%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP543-1 : 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 : n027.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 06:26:28 PM UTC 2025
% Result : Unsatisfiable 12.19s 4.50s
% Output : CNFRefutation 12.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 98 ( 98 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > divide > #nlpp > inverse > identity > c3 > b3 > a3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a3,type,
a3: $i ).
tff(c3,type,
c3: $i ).
tff(divide,type,
divide: ( $i * $i ) > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b3,type,
b3: $i ).
tff(identity,type,
identity: $i ).
tff(f_27,axiom,
! [A] : ( inverse(A) = divide(identity,A) ),
file(unknown,unknown) ).
tff(f_25,axiom,
! [A,B] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
file(unknown,unknown) ).
tff(f_29,axiom,
! [A] : ( identity = divide(A,A) ),
file(unknown,unknown) ).
tff(f_23,axiom,
! [A,B,C] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
file(unknown,unknown) ).
tff(f_31,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file(unknown,unknown) ).
tff(c_6,plain,
! [A_6] : ( divide(identity,A_6) = inverse(A_6) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_4,plain,
! [A_4,B_5] : ( divide(A_4,divide(identity,B_5)) = multiply(A_4,B_5) ),
inference(cnfTransformation,[status(thm)],[f_25]) ).
tff(c_11,plain,
! [A_4,B_5] : ( divide(A_4,inverse(B_5)) = multiply(A_4,B_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4]) ).
tff(c_42,plain,
! [A_10,B_11] : ( divide(A_10,inverse(B_11)) = multiply(A_10,B_11) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4]) ).
tff(c_49,plain,
! [B_11] : ( inverse(inverse(B_11)) = multiply(identity,B_11) ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_6]) ).
tff(c_20,plain,
! [A_9] : ( divide(identity,A_9) = inverse(A_9) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_8,plain,
! [A_7] : ( divide(A_7,A_7) = identity ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_27,plain,
inverse(identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20,c_8]) ).
tff(c_70,plain,
! [B_12] : ( multiply(inverse(B_12),B_12) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_8]) ).
tff(c_77,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_27,c_70]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( divide(divide(identity,divide(divide(divide(A_1,B_2),C_3),A_1)),C_3) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_183,plain,
! [A_17,B_18,C_19] : ( divide(inverse(divide(divide(divide(A_17,B_18),C_19),A_17)),C_19) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2]) ).
tff(c_224,plain,
! [A_17,B_18] : ( divide(inverse(divide(identity,A_17)),divide(A_17,B_18)) = B_18 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_183]) ).
tff(c_305,plain,
! [A_23,B_24] : ( divide(multiply(identity,A_23),divide(A_23,B_24)) = B_24 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_224]) ).
tff(c_345,plain,
! [A_6] : ( divide(multiply(identity,identity),inverse(A_6)) = A_6 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_305]) ).
tff(c_355,plain,
! [A_6] : ( multiply(identity,A_6) = A_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_77,c_345]) ).
tff(c_419,plain,
! [B_11] : ( inverse(inverse(B_11)) = B_11 ),
inference(demodulation,[status(thm),theory(equality)],[c_355,c_49]) ).
tff(c_232,plain,
! [A_17,B_18] : ( divide(multiply(identity,A_17),divide(A_17,B_18)) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_224]) ).
tff(c_415,plain,
! [A_17,B_18] : ( divide(A_17,divide(A_17,B_18)) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_355,c_232]) ).
tff(c_214,plain,
! [A_17,B_18,B_5] : ( multiply(inverse(divide(divide(divide(A_17,B_18),inverse(B_5)),A_17)),B_5) = B_18 ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_183]) ).
tff(c_567,plain,
! [A_31,B_32,B_33] : ( multiply(inverse(divide(multiply(divide(A_31,B_32),B_33),A_31)),B_33) = B_32 ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_214]) ).
tff(c_611,plain,
! [B_33,A_7] : ( multiply(inverse(divide(multiply(identity,B_33),A_7)),B_33) = A_7 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_567]) ).
tff(c_765,plain,
! [B_38,A_39] : ( multiply(inverse(divide(B_38,A_39)),B_38) = A_39 ),
inference(demodulation,[status(thm),theory(equality)],[c_355,c_611]) ).
tff(c_1652,plain,
! [B_59,A_60] : ( multiply(inverse(B_59),A_60) = divide(A_60,B_59) ),
inference(superposition,[status(thm),theory(equality)],[c_415,c_765]) ).
tff(c_2103,plain,
! [A_68,B_69] : ( divide(A_68,inverse(B_69)) = multiply(B_69,A_68) ),
inference(superposition,[status(thm),theory(equality)],[c_419,c_1652]) ).
tff(c_220,plain,
! [C_19,A_7] : ( divide(inverse(divide(divide(identity,C_19),A_7)),C_19) = A_7 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_183]) ).
tff(c_233,plain,
! [C_20,A_21] : ( divide(inverse(divide(inverse(C_20),A_21)),C_20) = A_21 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_220]) ).
tff(c_269,plain,
! [A_21] : ( divide(inverse(divide(identity,A_21)),identity) = A_21 ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_233]) ).
tff(c_279,plain,
! [A_21] : ( divide(multiply(identity,A_21),identity) = A_21 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_269]) ).
tff(c_416,plain,
! [A_21] : ( divide(A_21,identity) = A_21 ),
inference(demodulation,[status(thm),theory(equality)],[c_355,c_279]) ).
tff(c_59,plain,
! [A_10] : ( multiply(A_10,identity) = divide(A_10,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_42]) ).
tff(c_442,plain,
! [A_10] : ( multiply(A_10,identity) = A_10 ),
inference(demodulation,[status(thm),theory(equality)],[c_416,c_59]) ).
tff(c_585,plain,
! [A_31,B_32] : ( inverse(divide(multiply(divide(A_31,B_32),identity),A_31)) = B_32 ),
inference(superposition,[status(thm),theory(equality)],[c_442,c_567]) ).
tff(c_812,plain,
! [A_40,B_41] : ( inverse(divide(divide(A_40,B_41),A_40)) = B_41 ),
inference(demodulation,[status(thm),theory(equality)],[c_442,c_585]) ).
tff(c_845,plain,
! [B_18,A_17] : ( inverse(divide(B_18,A_17)) = divide(A_17,B_18) ),
inference(superposition,[status(thm),theory(equality)],[c_415,c_812]) ).
tff(c_2109,plain,
! [B_69,A_68] : ( divide(inverse(B_69),A_68) = inverse(multiply(B_69,A_68)) ),
inference(superposition,[status(thm),theory(equality)],[c_2103,c_845]) ).
tff(c_1410,plain,
! [A_54,B_55,C_56] : ( divide(inverse(divide(divide(multiply(A_54,B_55),C_56),A_54)),C_56) = inverse(B_55) ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_183]) ).
tff(c_231,plain,
! [C_19,A_7] : ( divide(inverse(divide(inverse(C_19),A_7)),C_19) = A_7 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_220]) ).
tff(c_1438,plain,
! [B_55,A_54,C_56] : ( divide(inverse(inverse(B_55)),divide(divide(multiply(A_54,B_55),C_56),A_54)) = C_56 ),
inference(superposition,[status(thm),theory(equality)],[c_1410,c_231]) ).
tff(c_7697,plain,
! [B_135,A_136,C_137] : ( divide(B_135,divide(divide(multiply(A_136,B_135),C_137),A_136)) = C_137 ),
inference(demodulation,[status(thm),theory(equality)],[c_419,c_1438]) ).
tff(c_15573,plain,
! [A_199,B_200,B_201] : ( divide(multiply(A_199,B_200),B_201) = divide(B_200,divide(B_201,A_199)) ),
inference(superposition,[status(thm),theory(equality)],[c_415,c_7697]) ).
tff(c_1740,plain,
! [A_60,B_11] : ( divide(A_60,inverse(B_11)) = multiply(B_11,A_60) ),
inference(superposition,[status(thm),theory(equality)],[c_419,c_1652]) ).
tff(c_15660,plain,
! [B_200,B_11,A_199] : ( divide(B_200,divide(inverse(B_11),A_199)) = multiply(B_11,multiply(A_199,B_200)) ),
inference(superposition,[status(thm),theory(equality)],[c_15573,c_1740]) ).
tff(c_15848,plain,
! [B_200,B_11,A_199] : ( multiply(B_200,multiply(B_11,A_199)) = multiply(B_11,multiply(A_199,B_200)) ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_2109,c_15660]) ).
tff(c_656,plain,
! [A_35,B_36] : ( divide(A_35,divide(A_35,B_36)) = B_36 ),
inference(demodulation,[status(thm),theory(equality)],[c_355,c_232]) ).
tff(c_933,plain,
! [A_44,B_45] : ( divide(A_44,multiply(A_44,B_45)) = inverse(B_45) ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_656]) ).
tff(c_620,plain,
! [B_33,A_7] : ( multiply(inverse(divide(B_33,A_7)),B_33) = A_7 ),
inference(demodulation,[status(thm),theory(equality)],[c_355,c_611]) ).
tff(c_945,plain,
! [B_45,A_44] : ( multiply(inverse(inverse(B_45)),A_44) = multiply(A_44,B_45) ),
inference(superposition,[status(thm),theory(equality)],[c_933,c_620]) ).
tff(c_996,plain,
! [B_45,A_44] : ( multiply(B_45,A_44) = multiply(A_44,B_45) ),
inference(demodulation,[status(thm),theory(equality)],[c_419,c_945]) ).
tff(c_10,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_1006,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm),theory(equality)],[c_996,c_10]) ).
tff(c_30329,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_15848,c_1006]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP543-1 : TPTP v9.0.0. Released v2.6.0.
% 0.10/0.13 % 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 : n027.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 21:55:36 EDT 2025
% 0.12/0.33 % CPUTime :
% 12.19/4.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.19/4.51
% 12.19/4.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------