%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP013-1 : 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/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 : n024.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 06:24:45 PM UTC 2025
% Result : Unsatisfiable 3.95s 2.61s
% Output : CNFRefutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > multiply > #nlpp > inverse > identity > d > c > b > 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(b,type,
b: $i ).
tff(d,type,
d: $i ).
tff(identity,type,
identity: $i ).
tff(c,type,
c: $i ).
tff(f_97,axiom,
! [A] : product(A,A,identity),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X] : product(X,inverse(X),identity),
file(unknown,unknown) ).
tff(f_104,axiom,
! [A,B,C] :
( ~ product(inverse(A),inverse(B),C)
| product(A,C,B) ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_99,axiom,
product(inverse(a),inverse(b),d),
file(unknown,unknown) ).
tff(f_98,axiom,
product(a,b,c),
file(unknown,unknown) ).
tff(f_106,axiom,
~ product(c,d,identity),
file(unknown,unknown) ).
tff(c_18,plain,
! [A_23] : product(A_23,A_23,identity),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_8,plain,
! [X_4] : product(X_4,inverse(X_4),identity),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_155,plain,
! [A_44,C_45,B_46] :
( product(A_44,C_45,B_46)
| ~ product(inverse(A_44),inverse(B_46),C_45) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_184,plain,
! [A_44] : product(A_44,identity,inverse(A_44)),
inference(resolution,[status(thm)],[c_8,c_155]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_33,plain,
! [Z_34,W_35,X_36,Y_37] :
( ( Z_34 = W_35 )
| ~ product(X_36,Y_37,W_35)
| ~ product(X_36,Y_37,Z_34) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_252,plain,
! [Z_55,X_56] :
( ( Z_55 = X_56 )
| ~ product(X_56,identity,Z_55) ),
inference(resolution,[status(thm)],[c_4,c_33]) ).
tff(c_278,plain,
! [A_44] : ( inverse(A_44) = A_44 ),
inference(resolution,[status(thm)],[c_184,c_252]) ).
tff(c_22,plain,
product(inverse(a),inverse(b),d),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_293,plain,
product(a,b,d),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_278,c_22]) ).
tff(c_20,plain,
product(a,b,c),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_371,plain,
! [Z_65] :
( ( c = Z_65 )
| ~ product(a,b,Z_65) ),
inference(resolution,[status(thm)],[c_20,c_33]) ).
tff(c_382,plain,
d = c,
inference(resolution,[status(thm)],[c_293,c_371]) ).
tff(c_26,plain,
~ product(c,d,identity),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_388,plain,
~ product(c,c,identity),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_26]) ).
tff(c_392,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18,c_388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP013-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % 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
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 21:10:21 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.95/2.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.95/2.62
% 3.95/2.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------