%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP035-3 : 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 : n031.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 06:24:50 PM UTC 2025
% Result : Unsatisfiable 4.39s 2.14s
% Output : CNFRefutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 81 ( 43 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > subgroup_member > multiply > #nlpp > inverse > identity > c > b > 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(b,type,
b: $i ).
tff(identity,type,
identity: $i ).
tff(subgroup_member,type,
subgroup_member: $i > $o ).
tff(c,type,
c: $i ).
tff(f_132,axiom,
subgroup_member(b),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X] : product(X,inverse(X),identity),
file(unknown,unknown) ).
tff(f_128,axiom,
! [A,B,C] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_135,axiom,
~ subgroup_member(c),
file(unknown,unknown) ).
tff(f_131,axiom,
subgroup_member(a),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_133,axiom,
product(a,b,c),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_92,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(inverse(X),X,identity),
file(unknown,unknown) ).
tff(c_22,plain,
subgroup_member(b),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_8,plain,
! [X_4] : product(X_4,inverse(X_4),identity),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_144,plain,
! [C_42,A_43,B_44] :
( subgroup_member(C_42)
| ~ product(A_43,inverse(B_44),C_42)
| ~ subgroup_member(B_44)
| ~ subgroup_member(A_43) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_165,plain,
! [X_4] :
( subgroup_member(identity)
| ~ subgroup_member(X_4) ),
inference(resolution,[status(thm)],[c_8,c_144]) ).
tff(c_167,plain,
! [X_4] : ~ subgroup_member(X_4),
inference(splitLeft,[status(thm)],[c_165]) ).
tff(c_171,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_167,c_22]) ).
tff(c_172,plain,
subgroup_member(identity),
inference(splitRight,[status(thm)],[c_165]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_166,plain,
! [B_44] :
( subgroup_member(inverse(B_44))
| ~ subgroup_member(B_44)
| ~ subgroup_member(identity) ),
inference(resolution,[status(thm)],[c_2,c_144]) ).
tff(c_257,plain,
! [B_44] :
( subgroup_member(inverse(B_44))
| ~ subgroup_member(B_44) ),
inference(demodulation,[status(thm),theory(equality)],[c_172,c_166]) ).
tff(c_26,plain,
~ subgroup_member(c),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_20,plain,
subgroup_member(a),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_10,plain,
! [X_5,Y_6] : product(X_5,Y_6,multiply(X_5,Y_6)),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_24,plain,
product(a,b,c),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_32,plain,
! [Z_32,W_33,X_34,Y_35] :
( ( Z_32 = W_33 )
| ~ product(X_34,Y_35,W_33)
| ~ product(X_34,Y_35,Z_32) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_192,plain,
! [Z_51] :
( ( c = Z_51 )
| ~ product(a,b,Z_51) ),
inference(resolution,[status(thm)],[c_24,c_32]) ).
tff(c_200,plain,
multiply(a,b) = c,
inference(resolution,[status(thm)],[c_10,c_192]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_264,plain,
! [X_57,Z_61,U_58,W_60,Y_56,V_59] :
( product(U_58,Z_61,W_60)
| ~ product(X_57,V_59,W_60)
| ~ product(Y_56,Z_61,V_59)
| ~ product(X_57,Y_56,U_58) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_667,plain,
! [U_91,Z_92,X_93,Y_94] :
( product(U_91,Z_92,X_93)
| ~ product(Y_94,Z_92,identity)
| ~ product(X_93,Y_94,U_91) ),
inference(resolution,[status(thm)],[c_4,c_264]) ).
tff(c_705,plain,
! [U_97,X_98,X_99] :
( product(U_97,inverse(X_98),X_99)
| ~ product(X_99,X_98,U_97) ),
inference(resolution,[status(thm)],[c_8,c_667]) ).
tff(c_50,plain,
! [Z_32,X_1] :
( ( Z_32 = X_1 )
| ~ product(identity,X_1,Z_32) ),
inference(resolution,[status(thm)],[c_2,c_32]) ).
tff(c_793,plain,
! [X_103,X_104] :
( ( inverse(X_103) = X_104 )
| ~ product(X_104,X_103,identity) ),
inference(resolution,[status(thm)],[c_705,c_50]) ).
tff(c_815,plain,
! [X_4] : ( inverse(inverse(X_4)) = X_4 ),
inference(resolution,[status(thm)],[c_8,c_793]) ).
tff(c_6,plain,
! [X_3] : product(inverse(X_3),X_3,identity),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_949,plain,
! [U_114,X_115,X_116] :
( product(U_114,X_115,X_116)
| ~ product(X_116,inverse(X_115),U_114) ),
inference(resolution,[status(thm)],[c_6,c_667]) ).
tff(c_982,plain,
! [X_117,X_118] : product(multiply(X_117,inverse(X_118)),X_118,X_117),
inference(resolution,[status(thm)],[c_10,c_949]) ).
tff(c_1157,plain,
! [X_121,X_122] : product(multiply(X_121,X_122),inverse(X_122),X_121),
inference(superposition,[status(thm),theory(equality)],[c_815,c_982]) ).
tff(c_1204,plain,
product(c,inverse(b),a),
inference(superposition,[status(thm),theory(equality)],[c_200,c_1157]) ).
tff(c_45,plain,
! [X_5,Y_6,Z_32] :
( ( multiply(X_5,Y_6) = Z_32 )
| ~ product(X_5,Y_6,Z_32) ),
inference(resolution,[status(thm)],[c_10,c_32]) ).
tff(c_1262,plain,
multiply(c,inverse(b)) = a,
inference(resolution,[status(thm)],[c_1204,c_45]) ).
tff(c_18,plain,
! [C_25,A_23,B_24] :
( subgroup_member(C_25)
| ~ product(A_23,inverse(B_24),C_25)
| ~ subgroup_member(B_24)
| ~ subgroup_member(A_23) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_1035,plain,
! [X_117,B_24] :
( subgroup_member(X_117)
| ~ subgroup_member(B_24)
| ~ subgroup_member(multiply(X_117,inverse(inverse(B_24)))) ),
inference(resolution,[status(thm)],[c_982,c_18]) ).
tff(c_1428,plain,
! [X_131,B_132] :
( subgroup_member(X_131)
| ~ subgroup_member(B_132)
| ~ subgroup_member(multiply(X_131,B_132)) ),
inference(demodulation,[status(thm),theory(equality)],[c_815,c_1035]) ).
tff(c_1434,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(a) ),
inference(superposition,[status(thm),theory(equality)],[c_1262,c_1428]) ).
tff(c_1457,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_1434]) ).
tff(c_1458,plain,
~ subgroup_member(inverse(b)),
inference(negUnitSimplification,[status(thm)],[c_26,c_1457]) ).
tff(c_1471,plain,
~ subgroup_member(b),
inference(resolution,[status(thm)],[c_257,c_1458]) ).
tff(c_1475,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1471]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP035-3 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % 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 : n031.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 21:12:52 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.39/2.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.45/2.15
% 4.45/2.15 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------