%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP459-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n026.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 06:26:17 PM UTC 2025
% Result : Unsatisfiable 8.90s 3.85s
% Output : CNFRefutation 9.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 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 : 73 ( 73 !; 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(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),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_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_2,plain,
! [A_1,B_2,C_3] : ( divide(divide(divide(A_1,A_1),divide(A_1,divide(B_2,divide(divide(identity,A_1),C_3)))),C_3) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_183,plain,
! [A_17,B_18,C_19] : ( divide(inverse(divide(A_17,divide(B_18,divide(inverse(A_17),C_19)))),C_19) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_8,c_2]) ).
tff(c_498,plain,
! [A_27,B_28] : ( divide(inverse(divide(A_27,divide(B_28,identity))),inverse(A_27)) = B_28 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_183]) ).
tff(c_558,plain,
! [B_28] : ( divide(inverse(identity),inverse(divide(B_28,identity))) = B_28 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_498]) ).
tff(c_567,plain,
! [B_28] : ( multiply(identity,divide(B_28,identity)) = B_28 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_27,c_558]) ).
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_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_229,plain,
! [B_18,C_19] : ( divide(inverse(inverse(divide(B_18,divide(inverse(identity),C_19)))),C_19) = B_18 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_183]) ).
tff(c_244,plain,
! [B_18,C_19] : ( divide(multiply(identity,multiply(B_18,C_19)),C_19) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_11,c_6,c_27,c_229]) ).
tff(c_569,plain,
! [B_29] : ( multiply(identity,divide(B_29,identity)) = B_29 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_27,c_558]) ).
tff(c_585,plain,
! [B_18] : ( multiply(identity,multiply(B_18,identity)) = multiply(identity,B_18) ),
inference(superposition,[status(thm),theory(equality)],[c_244,c_569]) ).
tff(c_601,plain,
! [B_18] : ( multiply(identity,B_18) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_567,c_59,c_585]) ).
tff(c_662,plain,
! [B_18,C_19] : ( divide(multiply(B_18,C_19),C_19) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_601,c_244]) ).
tff(c_665,plain,
! [B_11] : ( inverse(inverse(B_11)) = B_11 ),
inference(demodulation,[status(thm),theory(equality)],[c_601,c_49]) ).
tff(c_245,plain,
! [B_20,C_21] : ( divide(multiply(identity,multiply(B_20,C_21)),C_21) = B_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_11,c_6,c_27,c_229]) ).
tff(c_268,plain,
! [A_10] : ( divide(multiply(identity,divide(A_10,identity)),identity) = A_10 ),
inference(superposition,[status(thm),theory(equality)],[c_59,c_245]) ).
tff(c_568,plain,
! [A_10] : ( divide(A_10,identity) = A_10 ),
inference(demodulation,[status(thm),theory(equality)],[c_567,c_268]) ).
tff(c_53,plain,
! [B_11] : ( multiply(inverse(B_11),B_11) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_8]) ).
tff(c_218,plain,
! [A_17,B_18,B_5] : ( multiply(inverse(divide(A_17,divide(B_18,divide(inverse(A_17),inverse(B_5))))),B_5) = B_18 ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_183]) ).
tff(c_1032,plain,
! [A_44,B_45,B_46] : ( multiply(inverse(divide(A_44,divide(B_45,multiply(inverse(A_44),B_46)))),B_46) = B_45 ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_218]) ).
tff(c_1091,plain,
! [B_11,B_45] : ( multiply(inverse(divide(B_11,divide(B_45,identity))),B_11) = B_45 ),
inference(superposition,[status(thm),theory(equality)],[c_53,c_1032]) ).
tff(c_1181,plain,
! [B_49,B_50] : ( multiply(inverse(divide(B_49,B_50)),B_49) = B_50 ),
inference(demodulation,[status(thm),theory(equality)],[c_568,c_1091]) ).
tff(c_1201,plain,
! [B_49,B_50] : ( inverse(divide(B_49,B_50)) = divide(B_50,B_49) ),
inference(superposition,[status(thm),theory(equality)],[c_1181,c_662]) ).
tff(c_197,plain,
! [A_17,B_18,B_5] : ( multiply(inverse(divide(A_17,divide(B_18,divide(inverse(A_17),inverse(B_5))))),B_5) = B_18 ),
inference(superposition,[status(thm),theory(equality)],[c_183,c_11]) ).
tff(c_239,plain,
! [A_17,B_18,B_5] : ( multiply(inverse(divide(A_17,divide(B_18,multiply(inverse(A_17),B_5)))),B_5) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_197]) ).
tff(c_1567,plain,
! [B_59,A_60,B_61] : ( multiply(divide(divide(B_59,multiply(inverse(A_60),B_61)),A_60),B_61) = B_59 ),
inference(demodulation,[status(thm),theory(equality)],[c_1201,c_239]) ).
tff(c_1641,plain,
! [B_59,B_11,B_61] : ( multiply(divide(divide(B_59,multiply(B_11,B_61)),inverse(B_11)),B_61) = B_59 ),
inference(superposition,[status(thm),theory(equality)],[c_665,c_1567]) ).
tff(c_5186,plain,
! [B_123,B_124,B_125] : ( multiply(multiply(divide(B_123,multiply(B_124,B_125)),B_124),B_125) = B_123 ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_1641]) ).
tff(c_5332,plain,
! [B_18,B_124,B_125] : ( multiply(multiply(B_18,B_124),B_125) = multiply(B_18,multiply(B_124,B_125)) ),
inference(superposition,[status(thm),theory(equality)],[c_662,c_5186]) ).
tff(c_10,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_10017,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5332,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP459-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.10 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.29 % Computer : n026.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Apr 7 21:51:38 EDT 2025
% 0.09/0.30 % CPUTime :
% 8.90/3.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.90/3.86
% 8.90/3.86 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------