%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP030-1 : 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 : n003.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 3.24s 1.82s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 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 : 47 ( 47 !; 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_97,axiom,
~ product(a,identity,a),
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_28,plain,
! [V_32,X_33,U_31,Z_29,W_30,Y_34] :
( product(X_33,V_32,W_30)
| ~ product(U_31,Z_29,W_30)
| ~ product(Y_34,Z_29,V_32)
| ~ product(X_33,Y_34,U_31) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_144,plain,
! [X_58,V_59,A_60,Y_61] :
( product(X_58,V_59,A_60)
| ~ product(Y_61,A_60,V_59)
| ~ product(X_58,Y_61,identity) ),
inference(resolution,[status(thm)],[c_10,c_28]) ).
tff(c_236,plain,
! [X_68,A_69] :
( product(X_68,identity,A_69)
| ~ product(X_68,inverse(A_69),identity) ),
inference(resolution,[status(thm)],[c_12,c_144]) ).
tff(c_241,plain,
! [A_69] : product(inverse(inverse(A_69)),identity,A_69),
inference(resolution,[status(thm)],[c_12,c_236]) ).
tff(c_345,plain,
! [X_73,V_74,Y_75,A_76] :
( product(X_73,V_74,identity)
| ~ product(Y_75,A_76,V_74)
| ~ product(X_73,Y_75,inverse(A_76)) ),
inference(resolution,[status(thm)],[c_12,c_28]) ).
tff(c_377,plain,
! [X_79,A_80] :
( product(X_79,A_80,identity)
| ~ product(X_79,identity,inverse(A_80)) ),
inference(resolution,[status(thm)],[c_10,c_345]) ).
tff(c_386,plain,
! [A_81] : product(inverse(inverse(inverse(A_81))),A_81,identity),
inference(resolution,[status(thm)],[c_241,c_377]) ).
tff(c_152,plain,
! [X_58,A_20] :
( product(X_58,identity,A_20)
| ~ product(X_58,inverse(A_20),identity) ),
inference(resolution,[status(thm)],[c_12,c_144]) ).
tff(c_454,plain,
! [A_83] : product(inverse(inverse(inverse(inverse(A_83)))),identity,A_83),
inference(resolution,[status(thm)],[c_386,c_152]) ).
tff(c_242,plain,
! [A_70] : product(inverse(inverse(A_70)),identity,A_70),
inference(resolution,[status(thm)],[c_12,c_236]) ).
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_265,plain,
! [Z_5,A_70] :
( ( Z_5 = A_70 )
| ~ product(inverse(inverse(A_70)),identity,Z_5) ),
inference(resolution,[status(thm)],[c_242,c_4]) ).
tff(c_484,plain,
! [A_83] : ( inverse(inverse(A_83)) = A_83 ),
inference(resolution,[status(thm)],[c_454,c_265]) ).
tff(c_419,plain,
! [A_20] : product(inverse(inverse(inverse(inverse(A_20)))),identity,A_20),
inference(resolution,[status(thm)],[c_386,c_152]) ).
tff(c_496,plain,
! [A_20] : product(A_20,identity,A_20),
inference(demodulation,[status(thm),theory(equality)],[c_484,c_484,c_419]) ).
tff(c_14,plain,
~ product(a,identity,a),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_545,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_496,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP030-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : n003.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 21:12:18 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.24/1.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.24/1.82
% 3.24/1.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------