%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP031-1 : 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 : n002.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 06:24:49 PM UTC 2025
% Result : Unsatisfiable 3.21s 1.88s
% Output : CNFRefutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 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 : 48 ( 48 !; 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_95,axiom,
! [A] : product(inverse(A),A,identity),
file(unknown,unknown) ).
tff(f_93,axiom,
! [A] : product(identity,A,A),
file(unknown,unknown) ).
tff(f_78,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(f_67,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
! [A] : ~ product(a,A,identity),
file(unknown,unknown) ).
tff(c_12,plain,
! [A_20] : product(inverse(A_20),A_20,identity),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_10,plain,
! [A_19] : product(identity,A_19,A_19),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_29,plain,
! [Y_36,W_32,Z_31,U_33,V_34,X_35] :
( product(X_35,V_34,W_32)
| ~ product(U_33,Z_31,W_32)
| ~ product(Y_36,Z_31,V_34)
| ~ product(X_35,Y_36,U_33) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_145,plain,
! [X_60,V_61,A_62,Y_63] :
( product(X_60,V_61,A_62)
| ~ product(Y_63,A_62,V_61)
| ~ product(X_60,Y_63,identity) ),
inference(resolution,[status(thm)],[c_10,c_29]) ).
tff(c_237,plain,
! [X_70,A_71] :
( product(X_70,identity,A_71)
| ~ product(X_70,inverse(A_71),identity) ),
inference(resolution,[status(thm)],[c_12,c_145]) ).
tff(c_242,plain,
! [A_71] : product(inverse(inverse(A_71)),identity,A_71),
inference(resolution,[status(thm)],[c_12,c_237]) ).
tff(c_346,plain,
! [X_75,V_76,Y_77,A_78] :
( product(X_75,V_76,identity)
| ~ product(Y_77,A_78,V_76)
| ~ product(X_75,Y_77,inverse(A_78)) ),
inference(resolution,[status(thm)],[c_12,c_29]) ).
tff(c_378,plain,
! [X_81,A_82] :
( product(X_81,A_82,identity)
| ~ product(X_81,identity,inverse(A_82)) ),
inference(resolution,[status(thm)],[c_10,c_346]) ).
tff(c_387,plain,
! [A_83] : product(inverse(inverse(inverse(A_83))),A_83,identity),
inference(resolution,[status(thm)],[c_242,c_378]) ).
tff(c_153,plain,
! [X_60,A_20] :
( product(X_60,identity,A_20)
| ~ product(X_60,inverse(A_20),identity) ),
inference(resolution,[status(thm)],[c_12,c_145]) ).
tff(c_455,plain,
! [A_85] : product(inverse(inverse(inverse(inverse(A_85)))),identity,A_85),
inference(resolution,[status(thm)],[c_387,c_153]) ).
tff(c_243,plain,
! [A_72] : product(inverse(inverse(A_72)),identity,A_72),
inference(resolution,[status(thm)],[c_12,c_237]) ).
tff(c_4,plain,
! [Z_5,W_6,X_3,Y_4] :
( ( Z_5 = W_6 )
| ~ product(X_3,Y_4,W_6)
| ~ product(X_3,Y_4,Z_5) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_266,plain,
! [Z_5,A_72] :
( ( Z_5 = A_72 )
| ~ product(inverse(inverse(A_72)),identity,Z_5) ),
inference(resolution,[status(thm)],[c_243,c_4]) ).
tff(c_505,plain,
! [A_86] : ( inverse(inverse(A_86)) = A_86 ),
inference(resolution,[status(thm)],[c_455,c_266]) ).
tff(c_645,plain,
! [A_93] : product(A_93,inverse(A_93),identity),
inference(superposition,[status(thm),theory(equality)],[c_505,c_12]) ).
tff(c_14,plain,
! [A_21] : ~ product(a,A_21,identity),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_700,plain,
$false,
inference(resolution,[status(thm)],[c_645,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP031-1 : 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 : n002.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 21:12:46 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.21/1.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.21/1.89
% 3.21/1.89 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------