%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP566-1 : 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 : n017.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 06:26:32 PM UTC 2025
% Result : Unsatisfiable 3.54s 2.03s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 50 ( 50 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > identity > a2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(inverse,type,
inverse: $i > $i ).
tff(double_divide,type,
double_divide: ( $i * $i ) > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(a2,type,
a2: $i ).
tff(identity,type,
identity: $i ).
tff(f_27,axiom,
! [A] : ( inverse(A) = double_divide(A,identity) ),
file(unknown,unknown) ).
tff(f_29,axiom,
! [A] : ( identity = double_divide(A,inverse(A)) ),
file(unknown,unknown) ).
tff(f_23,axiom,
! [A,B,C] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ),
file(unknown,unknown) ).
tff(f_25,axiom,
! [A,B] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file(unknown,unknown) ).
tff(f_31,axiom,
multiply(identity,a2) != a2,
file(unknown,unknown) ).
tff(c_6,plain,
! [A_6] : ( double_divide(A_6,identity) = inverse(A_6) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_8,plain,
! [A_7] : ( double_divide(A_7,inverse(A_7)) = identity ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( double_divide(double_divide(A_1,double_divide(double_divide(B_2,double_divide(A_1,C_3)),double_divide(identity,C_3))),double_divide(identity,identity)) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_65,plain,
! [A_13,B_14,C_15] : ( double_divide(double_divide(A_13,double_divide(double_divide(B_14,double_divide(A_13,C_15)),double_divide(identity,C_15))),inverse(identity)) = B_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2]) ).
tff(c_90,plain,
! [A_13,B_14] : ( double_divide(double_divide(A_13,double_divide(double_divide(B_14,double_divide(A_13,identity)),inverse(identity))),inverse(identity)) = B_14 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_65]) ).
tff(c_522,plain,
! [A_32,B_33] : ( double_divide(double_divide(A_32,double_divide(double_divide(B_33,inverse(A_32)),inverse(identity))),inverse(identity)) = B_33 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_90]) ).
tff(c_570,plain,
! [A_7] : ( double_divide(double_divide(A_7,double_divide(identity,inverse(identity))),inverse(identity)) = A_7 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_522]) ).
tff(c_575,plain,
! [A_7] : ( double_divide(inverse(A_7),inverse(identity)) = A_7 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_8,c_570]) ).
tff(c_28,plain,
! [B_10,A_11] : ( double_divide(double_divide(B_10,A_11),identity) = multiply(A_11,B_10) ),
inference(cnfTransformation,[status(thm)],[f_25]) ).
tff(c_108,plain,
! [B_16,A_17] : ( inverse(double_divide(B_16,A_17)) = multiply(A_17,B_16) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).
tff(c_129,plain,
! [A_6] : ( inverse(inverse(A_6)) = multiply(identity,A_6) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_108]) ).
tff(c_576,plain,
! [A_34] : ( double_divide(inverse(A_34),inverse(identity)) = A_34 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_8,c_570]) ).
tff(c_641,plain,
! [A_36] : ( double_divide(multiply(identity,A_36),inverse(identity)) = inverse(A_36) ),
inference(superposition,[status(thm),theory(equality)],[c_129,c_576]) ).
tff(c_105,plain,
! [A_13,B_14] : ( double_divide(double_divide(A_13,double_divide(double_divide(B_14,inverse(A_13)),inverse(identity))),inverse(identity)) = B_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_90]) ).
tff(c_647,plain,
! [A_36] : ( double_divide(double_divide(identity,double_divide(inverse(A_36),inverse(identity))),inverse(identity)) = multiply(identity,A_36) ),
inference(superposition,[status(thm),theory(equality)],[c_641,c_105]) ).
tff(c_875,plain,
! [A_43] : ( double_divide(double_divide(identity,A_43),inverse(identity)) = multiply(identity,A_43) ),
inference(demodulation,[status(thm),theory(equality)],[c_575,c_647]) ).
tff(c_951,plain,
double_divide(inverse(identity),inverse(identity)) = multiply(identity,identity),
inference(superposition,[status(thm),theory(equality)],[c_6,c_875]) ).
tff(c_966,plain,
multiply(identity,identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_575,c_951]) ).
tff(c_52,plain,
! [A_7] : ( multiply(inverse(A_7),A_7) = double_divide(identity,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_28]) ).
tff(c_57,plain,
! [A_7] : ( multiply(inverse(A_7),A_7) = inverse(identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_52]) ).
tff(c_49,plain,
! [B_10,A_11] : ( inverse(double_divide(B_10,A_11)) = multiply(A_11,B_10) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).
tff(c_684,plain,
! [A_37,B_38] : ( double_divide(multiply(A_37,B_38),inverse(identity)) = double_divide(B_38,A_37) ),
inference(superposition,[status(thm),theory(equality)],[c_49,c_576]) ).
tff(c_706,plain,
! [A_37,B_38] : ( multiply(inverse(identity),multiply(A_37,B_38)) = inverse(double_divide(B_38,A_37)) ),
inference(superposition,[status(thm),theory(equality)],[c_684,c_49]) ).
tff(c_740,plain,
! [A_37,B_38] : ( multiply(inverse(identity),multiply(A_37,B_38)) = multiply(A_37,B_38) ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_706]) ).
tff(c_971,plain,
multiply(inverse(identity),identity) = multiply(identity,identity),
inference(superposition,[status(thm),theory(equality)],[c_966,c_740]) ).
tff(c_995,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_966,c_57,c_971]) ).
tff(c_1094,plain,
! [A_46] : ( multiply(inverse(A_46),A_46) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_995,c_57]) ).
tff(c_86,plain,
! [A_6,B_14] : ( double_divide(double_divide(A_6,double_divide(double_divide(B_14,inverse(A_6)),double_divide(identity,identity))),inverse(identity)) = B_14 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_65]) ).
tff(c_104,plain,
! [A_6,B_14] : ( double_divide(double_divide(A_6,double_divide(double_divide(B_14,inverse(A_6)),inverse(identity))),inverse(identity)) = B_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_86]) ).
tff(c_1043,plain,
! [A_6,B_14] : ( multiply(multiply(inverse(A_6),B_14),A_6) = B_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_995,c_49,c_6,c_995,c_104]) ).
tff(c_1099,plain,
! [A_46] : ( multiply(identity,A_46) = A_46 ),
inference(superposition,[status(thm),theory(equality)],[c_1094,c_1043]) ).
tff(c_10,plain,
multiply(identity,a2) != a2,
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_1127,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1099,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP566-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.12 % 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
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 21:55:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.54/2.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.54/2.04
% 3.54/2.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------