%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : BOO012-1 : 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 : n019.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 05:45:03 PM UTC 2025
% Result : Unsatisfiable 20.62s 8.82s
% Output : CNFRefutation 20.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 12 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 84 ( 43 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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; 3 con; 0-2 aty)
% Number of variables : 103 ( 103 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > multiply > add > #nlpp > inverse > 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(add,type,
add: ( $i * $i ) > $i ).
tff(f_180,axiom,
! [X] : sum(inverse(X),X,multiplicative_identity),
file(unknown,unknown) ).
tff(f_46,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file(unknown,unknown) ).
tff(f_195,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| ( U = V ) ),
file(unknown,unknown) ).
tff(f_182,axiom,
! [X] : sum(X,inverse(X),multiplicative_identity),
file(unknown,unknown) ).
tff(f_184,axiom,
! [X] : product(inverse(X),X,additive_identity),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] : sum(X,additive_identity,X),
file(unknown,unknown) ).
tff(f_136,axiom,
! [V3,Z,V1,X,Y,V2,V4] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3)
| ~ sum(X,V3,V4)
| product(V1,V2,V4) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X] : product(X,multiplicative_identity,X),
file(unknown,unknown) ).
tff(f_203,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [X] : product(multiplicative_identity,X,X),
file(unknown,unknown) ).
tff(f_150,axiom,
! [V3,Z,V1,X,Y,V2,V4] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3)
| ~ product(V1,V2,V4)
| sum(X,V3,V4) ),
file(unknown,unknown) ).
tff(f_207,axiom,
inverse(inverse(x)) != x,
file(unknown,unknown) ).
tff(c_34,plain,
! [X_71] : sum(inverse(X_71),X_71,multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_2,plain,
! [X_1,Y_2] : sum(X_1,Y_2,add(X_1,Y_2)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
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_53]) ).
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_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_195]) ).
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_36,plain,
! [X_72] : sum(X_72,inverse(X_72),multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_38,plain,
! [X_73] : product(inverse(X_73),X_73,additive_identity),
inference(cnfTransformation,[status(thm)],[f_184]) ).
tff(c_12,plain,
! [X_12] : sum(X_12,additive_identity,X_12),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_610,plain,
! [V1_152,V2_150,V4_154,V3_148,Z_151,Y_149,X_153] :
( product(V1_152,V2_150,V4_154)
| ~ sum(X_153,V3_148,V4_154)
| ~ product(Y_149,Z_151,V3_148)
| ~ sum(X_153,Z_151,V2_150)
| ~ sum(X_153,Y_149,V1_152) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_3826,plain,
! [V2_382,X_383,Z_384,V1_386,Y_385] :
( product(V1_386,V2_382,X_383)
| ~ product(Y_385,Z_384,additive_identity)
| ~ sum(X_383,Z_384,V2_382)
| ~ sum(X_383,Y_385,V1_386) ),
inference(resolution,[status(thm)],[c_12,c_610]) ).
tff(c_43119,plain,
! [V1_1061,V2_1062,X_1063,X_1064] :
( product(V1_1061,V2_1062,X_1063)
| ~ sum(X_1063,X_1064,V2_1062)
| ~ sum(X_1063,inverse(X_1064),V1_1061) ),
inference(resolution,[status(thm)],[c_38,c_3826]) ).
tff(c_51193,plain,
! [V1_1132,X_1133] :
( product(V1_1132,multiplicative_identity,X_1133)
| ~ sum(X_1133,inverse(inverse(X_1133)),V1_1132) ),
inference(resolution,[status(thm)],[c_36,c_43119]) ).
tff(c_51391,plain,
! [Y_2] : product(add(inverse(inverse(Y_2)),Y_2),multiplicative_identity,Y_2),
inference(resolution,[status(thm)],[c_68,c_51193]) ).
tff(c_51466,plain,
! [Y_1134] : product(add(Y_1134,inverse(inverse(Y_1134))),multiplicative_identity,Y_1134),
inference(demodulation,[status(thm),theory(equality)],[c_863,c_51391]) ).
tff(c_16,plain,
! [X_14] : product(X_14,multiplicative_identity,X_14),
inference(cnfTransformation,[status(thm)],[f_66]) ).
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_203]) ).
tff(c_125,plain,
! [X_14,U_106] :
( ( X_14 = U_106 )
| ~ product(X_14,multiplicative_identity,U_106) ),
inference(resolution,[status(thm)],[c_16,c_107]) ).
tff(c_51845,plain,
! [Y_1135] : ( add(Y_1135,inverse(inverse(Y_1135))) = Y_1135 ),
inference(resolution,[status(thm)],[c_51466,c_125]) ).
tff(c_51887,plain,
! [Y_1135] : sum(inverse(inverse(Y_1135)),Y_1135,Y_1135),
inference(superposition,[status(thm),theory(equality)],[c_51845,c_68]) ).
tff(c_14,plain,
! [X_13] : product(multiplicative_identity,X_13,X_13),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_1148,plain,
! [V3_211,Z_209,Y_212,V4_213,V2_208,V1_210,X_214] :
( sum(X_214,V3_211,V4_213)
| ~ product(V1_210,V2_208,V4_213)
| ~ product(Y_212,Z_209,V3_211)
| ~ sum(X_214,Z_209,V2_208)
| ~ sum(X_214,Y_212,V1_210) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_1727,plain,
! [X_260,Z_259,Y_258,X_261,V3_262] :
( sum(X_260,V3_262,X_261)
| ~ product(Y_258,Z_259,V3_262)
| ~ sum(X_260,Z_259,X_261)
| ~ sum(X_260,Y_258,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_14,c_1148]) ).
tff(c_57906,plain,
! [X_1165,X_1166,X_1167] :
( sum(X_1165,additive_identity,X_1166)
| ~ sum(X_1165,X_1167,X_1166)
| ~ sum(X_1165,inverse(X_1167),multiplicative_identity) ),
inference(resolution,[status(thm)],[c_38,c_1727]) ).
tff(c_57928,plain,
! [Y_1135] :
( sum(inverse(inverse(Y_1135)),additive_identity,Y_1135)
| ~ sum(inverse(inverse(Y_1135)),inverse(Y_1135),multiplicative_identity) ),
inference(resolution,[status(thm)],[c_51887,c_57906]) ).
tff(c_58140,plain,
! [Y_1168] : sum(inverse(inverse(Y_1168)),additive_identity,Y_1168),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_57928]) ).
tff(c_208,plain,
! [X_12,U_113] :
( ( X_12 = U_113 )
| ~ sum(X_12,additive_identity,U_113) ),
inference(resolution,[status(thm)],[c_12,c_190]) ).
tff(c_58436,plain,
! [Y_1168] : ( inverse(inverse(Y_1168)) = Y_1168 ),
inference(resolution,[status(thm)],[c_58140,c_208]) ).
tff(c_46,plain,
inverse(inverse(x)) != x,
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_58488,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58436,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : BOO012-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.13 % 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 : n019.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 15:22:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 20.62/8.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.62/8.83
% 20.62/8.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------