%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP592-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 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 : n012.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 06:26:36 PM UTC 2025
% Result : Unsatisfiable 5.29s 2.24s
% Output : CNFRefutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 107 ( 107 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(double_divide,type,
double_divide: ( $i * $i ) > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(f_26,axiom,
! [A,B] : ( multiply(A,B) = inverse(double_divide(B,A)) ),
file(unknown,unknown) ).
tff(f_24,axiom,
! [A,B,C] : ( double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C ),
file(unknown,unknown) ).
tff(f_28,axiom,
multiply(a,b) != multiply(b,a),
file(unknown,unknown) ).
tff(c_4,plain,
! [B_5,A_4] : ( inverse(double_divide(B_5,A_4)) = multiply(A_4,B_5) ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( double_divide(inverse(double_divide(double_divide(A_1,B_2),inverse(double_divide(A_1,inverse(C_3))))),B_2) = C_3 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_17,plain,
! [C_8,A_9,B_10] : ( double_divide(multiply(multiply(inverse(C_8),A_9),double_divide(A_9,B_10)),B_10) = C_8 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_2]) ).
tff(c_38,plain,
! [B_11,C_12,A_13] : ( multiply(B_11,multiply(multiply(inverse(C_12),A_13),double_divide(A_13,B_11))) = inverse(C_12) ),
inference(superposition,[status(thm),theory(equality)],[c_17,c_4]) ).
tff(c_62,plain,
! [B_11,A_4,B_5,A_13] : ( multiply(B_11,multiply(multiply(multiply(A_4,B_5),A_13),double_divide(A_13,B_11))) = inverse(double_divide(B_5,A_4)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_38]) ).
tff(c_65,plain,
! [B_11,A_4,B_5,A_13] : ( multiply(B_11,multiply(multiply(multiply(A_4,B_5),A_13),double_divide(A_13,B_11))) = multiply(A_4,B_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_62]) ).
tff(c_26,plain,
! [B_10,C_8,A_9] : ( multiply(B_10,multiply(multiply(inverse(C_8),A_9),double_divide(A_9,B_10))) = inverse(C_8) ),
inference(superposition,[status(thm),theory(equality)],[c_17,c_4]) ).
tff(c_7,plain,
! [C_3,A_1,B_2] : ( double_divide(multiply(multiply(inverse(C_3),A_1),double_divide(A_1,B_2)),B_2) = C_3 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_2]) ).
tff(c_102,plain,
! [C_18,C_19,A_20,B_21] : ( double_divide(multiply(multiply(inverse(C_18),multiply(multiply(inverse(C_19),A_20),double_divide(A_20,B_21))),C_19),B_21) = C_18 ),
inference(superposition,[status(thm),theory(equality)],[c_17,c_7]) ).
tff(c_149,plain,
! [C_22,C_23] : ( double_divide(multiply(inverse(C_22),C_22),inverse(C_23)) = C_23 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_102]) ).
tff(c_179,plain,
! [C_24,C_25] : ( multiply(inverse(C_24),multiply(inverse(C_25),C_25)) = inverse(C_24) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_4]) ).
tff(c_137,plain,
! [C_8,C_18] : ( double_divide(multiply(inverse(C_8),C_8),inverse(C_18)) = C_18 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_102]) ).
tff(c_220,plain,
! [C_26,C_27] : ( double_divide(inverse(multiply(inverse(C_26),C_26)),inverse(C_27)) = C_27 ),
inference(superposition,[status(thm),theory(equality)],[c_179,c_137]) ).
tff(c_238,plain,
! [C_27,C_26] : ( multiply(inverse(C_27),inverse(multiply(inverse(C_26),C_26))) = inverse(C_27) ),
inference(superposition,[status(thm),theory(equality)],[c_220,c_4]) ).
tff(c_190,plain,
! [C_25,C_18] : ( double_divide(inverse(multiply(inverse(C_25),C_25)),inverse(C_18)) = C_18 ),
inference(superposition,[status(thm),theory(equality)],[c_179,c_137]) ).
tff(c_167,plain,
! [C_23,C_22] : ( multiply(inverse(C_23),multiply(inverse(C_22),C_22)) = inverse(C_23) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_4]) ).
tff(c_348,plain,
! [C_32,A_33,B_34] : ( double_divide(multiply(inverse(C_32),C_32),multiply(A_33,B_34)) = double_divide(B_34,A_33) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_149]) ).
tff(c_363,plain,
! [C_3,C_32,B_34,A_33] : ( double_divide(multiply(multiply(inverse(C_3),multiply(inverse(C_32),C_32)),double_divide(B_34,A_33)),multiply(A_33,B_34)) = C_3 ),
inference(superposition,[status(thm),theory(equality)],[c_348,c_7]) ).
tff(c_479,plain,
! [C_38,B_39,A_40] : ( double_divide(multiply(inverse(C_38),double_divide(B_39,A_40)),multiply(A_40,B_39)) = C_38 ),
inference(demodulation,[status(thm),theory(equality)],[c_167,c_363]) ).
tff(c_532,plain,
! [C_38,C_18,C_25] : ( double_divide(multiply(inverse(C_38),C_18),multiply(inverse(C_18),inverse(multiply(inverse(C_25),C_25)))) = C_38 ),
inference(superposition,[status(thm),theory(equality)],[c_190,c_479]) ).
tff(c_564,plain,
! [C_41,C_42] : ( double_divide(multiply(inverse(C_41),C_42),inverse(C_42)) = C_41 ),
inference(demodulation,[status(thm),theory(equality)],[c_238,c_532]) ).
tff(c_621,plain,
! [C_43,C_44] : ( multiply(inverse(C_43),multiply(inverse(C_44),C_43)) = inverse(C_44) ),
inference(superposition,[status(thm),theory(equality)],[c_564,c_4]) ).
tff(c_559,plain,
! [C_38,C_18] : ( double_divide(multiply(inverse(C_38),C_18),inverse(C_18)) = C_38 ),
inference(demodulation,[status(thm),theory(equality)],[c_238,c_532]) ).
tff(c_1126,plain,
! [C_55,C_56] : ( double_divide(inverse(C_55),inverse(multiply(inverse(C_55),C_56))) = C_56 ),
inference(superposition,[status(thm),theory(equality)],[c_621,c_559]) ).
tff(c_1150,plain,
! [C_25,C_56] : ( multiply(inverse(multiply(inverse(C_25),C_25)),C_56) = C_56 ),
inference(superposition,[status(thm),theory(equality)],[c_1126,c_190]) ).
tff(c_601,plain,
! [C_23,C_22] : ( double_divide(inverse(C_23),inverse(multiply(inverse(C_22),C_22))) = C_23 ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_564]) ).
tff(c_1223,plain,
! [C_57,C_58] : ( multiply(inverse(multiply(inverse(C_57),C_57)),C_58) = C_58 ),
inference(superposition,[status(thm),theory(equality)],[c_1126,c_190]) ).
tff(c_1396,plain,
! [C_59,C_60] : ( multiply(inverse(C_59),C_59) = double_divide(C_60,inverse(C_60)) ),
inference(superposition,[status(thm),theory(equality)],[c_1223,c_559]) ).
tff(c_1402,plain,
! [C_60,C_56] : ( multiply(inverse(double_divide(C_60,inverse(C_60))),C_56) = C_56 ),
inference(superposition,[status(thm),theory(equality)],[c_1396,c_1150]) ).
tff(c_1563,plain,
! [C_61,C_62] : ( multiply(multiply(inverse(C_61),C_61),C_62) = C_62 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1402]) ).
tff(c_1802,plain,
! [B_67,C_68] : ( multiply(B_67,double_divide(C_68,B_67)) = inverse(C_68) ),
inference(superposition,[status(thm),theory(equality)],[c_1563,c_26]) ).
tff(c_1915,plain,
! [C_22,C_23] : ( multiply(inverse(multiply(inverse(C_22),C_22)),C_23) = inverse(inverse(C_23)) ),
inference(superposition,[status(thm),theory(equality)],[c_601,c_1802]) ).
tff(c_1957,plain,
! [C_23] : ( inverse(inverse(C_23)) = C_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_1150,c_1915]) ).
tff(c_1607,plain,
! [B_10,C_61] : ( multiply(B_10,double_divide(C_61,B_10)) = inverse(C_61) ),
inference(superposition,[status(thm),theory(equality)],[c_1563,c_26]) ).
tff(c_1961,plain,
! [C_69] : ( inverse(inverse(C_69)) = C_69 ),
inference(demodulation,[status(thm),theory(equality)],[c_1150,c_1915]) ).
tff(c_630,plain,
! [C_44,C_43] : ( double_divide(inverse(C_44),inverse(multiply(inverse(C_44),C_43))) = C_43 ),
inference(superposition,[status(thm),theory(equality)],[c_621,c_559]) ).
tff(c_1985,plain,
! [C_69,C_43] : ( double_divide(C_69,inverse(multiply(inverse(inverse(C_69)),C_43))) = C_43 ),
inference(superposition,[status(thm),theory(equality)],[c_1961,c_630]) ).
tff(c_2256,plain,
! [C_74,C_75] : ( double_divide(C_74,inverse(multiply(C_74,C_75))) = C_75 ),
inference(demodulation,[status(thm),theory(equality)],[c_1957,c_1985]) ).
tff(c_2317,plain,
! [B_10,C_61] : ( double_divide(B_10,inverse(inverse(C_61))) = double_divide(C_61,B_10) ),
inference(superposition,[status(thm),theory(equality)],[c_1607,c_2256]) ).
tff(c_2387,plain,
! [C_76,B_77] : ( double_divide(C_76,B_77) = double_divide(B_77,C_76) ),
inference(demodulation,[status(thm),theory(equality)],[c_1957,c_2317]) ).
tff(c_3578,plain,
! [B_94,C_95] : ( inverse(double_divide(B_94,C_95)) = multiply(B_94,C_95) ),
inference(superposition,[status(thm),theory(equality)],[c_2387,c_4]) ).
tff(c_3662,plain,
! [B_10,B_94,C_95,A_9] : ( multiply(B_10,multiply(multiply(multiply(B_94,C_95),A_9),double_divide(A_9,B_10))) = inverse(double_divide(B_94,C_95)) ),
inference(superposition,[status(thm),theory(equality)],[c_3578,c_26]) ).
tff(c_3729,plain,
! [C_95,B_94] : ( multiply(C_95,B_94) = multiply(B_94,C_95) ),
inference(demodulation,[status(thm),theory(equality)],[c_65,c_4,c_3662]) ).
tff(c_6,plain,
multiply(b,a) != multiply(a,b),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_3753,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3729,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP592-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.00/0.09 % 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
% 0.09/0.28 % Computer : n012.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Apr 7 21:56:45 EDT 2025
% 0.09/0.28 % CPUTime :
% 5.29/2.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.29/2.24
% 5.29/2.24 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------