TSTP Solution File: HEN009-3 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : HEN009-3 : TPTP v8.1.2. 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 : n005.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 10:42:18 EDT 2023
% Result : Unsatisfiable 6.53s 2.63s
% Output : CNFRefutation 6.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 89 ( 55 unt; 8 typ; 0 def)
% Number of atoms : 114 ( 70 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 35 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 68 (; 68 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_equal > divide > #nlpp > zero > identity > d > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(less_equal,type,
less_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(divide,type,
divide: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(d,type,
d: $i ).
tff(identity,type,
identity: $i ).
tff(zero,type,
zero: $i ).
tff(c,type,
c: $i ).
tff(f_84,axiom,
b != d,
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
! [X] : less_equal(X,identity),
file(unknown,unknown) ).
tff(f_82,axiom,
divide(identity,c) = d,
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_81,axiom,
divide(identity,b) = c,
file(unknown,unknown) ).
tff(f_80,axiom,
divide(identity,a) = b,
file(unknown,unknown) ).
tff(c_24,plain,
d != b,
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_10,plain,
! [X_10] : less_equal(zero,X_10),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_53,plain,
! [X_18,Y_19] :
( ( divide(X_18,Y_19) = zero )
| ~ less_equal(X_18,Y_19) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_64,plain,
! [X_10] : ( divide(zero,X_10) = zero ),
inference(resolution,[status(thm)],[c_10,c_53]) ).
tff(c_14,plain,
! [X_13] : less_equal(X_13,identity),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_65,plain,
! [X_13] : ( divide(X_13,identity) = zero ),
inference(resolution,[status(thm)],[c_14,c_53]) ).
tff(c_22,plain,
divide(identity,c) = d,
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_191,plain,
! [X_30,Z_31,Y_32] : less_equal(divide(divide(X_30,Z_31),divide(Y_32,Z_31)),divide(divide(X_30,Y_32),Z_31)),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_249,plain,
! [X_30] : less_equal(divide(divide(X_30,c),d),divide(divide(X_30,identity),c)),
inference(superposition,[status(thm),theory(equality)],[c_22,c_191]) ).
tff(c_308,plain,
! [X_35] : less_equal(divide(divide(X_35,c),d),zero),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_65,c_249]) ).
tff(c_148,plain,
! [Y_26,X_27] :
( ( Y_26 = X_27 )
| ~ less_equal(Y_26,X_27)
| ~ less_equal(X_27,Y_26) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_159,plain,
! [X_10] :
( ( zero = X_10 )
| ~ less_equal(X_10,zero) ),
inference(resolution,[status(thm)],[c_10,c_148]) ).
tff(c_328,plain,
! [X_35] : ( divide(divide(X_35,c),d) = zero ),
inference(resolution,[status(thm)],[c_308,c_159]) ).
tff(c_6,plain,
! [X_5,Y_6] : less_equal(divide(X_5,Y_6),X_5),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_63,plain,
! [X_5,Y_6] : ( divide(divide(X_5,Y_6),X_5) = zero ),
inference(resolution,[status(thm)],[c_6,c_53]) ).
tff(c_877,plain,
! [X_46,Y_47] : less_equal(divide(divide(X_46,X_46),divide(Y_47,X_46)),zero),
inference(superposition,[status(thm),theory(equality)],[c_63,c_191]) ).
tff(c_968,plain,
! [X_48] : less_equal(divide(divide(X_48,X_48),zero),zero),
inference(superposition,[status(thm),theory(equality)],[c_63,c_877]) ).
tff(c_4,plain,
! [X_3,Y_4] :
( less_equal(X_3,Y_4)
| ( divide(X_3,Y_4) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_157,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ less_equal(Y_4,X_3)
| ( divide(X_3,Y_4) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_148]) ).
tff(c_971,plain,
! [X_48] :
( ( divide(divide(X_48,X_48),zero) = zero )
| ( divide(zero,divide(divide(X_48,X_48),zero)) != zero ) ),
inference(resolution,[status(thm)],[c_968,c_157]) ).
tff(c_1049,plain,
! [X_50] : ( divide(divide(X_50,X_50),zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_971]) ).
tff(c_161,plain,
! [X_28] :
( ( zero = X_28 )
| ~ less_equal(X_28,zero) ),
inference(resolution,[status(thm)],[c_10,c_148]) ).
tff(c_174,plain,
! [X_3] :
( ( zero = X_3 )
| ( divide(X_3,zero) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_161]) ).
tff(c_1102,plain,
! [X_50] : ( divide(X_50,X_50) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_1049,c_174]) ).
tff(c_20,plain,
divide(identity,b) = c,
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_1390,plain,
! [Z_53] : less_equal(divide(divide(identity,Z_53),divide(b,Z_53)),divide(c,Z_53)),
inference(superposition,[status(thm),theory(equality)],[c_20,c_191]) ).
tff(c_1431,plain,
less_equal(divide(d,divide(b,c)),divide(c,c)),
inference(superposition,[status(thm),theory(equality)],[c_22,c_1390]) ).
tff(c_1445,plain,
less_equal(divide(d,divide(b,c)),zero),
inference(demodulation,[status(thm),theory(equality)],[c_1102,c_1431]) ).
tff(c_1448,plain,
( ( divide(d,divide(b,c)) = zero )
| ( divide(zero,divide(d,divide(b,c))) != zero ) ),
inference(resolution,[status(thm)],[c_1445,c_157]) ).
tff(c_1459,plain,
divide(d,divide(b,c)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_64,c_1448]) ).
tff(c_683,plain,
! [Y_41,X_42] :
( ( Y_41 = X_42 )
| ~ less_equal(Y_41,X_42)
| ( divide(X_42,Y_41) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_148]) ).
tff(c_4291,plain,
! [Y_76,X_77] :
( ( Y_76 = X_77 )
| ( divide(Y_76,X_77) != zero )
| ( divide(X_77,Y_76) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_683]) ).
tff(c_4311,plain,
( ( divide(b,c) = d )
| ( divide(divide(b,c),d) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_1459,c_4291]) ).
tff(c_4342,plain,
divide(b,c) = d,
inference(demodulation,[status(thm),theory(equality)],[c_328,c_4311]) ).
tff(c_4629,plain,
divide(d,b) = zero,
inference(superposition,[status(thm),theory(equality)],[c_4342,c_63]) ).
tff(c_18,plain,
divide(identity,a) = b,
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_258,plain,
! [X_30] : less_equal(divide(divide(X_30,a),b),divide(divide(X_30,identity),a)),
inference(superposition,[status(thm),theory(equality)],[c_18,c_191]) ).
tff(c_336,plain,
! [X_36] : less_equal(divide(divide(X_36,a),b),zero),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_65,c_258]) ).
tff(c_356,plain,
! [X_36] : ( divide(divide(X_36,a),b) = zero ),
inference(resolution,[status(thm)],[c_336,c_159]) ).
tff(c_240,plain,
! [X_30] : less_equal(divide(divide(X_30,b),c),divide(divide(X_30,identity),b)),
inference(superposition,[status(thm),theory(equality)],[c_20,c_191]) ).
tff(c_543,plain,
! [X_39] : less_equal(divide(divide(X_39,b),c),zero),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_65,c_240]) ).
tff(c_567,plain,
! [X_39] : ( divide(divide(X_39,b),c) = zero ),
inference(resolution,[status(thm)],[c_543,c_159]) ).
tff(c_355,plain,
less_equal(divide(b,b),zero),
inference(superposition,[status(thm),theory(equality)],[c_18,c_336]) ).
tff(c_411,plain,
divide(b,b) = zero,
inference(resolution,[status(thm)],[c_355,c_159]) ).
tff(c_783,plain,
! [Z_45] : less_equal(divide(divide(identity,Z_45),divide(a,Z_45)),divide(b,Z_45)),
inference(superposition,[status(thm),theory(equality)],[c_18,c_191]) ).
tff(c_809,plain,
less_equal(divide(c,divide(a,b)),divide(b,b)),
inference(superposition,[status(thm),theory(equality)],[c_20,c_783]) ).
tff(c_823,plain,
less_equal(divide(c,divide(a,b)),zero),
inference(demodulation,[status(thm),theory(equality)],[c_411,c_809]) ).
tff(c_826,plain,
( ( divide(c,divide(a,b)) = zero )
| ( divide(zero,divide(c,divide(a,b))) != zero ) ),
inference(resolution,[status(thm)],[c_823,c_157]) ).
tff(c_837,plain,
divide(c,divide(a,b)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_64,c_826]) ).
tff(c_4315,plain,
( ( divide(a,b) = c )
| ( divide(divide(a,b),c) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_837,c_4291]) ).
tff(c_4349,plain,
divide(a,b) = c,
inference(demodulation,[status(thm),theory(equality)],[c_567,c_4315]) ).
tff(c_4421,plain,
divide(c,a) = zero,
inference(superposition,[status(thm),theory(equality)],[c_4349,c_63]) ).
tff(c_1009,plain,
! [Y_49] : less_equal(divide(b,divide(Y_49,a)),divide(divide(identity,Y_49),a)),
inference(superposition,[status(thm),theory(equality)],[c_18,c_191]) ).
tff(c_1035,plain,
less_equal(divide(b,divide(c,a)),divide(d,a)),
inference(superposition,[status(thm),theory(equality)],[c_22,c_1009]) ).
tff(c_4476,plain,
less_equal(divide(b,zero),divide(d,a)),
inference(demodulation,[status(thm),theory(equality)],[c_4421,c_1035]) ).
tff(c_2,plain,
! [X_1,Y_2] :
( ( divide(X_1,Y_2) = zero )
| ~ less_equal(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_4795,plain,
divide(divide(b,zero),divide(d,a)) = zero,
inference(resolution,[status(thm)],[c_4476,c_2]) ).
tff(c_12,plain,
! [Y_12,X_11] :
( ( Y_12 = X_11 )
| ~ less_equal(Y_12,X_11)
| ~ less_equal(X_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_262,plain,
! [X_30,Z_31,Y_32] :
( ( divide(divide(X_30,Z_31),divide(Y_32,Z_31)) = divide(divide(X_30,Y_32),Z_31) )
| ~ less_equal(divide(divide(X_30,Y_32),Z_31),divide(divide(X_30,Z_31),divide(Y_32,Z_31))) ),
inference(resolution,[status(thm)],[c_191,c_12]) ).
tff(c_4817,plain,
( ( divide(divide(b,divide(d,a)),divide(zero,divide(d,a))) = divide(divide(b,zero),divide(d,a)) )
| ~ less_equal(zero,divide(divide(b,divide(d,a)),divide(zero,divide(d,a)))) ),
inference(superposition,[status(thm),theory(equality)],[c_4795,c_262]) ).
tff(c_4870,plain,
divide(divide(b,divide(d,a)),zero) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_4795,c_64,c_4817]) ).
tff(c_700,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ( divide(Y_4,X_3) != zero )
| ( divide(X_3,Y_4) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_683]) ).
tff(c_5357,plain,
( ( divide(b,divide(d,a)) = zero )
| ( divide(zero,divide(b,divide(d,a))) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_4870,c_700]) ).
tff(c_5425,plain,
divide(b,divide(d,a)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_64,c_5357]) ).
tff(c_5452,plain,
( ( divide(d,a) = b )
| ( divide(divide(d,a),b) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_5425,c_700]) ).
tff(c_5515,plain,
divide(d,a) = b,
inference(demodulation,[status(thm),theory(equality)],[c_356,c_5452]) ).
tff(c_701,plain,
! [X_5,Y_6] :
( ( divide(X_5,Y_6) = X_5 )
| ( divide(X_5,divide(X_5,Y_6)) != zero ) ),
inference(resolution,[status(thm)],[c_6,c_683]) ).
tff(c_5545,plain,
( ( divide(d,a) = d )
| ( divide(d,b) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_5515,c_701]) ).
tff(c_5602,plain,
d = b,
inference(demodulation,[status(thm),theory(equality)],[c_4629,c_5515,c_5545]) ).
tff(c_5604,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_5602]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HEN009-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % 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
% 0.19/0.36 % Computer : n005.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Thu Aug 3 13:07:12 EDT 2023
% 0.21/0.36 % CPUTime :
% 6.53/2.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.53/2.64
% 6.53/2.64 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.77/2.69
% 6.77/2.69 Inference rules
% 6.77/2.69 ----------------------
% 6.77/2.69 #Ref : 0
% 6.77/2.69 #Sup : 1402
% 6.77/2.69 #Fact : 0
% 6.77/2.69 #Define : 0
% 6.77/2.69 #Split : 4
% 6.77/2.69 #Chain : 0
% 6.77/2.69 #Close : 0
% 6.77/2.69
% 6.77/2.69 Ordering : KBO
% 6.77/2.69
% 6.77/2.69 Simplification rules
% 6.77/2.69 ----------------------
% 6.77/2.69 #Subsume : 123
% 6.77/2.69 #Demod : 1657
% 6.77/2.69 #Tautology : 800
% 6.77/2.69 #SimpNegUnit : 35
% 6.77/2.69 #BackRed : 38
% 6.77/2.69
% 6.77/2.69 #Partial instantiations: 0
% 6.77/2.69 #Strategies tried : 1
% 6.77/2.69
% 6.77/2.69 Timing (in seconds)
% 6.77/2.69 ----------------------
% 6.77/2.69 Preprocessing : 0.47
% 6.77/2.69 Parsing : 0.24
% 6.77/2.69 CNF conversion : 0.03
% 6.77/2.69 Main loop : 1.11
% 6.77/2.69 Inferencing : 0.35
% 6.77/2.69 Reduction : 0.47
% 6.77/2.69 Demodulation : 0.36
% 6.77/2.69 BG Simplification : 0.03
% 6.77/2.69 Subsumption : 0.18
% 6.77/2.69 Abstraction : 0.04
% 6.77/2.69 MUC search : 0.00
% 6.77/2.69 Cooper : 0.00
% 6.77/2.69 Total : 1.65
% 6.77/2.70 Index Insertion : 0.00
% 6.77/2.70 Index Deletion : 0.00
% 6.77/2.70 Index Matching : 0.00
% 6.77/2.70 BG Taut test : 0.00
%------------------------------------------------------------------------------