%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP003-1 : 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 06:24:42 PM UTC 2025
% Result : Unsatisfiable 3.25s 1.85s
% Output : CNFRefutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 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 : 45 ( 45 !; 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_28,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_30,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_41,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_52,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_54,axiom,
~ product(a,identity,a),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : product(inverse(X_1),X_1,identity),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_4,plain,
! [X_2] : product(identity,X_2,X_2),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_13,plain,
! [Z_21,U_19,W_20,Y_22,V_18,X_17] :
( product(X_17,V_18,W_20)
| ~ product(U_19,Z_21,W_20)
| ~ product(Y_22,Z_21,V_18)
| ~ product(X_17,Y_22,U_19) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_20,plain,
! [X_23,V_24,X_25,Y_26] :
( product(X_23,V_24,X_25)
| ~ product(Y_26,X_25,V_24)
| ~ product(X_23,Y_26,identity) ),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_59,plain,
! [X_36,X_37] :
( product(X_36,identity,X_37)
| ~ product(X_36,inverse(X_37),identity) ),
inference(resolution,[status(thm)],[c_2,c_20]) ).
tff(c_64,plain,
! [X_37] : product(inverse(inverse(X_37)),identity,X_37),
inference(resolution,[status(thm)],[c_2,c_59]) ).
tff(c_27,plain,
! [W_27,U_31,Z_32,V_30,X_28,Y_29] :
( product(U_31,Z_32,W_27)
| ~ product(X_28,V_30,W_27)
| ~ product(Y_29,Z_32,V_30)
| ~ product(X_28,Y_29,U_31) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_403,plain,
! [U_72,Z_73,Y_74,X_75] :
( product(U_72,Z_73,identity)
| ~ product(Y_74,Z_73,X_75)
| ~ product(inverse(X_75),Y_74,U_72) ),
inference(resolution,[status(thm)],[c_2,c_27]) ).
tff(c_437,plain,
! [U_76,X_77] :
( product(U_76,X_77,identity)
| ~ product(inverse(X_77),identity,U_76) ),
inference(resolution,[status(thm)],[c_4,c_403]) ).
tff(c_488,plain,
! [X_78] : product(X_78,inverse(X_78),identity),
inference(resolution,[status(thm)],[c_64,c_437]) ).
tff(c_25,plain,
! [X_23,X_1] :
( product(X_23,identity,X_1)
| ~ product(X_23,inverse(X_1),identity) ),
inference(resolution,[status(thm)],[c_2,c_20]) ).
tff(c_529,plain,
! [X_78] : product(X_78,identity,X_78),
inference(resolution,[status(thm)],[c_488,c_25]) ).
tff(c_10,plain,
~ product(a,identity,a),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_535,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_529,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP003-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % 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 : n016.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 21:09:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.25/1.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.25/1.85
% 3.25/1.85 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------