%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP004-1 : 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 : n032.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 3.14s 1.83s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 44 ( 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > #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(identity,type,
identity: $i ).
tff(f_29,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_31,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_42,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_53,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_56,axiom,
! [X] : ~ product(a,X,identity),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : product(inverse(X_1),X_1,identity),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_4,plain,
! [X_2] : product(identity,X_2,X_2),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_14,plain,
! [X_19,V_20,Z_23,U_21,Y_24,W_22] :
( product(X_19,V_20,W_22)
| ~ product(U_21,Z_23,W_22)
| ~ product(Y_24,Z_23,V_20)
| ~ product(X_19,Y_24,U_21) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_21,plain,
! [X_25,V_26,X_27,Y_28] :
( product(X_25,V_26,X_27)
| ~ product(Y_28,X_27,V_26)
| ~ product(X_25,Y_28,identity) ),
inference(resolution,[status(thm)],[c_4,c_14]) ).
tff(c_60,plain,
! [X_38,X_39] :
( product(X_38,identity,X_39)
| ~ product(X_38,inverse(X_39),identity) ),
inference(resolution,[status(thm)],[c_2,c_21]) ).
tff(c_65,plain,
! [X_39] : product(inverse(inverse(X_39)),identity,X_39),
inference(resolution,[status(thm)],[c_2,c_60]) ).
tff(c_28,plain,
! [V_32,Y_31,W_29,Z_34,X_30,U_33] :
( product(U_33,Z_34,W_29)
| ~ product(X_30,V_32,W_29)
| ~ product(Y_31,Z_34,V_32)
| ~ product(X_30,Y_31,U_33) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_404,plain,
! [U_74,Z_75,Y_76,X_77] :
( product(U_74,Z_75,identity)
| ~ product(Y_76,Z_75,X_77)
| ~ product(inverse(X_77),Y_76,U_74) ),
inference(resolution,[status(thm)],[c_2,c_28]) ).
tff(c_438,plain,
! [U_78,X_79] :
( product(U_78,X_79,identity)
| ~ product(inverse(X_79),identity,U_78) ),
inference(resolution,[status(thm)],[c_4,c_404]) ).
tff(c_489,plain,
! [X_80] : product(X_80,inverse(X_80),identity),
inference(resolution,[status(thm)],[c_65,c_438]) ).
tff(c_10,plain,
! [X_15] : ~ product(a,X_15,identity),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_538,plain,
$false,
inference(resolution,[status(thm)],[c_489,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP004-1 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.09 % 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
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Apr 7 21:09:30 EDT 2025
% 0.09/0.28 % CPUTime :
% 3.14/1.83 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.14/1.84
% 3.14/1.84 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------