%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP008-1 : 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 : n018.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 06:24:43 PM UTC 2025
% Result : Unsatisfiable 3.46s 2.02s
% Output : CNFRefutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 16 ~; 21 |; 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > q > multiply > #nlpp > j > inverse > h > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse,type,
inverse: $i > $i ).
tff(q,type,
q: $i > $o ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(h,type,
h: $i > $i ).
tff(identity,type,
identity: $i ).
tff(j,type,
j: $i > $i ).
tff(f_118,axiom,
~ q(identity),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_108,axiom,
! [A] :
( product(j(A),A,h(A))
| product(A,j(A),h(A))
| q(A) ),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
! [A] :
( ~ product(j(A),A,h(A))
| ~ product(A,j(A),h(A))
| q(A) ),
file(unknown,unknown) ).
tff(c_24,plain,
~ q(identity),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_298,plain,
! [A_56] :
( q(A_56)
| product(A_56,j(A_56),h(A_56))
| product(j(A_56),A_56,h(A_56)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_30,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_70]) ).
tff(c_45,plain,
! [Z_34,X_2] :
( ( Z_34 = X_2 )
| ~ product(X_2,identity,Z_34) ),
inference(resolution,[status(thm)],[c_4,c_30]) ).
tff(c_305,plain,
( ( j(identity) = h(identity) )
| q(identity)
| product(identity,j(identity),h(identity)) ),
inference(resolution,[status(thm)],[c_298,c_45]) ).
tff(c_313,plain,
( ( j(identity) = h(identity) )
| product(identity,j(identity),h(identity)) ),
inference(negUnitSimplification,[status(thm)],[c_24,c_305]) ).
tff(c_385,plain,
product(identity,j(identity),h(identity)),
inference(splitLeft,[status(thm)],[c_313]) ).
tff(c_44,plain,
! [Z_34,X_1] :
( ( Z_34 = X_1 )
| ~ product(identity,X_1,Z_34) ),
inference(resolution,[status(thm)],[c_2,c_30]) ).
tff(c_403,plain,
j(identity) = h(identity),
inference(resolution,[status(thm)],[c_385,c_44]) ).
tff(c_22,plain,
! [A_27] :
( q(A_27)
| ~ product(A_27,j(A_27),h(A_27))
| ~ product(j(A_27),A_27,h(A_27)) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_438,plain,
( q(identity)
| ~ product(identity,j(identity),h(identity))
| ~ product(h(identity),identity,h(identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_403,c_22]) ).
tff(c_444,plain,
q(identity),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_403,c_438]) ).
tff(c_446,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_444]) ).
tff(c_447,plain,
j(identity) = h(identity),
inference(splitRight,[status(thm)],[c_313]) ).
tff(c_455,plain,
( q(identity)
| ~ product(identity,j(identity),h(identity))
| ~ product(h(identity),identity,h(identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_447,c_22]) ).
tff(c_461,plain,
q(identity),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_447,c_455]) ).
tff(c_463,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : GRP008-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.09 % 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
% 0.09/0.30 % Computer : n018.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Apr 7 21:09:47 EDT 2025
% 0.09/0.30 % CPUTime :
% 3.46/2.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.46/2.02
% 3.46/2.02 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------