%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : BOO010-1 : 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 : 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 05:45:02 PM UTC 2025
% Result : Unsatisfiable 252.62s 223.64s
% Output : CNFRefutation 252.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 94 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 98 ( 50 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 126 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > multiply > add > #nlpp > inverse > y > x > multiplicative_identity > additive_identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(x,type,
x: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(y,type,
y: $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(f_51,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X] : product(multiplicative_identity,X,X),
file(unknown,unknown) ).
tff(f_206,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) ),
file(unknown,unknown) ).
tff(f_183,axiom,
! [X] : sum(inverse(X),X,multiplicative_identity),
file(unknown,unknown) ).
tff(f_49,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X] : product(X,multiplicative_identity,X),
file(unknown,unknown) ).
tff(f_181,axiom,
! [V3,Z,V1,X,Y,V2,V4] :
( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ product(V1,V2,V4)
| sum(V3,X,V4) ),
file(unknown,unknown) ).
tff(f_198,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| ( U = V ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [V3,Z,V1,X,Y,V2,V4] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ),
file(unknown,unknown) ).
tff(f_210,axiom,
~ sum(x,multiply(x,y),x),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4] : product(X_3,Y_4,multiply(X_3,Y_4)),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_82,plain,
! [Y_100,X_101,Z_102] :
( product(Y_100,X_101,Z_102)
| ~ product(X_101,Y_100,Z_102) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_93,plain,
! [Y_4,X_3] : product(Y_4,X_3,multiply(X_3,Y_4)),
inference(resolution,[status(thm)],[c_4,c_82]) ).
tff(c_14,plain,
! [X_13] : product(multiplicative_identity,X_13,X_13),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_107,plain,
! [V_105,U_106,X_107,Y_108] :
( ( V_105 = U_106 )
| ~ product(X_107,Y_108,V_105)
| ~ product(X_107,Y_108,U_106) ),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_126,plain,
! [X_109,U_110] :
( ( X_109 = U_110 )
| ~ product(multiplicative_identity,X_109,U_110) ),
inference(resolution,[status(thm)],[c_14,c_107]) ).
tff(c_146,plain,
! [X_3] : ( multiply(X_3,multiplicative_identity) = X_3 ),
inference(resolution,[status(thm)],[c_93,c_126]) ).
tff(c_34,plain,
! [X_71] : sum(inverse(X_71),X_71,multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_2,plain,
! [X_1,Y_2] : sum(X_1,Y_2,add(X_1,Y_2)),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_57,plain,
! [Y_95,X_96,Z_97] :
( sum(Y_95,X_96,Z_97)
| ~ sum(X_96,Y_95,Z_97) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_68,plain,
! [Y_2,X_1] : sum(Y_2,X_1,add(X_1,Y_2)),
inference(resolution,[status(thm)],[c_2,c_57]) ).
tff(c_16,plain,
! [X_14] : product(X_14,multiplicative_identity,X_14),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_610,plain,
! [Y_152,V3_150,V2_153,V1_148,X_154,Z_151,V4_149] :
( sum(V3_150,X_154,V4_149)
| ~ product(V1_148,V2_153,V4_149)
| ~ product(Y_152,Z_151,V3_150)
| ~ sum(Z_151,X_154,V2_153)
| ~ sum(Y_152,X_154,V1_148) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_1056,plain,
! [Z_190,X_189,V3_192,X_188,Y_191] :
( sum(V3_192,X_188,X_189)
| ~ product(Y_191,Z_190,V3_192)
| ~ sum(Z_190,X_188,X_189)
| ~ sum(Y_191,X_188,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_14,c_610]) ).
tff(c_1075,plain,
! [X_193,X_194,X_195] :
( sum(X_193,X_194,X_195)
| ~ sum(multiplicative_identity,X_194,X_195)
| ~ sum(X_193,X_194,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_16,c_1056]) ).
tff(c_1093,plain,
! [X_196,X_197] :
( sum(X_196,X_197,add(X_197,multiplicative_identity))
| ~ sum(X_196,X_197,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_68,c_1075]) ).
tff(c_190,plain,
! [V_112,U_113,X_114,Y_115] :
( ( V_112 = U_113 )
| ~ sum(X_114,Y_115,V_112)
| ~ sum(X_114,Y_115,U_113) ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_206,plain,
! [U_113,X_71] :
( ( multiplicative_identity = U_113 )
| ~ sum(inverse(X_71),X_71,U_113) ),
inference(resolution,[status(thm)],[c_34,c_190]) ).
tff(c_1106,plain,
! [X_197] :
( ( add(X_197,multiplicative_identity) = multiplicative_identity )
| ~ sum(inverse(X_197),X_197,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_1093,c_206]) ).
tff(c_1180,plain,
! [X_205] : ( add(X_205,multiplicative_identity) = multiplicative_identity ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_1106]) ).
tff(c_844,plain,
! [X_170,Y_171,U_172] :
( ( add(X_170,Y_171) = U_172 )
| ~ sum(X_170,Y_171,U_172) ),
inference(resolution,[status(thm)],[c_2,c_190]) ).
tff(c_863,plain,
! [Y_2,X_1] : ( add(Y_2,X_1) = add(X_1,Y_2) ),
inference(resolution,[status(thm)],[c_68,c_844]) ).
tff(c_1185,plain,
! [X_205] : ( add(multiplicative_identity,X_205) = multiplicative_identity ),
inference(superposition,[status(thm),theory(equality)],[c_1180,c_863]) ).
tff(c_1037,plain,
! [Z_183,V3_185,V4_181,X_184,Y_187,V2_182,V1_186] :
( sum(V1_186,V2_182,V4_181)
| ~ product(X_184,V3_185,V4_181)
| ~ sum(Y_187,Z_183,V3_185)
| ~ product(X_184,Z_183,V2_182)
| ~ product(X_184,Y_187,V1_186) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_12215,plain,
! [V1_731,X_733,Y_734,Y_730,V2_735,Z_732] :
( sum(V1_731,V2_735,multiply(X_733,Y_734))
| ~ sum(Y_730,Z_732,Y_734)
| ~ product(X_733,Z_732,V2_735)
| ~ product(X_733,Y_730,V1_731) ),
inference(resolution,[status(thm)],[c_4,c_1037]) ).
tff(c_175342,plain,
! [Y_2092,X_2090,V2_2091,X_2089,V1_2088] :
( sum(V1_2088,V2_2091,multiply(X_2090,add(X_2089,Y_2092)))
| ~ product(X_2090,X_2089,V2_2091)
| ~ product(X_2090,Y_2092,V1_2088) ),
inference(resolution,[status(thm)],[c_68,c_12215]) ).
tff(c_203,plain,
! [X_1,Y_2,U_113] :
( ( add(X_1,Y_2) = U_113 )
| ~ sum(Y_2,X_1,U_113) ),
inference(resolution,[status(thm)],[c_68,c_190]) ).
tff(c_860698,plain,
! [Y_5453,X_5456,V1_5454,V2_5457,X_5455] :
( ( multiply(X_5456,add(X_5455,Y_5453)) = add(V2_5457,V1_5454) )
| ~ product(X_5456,X_5455,V2_5457)
| ~ product(X_5456,Y_5453,V1_5454) ),
inference(resolution,[status(thm)],[c_175342,c_203]) ).
tff(c_861074,plain,
! [X_14,Y_5453,V1_5454] :
( ( multiply(X_14,add(multiplicative_identity,Y_5453)) = add(X_14,V1_5454) )
| ~ product(X_14,Y_5453,V1_5454) ),
inference(resolution,[status(thm)],[c_16,c_860698]) ).
tff(c_861367,plain,
! [X_5458,V1_5459,Y_5460] :
( ( add(X_5458,V1_5459) = X_5458 )
| ~ product(X_5458,Y_5460,V1_5459) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_1185,c_861074]) ).
tff(c_863471,plain,
! [X_5463,Y_5464] : ( add(X_5463,multiply(X_5463,Y_5464)) = X_5463 ),
inference(resolution,[status(thm)],[c_4,c_861367]) ).
tff(c_864178,plain,
! [X_5463,Y_5464] : sum(X_5463,multiply(X_5463,Y_5464),X_5463),
inference(superposition,[status(thm),theory(equality)],[c_863471,c_2]) ).
tff(c_46,plain,
~ sum(x,multiply(x,y),x),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_866174,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_864178,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : BOO010-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.12/0.33 % Computer : n023.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 15:22:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 252.62/223.64 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 252.62/223.65
% 252.62/223.65 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------