TSTP Solution File: FLD008-4 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : FLD008-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n009.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 : Tue Aug 22 10:37:26 EDT 2023
% Result : Unsatisfiable 14.83s 5.72s
% Output : CNFRefutation 14.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 31
% Syntax : Number of formulae : 105 ( 38 unt; 14 typ; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 194 ( 102 ~; 92 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 94 (; 94 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > d > c > b > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(additive_inverse,type,
additive_inverse: $i > $i ).
tff(b,type,
b: $i ).
tff(defined,type,
defined: $i > $o ).
tff(multiplicative_inverse,type,
multiplicative_inverse: $i > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(d,type,
d: $i ).
tff(c,type,
c: $i ).
tff(f_256,axiom,
~ sum(additive_identity,additive_inverse(c),d),
file(unknown,unknown) ).
tff(f_251,axiom,
defined(c),
file(unknown,unknown) ).
tff(f_164,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_252,axiom,
defined(d),
file(unknown,unknown) ).
tff(f_222,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_204,axiom,
! [X,Y] :
( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_253,axiom,
sum(a,b,c),
file(unknown,unknown) ).
tff(f_250,axiom,
defined(b),
file(unknown,unknown) ).
tff(f_68,axiom,
! [W,U,Z,X,Y,V] :
( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_159,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_233,axiom,
! [U,Z,X,Y,V] :
( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) ),
file(unknown,unknown) ).
tff(f_254,axiom,
sum(additive_inverse(a),additive_inverse(b),d),
file(unknown,unknown) ).
tff(f_57,axiom,
! [W,U,Z,X,Y,V] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file(unknown,unknown) ).
tff(c_66,plain,
~ sum(additive_identity,additive_inverse(c),d),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_58,plain,
defined(c),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_30,plain,
! [X_51] :
( ~ defined(X_51)
| defined(additive_inverse(X_51)) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_60,plain,
defined(d),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_46,plain,
! [Y_65,X_64] :
( ~ defined(Y_65)
| ~ defined(X_64)
| less_or_equal(Y_65,X_64)
| less_or_equal(X_64,Y_65) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_112,plain,
! [Y_95,X_96] :
( ~ less_or_equal(Y_95,X_96)
| ~ less_or_equal(X_96,Y_95)
| sum(additive_identity,X_96,Y_95) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_122,plain,
( ~ less_or_equal(d,additive_inverse(c))
| ~ less_or_equal(additive_inverse(c),d) ),
inference(resolution,[status(thm)],[c_112,c_66]) ).
tff(c_125,plain,
~ less_or_equal(additive_inverse(c),d),
inference(splitLeft,[status(thm)],[c_122]) ).
tff(c_151,plain,
( ~ defined(additive_inverse(c))
| ~ defined(d)
| less_or_equal(d,additive_inverse(c)) ),
inference(resolution,[status(thm)],[c_46,c_125]) ).
tff(c_157,plain,
( ~ defined(additive_inverse(c))
| less_or_equal(d,additive_inverse(c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_151]) ).
tff(c_165,plain,
~ defined(additive_inverse(c)),
inference(splitLeft,[status(thm)],[c_157]) ).
tff(c_168,plain,
~ defined(c),
inference(resolution,[status(thm)],[c_30,c_165]) ).
tff(c_172,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_168]) ).
tff(c_174,plain,
defined(additive_inverse(c)),
inference(splitRight,[status(thm)],[c_157]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_73,plain,
! [X_82,Y_83,Z_84] :
( ~ sum(X_82,Y_83,Z_84)
| sum(Y_83,X_82,Z_84) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_83,plain,
! [X_13] :
( sum(X_13,additive_identity,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_73]) ).
tff(c_62,plain,
sum(a,b,c),
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_56,plain,
defined(b),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_393,plain,
! [X_133,Y_134,Z_129,V_132,W_130,U_131] :
( ~ sum(X_133,V_132,W_130)
| ~ sum(Y_134,Z_129,V_132)
| ~ sum(X_133,Y_134,U_131)
| sum(U_131,Z_129,W_130) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_3596,plain,
! [Y_270,Z_271,U_272] :
( ~ sum(Y_270,Z_271,b)
| ~ sum(a,Y_270,U_272)
| sum(U_272,Z_271,c) ),
inference(resolution,[status(thm)],[c_62,c_393]) ).
tff(c_3605,plain,
! [U_272] :
( ~ sum(a,b,U_272)
| sum(U_272,additive_identity,c)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_83,c_3596]) ).
tff(c_3812,plain,
! [U_275] :
( ~ sum(a,b,U_275)
| sum(U_275,additive_identity,c) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_3605]) ).
tff(c_3831,plain,
sum(c,additive_identity,c),
inference(resolution,[status(thm)],[c_62,c_3812]) ).
tff(c_10,plain,
! [X_16,Y_15,Z_17] :
( ~ sum(X_16,Y_15,Z_17)
| sum(Y_15,X_16,Z_17) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_3852,plain,
sum(additive_identity,c,c),
inference(resolution,[status(thm)],[c_3831,c_10]) ).
tff(c_8,plain,
! [X_14] :
( ~ defined(X_14)
| sum(additive_inverse(X_14),X_14,additive_identity) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_6454,plain,
! [Y_337,Z_338,X_339,U_340] :
( ~ sum(Y_337,Z_338,X_339)
| ~ sum(additive_inverse(X_339),Y_337,U_340)
| sum(U_340,Z_338,additive_identity)
| ~ defined(X_339) ),
inference(resolution,[status(thm)],[c_8,c_393]) ).
tff(c_6496,plain,
! [U_340] :
( ~ sum(additive_inverse(c),additive_identity,U_340)
| sum(U_340,c,additive_identity)
| ~ defined(c) ),
inference(resolution,[status(thm)],[c_3852,c_6454]) ).
tff(c_21942,plain,
! [U_547] :
( ~ sum(additive_inverse(c),additive_identity,U_547)
| sum(U_547,c,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_6496]) ).
tff(c_21958,plain,
( sum(additive_inverse(c),c,additive_identity)
| ~ defined(additive_inverse(c)) ),
inference(resolution,[status(thm)],[c_83,c_21942]) ).
tff(c_21968,plain,
sum(additive_inverse(c),c,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_174,c_21958]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_28,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_282,plain,
! [V_125,X_122,Z_123,Y_124,U_121] :
( ~ sum(Y_124,Z_123,V_125)
| ~ sum(X_122,Z_123,U_121)
| ~ less_or_equal(X_122,Y_124)
| less_or_equal(U_121,V_125) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_331,plain,
! [X_127,U_128] :
( ~ sum(X_127,b,U_128)
| ~ less_or_equal(X_127,a)
| less_or_equal(U_128,c) ),
inference(resolution,[status(thm)],[c_62,c_282]) ).
tff(c_347,plain,
( ~ less_or_equal(additive_inverse(b),a)
| less_or_equal(additive_identity,c)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_8,c_331]) ).
tff(c_364,plain,
( ~ less_or_equal(additive_inverse(b),a)
| less_or_equal(additive_identity,c) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_347]) ).
tff(c_496,plain,
~ less_or_equal(additive_inverse(b),a),
inference(splitLeft,[status(thm)],[c_364]) ).
tff(c_499,plain,
( ~ defined(additive_inverse(b))
| ~ defined(a)
| less_or_equal(a,additive_inverse(b)) ),
inference(resolution,[status(thm)],[c_46,c_496]) ).
tff(c_505,plain,
( ~ defined(additive_inverse(b))
| less_or_equal(a,additive_inverse(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_499]) ).
tff(c_546,plain,
~ defined(additive_inverse(b)),
inference(splitLeft,[status(thm)],[c_505]) ).
tff(c_549,plain,
~ defined(b),
inference(resolution,[status(thm)],[c_30,c_546]) ).
tff(c_553,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_56,c_549]) ).
tff(c_555,plain,
defined(additive_inverse(b)),
inference(splitRight,[status(thm)],[c_505]) ).
tff(c_64,plain,
sum(additive_inverse(a),additive_inverse(b),d),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_3131,plain,
! [X_254,X_255,U_256] :
( ~ sum(X_254,X_255,U_256)
| ~ less_or_equal(X_254,additive_identity)
| less_or_equal(U_256,X_255)
| ~ defined(X_255) ),
inference(resolution,[status(thm)],[c_6,c_282]) ).
tff(c_3164,plain,
( ~ less_or_equal(additive_inverse(a),additive_identity)
| less_or_equal(d,additive_inverse(b))
| ~ defined(additive_inverse(b)) ),
inference(resolution,[status(thm)],[c_64,c_3131]) ).
tff(c_3186,plain,
( ~ less_or_equal(additive_inverse(a),additive_identity)
| less_or_equal(d,additive_inverse(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_555,c_3164]) ).
tff(c_3481,plain,
~ less_or_equal(additive_inverse(a),additive_identity),
inference(splitLeft,[status(thm)],[c_3186]) ).
tff(c_3532,plain,
( ~ defined(additive_inverse(a))
| ~ defined(additive_identity)
| less_or_equal(additive_identity,additive_inverse(a)) ),
inference(resolution,[status(thm)],[c_46,c_3481]) ).
tff(c_3539,plain,
( ~ defined(additive_inverse(a))
| less_or_equal(additive_identity,additive_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_3532]) ).
tff(c_3559,plain,
~ defined(additive_inverse(a)),
inference(splitLeft,[status(thm)],[c_3539]) ).
tff(c_3563,plain,
~ defined(a),
inference(resolution,[status(thm)],[c_30,c_3559]) ).
tff(c_3567,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_3563]) ).
tff(c_3569,plain,
defined(additive_inverse(a)),
inference(splitRight,[status(thm)],[c_3539]) ).
tff(c_509,plain,
! [Z_142,W_147,U_145,Y_143,X_146,V_144] :
( ~ sum(U_145,Z_142,W_147)
| ~ sum(Y_143,Z_142,V_144)
| ~ sum(X_146,Y_143,U_145)
| sum(X_146,V_144,W_147) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_5448,plain,
! [Y_317,X_318,V_319,X_320] :
( ~ sum(Y_317,X_318,V_319)
| ~ sum(X_320,Y_317,additive_identity)
| sum(X_320,V_319,X_318)
| ~ defined(X_318) ),
inference(resolution,[status(thm)],[c_6,c_509]) ).
tff(c_5516,plain,
! [X_320] :
( ~ sum(X_320,a,additive_identity)
| sum(X_320,c,b)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_62,c_5448]) ).
tff(c_5630,plain,
! [X_322] :
( ~ sum(X_322,a,additive_identity)
| sum(X_322,c,b) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_5516]) ).
tff(c_6106,plain,
! [X_331] :
( sum(c,X_331,b)
| ~ sum(X_331,a,additive_identity) ),
inference(resolution,[status(thm)],[c_5630,c_10]) ).
tff(c_6112,plain,
( sum(c,additive_inverse(a),b)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_8,c_6106]) ).
tff(c_6118,plain,
sum(c,additive_inverse(a),b),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_6112]) ).
tff(c_543,plain,
! [Y_143,X_13,V_144,X_146] :
( ~ sum(Y_143,X_13,V_144)
| ~ sum(X_146,Y_143,additive_identity)
| sum(X_146,V_144,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_509]) ).
tff(c_6122,plain,
! [X_146] :
( ~ sum(X_146,c,additive_identity)
| sum(X_146,b,additive_inverse(a))
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[c_6118,c_543]) ).
tff(c_23211,plain,
! [X_559] :
( ~ sum(X_559,c,additive_identity)
| sum(X_559,b,additive_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_3569,c_6122]) ).
tff(c_82,plain,
! [X_14] :
( sum(X_14,additive_inverse(X_14),additive_identity)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_73]) ).
tff(c_5314,plain,
! [Y_313,V_314,X_315] :
( ~ sum(Y_313,additive_inverse(b),V_314)
| ~ sum(X_315,Y_313,additive_inverse(a))
| sum(X_315,V_314,d) ),
inference(resolution,[status(thm)],[c_64,c_509]) ).
tff(c_5326,plain,
! [X_315] :
( ~ sum(X_315,b,additive_inverse(a))
| sum(X_315,additive_identity,d)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_82,c_5314]) ).
tff(c_5344,plain,
! [X_315] :
( ~ sum(X_315,b,additive_inverse(a))
| sum(X_315,additive_identity,d) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_5326]) ).
tff(c_23524,plain,
! [X_561] :
( sum(X_561,additive_identity,d)
| ~ sum(X_561,c,additive_identity) ),
inference(resolution,[status(thm)],[c_23211,c_5344]) ).
tff(c_23544,plain,
sum(additive_inverse(c),additive_identity,d),
inference(resolution,[status(thm)],[c_21968,c_23524]) ).
tff(c_23683,plain,
sum(additive_identity,additive_inverse(c),d),
inference(resolution,[status(thm)],[c_23544,c_10]) ).
tff(c_23729,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66,c_23683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD008-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % 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
% 0.16/0.34 % Computer : n009.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 3 19:53:54 EDT 2023
% 0.16/0.35 % CPUTime :
% 14.83/5.72 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.83/5.73
% 14.83/5.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.83/5.77
% 14.83/5.77 Inference rules
% 14.83/5.77 ----------------------
% 14.83/5.77 #Ref : 0
% 14.83/5.77 #Sup : 5402
% 14.83/5.77 #Fact : 16
% 14.83/5.77 #Define : 0
% 14.83/5.77 #Split : 43
% 14.83/5.77 #Chain : 0
% 14.83/5.77 #Close : 0
% 14.83/5.77
% 14.83/5.77 Ordering : KBO
% 14.83/5.77
% 14.83/5.77 Simplification rules
% 14.83/5.77 ----------------------
% 14.83/5.77 #Subsume : 985
% 14.83/5.77 #Demod : 3183
% 14.83/5.77 #Tautology : 786
% 14.83/5.77 #SimpNegUnit : 125
% 14.83/5.77 #BackRed : 0
% 14.83/5.77
% 14.83/5.77 #Partial instantiations: 0
% 14.83/5.77 #Strategies tried : 1
% 14.83/5.77
% 14.83/5.77 Timing (in seconds)
% 14.83/5.77 ----------------------
% 14.83/5.78 Preprocessing : 0.49
% 14.83/5.78 Parsing : 0.27
% 14.83/5.78 CNF conversion : 0.03
% 14.83/5.78 Main loop : 4.21
% 14.83/5.78 Inferencing : 0.96
% 14.83/5.78 Reduction : 1.64
% 14.83/5.78 Demodulation : 1.21
% 14.83/5.78 BG Simplification : 0.06
% 14.83/5.78 Subsumption : 1.23
% 14.83/5.78 Abstraction : 0.07
% 14.83/5.78 MUC search : 0.00
% 14.83/5.78 Cooper : 0.00
% 14.83/5.78 Total : 4.77
% 14.83/5.78 Index Insertion : 0.00
% 14.83/5.78 Index Deletion : 0.00
% 14.83/5.78 Index Matching : 0.00
% 14.83/5.78 BG Taut test : 0.00
%------------------------------------------------------------------------------