%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP424-1 : 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 : n028.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 06:26:12 PM UTC 2025
% Result : Unsatisfiable 9.08s 3.18s
% Output : CNFRefutation 9.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 16 ( 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 : 63 ( 63 !; 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] : ( multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = B ),
file(unknown,unknown) ).
tff(f_26,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file(unknown,unknown) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( multiply(inverse(multiply(inverse(multiply(A_1,inverse(multiply(inverse(B_2),C_3)))),multiply(A_1,inverse(C_3)))),inverse(multiply(inverse(C_3),C_3))) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_5,plain,
! [A_4,B_5,C_6] : ( multiply(inverse(multiply(inverse(multiply(A_4,inverse(multiply(inverse(B_5),C_6)))),multiply(A_4,inverse(C_6)))),inverse(multiply(inverse(C_6),C_6))) = B_5 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_26,plain,
! [A_1,B_2,C_3,B_5] : ( multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A_1,inverse(multiply(inverse(B_2),C_3)))),multiply(A_1,inverse(C_3)))),inverse(multiply(inverse(B_5),multiply(inverse(C_3),C_3))))),B_2)),inverse(multiply(inverse(multiply(inverse(C_3),C_3)),multiply(inverse(C_3),C_3)))) = B_5 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_5]) ).
tff(c_224,plain,
! [A_17,B_18,C_19,A_20] : ( multiply(inverse(multiply(inverse(multiply(A_17,inverse(B_18))),multiply(A_17,inverse(inverse(multiply(inverse(C_19),C_19)))))),inverse(multiply(inverse(inverse(multiply(inverse(C_19),C_19))),inverse(multiply(inverse(C_19),C_19))))) = multiply(inverse(multiply(A_20,inverse(multiply(inverse(B_18),C_19)))),multiply(A_20,inverse(C_19))) ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_313,plain,
! [A_20,B_2,C_19] : ( multiply(inverse(multiply(A_20,inverse(multiply(inverse(multiply(inverse(B_2),inverse(multiply(inverse(C_19),C_19)))),C_19)))),multiply(A_20,inverse(C_19))) = B_2 ),
inference(superposition,[status(thm),theory(equality)],[c_224,c_2]) ).
tff(c_8,plain,
! [A_1,B_5,C_6,A_4] : ( multiply(inverse(multiply(inverse(multiply(A_1,inverse(B_5))),multiply(A_1,inverse(inverse(multiply(inverse(C_6),C_6)))))),inverse(multiply(inverse(inverse(multiply(inverse(C_6),C_6))),inverse(multiply(inverse(C_6),C_6))))) = multiply(inverse(multiply(A_4,inverse(multiply(inverse(B_5),C_6)))),multiply(A_4,inverse(C_6))) ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_485,plain,
! [A_27,B_25,C_26,A_24] : ( multiply(inverse(multiply(A_27,inverse(multiply(inverse(B_25),C_26)))),multiply(A_27,inverse(C_26))) = multiply(inverse(multiply(A_24,inverse(multiply(inverse(B_25),C_26)))),multiply(A_24,inverse(C_26))) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_224]) ).
tff(c_620,plain,
! [A_24,B_2,A_20,C_19,A_27] : ( multiply(inverse(multiply(A_27,inverse(B_2))),multiply(A_27,inverse(multiply(A_20,inverse(C_19))))) = multiply(inverse(multiply(A_24,inverse(multiply(inverse(multiply(A_20,inverse(multiply(inverse(multiply(inverse(B_2),inverse(multiply(inverse(C_19),C_19)))),C_19)))),multiply(A_20,inverse(C_19)))))),multiply(A_24,inverse(multiply(A_20,inverse(C_19))))) ),
inference(superposition,[status(thm),theory(equality)],[c_313,c_485]) ).
tff(c_756,plain,
! [A_31,A_29,A_32,B_30,C_28] : ( multiply(inverse(multiply(A_32,inverse(B_30))),multiply(A_32,inverse(multiply(A_31,inverse(C_28))))) = multiply(inverse(multiply(A_29,inverse(B_30))),multiply(A_29,inverse(multiply(A_31,inverse(C_28))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_313,c_620]) ).
tff(c_1046,plain,
! [B_5,A_29,B_2,C_3,A_1,A_32,B_30] : ( multiply(inverse(multiply(A_32,inverse(B_30))),multiply(A_32,inverse(B_5))) = multiply(inverse(multiply(A_29,inverse(B_30))),multiply(A_29,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A_1,inverse(multiply(inverse(B_2),C_3)))),multiply(A_1,inverse(C_3)))),inverse(multiply(inverse(B_5),multiply(inverse(C_3),C_3))))),B_2)),inverse(multiply(inverse(multiply(inverse(C_3),C_3)),multiply(inverse(C_3),C_3))))))) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_756]) ).
tff(c_1133,plain,
! [A_36,B_34,B_35,A_33] : ( multiply(inverse(multiply(A_36,inverse(B_34))),multiply(A_36,inverse(B_35))) = multiply(inverse(multiply(A_33,inverse(B_34))),multiply(A_33,inverse(B_35))) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_1046]) ).
tff(c_3050,plain,
! [A_60,A_56,B_57,B_58,C_59] : ( multiply(inverse(multiply(inverse(multiply(inverse(multiply(A_60,inverse(multiply(inverse(B_57),C_59)))),multiply(A_60,inverse(C_59)))),inverse(B_58))),B_57) = multiply(inverse(multiply(A_56,inverse(B_58))),multiply(A_56,inverse(multiply(inverse(C_59),C_59)))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1133]) ).
tff(c_3751,plain,
! [A_61,C_62,B_63] : ( multiply(inverse(multiply(A_61,inverse(multiply(inverse(C_62),C_62)))),multiply(A_61,inverse(multiply(inverse(C_62),C_62)))) = multiply(inverse(B_63),B_63) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_3050]) ).
tff(c_3719,plain,
! [A_56,C_3,B_2] : ( multiply(inverse(multiply(A_56,inverse(multiply(inverse(C_3),C_3)))),multiply(A_56,inverse(multiply(inverse(C_3),C_3)))) = multiply(inverse(B_2),B_2) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_3050]) ).
tff(c_4344,plain,
! [B_65,B_64] : ( multiply(inverse(B_65),B_65) = multiply(inverse(B_64),B_64) ),
inference(superposition,[status(thm),theory(equality)],[c_3751,c_3719]) ).
tff(c_4,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_4922,plain,
! [B_64] : ( multiply(inverse(a1),a1) != multiply(inverse(B_64),B_64) ),
inference(superposition,[status(thm),theory(equality)],[c_4344,c_4]) ).
tff(c_4979,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_4922]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP424-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.13 % 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
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 7 21:49:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 9.08/3.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.08/3.19
% 9.08/3.19 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------