%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP031-2 : 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 : n026.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 6.27s 2.50s
% Output : CNFRefutation 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 ( 2 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 > equalish > 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(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(f_66,axiom,
! [A] : product(A,inverse(A),identity),
file(unknown,unknown) ).
tff(f_68,axiom,
! [A] : product(A,identity,A),
file(unknown,unknown) ).
tff(f_64,axiom,
! [W,U,Z,X,Y,V] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file(unknown,unknown) ).
tff(f_53,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_71,axiom,
! [A] : ~ product(A,a,identity),
file(unknown,unknown) ).
tff(c_10,plain,
! [A_19] : product(A_19,inverse(A_19),identity),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_12,plain,
! [A_20] : product(A_20,identity,A_20),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_29,plain,
! [X_33,U_31,Z_32,V_36,W_34,Y_35] :
( product(U_31,Z_32,W_34)
| ~ product(X_33,V_36,W_34)
| ~ product(Y_35,Z_32,V_36)
| ~ product(X_33,Y_35,U_31) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_74,plain,
! [U_53,Z_54,A_55,Y_56] :
( product(U_53,Z_54,A_55)
| ~ product(Y_56,Z_54,identity)
| ~ product(A_55,Y_56,U_53) ),
inference(resolution,[status(thm)],[c_12,c_29]) ).
tff(c_80,plain,
! [U_53,A_19,A_55] :
( product(U_53,inverse(A_19),A_55)
| ~ product(A_55,A_19,U_53) ),
inference(resolution,[status(thm)],[c_10,c_74]) ).
tff(c_51,plain,
! [W_42,U_43,X_45,V_44,Z_41,Y_46] :
( product(X_45,V_44,W_42)
| ~ product(U_43,Z_41,W_42)
| ~ product(Y_46,Z_41,V_44)
| ~ product(X_45,Y_46,U_43) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_197,plain,
! [X_76,V_77,Y_78,A_79] :
( product(X_76,V_77,identity)
| ~ product(Y_78,inverse(A_79),V_77)
| ~ product(X_76,Y_78,A_79) ),
inference(resolution,[status(thm)],[c_10,c_51]) ).
tff(c_4199,plain,
! [X_270,A_271,U_272,A_273] :
( product(X_270,A_271,identity)
| ~ product(X_270,U_272,A_273)
| ~ product(A_271,A_273,U_272) ),
inference(resolution,[status(thm)],[c_80,c_197]) ).
tff(c_4344,plain,
! [A_274,A_275] :
( product(A_274,A_275,identity)
| ~ product(A_275,A_274,identity) ),
inference(resolution,[status(thm)],[c_12,c_4199]) ).
tff(c_4438,plain,
! [A_276] : product(inverse(A_276),A_276,identity),
inference(resolution,[status(thm)],[c_10,c_4344]) ).
tff(c_14,plain,
! [A_21] : ~ product(A_21,a,identity),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_4584,plain,
$false,
inference(resolution,[status(thm)],[c_4438,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP031-2 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % 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 : n026.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 21:12:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 6.27/2.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.27/2.51
% 6.27/2.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------