%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP607-1 : 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 : 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 06:26:38 PM UTC 2025
% Result : Unsatisfiable 72.88s 52.35s
% Output : CNFRefutation 73.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 112 ( 112 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > c3 > b3 > a3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a3,type,
a3: $i ).
tff(c3,type,
c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(double_divide,type,
double_divide: ( $i * $i ) > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b3,type,
b3: $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(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B ),
file(unknown,unknown) ).
tff(f_27,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
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(inverse(double_divide(A_1,inverse(double_divide(inverse(B_2),double_divide(A_1,C_3))))),C_3) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_17,plain,
! [A_8,C_9,B_10] : ( double_divide(multiply(multiply(double_divide(A_8,C_9),inverse(B_10)),A_8),C_9) = B_10 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_2]) ).
tff(c_26,plain,
! [C_9,A_8,B_10] : ( multiply(C_9,multiply(multiply(double_divide(A_8,C_9),inverse(B_10)),A_8)) = inverse(B_10) ),
inference(superposition,[status(thm),theory(equality)],[c_17,c_4]) ).
tff(c_7,plain,
! [A_1,C_3,B_2] : ( double_divide(multiply(multiply(double_divide(A_1,C_3),inverse(B_2)),A_1),C_3) = B_2 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_2]) ).
tff(c_90,plain,
! [B_18,B_19,A_20,C_21] : ( double_divide(multiply(multiply(B_18,inverse(B_19)),multiply(multiply(double_divide(A_20,C_21),inverse(B_18)),A_20)),C_21) = B_19 ),
inference(superposition,[status(thm),theory(equality)],[c_17,c_7]) ).
tff(c_133,plain,
! [B_22,B_23] : ( double_divide(inverse(B_22),multiply(B_22,inverse(B_23))) = B_23 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_90]) ).
tff(c_163,plain,
! [B_24,B_25] : ( multiply(multiply(B_24,inverse(B_25)),inverse(B_24)) = inverse(B_25) ),
inference(superposition,[status(thm),theory(equality)],[c_133,c_4]) ).
tff(c_187,plain,
! [B_24,A_4,B_5] : ( multiply(multiply(B_24,multiply(A_4,B_5)),inverse(B_24)) = inverse(double_divide(B_5,A_4)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_163]) ).
tff(c_419,plain,
! [B_38,A_39,B_40] : ( multiply(multiply(B_38,multiply(A_39,B_40)),inverse(B_38)) = multiply(A_39,B_40) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_187]) ).
tff(c_121,plain,
! [B_10,B_19] : ( double_divide(inverse(B_10),multiply(B_10,inverse(B_19))) = B_19 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_90]) ).
tff(c_172,plain,
! [B_24,B_25] : ( double_divide(inverse(multiply(B_24,inverse(B_25))),inverse(B_25)) = B_24 ),
inference(superposition,[status(thm),theory(equality)],[c_163,c_121]) ).
tff(c_1038,plain,
! [A_58,B_59,B_60] : ( double_divide(inverse(multiply(A_58,B_59)),inverse(B_60)) = multiply(B_60,multiply(A_58,B_59)) ),
inference(superposition,[status(thm),theory(equality)],[c_419,c_172]) ).
tff(c_1054,plain,
! [B_60,A_58] : ( multiply(B_60,multiply(A_58,inverse(B_60))) = A_58 ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_172]) ).
tff(c_1113,plain,
! [B_61,A_62] : ( multiply(B_61,multiply(A_62,inverse(B_61))) = A_62 ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_172]) ).
tff(c_194,plain,
! [B_24,A_4,B_5] : ( multiply(multiply(B_24,multiply(A_4,B_5)),inverse(B_24)) = multiply(A_4,B_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_187]) ).
tff(c_1154,plain,
! [B_24,A_62,B_61] : ( multiply(multiply(B_24,A_62),inverse(B_24)) = multiply(B_61,multiply(A_62,inverse(B_61))) ),
inference(superposition,[status(thm),theory(equality)],[c_1113,c_194]) ).
tff(c_1221,plain,
! [B_24,A_62] : ( multiply(multiply(B_24,A_62),inverse(B_24)) = A_62 ),
inference(demodulation,[status(thm),theory(equality)],[c_1054,c_1154]) ).
tff(c_1732,plain,
! [C_77,B_78] : ( multiply(double_divide(inverse(C_77),C_77),inverse(B_78)) = inverse(B_78) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1113]) ).
tff(c_1826,plain,
! [B_79,C_80] : ( multiply(B_79,inverse(B_79)) = double_divide(inverse(C_80),C_80) ),
inference(superposition,[status(thm),theory(equality)],[c_1732,c_1054]) ).
tff(c_1867,plain,
! [B_79,C_80] : ( multiply(B_79,double_divide(inverse(C_80),C_80)) = B_79 ),
inference(superposition,[status(thm),theory(equality)],[c_1826,c_1054]) ).
tff(c_1755,plain,
! [B_78,C_77] : ( multiply(B_78,inverse(B_78)) = double_divide(inverse(C_77),C_77) ),
inference(superposition,[status(thm),theory(equality)],[c_1732,c_1054]) ).
tff(c_1779,plain,
! [C_77,B_78] : ( double_divide(inverse(double_divide(inverse(C_77),C_77)),inverse(B_78)) = B_78 ),
inference(superposition,[status(thm),theory(equality)],[c_1732,c_121]) ).
tff(c_1818,plain,
! [C_77,B_78] : ( double_divide(multiply(C_77,inverse(C_77)),inverse(B_78)) = B_78 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1779]) ).
tff(c_2375,plain,
! [C_91,B_92] : ( double_divide(double_divide(inverse(C_91),C_91),inverse(B_92)) = B_92 ),
inference(demodulation,[status(thm),theory(equality)],[c_1755,c_1818]) ).
tff(c_2405,plain,
! [B_92,B_2,C_91] : ( double_divide(multiply(multiply(B_92,inverse(B_2)),double_divide(inverse(C_91),C_91)),inverse(B_92)) = B_2 ),
inference(superposition,[status(thm),theory(equality)],[c_2375,c_7]) ).
tff(c_3213,plain,
! [B_101,B_102] : ( double_divide(multiply(B_101,inverse(B_102)),inverse(B_101)) = B_102 ),
inference(demodulation,[status(thm),theory(equality)],[c_1867,c_2405]) ).
tff(c_3301,plain,
! [A_103,B_104] : ( double_divide(A_103,inverse(multiply(B_104,A_103))) = B_104 ),
inference(superposition,[status(thm),theory(equality)],[c_1221,c_3213]) ).
tff(c_195,plain,
! [B_26,B_27] : ( double_divide(inverse(multiply(B_26,inverse(B_27))),inverse(B_27)) = B_26 ),
inference(superposition,[status(thm),theory(equality)],[c_163,c_121]) ).
tff(c_230,plain,
! [B_28,B_29] : ( multiply(inverse(B_28),inverse(multiply(B_29,inverse(B_28)))) = inverse(B_29) ),
inference(superposition,[status(thm),theory(equality)],[c_195,c_4]) ).
tff(c_239,plain,
! [B_29,B_28] : ( double_divide(inverse(inverse(B_29)),inverse(multiply(B_29,inverse(B_28)))) = inverse(B_28) ),
inference(superposition,[status(thm),theory(equality)],[c_230,c_172]) ).
tff(c_3332,plain,
! [B_104] : ( inverse(inverse(B_104)) = B_104 ),
inference(superposition,[status(thm),theory(equality)],[c_3301,c_239]) ).
tff(c_437,plain,
! [A_39,B_40,B_38] : ( double_divide(inverse(multiply(A_39,B_40)),inverse(B_38)) = multiply(B_38,multiply(A_39,B_40)) ),
inference(superposition,[status(thm),theory(equality)],[c_419,c_172]) ).
tff(c_1119,plain,
! [B_38,B_61,A_62] : ( multiply(B_38,multiply(B_61,multiply(A_62,inverse(B_61)))) = double_divide(inverse(A_62),inverse(B_38)) ),
inference(superposition,[status(thm),theory(equality)],[c_1113,c_437]) ).
tff(c_1212,plain,
! [A_62,B_38] : ( double_divide(inverse(A_62),inverse(B_38)) = multiply(B_38,A_62) ),
inference(demodulation,[status(thm),theory(equality)],[c_1054,c_1119]) ).
tff(c_4894,plain,
! [B_125,A_126] : ( multiply(multiply(B_125,inverse(A_126)),A_126) = B_125 ),
inference(superposition,[status(thm),theory(equality)],[c_3301,c_1212]) ).
tff(c_4946,plain,
! [B_125,B_60] : ( multiply(B_125,inverse(inverse(B_60))) = multiply(B_60,B_125) ),
inference(superposition,[status(thm),theory(equality)],[c_4894,c_1054]) ).
tff(c_5050,plain,
! [B_60,B_125] : ( multiply(B_60,B_125) = multiply(B_125,B_60) ),
inference(demodulation,[status(thm),theory(equality)],[c_3332,c_4946]) ).
tff(c_54,plain,
! [A_14,C_15,A_16,B_17] : ( double_divide(multiply(multiply(double_divide(A_14,C_15),multiply(A_16,B_17)),A_14),C_15) = double_divide(B_17,A_16) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17]) ).
tff(c_69,plain,
! [C_15,A_14,A_16,B_17] : ( multiply(C_15,multiply(multiply(double_divide(A_14,C_15),multiply(A_16,B_17)),A_14)) = inverse(double_divide(B_17,A_16)) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_4]) ).
tff(c_87,plain,
! [C_15,A_14,A_16,B_17] : ( multiply(C_15,multiply(multiply(double_divide(A_14,C_15),multiply(A_16,B_17)),A_14)) = multiply(A_16,B_17) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_69]) ).
tff(c_1138,plain,
! [A_62,A_14,C_15] : ( multiply(A_62,inverse(double_divide(A_14,C_15))) = multiply(C_15,multiply(A_62,A_14)) ),
inference(superposition,[status(thm),theory(equality)],[c_1113,c_87]) ).
tff(c_1217,plain,
! [C_15,A_62,A_14] : ( multiply(C_15,multiply(A_62,A_14)) = multiply(A_62,multiply(C_15,A_14)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1138]) ).
tff(c_6,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_5073,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm),theory(equality)],[c_5050,c_6]) ).
tff(c_184687,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm),theory(equality)],[c_1217,c_5073]) ).
tff(c_184697,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5050,c_184687]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : GRP607-1 : TPTP v9.0.0. Released v2.6.0.
% 0.02/0.09 % 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
% 0.07/0.28 % Computer : n012.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Mon Apr 7 21:57:00 EDT 2025
% 0.07/0.28 % CPUTime :
% 72.88/52.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 72.88/52.36
% 72.88/52.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------