]) ).
tff(c_12274,plain,
! [B_195,C_196,B_5] : ( multiply(multiply(B_195,C_196),B_5) = multiply(B_195,multiply(C_196,B_5)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12108]) ).
tff(c_10,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_12827,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12274,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP498-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.13 % 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
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 21:53:32 EDT 2025
% 0.12/0.33 % CPUTime :
% 8.09/3.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.09/3.01
% 8.09/3.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------