%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP581-1 : 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 : n013.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 3.22s 1.82s
% Output : CNFRefutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 25 ( 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > identity > 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(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_25,axiom,
! [A,B] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file(unknown,unknown) ).
tff(f_31,axiom,
multiply(inverse(a1),a1) != identity,
file(unknown,unknown) ).
tff(f_23,axiom,
! [A,B,C] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ),
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_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_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_10,plain,
multiply(inverse(a1),a1) != identity,
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_58,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_57,c_10]) ).
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_2,plain,
! [A_1,B_2,C_3] : ( double_divide(double_divide(A_1,double_divide(double_divide(identity,B_2),double_divide(C_3,double_divide(B_2,A_1)))),double_divide(identity,identity)) = C_3 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_66,plain,
! [A_13,B_14,C_15] : ( double_divide(double_divide(A_13,double_divide(double_divide(identity,B_14),double_divide(C_15,double_divide(B_14,A_13)))),inverse(identity)) = C_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2]) ).
tff(c_551,plain,
! [A_33,C_34] : ( double_divide(double_divide(identity,double_divide(double_divide(identity,A_33),double_divide(C_34,inverse(A_33)))),inverse(identity)) = C_34 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_66]) ).
tff(c_610,plain,
! [A_7] : ( double_divide(double_divide(identity,double_divide(double_divide(identity,A_7),identity)),inverse(identity)) = A_7 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_551]) ).
tff(c_622,plain,
! [A_35] : ( double_divide(double_divide(identity,multiply(A_35,identity)),inverse(identity)) = A_35 ),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_610]) ).
tff(c_656,plain,
double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = inverse(identity),
inference(superposition,[status(thm),theory(equality)],[c_57,c_622]) ).
tff(c_661,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_656]) ).
tff(c_663,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_58,c_661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP581-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % 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
% 0.12/0.31 % Computer : n013.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Apr 7 21:56:47 EDT 2025
% 0.12/0.32 % CPUTime :
% 3.22/1.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.22/1.82
% 3.22/1.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------