%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP585-1 : 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 : n031.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 06:26:34 PM UTC 2025
% Result : Unsatisfiable 12.58s 4.30s
% Output : CNFRefutation 12.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 101 ( 101 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > b1 > a1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a1,type,
a1: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(double_divide,type,
double_divide: ( $i * $i ) > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b1,type,
b1: $i ).
tff(f_25,axiom,
! [A,B] : ( multiply(A,B) = inverse(double_divide(B,A)) ),
file(unknown,unknown) ).
tff(f_23,axiom,
! [A,B,C] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C ),
file(unknown,unknown) ).
tff(f_27,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
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_25]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( double_divide(A_1,inverse(double_divide(inverse(double_divide(double_divide(A_1,B_2),inverse(C_3))),B_2))) = C_3 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_17,plain,
! [A_8,B_9,C_10] : ( double_divide(A_8,multiply(B_9,multiply(inverse(C_10),double_divide(A_8,B_9)))) = C_10 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_2]) ).
tff(c_26,plain,
! [B_9,C_10,A_8] : ( multiply(multiply(B_9,multiply(inverse(C_10),double_divide(A_8,B_9))),A_8) = inverse(C_10) ),
inference(superposition,[status(thm),theory(equality)],[c_17,c_4]) ).
tff(c_7,plain,
! [A_1,B_2,C_3] : ( double_divide(A_1,multiply(B_2,multiply(inverse(C_3),double_divide(A_1,B_2)))) = C_3 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_2]) ).
tff(c_90,plain,
! [A_18,B_19,C_20,C_21] : ( double_divide(A_18,multiply(multiply(B_19,multiply(inverse(C_20),double_divide(A_18,B_19))),multiply(inverse(C_21),C_20))) = C_21 ),
inference(superposition,[status(thm),theory(equality)],[c_17,c_7]) ).
tff(c_133,plain,
! [C_22,C_23] : ( double_divide(multiply(inverse(C_22),C_23),inverse(C_23)) = C_22 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_90]) ).
tff(c_306,plain,
! [A_32,B_33,C_34] : ( double_divide(multiply(multiply(A_32,B_33),C_34),inverse(C_34)) = double_divide(B_33,A_32) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_133]) ).
tff(c_324,plain,
! [C_34,A_32,B_33] : ( multiply(inverse(C_34),multiply(multiply(A_32,B_33),C_34)) = inverse(double_divide(B_33,A_32)) ),
inference(superposition,[status(thm),theory(equality)],[c_306,c_4]) ).
tff(c_419,plain,
! [C_38,A_39,B_40] : ( multiply(inverse(C_38),multiply(multiply(A_39,B_40),C_38)) = multiply(A_39,B_40) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_324]) ).
tff(c_163,plain,
! [C_24,C_25] : ( multiply(inverse(C_24),multiply(inverse(C_25),C_24)) = inverse(C_25) ),
inference(superposition,[status(thm),theory(equality)],[c_133,c_4]) ).
tff(c_121,plain,
! [C_21,C_10] : ( double_divide(multiply(inverse(C_21),C_10),inverse(C_10)) = C_21 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_90]) ).
tff(c_172,plain,
! [C_25,C_24] : ( double_divide(inverse(C_25),inverse(multiply(inverse(C_25),C_24))) = C_24 ),
inference(superposition,[status(thm),theory(equality)],[c_163,c_121]) ).
tff(c_1038,plain,
! [C_58,A_59,B_60] : ( double_divide(inverse(C_58),inverse(multiply(A_59,B_60))) = multiply(multiply(A_59,B_60),C_58) ),
inference(superposition,[status(thm),theory(equality)],[c_419,c_172]) ).
tff(c_1054,plain,
! [C_58,B_60] : ( multiply(multiply(inverse(C_58),B_60),C_58) = B_60 ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_172]) ).
tff(c_1113,plain,
! [C_61,B_62] : ( multiply(multiply(inverse(C_61),B_62),C_61) = B_62 ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_172]) ).
tff(c_344,plain,
! [C_34,A_32,B_33] : ( multiply(inverse(C_34),multiply(multiply(A_32,B_33),C_34)) = multiply(A_32,B_33) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_324]) ).
tff(c_1154,plain,
! [C_61,B_62,C_34] : ( multiply(multiply(inverse(C_61),B_62),C_61) = multiply(inverse(C_34),multiply(B_62,C_34)) ),
inference(superposition,[status(thm),theory(equality)],[c_1113,c_344]) ).
tff(c_1221,plain,
! [C_34,B_62] : ( multiply(inverse(C_34),multiply(B_62,C_34)) = B_62 ),
inference(demodulation,[status(thm),theory(equality)],[c_1054,c_1154]) ).
tff(c_1732,plain,
! [C_77,A_78] : ( multiply(inverse(C_77),double_divide(A_78,inverse(A_78))) = inverse(C_77) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1113]) ).
tff(c_1826,plain,
! [C_79,A_80] : ( multiply(inverse(C_79),C_79) = double_divide(A_80,inverse(A_80)) ),
inference(superposition,[status(thm),theory(equality)],[c_1732,c_1054]) ).
tff(c_1867,plain,
! [A_80,C_79] : ( multiply(double_divide(A_80,inverse(A_80)),C_79) = C_79 ),
inference(superposition,[status(thm),theory(equality)],[c_1826,c_1054]) ).
tff(c_1755,plain,
! [C_77,A_78] : ( multiply(inverse(C_77),C_77) = double_divide(A_78,inverse(A_78)) ),
inference(superposition,[status(thm),theory(equality)],[c_1732,c_1054]) ).
tff(c_160,plain,
! [C_22,B_5,A_4] : ( double_divide(multiply(inverse(C_22),double_divide(B_5,A_4)),multiply(A_4,B_5)) = C_22 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_133]) ).
tff(c_1770,plain,
! [C_77,A_78] : ( double_divide(inverse(C_77),multiply(inverse(A_78),A_78)) = C_77 ),
inference(superposition,[status(thm),theory(equality)],[c_1732,c_160]) ).
tff(c_2274,plain,
! [C_89,A_90] : ( double_divide(inverse(C_89),double_divide(A_90,inverse(A_90))) = C_89 ),
inference(demodulation,[status(thm),theory(equality)],[c_1755,c_1770]) ).
tff(c_2304,plain,
! [C_89,A_90,C_3] : ( double_divide(inverse(C_89),multiply(double_divide(A_90,inverse(A_90)),multiply(inverse(C_3),C_89))) = C_3 ),
inference(superposition,[status(thm),theory(equality)],[c_2274,c_7]) ).
tff(c_2529,plain,
! [C_96,C_97] : ( double_divide(inverse(C_96),multiply(inverse(C_97),C_96)) = C_97 ),
inference(demodulation,[status(thm),theory(equality)],[c_1867,c_2304]) ).
tff(c_2602,plain,
! [B_98,C_99] : ( double_divide(inverse(multiply(B_98,C_99)),B_98) = C_99 ),
inference(superposition,[status(thm),theory(equality)],[c_1221,c_2529]) ).
tff(c_195,plain,
! [C_26,C_27] : ( double_divide(inverse(C_26),inverse(multiply(inverse(C_26),C_27))) = C_27 ),
inference(superposition,[status(thm),theory(equality)],[c_163,c_121]) ).
tff(c_230,plain,
! [C_28,C_29] : ( multiply(inverse(multiply(inverse(C_28),C_29)),inverse(C_28)) = inverse(C_29) ),
inference(superposition,[status(thm),theory(equality)],[c_195,c_4]) ).
tff(c_239,plain,
! [C_28,C_29] : ( double_divide(inverse(multiply(inverse(C_28),C_29)),inverse(inverse(C_29))) = inverse(C_28) ),
inference(superposition,[status(thm),theory(equality)],[c_230,c_172]) ).
tff(c_2633,plain,
! [C_99] : ( inverse(inverse(C_99)) = C_99 ),
inference(superposition,[status(thm),theory(equality)],[c_2602,c_239]) ).
tff(c_437,plain,
! [C_38,A_39,B_40] : ( double_divide(inverse(C_38),inverse(multiply(A_39,B_40))) = multiply(multiply(A_39,B_40),C_38) ),
inference(superposition,[status(thm),theory(equality)],[c_419,c_172]) ).
tff(c_1119,plain,
! [C_61,B_62,C_38] : ( multiply(multiply(multiply(inverse(C_61),B_62),C_61),C_38) = double_divide(inverse(C_38),inverse(B_62)) ),
inference(superposition,[status(thm),theory(equality)],[c_1113,c_437]) ).
tff(c_1212,plain,
! [C_38,B_62] : ( double_divide(inverse(C_38),inverse(B_62)) = multiply(B_62,C_38) ),
inference(demodulation,[status(thm),theory(equality)],[c_1054,c_1119]) ).
tff(c_4068,plain,
! [B_120,C_121] : ( multiply(B_120,multiply(inverse(B_120),C_121)) = C_121 ),
inference(superposition,[status(thm),theory(equality)],[c_2602,c_1212]) ).
tff(c_4124,plain,
! [C_58,C_121] : ( multiply(inverse(inverse(C_58)),C_121) = multiply(C_121,C_58) ),
inference(superposition,[status(thm),theory(equality)],[c_4068,c_1054]) ).
tff(c_4222,plain,
! [C_58,C_121] : ( multiply(C_58,C_121) = multiply(C_121,C_58) ),
inference(demodulation,[status(thm),theory(equality)],[c_2633,c_4124]) ).
tff(c_6,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_2336,plain,
! [A_91] : ( multiply(inverse(a1),a1) != double_divide(A_91,inverse(A_91)) ),
inference(superposition,[status(thm),theory(equality)],[c_1826,c_6]) ).
tff(c_2338,plain,
! [C_77] : ( multiply(inverse(a1),a1) != multiply(inverse(C_77),C_77) ),
inference(superposition,[status(thm),theory(equality)],[c_1755,c_2336]) ).
tff(c_15837,plain,
! [C_77] : ( multiply(a1,inverse(a1)) != multiply(C_77,inverse(C_77)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4222,c_4222,c_2338]) ).
tff(c_15841,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_15837]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP585-1 : TPTP v9.0.0. Released v2.6.0.
% 0.14/0.14 % 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
% 0.16/0.35 % Computer : n031.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Mon Apr 7 21:56:52 EDT 2025
% 0.16/0.36 % CPUTime :
% 12.58/4.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.58/4.31
% 12.58/4.31 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------