%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP407-1 : 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 : n008.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 06:26:10 PM UTC 2025
% Result : Unsatisfiable 24.60s 10.71s
% Output : CNFRefutation 24.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 46 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 14 ( 3 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 125 ( 125 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > b2 > a2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(b2,type,
b2: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(a2,type,
a2: $i ).
tff(f_24,axiom,
! [A,B,C] : ( multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = C ),
file(unknown,unknown) ).
tff(f_26,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file(unknown,unknown) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( multiply(A_1,inverse(multiply(inverse(multiply(inverse(multiply(A_1,B_2)),C_3)),multiply(inverse(B_2),multiply(inverse(B_2),B_2))))) = C_3 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_5,plain,
! [A_4,B_5,C_6] : ( multiply(A_4,inverse(multiply(inverse(multiply(inverse(multiply(A_4,B_5)),C_6)),multiply(inverse(B_5),multiply(inverse(B_5),B_5))))) = C_6 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_28,plain,
! [A_7,C_8,B_9,B_10] : ( multiply(A_7,inverse(multiply(inverse(C_8),multiply(inverse(B_9),multiply(inverse(B_9),B_9))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A_7,B_9)),B_10)),C_8)),multiply(inverse(B_10),multiply(inverse(B_10),B_10)))) ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_165,plain,
! [A_1,B_2,B_10,C_3] : ( inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A_1,B_2)),B_10)),multiply(inverse(multiply(A_1,B_2)),C_3))),multiply(inverse(B_10),multiply(inverse(B_10),B_10)))) = C_3 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_28]) ).
tff(c_246,plain,
! [A_14,B_15,B_16,C_17] : ( inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A_14,B_15)),B_16)),multiply(inverse(multiply(A_14,B_15)),C_17))),multiply(inverse(B_16),multiply(inverse(B_16),B_16)))) = C_17 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_28]) ).
tff(c_249,plain,
! [B_16,C_3,B_10,A_14,C_17,B_15] : ( inverse(multiply(inverse(multiply(inverse(multiply(C_17,B_10)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A_14,B_15)),B_16)),multiply(inverse(multiply(A_14,B_15)),C_17))),multiply(inverse(B_16),multiply(inverse(B_16),B_16)))),C_3))),multiply(inverse(B_10),multiply(inverse(B_10),B_10)))) = C_3 ),
inference(superposition,[status(thm),theory(equality)],[c_246,c_165]) ).
tff(c_437,plain,
! [C_18,B_19,C_20] : ( inverse(multiply(inverse(multiply(inverse(multiply(C_18,B_19)),multiply(C_18,C_20))),multiply(inverse(B_19),multiply(inverse(B_19),B_19)))) = C_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_165,c_249]) ).
tff(c_8536,plain,
! [C_77,B_78,C_79] : ( multiply(inverse(multiply(C_77,B_78)),inverse(multiply(C_79,multiply(inverse(multiply(C_77,C_79)),multiply(inverse(multiply(C_77,C_79)),multiply(C_77,C_79)))))) = multiply(inverse(B_78),multiply(inverse(B_78),B_78)) ),
inference(superposition,[status(thm),theory(equality)],[c_437,c_2]) ).
tff(c_95,plain,
! [A_7,B_9,C_8] : ( multiply(inverse(multiply(A_7,B_9)),multiply(A_7,inverse(multiply(inverse(C_8),multiply(inverse(B_9),multiply(inverse(B_9),B_9)))))) = C_8 ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_2]) ).
tff(c_8977,plain,
! [C_77,B_78,C_8] : ( multiply(inverse(multiply(inverse(multiply(C_77,B_78)),multiply(C_77,inverse(C_8)))),multiply(inverse(B_78),multiply(inverse(B_78),B_78))) = C_8 ),
inference(superposition,[status(thm),theory(equality)],[c_8536,c_95]) ).
tff(c_410,plain,
! [C_17,B_10,C_3] : ( inverse(multiply(inverse(multiply(inverse(multiply(C_17,B_10)),multiply(C_17,C_3))),multiply(inverse(B_10),multiply(inverse(B_10),B_10)))) = C_3 ),
inference(demodulation,[status(thm),theory(equality)],[c_165,c_249]) ).
tff(c_579,plain,
! [C_21,B_22,C_23,A_24] : ( multiply(inverse(multiply(C_21,B_22)),multiply(C_21,C_23)) = multiply(inverse(multiply(A_24,B_22)),multiply(A_24,C_23)) ),
inference(superposition,[status(thm),theory(equality)],[c_437,c_95]) ).
tff(c_11943,plain,
! [C_95,C_94,C_97,B_96,C_93] : ( multiply(inverse(multiply(C_93,multiply(inverse(B_96),multiply(inverse(B_96),B_96)))),multiply(C_93,C_95)) = multiply(C_97,multiply(inverse(multiply(inverse(multiply(C_94,B_96)),multiply(C_94,C_97))),C_95)) ),
inference(superposition,[status(thm),theory(equality)],[c_410,c_579]) ).
tff(c_13322,plain,
! [C_98,B_99,C_100] : ( multiply(inverse(multiply(C_98,multiply(inverse(B_99),multiply(inverse(B_99),B_99)))),multiply(C_98,multiply(inverse(B_99),multiply(inverse(B_99),B_99)))) = multiply(inverse(C_100),C_100) ),
inference(superposition,[status(thm),theory(equality)],[c_8977,c_11943]) ).
tff(c_12822,plain,
! [C_93,B_78,C_8] : ( multiply(inverse(multiply(C_93,multiply(inverse(B_78),multiply(inverse(B_78),B_78)))),multiply(C_93,multiply(inverse(B_78),multiply(inverse(B_78),B_78)))) = multiply(inverse(C_8),C_8) ),
inference(superposition,[status(thm),theory(equality)],[c_8977,c_11943]) ).
tff(c_13348,plain,
! [C_8,C_100] : ( multiply(inverse(C_8),C_8) = multiply(inverse(C_100),C_100) ),
inference(superposition,[status(thm),theory(equality)],[c_13322,c_12822]) ).
tff(c_14670,plain,
! [C_102,C_101] : ( multiply(inverse(C_102),C_102) = multiply(inverse(C_101),C_101) ),
inference(superposition,[status(thm),theory(equality)],[c_13322,c_12822]) ).
tff(c_12,plain,
! [A_1,C_6,B_2,B_5] : ( multiply(A_1,inverse(multiply(inverse(C_6),multiply(inverse(B_2),multiply(inverse(B_2),B_2))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A_1,B_2)),B_5)),C_6)),multiply(inverse(B_5),multiply(inverse(B_5),B_5)))) ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_15609,plain,
! [A_1,B_2,B_5,C_101] : ( multiply(A_1,inverse(multiply(inverse(multiply(inverse(multiply(A_1,B_2)),B_5)),multiply(inverse(B_2),multiply(inverse(B_2),B_2))))) = inverse(multiply(inverse(multiply(inverse(C_101),C_101)),multiply(inverse(B_5),multiply(inverse(B_5),B_5)))) ),
inference(superposition,[status(thm),theory(equality)],[c_14670,c_12]) ).
tff(c_15847,plain,
! [C_104,B_105] : ( inverse(multiply(inverse(multiply(inverse(C_104),C_104)),multiply(inverse(B_105),multiply(inverse(B_105),B_105)))) = B_105 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15609]) ).
tff(c_1262,plain,
! [A_29,B_30,C_31,B_32] : ( multiply(inverse(multiply(A_29,B_30)),multiply(A_29,inverse(multiply(inverse(multiply(C_31,B_32)),multiply(C_31,multiply(inverse(B_30),B_30)))))) = multiply(inverse(B_30),B_32) ),
inference(superposition,[status(thm),theory(equality)],[c_579,c_95]) ).
tff(c_5532,plain,
! [B_65,B_66,C_67] : ( inverse(multiply(inverse(multiply(inverse(B_65),B_66)),multiply(inverse(B_65),multiply(inverse(B_65),B_65)))) = inverse(multiply(inverse(multiply(C_67,B_66)),multiply(C_67,multiply(inverse(B_65),B_65)))) ),
inference(superposition,[status(thm),theory(equality)],[c_1262,c_410]) ).
tff(c_1323,plain,
! [B_30,B_32,C_31] : ( inverse(multiply(inverse(multiply(inverse(B_30),B_32)),multiply(inverse(B_30),multiply(inverse(B_30),B_30)))) = inverse(multiply(inverse(multiply(C_31,B_32)),multiply(C_31,multiply(inverse(B_30),B_30)))) ),
inference(superposition,[status(thm),theory(equality)],[c_1262,c_410]) ).
tff(c_5568,plain,
! [C_67,B_66,B_65,C_31] : ( inverse(multiply(inverse(multiply(C_67,B_66)),multiply(C_67,multiply(inverse(B_65),B_65)))) = inverse(multiply(inverse(multiply(C_31,B_66)),multiply(C_31,multiply(inverse(B_65),B_65)))) ),
inference(superposition,[status(thm),theory(equality)],[c_5532,c_1323]) ).
tff(c_18724,plain,
! [C_112,B_113] : ( inverse(multiply(inverse(multiply(C_112,B_113)),multiply(C_112,multiply(inverse(B_113),B_113)))) = B_113 ),
inference(superposition,[status(thm),theory(equality)],[c_15847,c_5568]) ).
tff(c_19181,plain,
! [C_112,C_8,C_100] : ( inverse(multiply(inverse(multiply(C_112,C_8)),multiply(C_112,multiply(inverse(C_100),C_100)))) = C_8 ),
inference(superposition,[status(thm),theory(equality)],[c_13348,c_18724]) ).
tff(c_652,plain,
! [A_7,B_9,C_21,B_22] : ( multiply(inverse(multiply(A_7,B_9)),multiply(A_7,inverse(multiply(inverse(multiply(C_21,B_22)),multiply(C_21,multiply(inverse(B_9),B_9)))))) = multiply(inverse(B_9),B_22) ),
inference(superposition,[status(thm),theory(equality)],[c_579,c_95]) ).
tff(c_20192,plain,
! [A_7,B_9,B_22] : ( multiply(inverse(multiply(A_7,B_9)),multiply(A_7,B_22)) = multiply(inverse(B_9),B_22) ),
inference(demodulation,[status(thm),theory(equality)],[c_19181,c_652]) ).
tff(c_31352,plain,
! [C_8,C_100] : ( inverse(multiply(inverse(C_8),multiply(inverse(C_100),C_100))) = C_8 ),
inference(demodulation,[status(thm),theory(equality)],[c_20192,c_19181]) ).
tff(c_31935,plain,
! [C_150,C_151] : ( inverse(multiply(inverse(C_150),multiply(inverse(C_151),C_151))) = C_150 ),
inference(demodulation,[status(thm),theory(equality)],[c_20192,c_19181]) ).
tff(c_32260,plain,
! [C_150,C_8,C_151] : ( multiply(C_150,multiply(inverse(C_150),inverse(multiply(inverse(C_8),multiply(inverse(multiply(inverse(C_151),C_151)),multiply(inverse(multiply(inverse(C_151),C_151)),multiply(inverse(C_151),C_151))))))) = C_8 ),
inference(superposition,[status(thm),theory(equality)],[c_31935,c_95]) ).
tff(c_34451,plain,
! [C_157,C_158] : ( multiply(C_157,multiply(inverse(C_157),C_158)) = C_158 ),
inference(demodulation,[status(thm),theory(equality)],[c_31352,c_20192,c_20192,c_32260]) ).
tff(c_34814,plain,
! [C_159] : ( inverse(inverse(C_159)) = C_159 ),
inference(superposition,[status(thm),theory(equality)],[c_34451,c_31352]) ).
tff(c_32543,plain,
! [C_150,C_8] : ( multiply(C_150,multiply(inverse(C_150),C_8)) = C_8 ),
inference(demodulation,[status(thm),theory(equality)],[c_31352,c_20192,c_20192,c_32260]) ).
tff(c_34823,plain,
! [C_159,C_8] : ( multiply(inverse(C_159),multiply(C_159,C_8)) = C_8 ),
inference(superposition,[status(thm),theory(equality)],[c_34814,c_32543]) ).
tff(c_34481,plain,
! [C_8] : ( inverse(inverse(C_8)) = C_8 ),
inference(superposition,[status(thm),theory(equality)],[c_34451,c_31352]) ).
tff(c_20193,plain,
! [C_116,C_117,C_118] : ( inverse(multiply(inverse(multiply(C_116,C_117)),multiply(C_116,multiply(inverse(C_118),C_118)))) = C_117 ),
inference(superposition,[status(thm),theory(equality)],[c_13348,c_18724]) ).
tff(c_20634,plain,
! [C_118,C_8] : ( multiply(inverse(C_118),C_118) = inverse(multiply(inverse(C_8),C_8)) ),
inference(superposition,[status(thm),theory(equality)],[c_13348,c_20193]) ).
tff(c_35877,plain,
! [C_170,C_171] : ( multiply(C_170,inverse(multiply(inverse(C_171),C_171))) = C_170 ),
inference(superposition,[status(thm),theory(equality)],[c_20634,c_34451]) ).
tff(c_35914,plain,
! [C_171,B_22,C_170] : ( multiply(inverse(inverse(multiply(inverse(C_171),C_171))),B_22) = multiply(inverse(C_170),multiply(C_170,B_22)) ),
inference(superposition,[status(thm),theory(equality)],[c_35877,c_20192]) ).
tff(c_36068,plain,
! [C_171,B_22] : ( multiply(multiply(inverse(C_171),C_171),B_22) = B_22 ),
inference(demodulation,[status(thm),theory(equality)],[c_34823,c_34481,c_35914]) ).
tff(c_4,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_15634,plain,
! [C_102] : ( multiply(multiply(inverse(C_102),C_102),a2) != a2 ),
inference(superposition,[status(thm),theory(equality)],[c_14670,c_4]) ).
tff(c_36551,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36068,c_15634]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP407-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 21:47:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 24.60/10.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.72/10.72
% 24.72/10.72 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------