%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP551-1 : 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 : n009.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 06:26:29 PM UTC 2025
% Result : Unsatisfiable 12.27s 4.16s
% Output : CNFRefutation 12.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 51 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 : 5 ( 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 : 87 ( 87 !; 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,A),divide(divide(divide(B,A),C),B)) = C ),
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_8,plain,
! [A_7] : ( divide(A_7,A_7) = identity ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( divide(divide(identity,A_1),divide(divide(divide(B_2,A_1),C_3),B_2)) = C_3 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_183,plain,
! [A_17,B_18,C_19] : ( divide(inverse(A_17),divide(divide(divide(B_18,A_17),C_19),B_18)) = C_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2]) ).
tff(c_218,plain,
! [A_7,C_19] : ( divide(inverse(A_7),divide(divide(identity,C_19),A_7)) = C_19 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_183]) ).
tff(c_229,plain,
! [A_7,C_19] : ( divide(inverse(A_7),divide(inverse(C_19),A_7)) = C_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_218]) ).
tff(c_20,plain,
! [A_9] : ( divide(identity,A_9) = inverse(A_9) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_27,plain,
inverse(identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20,c_8]) ).
tff(c_329,plain,
! [A_24,C_25] : ( divide(inverse(A_24),divide(divide(inverse(A_24),C_25),identity)) = C_25 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_183]) ).
tff(c_367,plain,
! [A_24] : ( divide(inverse(A_24),divide(identity,identity)) = inverse(A_24) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_329]) ).
tff(c_376,plain,
! [A_24] : ( divide(inverse(A_24),identity) = inverse(A_24) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_367]) ).
tff(c_360,plain,
! [C_25] : ( divide(identity,divide(divide(inverse(identity),C_25),identity)) = C_25 ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_329]) ).
tff(c_374,plain,
! [C_25] : ( inverse(divide(inverse(C_25),identity)) = C_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_27,c_360]) ).
tff(c_423,plain,
! [C_25] : ( inverse(inverse(C_25)) = C_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_376,c_374]) ).
tff(c_222,plain,
! [A_17,B_18] : ( divide(inverse(A_17),divide(identity,B_18)) = divide(B_18,A_17) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_183]) ).
tff(c_231,plain,
! [A_20,B_21] : ( multiply(inverse(A_20),B_21) = divide(B_21,A_20) ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_6,c_222]) ).
tff(c_258,plain,
! [B_21] : ( multiply(identity,B_21) = divide(B_21,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_231]) ).
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_268,plain,
! [B_11] : ( inverse(inverse(B_11)) = divide(B_11,identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_258,c_49]) ).
tff(c_500,plain,
! [B_29] : ( divide(B_29,identity) = B_29 ),
inference(demodulation,[status(thm),theory(equality)],[c_423,c_268]) ).
tff(c_12,plain,
! [A_1,B_2,C_3] : ( divide(inverse(A_1),divide(divide(divide(B_2,A_1),C_3),B_2)) = C_3 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2]) ).
tff(c_506,plain,
! [B_29,C_3] : ( divide(inverse(identity),divide(divide(B_29,C_3),B_29)) = C_3 ),
inference(superposition,[status(thm),theory(equality)],[c_500,c_12]) ).
tff(c_944,plain,
! [B_43,C_44] : ( inverse(divide(divide(B_43,C_44),B_43)) = C_44 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_27,c_506]) ).
tff(c_998,plain,
! [C_19,A_7] : ( inverse(divide(C_19,inverse(A_7))) = divide(inverse(C_19),A_7) ),
inference(superposition,[status(thm),theory(equality)],[c_229,c_944]) ).
tff(c_1027,plain,
! [C_19,A_7] : ( divide(inverse(C_19),A_7) = inverse(multiply(C_19,A_7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_998]) ).
tff(c_230,plain,
! [A_17,B_18] : ( multiply(inverse(A_17),B_18) = divide(B_18,A_17) ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_6,c_222]) ).
tff(c_542,plain,
! [A_30,C_31] : ( divide(inverse(A_30),divide(inverse(C_31),A_30)) = C_31 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_218]) ).
tff(c_574,plain,
! [B_5,C_31] : ( divide(inverse(inverse(B_5)),multiply(inverse(C_31),B_5)) = C_31 ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_542]) ).
tff(c_590,plain,
! [B_5,C_31] : ( divide(B_5,divide(B_5,C_31)) = C_31 ),
inference(demodulation,[status(thm),theory(equality)],[c_423,c_230,c_574]) ).
tff(c_449,plain,
! [B_11] : ( divide(B_11,identity) = B_11 ),
inference(demodulation,[status(thm),theory(equality)],[c_423,c_268]) ).
tff(c_498,plain,
! [B_21] : ( multiply(identity,B_21) = B_21 ),
inference(demodulation,[status(thm),theory(equality)],[c_449,c_258]) ).
tff(c_201,plain,
! [B_5,A_4,C_19] : ( divide(inverse(inverse(B_5)),divide(divide(multiply(A_4,B_5),C_19),A_4)) = C_19 ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_183]) ).
tff(c_228,plain,
! [B_5,A_4,C_19] : ( divide(multiply(identity,B_5),divide(divide(multiply(A_4,B_5),C_19),A_4)) = C_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_201]) ).
tff(c_1816,plain,
! [B_62,A_63,C_64] : ( divide(B_62,divide(divide(multiply(A_63,B_62),C_64),A_63)) = C_64 ),
inference(demodulation,[status(thm),theory(equality)],[c_498,c_228]) ).
tff(c_16356,plain,
! [A_198,B_199,C_200] : ( divide(multiply(A_198,B_199),C_200) = divide(B_199,divide(C_200,A_198)) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_1816]) ).
tff(c_450,plain,
! [C_28] : ( inverse(inverse(C_28)) = C_28 ),
inference(demodulation,[status(thm),theory(equality)],[c_376,c_374]) ).
tff(c_468,plain,
! [B_18,C_28] : ( divide(B_18,inverse(C_28)) = multiply(C_28,B_18) ),
inference(superposition,[status(thm),theory(equality)],[c_450,c_230]) ).
tff(c_16507,plain,
! [B_199,C_28,A_198] : ( divide(B_199,divide(inverse(C_28),A_198)) = multiply(C_28,multiply(A_198,B_199)) ),
inference(superposition,[status(thm),theory(equality)],[c_16356,c_468]) ).
tff(c_16697,plain,
! [C_28,A_198,B_199] : ( multiply(C_28,multiply(A_198,B_199)) = multiply(B_199,multiply(C_28,A_198)) ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_1027,c_16507]) ).
tff(c_1101,plain,
! [B_47,C_48] : ( divide(B_47,inverse(C_48)) = multiply(C_48,B_47) ),
inference(superposition,[status(thm),theory(equality)],[c_450,c_230]) ).
tff(c_1144,plain,
! [C_48,B_47] : ( multiply(C_48,B_47) = multiply(B_47,C_48) ),
inference(superposition,[status(thm),theory(equality)],[c_1101,c_11]) ).
tff(c_10,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_1193,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm),theory(equality)],[c_1144,c_10]) ).
tff(c_22862,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16697,c_16697,c_1193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP551-1 : 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
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 21:55:11 EDT 2025
% 0.14/0.34 % CPUTime :
% 12.27/4.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.27/4.17
% 12.27/4.17 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------