%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP010-1 : 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 : n016.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 06:24:44 PM UTC 2025
% Result : Unsatisfiable 3.17s 1.89s
% Output : CNFRefutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 43 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > multiply > #nlpp > inverse > identity > 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(identity,type,
identity: $i ).
tff(f_97,axiom,
~ product(b,a,identity),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X] : product(X,identity,X),
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_95,axiom,
product(a,b,identity),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_81,axiom,
! [W,U,Z,X,Y,V] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ),
file(unknown,unknown) ).
tff(c_20,plain,
~ product(b,a,identity),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_6,plain,
! [X_3] : product(inverse(X_3),X_3,identity),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_10,plain,
! [X_5,Y_6] : product(X_5,Y_6,multiply(X_5,Y_6)),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_26,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_70]) ).
tff(c_111,plain,
! [Z_42,X_43] :
( ( Z_42 = X_43 )
| ~ product(X_43,identity,Z_42) ),
inference(resolution,[status(thm)],[c_4,c_26]) ).
tff(c_127,plain,
! [X_5] : ( multiply(X_5,identity) = X_5 ),
inference(resolution,[status(thm)],[c_10,c_111]) ).
tff(c_18,plain,
product(a,b,identity),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_168,plain,
! [Y_47,W_46,U_48,Z_50,V_51,X_49] :
( product(X_49,V_51,W_46)
| ~ product(U_48,Z_50,W_46)
| ~ product(Y_47,Z_50,V_51)
| ~ product(X_49,Y_47,U_48) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_460,plain,
! [X_76,V_77,X_78,Y_79] :
( product(X_76,V_77,X_78)
| ~ product(Y_79,X_78,V_77)
| ~ product(X_76,Y_79,identity) ),
inference(resolution,[status(thm)],[c_2,c_168]) ).
tff(c_504,plain,
! [X_82] :
( product(X_82,identity,b)
| ~ product(X_82,a,identity) ),
inference(resolution,[status(thm)],[c_18,c_460]) ).
tff(c_39,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_26]) ).
tff(c_514,plain,
! [X_82] :
( ( multiply(X_82,identity) = b )
| ~ product(X_82,a,identity) ),
inference(resolution,[status(thm)],[c_504,c_39]) ).
tff(c_544,plain,
! [X_83] :
( ( b = X_83 )
| ~ product(X_83,a,identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_127,c_514]) ).
tff(c_549,plain,
inverse(a) = b,
inference(resolution,[status(thm)],[c_6,c_544]) ).
tff(c_568,plain,
product(b,a,identity),
inference(superposition,[status(thm),theory(equality)],[c_549,c_6]) ).
tff(c_574,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP010-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % 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
% 0.12/0.34 % Computer : n016.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 21:10:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.17/1.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.17/1.90
% 3.17/1.90 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------