%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP418-1 : 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 : n017.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 06:26:11 PM UTC 2025
% Result : Unsatisfiable 62.08s 21.05s
% Output : CNFRefutation 62.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of formulae : 39 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 24 ( 4 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 : 139 ( 139 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > b1 > a1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a1,type,
a1: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b1,type,
b1: $i ).
tff(f_24,axiom,
! [A,B,C] : ( inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = B ),
file(unknown,unknown) ).
tff(f_26,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file(unknown,unknown) ).
tff(c_5,plain,
! [A_4,B_5,C_6] : ( inverse(multiply(inverse(multiply(A_4,inverse(multiply(inverse(B_5),inverse(multiply(C_6,inverse(multiply(inverse(C_6),C_6)))))))),multiply(A_4,C_6))) = B_5 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( inverse(multiply(inverse(multiply(A_1,inverse(multiply(inverse(B_2),inverse(multiply(C_3,inverse(multiply(inverse(C_3),C_3)))))))),multiply(A_1,C_3))) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_8,plain,
! [B_5,A_4,C_3,A_1,C_6] : ( multiply(inverse(multiply(A_4,inverse(multiply(inverse(B_5),inverse(multiply(C_6,inverse(multiply(inverse(C_6),C_6)))))))),multiply(A_4,C_6)) = inverse(multiply(inverse(multiply(A_1,inverse(multiply(B_5,inverse(multiply(C_3,inverse(multiply(inverse(C_3),C_3)))))))),multiply(A_1,C_3))) ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_76,plain,
! [A_12,B_13,C_14] : ( inverse(inverse(multiply(inverse(multiply(A_12,inverse(multiply(B_13,inverse(multiply(C_14,inverse(multiply(inverse(C_14),C_14)))))))),multiply(A_12,C_14)))) = B_13 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_2]) ).
tff(c_103,plain,
! [A_4,B_5,C_6] : ( inverse(multiply(inverse(multiply(A_4,inverse(multiply(inverse(B_5),inverse(multiply(C_6,inverse(multiply(inverse(C_6),C_6)))))))),multiply(A_4,C_6))) = B_5 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_76]) ).
tff(c_114,plain,
! [A_15,B_16,C_17] : ( inverse(multiply(inverse(multiply(A_15,inverse(multiply(inverse(B_16),inverse(multiply(C_17,inverse(multiply(inverse(C_17),C_17)))))))),multiply(A_15,C_17))) = B_16 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_76]) ).
tff(c_141,plain,
! [A_4,B_16,C_6] : ( multiply(inverse(multiply(A_4,inverse(multiply(inverse(inverse(B_16)),inverse(multiply(C_6,inverse(multiply(inverse(C_6),C_6)))))))),multiply(A_4,C_6)) = B_16 ),
inference(superposition,[status(thm),theory(equality)],[c_114,c_8]) ).
tff(c_26,plain,
! [A_1,B_2,C_3] : ( inverse(inverse(multiply(inverse(multiply(A_1,inverse(multiply(B_2,inverse(multiply(C_3,inverse(multiply(inverse(C_3),C_3)))))))),multiply(A_1,C_3)))) = B_2 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_2]) ).
tff(c_177,plain,
! [A_18,B_19,C_20] : ( multiply(inverse(multiply(A_18,inverse(multiply(inverse(inverse(B_19)),inverse(multiply(C_20,inverse(multiply(inverse(C_20),C_20)))))))),multiply(A_18,C_20)) = B_19 ),
inference(superposition,[status(thm),theory(equality)],[c_114,c_8]) ).
tff(c_1663,plain,
! [A_45,B_46,C_47,B_48] : ( inverse(multiply(inverse(multiply(inverse(multiply(A_45,inverse(multiply(inverse(inverse(B_46)),inverse(multiply(C_47,inverse(multiply(inverse(C_47),C_47)))))))),inverse(multiply(inverse(B_48),inverse(multiply(multiply(A_45,C_47),inverse(multiply(inverse(multiply(A_45,C_47)),multiply(A_45,C_47))))))))),B_46)) = B_48 ),
inference(superposition,[status(thm),theory(equality)],[c_177,c_103]) ).
tff(c_27,plain,
! [B_7,C_8,A_10,C_9,A_11] : ( multiply(inverse(multiply(A_11,inverse(multiply(inverse(B_7),inverse(multiply(C_8,inverse(multiply(inverse(C_8),C_8)))))))),multiply(A_11,C_8)) = inverse(multiply(inverse(multiply(A_10,inverse(multiply(B_7,inverse(multiply(C_9,inverse(multiply(inverse(C_9),C_9)))))))),multiply(A_10,C_9))) ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_69,plain,
! [B_5,A_10,C_3,A_1,C_9] : ( inverse(multiply(inverse(multiply(A_10,inverse(multiply(B_5,inverse(multiply(C_9,inverse(multiply(inverse(C_9),C_9)))))))),multiply(A_10,C_9))) = inverse(multiply(inverse(multiply(A_1,inverse(multiply(B_5,inverse(multiply(C_3,inverse(multiply(inverse(C_3),C_3)))))))),multiply(A_1,C_3))) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_27]) ).
tff(c_1762,plain,
! [A_10,C_3,C_47,A_1,A_45,C_9,B_48] : ( inverse(multiply(inverse(multiply(A_10,B_48)),multiply(A_10,C_9))) = inverse(multiply(inverse(multiply(A_1,inverse(multiply(inverse(multiply(inverse(multiply(A_45,inverse(multiply(inverse(inverse(inverse(multiply(C_9,inverse(multiply(inverse(C_9),C_9)))))),inverse(multiply(C_47,inverse(multiply(inverse(C_47),C_47)))))))),inverse(multiply(inverse(B_48),inverse(multiply(multiply(A_45,C_47),inverse(multiply(inverse(multiply(A_45,C_47)),multiply(A_45,C_47))))))))),inverse(multiply(C_3,inverse(multiply(inverse(C_3),C_3)))))))),multiply(A_1,C_3))) ),
inference(superposition,[status(thm),theory(equality)],[c_1663,c_69]) ).
tff(c_2785,plain,
! [A_61,C_62,A_63,B_60,C_59] : ( multiply(inverse(multiply(A_61,inverse(multiply(inverse(inverse(inverse(multiply(C_59,inverse(multiply(inverse(C_59),C_59)))))),inverse(multiply(C_62,inverse(multiply(inverse(C_62),C_62)))))))),inverse(multiply(inverse(B_60),inverse(multiply(multiply(A_61,C_62),inverse(multiply(inverse(multiply(A_61,C_62)),multiply(A_61,C_62)))))))) = inverse(multiply(inverse(multiply(A_63,B_60)),multiply(A_63,C_59))) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_8,c_1762]) ).
tff(c_3179,plain,
! [B_16,A_61,C_62,A_63,C_59] : ( multiply(inverse(inverse(multiply(inverse(multiply(A_63,inverse(B_16))),multiply(A_63,C_59)))),multiply(inverse(multiply(A_61,inverse(multiply(inverse(inverse(inverse(multiply(C_59,inverse(multiply(inverse(C_59),C_59)))))),inverse(multiply(C_62,inverse(multiply(inverse(C_62),C_62)))))))),multiply(A_61,C_62))) = B_16 ),
inference(superposition,[status(thm),theory(equality)],[c_2785,c_141]) ).
tff(c_3577,plain,
! [A_63,B_16,C_59] : ( multiply(inverse(inverse(multiply(inverse(multiply(A_63,inverse(B_16))),multiply(A_63,C_59)))),inverse(multiply(C_59,inverse(multiply(inverse(C_59),C_59))))) = B_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_3179]) ).
tff(c_210,plain,
! [A_4,B_16,C_6,B_19] : ( multiply(inverse(multiply(inverse(multiply(A_4,inverse(multiply(inverse(inverse(B_16)),inverse(multiply(C_6,inverse(multiply(inverse(C_6),C_6)))))))),inverse(multiply(inverse(inverse(B_19)),inverse(multiply(multiply(A_4,C_6),inverse(multiply(inverse(multiply(A_4,C_6)),multiply(A_4,C_6))))))))),B_16) = B_19 ),
inference(superposition,[status(thm),theory(equality)],[c_141,c_177]) ).
tff(c_2080,plain,
! [A_10,C_47,A_45,C_9,B_48] : ( multiply(inverse(multiply(A_45,inverse(multiply(inverse(inverse(inverse(multiply(C_9,inverse(multiply(inverse(C_9),C_9)))))),inverse(multiply(C_47,inverse(multiply(inverse(C_47),C_47)))))))),inverse(multiply(inverse(B_48),inverse(multiply(multiply(A_45,C_47),inverse(multiply(inverse(multiply(A_45,C_47)),multiply(A_45,C_47)))))))) = inverse(multiply(inverse(multiply(A_10,B_48)),multiply(A_10,C_9))) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_8,c_1762]) ).
tff(c_3596,plain,
! [A_67,B_65,C_66,A_64] : ( inverse(multiply(inverse(multiply(A_67,B_65)),multiply(A_67,C_66))) = inverse(multiply(inverse(multiply(A_64,B_65)),multiply(A_64,C_66))) ),
inference(superposition,[status(thm),theory(equality)],[c_2785,c_2080]) ).
tff(c_4421,plain,
! [B_70,C_68,A_72,A_71,A_69] : ( inverse(inverse(multiply(inverse(multiply(A_71,inverse(multiply(B_70,inverse(multiply(multiply(A_72,C_68),inverse(multiply(inverse(multiply(A_69,C_68)),multiply(A_69,C_68))))))))),multiply(A_71,multiply(A_72,C_68))))) = B_70 ),
inference(superposition,[status(thm),theory(equality)],[c_3596,c_26]) ).
tff(c_4622,plain,
! [B_16,B_70,A_4,C_6,A_72,A_71,B_19] : ( inverse(inverse(multiply(inverse(multiply(A_71,inverse(multiply(B_70,inverse(multiply(multiply(A_72,B_16),inverse(multiply(inverse(B_19),multiply(inverse(multiply(inverse(multiply(A_4,inverse(multiply(inverse(inverse(B_16)),inverse(multiply(C_6,inverse(multiply(inverse(C_6),C_6)))))))),inverse(multiply(inverse(inverse(B_19)),inverse(multiply(multiply(A_4,C_6),inverse(multiply(inverse(multiply(A_4,C_6)),multiply(A_4,C_6))))))))),B_16))))))))),multiply(A_71,multiply(A_72,B_16))))) = B_70 ),
inference(superposition,[status(thm),theory(equality)],[c_210,c_4421]) ).
tff(c_8500,plain,
! [B_98,A_99,B_96,B_100,A_97] : ( inverse(inverse(multiply(inverse(multiply(A_99,inverse(multiply(B_96,inverse(multiply(multiply(A_97,B_98),inverse(multiply(inverse(B_100),B_100)))))))),multiply(A_99,multiply(A_97,B_98))))) = B_96 ),
inference(demodulation,[status(thm),theory(equality)],[c_210,c_4622]) ).
tff(c_8889,plain,
! [B_16,A_4,A_99,C_6,B_96,B_100] : ( inverse(inverse(multiply(inverse(multiply(A_99,inverse(multiply(B_96,inverse(multiply(B_16,inverse(multiply(inverse(B_100),B_100)))))))),multiply(A_99,multiply(inverse(multiply(A_4,inverse(multiply(inverse(inverse(B_16)),inverse(multiply(C_6,inverse(multiply(inverse(C_6),C_6)))))))),multiply(A_4,C_6)))))) = B_96 ),
inference(superposition,[status(thm),theory(equality)],[c_141,c_8500]) ).
tff(c_9666,plain,
! [A_106,B_107,B_108,B_109] : ( inverse(inverse(multiply(inverse(multiply(A_106,inverse(multiply(B_107,inverse(multiply(B_108,inverse(multiply(inverse(B_109),B_109)))))))),multiply(A_106,B_108)))) = B_107 ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_8889]) ).
tff(c_10088,plain,
! [B_110,B_111,B_112] : ( multiply(B_110,inverse(multiply(B_111,inverse(multiply(inverse(B_112),B_112))))) = multiply(B_110,inverse(multiply(B_111,inverse(multiply(inverse(B_111),B_111))))) ),
inference(superposition,[status(thm),theory(equality)],[c_9666,c_3577]) ).
tff(c_3249,plain,
! [A_61,A_4,C_62,C_6,A_63,B_60,C_59] : ( multiply(inverse(multiply(A_4,inverse(multiply(inverse(inverse(B_60)),inverse(multiply(C_6,inverse(multiply(inverse(C_6),C_6)))))))),multiply(A_4,C_6)) = inverse(multiply(inverse(inverse(multiply(inverse(multiply(A_63,B_60)),multiply(A_63,C_59)))),multiply(inverse(multiply(A_61,inverse(multiply(inverse(inverse(inverse(multiply(C_59,inverse(multiply(inverse(C_59),C_59)))))),inverse(multiply(C_62,inverse(multiply(inverse(C_62),C_62)))))))),multiply(A_61,C_62)))) ),
inference(superposition,[status(thm),theory(equality)],[c_2785,c_8]) ).
tff(c_3581,plain,
! [A_63,B_60,C_59] : ( inverse(multiply(inverse(inverse(multiply(inverse(multiply(A_63,B_60)),multiply(A_63,C_59)))),inverse(multiply(C_59,inverse(multiply(inverse(C_59),C_59)))))) = B_60 ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_141,c_3249]) ).
tff(c_10324,plain,
! [B_110,B_111,B_112,C_59] : ( inverse(multiply(inverse(inverse(multiply(inverse(multiply(B_110,inverse(multiply(B_111,inverse(multiply(inverse(B_112),B_112)))))),multiply(B_110,C_59)))),inverse(multiply(C_59,inverse(multiply(inverse(C_59),C_59)))))) = inverse(multiply(B_111,inverse(multiply(inverse(B_111),B_111)))) ),
inference(superposition,[status(thm),theory(equality)],[c_10088,c_3581]) ).
tff(c_11031,plain,
! [B_113,B_114] : ( inverse(multiply(B_113,inverse(multiply(inverse(B_114),B_114)))) = inverse(multiply(B_113,inverse(multiply(inverse(B_113),B_113)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_3577,c_10324]) ).
tff(c_11226,plain,
! [B_113,B_114,C_59] : ( inverse(multiply(inverse(inverse(multiply(inverse(multiply(B_113,inverse(multiply(inverse(B_114),B_114)))),multiply(B_113,C_59)))),inverse(multiply(C_59,inverse(multiply(inverse(C_59),C_59)))))) = inverse(multiply(inverse(B_113),B_113)) ),
inference(superposition,[status(thm),theory(equality)],[c_11031,c_3581]) ).
tff(c_11983,plain,
! [B_116,B_115] : ( inverse(multiply(inverse(B_116),B_116)) = inverse(multiply(inverse(B_115),B_115)) ),
inference(demodulation,[status(thm),theory(equality)],[c_3577,c_11226]) ).
tff(c_31835,plain,
! [B_178,B_179] : ( inverse(multiply(inverse(inverse(multiply(inverse(B_178),B_178))),inverse(multiply(B_179,inverse(multiply(inverse(B_179),B_179)))))) = B_179 ),
inference(superposition,[status(thm),theory(equality)],[c_11983,c_3581]) ).
tff(c_32216,plain,
! [A_4,B_16,C_6,B_178] : ( multiply(inverse(multiply(inverse(multiply(A_4,inverse(multiply(inverse(inverse(B_16)),inverse(multiply(C_6,inverse(multiply(inverse(C_6),C_6)))))))),multiply(A_4,C_6))),B_16) = multiply(inverse(B_178),B_178) ),
inference(superposition,[status(thm),theory(equality)],[c_31835,c_210]) ).
tff(c_32755,plain,
! [B_181,B_180] : ( multiply(inverse(B_181),B_181) = multiply(inverse(B_180),B_180) ),
inference(demodulation,[status(thm),theory(equality)],[c_103,c_32216]) ).
tff(c_4,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_34667,plain,
! [B_181] : ( multiply(inverse(a1),a1) != multiply(inverse(B_181),B_181) ),
inference(superposition,[status(thm),theory(equality)],[c_32755,c_4]) ).
tff(c_34993,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_34667]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP418-1 : 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 : n017.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 21:47:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 62.08/21.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 62.08/21.06
% 62.08/21.06 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------