%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG002-1 : 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 : n008.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 08:31:12 PM UTC 2025
% Result : Unsatisfiable 5.35s 2.29s
% Output : CNFRefutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > multiply > add > #nlpp > additive_inverse > d > c > b > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(additive_inverse,type,
additive_inverse: $i > $i ).
tff(b,type,
b: $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(d,type,
d: $i ).
tff(c,type,
c: $i ).
tff(f_185,axiom,
b != c,
file(unknown,unknown) ).
tff(f_55,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file(unknown,unknown) ).
tff(f_182,axiom,
sum(a,b,d),
file(unknown,unknown) ).
tff(f_47,axiom,
! [X] : sum(additive_identity,X,X),
file(unknown,unknown) ).
tff(f_68,axiom,
! [W,U,Z,X,Y,V] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,W) ),
file(unknown,unknown) ).
tff(f_183,axiom,
sum(a,c,d),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file(unknown,unknown) ).
tff(f_84,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file(unknown,unknown) ).
tff(f_171,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| ( U = V ) ),
file(unknown,unknown) ).
tff(c_40,plain,
c != b,
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_10,plain,
! [X_7] : sum(additive_inverse(X_7),X_7,additive_identity),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_36,plain,
sum(a,b,d),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_2,plain,
! [X_1] : sum(additive_identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_250,plain,
! [Y_108,Z_111,V_109,W_106,X_107,U_110] :
( sum(X_107,V_109,W_106)
| ~ sum(U_110,Z_111,W_106)
| ~ sum(Y_108,Z_111,V_109)
| ~ sum(X_107,Y_108,U_110) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_775,plain,
! [X_151,V_152,X_153,Y_154] :
( sum(X_151,V_152,X_153)
| ~ sum(Y_154,X_153,V_152)
| ~ sum(X_151,Y_154,additive_identity) ),
inference(resolution,[status(thm)],[c_2,c_250]) ).
tff(c_802,plain,
! [X_151] :
( sum(X_151,d,b)
| ~ sum(X_151,a,additive_identity) ),
inference(resolution,[status(thm)],[c_36,c_775]) ).
tff(c_38,plain,
sum(a,c,d),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_919,plain,
! [X_171] :
( sum(X_171,d,c)
| ~ sum(X_171,a,additive_identity) ),
inference(resolution,[status(thm)],[c_38,c_775]) ).
tff(c_8,plain,
! [X_5,Y_6] : sum(X_5,Y_6,add(X_5,Y_6)),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_47,plain,
! [Y_80,X_81,Z_82] :
( sum(Y_80,X_81,Z_82)
| ~ sum(X_81,Y_80,Z_82) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_62,plain,
! [Y_6,X_5] : sum(Y_6,X_5,add(X_5,Y_6)),
inference(resolution,[status(thm)],[c_8,c_47]) ).
tff(c_96,plain,
! [V_92,U_93,X_94,Y_95] :
( ( V_92 = U_93 )
| ~ sum(X_94,Y_95,V_92)
| ~ sum(X_94,Y_95,U_93) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_117,plain,
! [X_5,Y_6,U_93] :
( ( add(X_5,Y_6) = U_93 )
| ~ sum(Y_6,X_5,U_93) ),
inference(resolution,[status(thm)],[c_62,c_96]) ).
tff(c_1996,plain,
! [X_234] :
( ( add(d,X_234) = c )
| ~ sum(X_234,a,additive_identity) ),
inference(resolution,[status(thm)],[c_919,c_117]) ).
tff(c_2001,plain,
add(d,additive_inverse(a)) = c,
inference(resolution,[status(thm)],[c_10,c_1996]) ).
tff(c_2071,plain,
sum(additive_inverse(a),d,c),
inference(superposition,[status(thm),theory(equality)],[c_2001,c_62]) ).
tff(c_32,plain,
! [V_67,U_66,X_64,Y_65] :
( ( V_67 = U_66 )
| ~ sum(X_64,Y_65,V_67)
| ~ sum(X_64,Y_65,U_66) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_2205,plain,
! [U_240] :
( ( c = U_240 )
| ~ sum(additive_inverse(a),d,U_240) ),
inference(resolution,[status(thm)],[c_2071,c_32]) ).
tff(c_2216,plain,
( ( c = b )
| ~ sum(additive_inverse(a),a,additive_identity) ),
inference(resolution,[status(thm)],[c_802,c_2205]) ).
tff(c_2242,plain,
c = b,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_2216]) ).
tff(c_2244,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_2242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % 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
% 0.13/0.34 % Computer : n008.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 : Tue Apr 8 18:14:33 EDT 2025
% 0.13/0.35 % CPUTime :
% 5.35/2.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.35/2.30
% 5.35/2.30 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------