%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP004-2 : 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/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 : n023.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 4.53s 2.23s
% Output : CNFRefutation 4.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 31 ~; 29 |; 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 64 !; 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_52,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| equalish(Z,W) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_96,axiom,
! [X,Y,W,Z] :
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) ),
file(unknown,unknown) ).
tff(f_77,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_88,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_100,axiom,
~ product(a,inverse(a),identity),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_20,plain,
! [Z_29,W_30,X_31,Y_32] :
( equalish(Z_29,W_30)
| ~ product(X_31,Y_32,W_30)
| ~ product(X_31,Y_32,Z_29) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_40,plain,
! [Z_37,X_38] :
( equalish(Z_37,X_38)
| ~ product(identity,X_38,Z_37) ),
inference(resolution,[status(thm)],[c_2,c_20]) ).
tff(c_49,plain,
! [X_1] : equalish(X_1,X_1),
inference(resolution,[status(thm)],[c_2,c_40]) ).
tff(c_4,plain,
! [X_2] : product(inverse(X_2),X_2,identity),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_30,plain,
! [W_33,Z_34,Y_35,X_36] :
( product(W_33,Z_34,Y_35)
| ~ product(W_33,Z_34,X_36)
| ~ equalish(X_36,Y_35) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_38,plain,
! [X_2,Y_35] :
( product(inverse(X_2),X_2,Y_35)
| ~ equalish(identity,Y_35) ),
inference(resolution,[status(thm)],[c_4,c_30]) ).
tff(c_52,plain,
! [U_45,Y_43,Z_46,X_42,W_41,V_44] :
( product(X_42,V_44,W_41)
| ~ product(U_45,Z_46,W_41)
| ~ product(Y_43,Z_46,V_44)
| ~ product(X_42,Y_43,U_45) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_237,plain,
! [X_76,V_77,X_78,Y_79] :
( product(X_76,V_77,X_78)
| ~ product(Y_79,X_78,V_77)
| ~ product(X_76,Y_79,identity) ),
inference(resolution,[status(thm)],[c_2,c_52]) ).
tff(c_512,plain,
! [X_99,X_100] :
( product(X_99,identity,X_100)
| ~ product(X_99,inverse(X_100),identity) ),
inference(resolution,[status(thm)],[c_4,c_237]) ).
tff(c_520,plain,
! [X_100] :
( product(inverse(inverse(X_100)),identity,X_100)
| ~ equalish(identity,identity) ),
inference(resolution,[status(thm)],[c_38,c_512]) ).
tff(c_532,plain,
! [X_100] : product(inverse(inverse(X_100)),identity,X_100),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_520]) ).
tff(c_114,plain,
! [V_60,X_58,Z_57,Y_61,W_56,U_59] :
( product(U_59,Z_57,W_56)
| ~ product(X_58,V_60,W_56)
| ~ product(Y_61,Z_57,V_60)
| ~ product(X_58,Y_61,U_59) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_836,plain,
! [U_115,Z_116,Y_117,X_118] :
( product(U_115,Z_116,identity)
| ~ product(Y_117,Z_116,X_118)
| ~ product(inverse(X_118),Y_117,U_115) ),
inference(resolution,[status(thm)],[c_4,c_114]) ).
tff(c_1729,plain,
! [U_144,X_145] :
( product(U_144,X_145,identity)
| ~ product(inverse(X_145),identity,U_144) ),
inference(resolution,[status(thm)],[c_2,c_836]) ).
tff(c_1789,plain,
! [X_100] : product(X_100,inverse(X_100),identity),
inference(resolution,[status(thm)],[c_532,c_1729]) ).
tff(c_16,plain,
~ product(a,inverse(a),identity),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_1801,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1789,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GRP004-2 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.12 % 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
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 7 21:09:39 EDT 2025
% 0.13/0.33 % CPUTime :
% 4.53/2.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.88/2.23
% 4.88/2.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------