%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP022-1 : TPTP v9.0.0. Released v1.0.0.
% 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 : 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 06:24:46 PM UTC 2025
% Result : Unsatisfiable 3.09s 1.82s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > multiply > #nlpp > inverse > identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(identity,type,
identity: $i ).
tff(f_63,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_94,axiom,
! [W,U,Z,X,Y,V] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file(unknown,unknown) ).
tff(f_98,axiom,
inverse(inverse(a)) != a,
file(unknown,unknown) ).
tff(c_10,plain,
! [X_5,Y_6] : product(X_5,Y_6,multiply(X_5,Y_6)),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_24,plain,
! [Z_29,W_30,X_31,Y_32] :
( ( Z_29 = W_30 )
| ~ product(X_31,Y_32,W_30)
| ~ product(X_31,Y_32,Z_29) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_40,plain,
! [Z_33,X_34] :
( ( Z_33 = X_34 )
| ~ product(identity,X_34,Z_33) ),
inference(resolution,[status(thm)],[c_2,c_24]) ).
tff(c_56,plain,
! [Y_6] : ( multiply(identity,Y_6) = Y_6 ),
inference(resolution,[status(thm)],[c_10,c_40]) ).
tff(c_6,plain,
! [X_3] : product(inverse(X_3),X_3,identity),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_74,plain,
! [W_39,Z_40,X_36,V_38,U_37,Y_35] :
( product(U_37,Z_40,W_39)
| ~ product(X_36,V_38,W_39)
| ~ product(Y_35,Z_40,V_38)
| ~ product(X_36,Y_35,U_37) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_281,plain,
! [U_60,Z_61,X_62,Y_63] :
( product(U_60,Z_61,X_62)
| ~ product(Y_63,Z_61,identity)
| ~ product(X_62,Y_63,U_60) ),
inference(resolution,[status(thm)],[c_4,c_74]) ).
tff(c_316,plain,
! [U_66,X_67,X_68] :
( product(U_66,X_67,X_68)
| ~ product(X_68,inverse(X_67),U_66) ),
inference(resolution,[status(thm)],[c_6,c_281]) ).
tff(c_341,plain,
! [X_69] : product(identity,X_69,inverse(inverse(X_69))),
inference(resolution,[status(thm)],[c_6,c_316]) ).
tff(c_35,plain,
! [X_5,Y_6,Z_29] :
( ( multiply(X_5,Y_6) = Z_29 )
| ~ product(X_5,Y_6,Z_29) ),
inference(resolution,[status(thm)],[c_10,c_24]) ).
tff(c_351,plain,
! [X_69] : ( inverse(inverse(X_69)) = multiply(identity,X_69) ),
inference(resolution,[status(thm)],[c_341,c_35]) ).
tff(c_376,plain,
! [X_69] : ( inverse(inverse(X_69)) = X_69 ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_351]) ).
tff(c_18,plain,
inverse(inverse(a)) != a,
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_390,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_376,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP022-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 21:10:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.09/1.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.09/1.83
% 3.09/1.83 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------