TSTP Solution File: NUN082+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUN082+2 : TPTP v8.1.2. Released v7.3.0.
% 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 : n032.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 10:53:25 EDT 2023
% Result : Theorem 3.54s 1.89s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 33
% Syntax : Number of formulae : 79 ( 36 unt; 24 typ; 0 def)
% Number of atoms : 97 ( 34 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 68 ( 26 ~; 17 |; 25 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 23 >; 15 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-2 aty)
% Number of variables : 107 (; 85 !; 22 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ r4 > r3 > r2 > r1 > #nlpp > #skF_11 > #skF_16 > #skF_6 > #skF_2 > #skF_18 > #skF_19 > #skF_3 > #skF_15 > #skF_12 > #skF_10 > #skF_1 > #skF_8 > #skF_13 > #skF_17 > #skF_14 > #skF_7 > #skF_9 > #skF_5 > #skF_4 > #skF_20
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(r2,type,
r2: ( $i * $i ) > $o ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(r3,type,
r3: ( $i * $i * $i ) > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(r4,type,
r4: ( $i * $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff(r1,type,
r1: $i > $o ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff(f_63,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& ( X19 != Y24 ) )
| ( r1(X19)
& ( X19 = Y24 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
tff(f_160,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& ( Y8 = Y18 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
tff(f_99,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( ~ r4(X16,X17,X18)
& ( X18 != Y23 ) )
| ( r4(X16,X17,X18)
& ( X18 = Y23 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4) ).
tff(f_128,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) )
& ( Y3 = Y2 ) )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).
tff(f_114,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) )
& ( Y5 = Y4 ) )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
tff(f_87,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ r3(X13,X14,X15)
& ( X15 != Y22 ) )
| ( r3(X13,X14,X15)
& ( X15 = Y22 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
tff(f_149,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) )
& ( Y9 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
tff(f_75,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ r2(X11,X12)
& ( X12 != Y21 ) )
| ( r2(X11,X12)
& ( X12 = Y21 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
tff(f_196,negated_conjecture,
~ ? [Y1,Y2] :
( ? [Y3] :
( r4(Y1,Y3,Y2)
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) ) )
& ? [Y5] :
( r1(Y5)
& ( Y2 = Y5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xtimesoneeqzero) ).
tff(c_7,plain,
r1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_68,plain,
! [X5_68] : r1('#skF_17'(X5_68)),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_111,plain,
! [X19_100] :
( ~ r1(X19_100)
| ( X19_100 = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_126,plain,
! [X5_68] : ( '#skF_17'(X5_68) = '#skF_1' ),
inference(resolution,[status(thm)],[c_68,c_111]) ).
tff(c_72,plain,
! [X5_68] : r1('#skF_16'(X5_68)),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_124,plain,
! [X5_68] : ( '#skF_16'(X5_68) = '#skF_1' ),
inference(resolution,[status(thm)],[c_72,c_111]) ).
tff(c_66,plain,
! [X5_68] : ( '#skF_15'(X5_68) = '#skF_17'(X5_68) ),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_70,plain,
! [X5_68] : r4(X5_68,'#skF_16'(X5_68),'#skF_15'(X5_68)),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_85,plain,
! [X5_68] : r4(X5_68,'#skF_16'(X5_68),'#skF_17'(X5_68)),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_70]) ).
tff(c_204,plain,
! [X5_68] : r4(X5_68,'#skF_1','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_124,c_85]) ).
tff(c_557,plain,
! [X16_184,X17_185,X18_186] :
( ~ r4(X16_184,X17_185,X18_186)
| ( X18_186 = '#skF_4'(X16_184,X17_185) ) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_574,plain,
! [X5_68] : ( '#skF_4'(X5_68,'#skF_1') = '#skF_1' ),
inference(resolution,[status(thm)],[c_204,c_557]) ).
tff(c_48,plain,
! [X2_39,X9_40] : r4(X2_39,X9_40,'#skF_12'(X2_39,X9_40)),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_571,plain,
! [X2_39,X9_40] : ( '#skF_12'(X2_39,X9_40) = '#skF_4'(X2_39,X9_40) ),
inference(resolution,[status(thm)],[c_48,c_557]) ).
tff(c_50,plain,
! [X2_39,X9_40] : r3('#skF_12'(X2_39,X9_40),X2_39,'#skF_9'(X2_39,X9_40)),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_682,plain,
! [X2_198,X9_199] : r3('#skF_4'(X2_198,X9_199),X2_198,'#skF_9'(X2_198,X9_199)),
inference(demodulation,[status(thm),theory(equality)],[c_571,c_50]) ).
tff(c_685,plain,
! [X5_68] : r3('#skF_1',X5_68,'#skF_9'(X5_68,'#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_574,c_682]) ).
tff(c_38,plain,
! [X1_23,X8_24] : r3(X1_23,X8_24,'#skF_8'(X1_23,X8_24)),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_522,plain,
! [X13_180,X14_181,X15_182] :
( ~ r3(X13_180,X14_181,X15_182)
| ( X15_182 = '#skF_3'(X13_180,X14_181) ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_540,plain,
! [X1_23,X8_24] : ( '#skF_3'(X1_23,X8_24) = '#skF_8'(X1_23,X8_24) ),
inference(resolution,[status(thm)],[c_38,c_522]) ).
tff(c_23,plain,
! [X13_9,X14_10,X15_15] :
( ~ r3(X13_9,X14_10,X15_15)
| ( X15_15 = '#skF_3'(X13_9,X14_10) ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_924,plain,
! [X13_227,X14_228,X15_229] :
( ~ r3(X13_227,X14_228,X15_229)
| ( X15_229 = '#skF_8'(X13_227,X14_228) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_540,c_23]) ).
tff(c_943,plain,
! [X5_230] : ( '#skF_8'('#skF_1',X5_230) = '#skF_9'(X5_230,'#skF_1') ),
inference(resolution,[status(thm)],[c_685,c_924]) ).
tff(c_589,plain,
! [X1_188,X8_189] : ( '#skF_3'(X1_188,X8_189) = '#skF_8'(X1_188,X8_189) ),
inference(resolution,[status(thm)],[c_38,c_522]) ).
tff(c_64,plain,
! [X4_63] : r1('#skF_14'(X4_63)),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_125,plain,
! [X4_63] : ( '#skF_14'(X4_63) = '#skF_1' ),
inference(resolution,[status(thm)],[c_64,c_111]) ).
tff(c_60,plain,
! [X4_63] : ( '#skF_13'(X4_63) = X4_63 ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_62,plain,
! [X4_63] : r3(X4_63,'#skF_14'(X4_63),'#skF_13'(X4_63)),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_86,plain,
! [X4_63] : r3(X4_63,'#skF_14'(X4_63),X4_63),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_62]) ).
tff(c_193,plain,
! [X4_63] : r3(X4_63,'#skF_1',X4_63),
inference(demodulation,[status(thm),theory(equality)],[c_125,c_86]) ).
tff(c_543,plain,
! [X4_63] : ( '#skF_3'(X4_63,'#skF_1') = X4_63 ),
inference(resolution,[status(thm)],[c_193,c_522]) ).
tff(c_596,plain,
! [X1_188] : ( '#skF_8'(X1_188,'#skF_1') = X1_188 ),
inference(superposition,[status(thm),theory(equality)],[c_589,c_543]) ).
tff(c_954,plain,
'#skF_9'('#skF_1','#skF_1') = '#skF_1',
inference(superposition,[status(thm),theory(equality)],[c_943,c_596]) ).
tff(c_56,plain,
! [X9_40,X2_39] : r2(X9_40,'#skF_11'(X2_39,X9_40)),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_212,plain,
! [X11_129,X12_130] :
( ~ r2(X11_129,X12_130)
| ( X12_130 = '#skF_2'(X11_129) ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_223,plain,
! [X2_39,X9_40] : ( '#skF_11'(X2_39,X9_40) = '#skF_2'(X9_40) ),
inference(resolution,[status(thm)],[c_56,c_212]) ).
tff(c_52,plain,
! [X2_39,X9_40] : ( '#skF_10'(X2_39,X9_40) = '#skF_9'(X2_39,X9_40) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_54,plain,
! [X2_39,X9_40] : r4(X2_39,'#skF_11'(X2_39,X9_40),'#skF_10'(X2_39,X9_40)),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_87,plain,
! [X2_39,X9_40] : r4(X2_39,'#skF_11'(X2_39,X9_40),'#skF_9'(X2_39,X9_40)),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54]) ).
tff(c_461,plain,
! [X2_167,X9_168] : r4(X2_167,'#skF_2'(X9_168),'#skF_9'(X2_167,X9_168)),
inference(demodulation,[status(thm),theory(equality)],[c_223,c_87]) ).
tff(c_16,plain,
! [X11_3] : r2(X11_3,'#skF_2'(X11_3)),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_138,plain,
! [Y5_102,Y4_103,Y3_104,Y1_105] :
( ~ r1(Y5_102)
| ~ r2(Y4_103,Y3_104)
| ~ r1(Y4_103)
| ~ r4(Y1_105,Y3_104,Y5_102) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_141,plain,
! [Y5_102,X11_3,Y1_105] :
( ~ r1(Y5_102)
| ~ r1(X11_3)
| ~ r4(Y1_105,'#skF_2'(X11_3),Y5_102) ),
inference(resolution,[status(thm)],[c_16,c_138]) ).
tff(c_471,plain,
! [X2_167,X9_168] :
( ~ r1('#skF_9'(X2_167,X9_168))
| ~ r1(X9_168) ),
inference(resolution,[status(thm)],[c_461,c_141]) ).
tff(c_987,plain,
( ~ r1('#skF_1')
| ~ r1('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_954,c_471]) ).
tff(c_994,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7,c_7,c_987]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUN082+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.09 % 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
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Thu Aug 3 18:40:36 EDT 2023
% 0.09/0.28 % CPUTime :
% 3.54/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.54/1.90
% 3.54/1.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.81/1.93
% 3.81/1.93 Inference rules
% 3.81/1.93 ----------------------
% 3.81/1.93 #Ref : 0
% 3.81/1.93 #Sup : 217
% 3.81/1.93 #Fact : 0
% 3.81/1.93 #Define : 0
% 3.81/1.93 #Split : 0
% 3.81/1.93 #Chain : 0
% 3.81/1.93 #Close : 0
% 3.81/1.93
% 3.81/1.93 Ordering : KBO
% 3.81/1.93
% 3.81/1.93 Simplification rules
% 3.81/1.93 ----------------------
% 3.81/1.93 #Subsume : 35
% 3.81/1.93 #Demod : 71
% 3.81/1.93 #Tautology : 98
% 3.81/1.93 #SimpNegUnit : 0
% 3.81/1.93 #BackRed : 23
% 3.81/1.93
% 3.81/1.93 #Partial instantiations: 0
% 3.81/1.93 #Strategies tried : 1
% 3.81/1.93
% 3.81/1.93 Timing (in seconds)
% 3.81/1.93 ----------------------
% 3.81/1.93 Preprocessing : 0.52
% 3.81/1.93 Parsing : 0.25
% 3.81/1.93 CNF conversion : 0.05
% 3.81/1.93 Main loop : 0.44
% 3.81/1.93 Inferencing : 0.17
% 3.81/1.93 Reduction : 0.13
% 3.81/1.93 Demodulation : 0.10
% 3.81/1.93 BG Simplification : 0.03
% 3.81/1.93 Subsumption : 0.08
% 3.81/1.93 Abstraction : 0.02
% 3.81/1.93 MUC search : 0.00
% 3.81/1.93 Cooper : 0.00
% 3.81/1.93 Total : 1.01
% 3.81/1.93 Index Insertion : 0.00
% 3.81/1.93 Index Deletion : 0.00
% 3.81/1.93 Index Matching : 0.00
% 3.81/1.94 BG Taut test : 0.00
%------------------------------------------------------------------------------