TSTP Solution File: NUN086+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUN086+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/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 : n011.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 3.94s 2.00s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 33
% Syntax : Number of formulae : 83 ( 40 unt; 24 typ; 0 def)
% Number of atoms : 108 ( 35 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 83 ( 34 ~; 23 |; 26 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 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 : 111 (; 89 !; 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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
tff(f_160,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& ( Y8 = Y18 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).
tff(f_75,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ r2(X11,X12)
& ( X12 != Y21 ) )
| ( r2(X11,X12)
& ( X12 = Y21 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
tff(f_199,negated_conjecture,
~ ? [Y1] :
( ? [Y2] :
( ? [Y3] :
( r1(Y3)
& r2(Y3,Y2) )
& ? [Y4] :
( r1(Y4)
& r4(Y4,Y2,Y1) ) )
& ? [Y5] :
( r1(Y5)
& ( Y1 = Y5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerotimesoneeqzero) ).
tff(c_7,plain,
r1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_63]) ).
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_458,plain,
! [X13_175,X14_176,X15_177] :
( ~ r3(X13_175,X14_176,X15_177)
| ( X15_177 = '#skF_3'(X13_175,X14_176) ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_504,plain,
! [X1_179,X8_180] : ( '#skF_3'(X1_179,X8_180) = '#skF_8'(X1_179,X8_180) ),
inference(resolution,[status(thm)],[c_38,c_458]) ).
tff(c_64,plain,
! [X4_63] : r1('#skF_14'(X4_63)),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_111,plain,
! [X19_103] :
( ~ r1(X19_103)
| ( X19_103 = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
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_187,plain,
! [X4_63] : r3(X4_63,'#skF_1',X4_63),
inference(demodulation,[status(thm),theory(equality)],[c_125,c_86]) ).
tff(c_487,plain,
! [X4_63] : ( '#skF_3'(X4_63,'#skF_1') = X4_63 ),
inference(resolution,[status(thm)],[c_187,c_458]) ).
tff(c_520,plain,
! [X1_181] : ( '#skF_8'(X1_181,'#skF_1') = X1_181 ),
inference(superposition,[status(thm),theory(equality)],[c_504,c_487]) ).
tff(c_40,plain,
! [X1_23,X8_24] : r2('#skF_8'(X1_23,X8_24),'#skF_5'(X1_23,X8_24)),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_529,plain,
! [X1_181] : r2(X1_181,'#skF_5'(X1_181,'#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_520,c_40]) ).
tff(c_68,plain,
! [X5_68] : r1('#skF_17'(X5_68)),
inference(cnfTransformation,[status(thm)],[f_160]) ).
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_199,plain,
! [X5_68] : r4(X5_68,'#skF_1','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_124,c_85]) ).
tff(c_394,plain,
! [X16_162,X17_163,X18_164] :
( ~ r4(X16_162,X17_163,X18_164)
| ( X18_164 = '#skF_4'(X16_162,X17_163) ) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_405,plain,
! [X5_68] : ( '#skF_4'(X5_68,'#skF_1') = '#skF_1' ),
inference(resolution,[status(thm)],[c_199,c_394]) ).
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_404,plain,
! [X2_39,X9_40] : ( '#skF_12'(X2_39,X9_40) = '#skF_4'(X2_39,X9_40) ),
inference(resolution,[status(thm)],[c_48,c_394]) ).
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_453,plain,
! [X2_172,X9_173] : r3('#skF_4'(X2_172,X9_173),X2_172,'#skF_9'(X2_172,X9_173)),
inference(demodulation,[status(thm),theory(equality)],[c_404,c_50]) ).
tff(c_456,plain,
! [X5_68] : r3('#skF_1',X5_68,'#skF_9'(X5_68,'#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_405,c_453]) ).
tff(c_591,plain,
! [X5_189] : ( '#skF_3'('#skF_1',X5_189) = '#skF_9'(X5_189,'#skF_1') ),
inference(resolution,[status(thm)],[c_456,c_458]) ).
tff(c_601,plain,
'#skF_9'('#skF_1','#skF_1') = '#skF_1',
inference(superposition,[status(thm),theory(equality)],[c_591,c_487]) ).
tff(c_360,plain,
! [X1_152,X8_153] : r2('#skF_8'(X1_152,X8_153),'#skF_5'(X1_152,X8_153)),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_14,plain,
! [X11_3,X12_8] :
( ~ r2(X11_3,X12_8)
| ( X12_8 = '#skF_2'(X11_3) ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_367,plain,
! [X1_152,X8_153] : ( '#skF_2'('#skF_8'(X1_152,X8_153)) = '#skF_5'(X1_152,X8_153) ),
inference(resolution,[status(thm)],[c_360,c_14]) ).
tff(c_526,plain,
! [X1_181] : ( '#skF_2'(X1_181) = '#skF_5'(X1_181,'#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_520,c_367]) ).
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_233,plain,
! [X11_137,X12_138] :
( ~ r2(X11_137,X12_138)
| ( X12_138 = '#skF_2'(X11_137) ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_244,plain,
! [X2_39,X9_40] : ( '#skF_11'(X2_39,X9_40) = '#skF_2'(X9_40) ),
inference(resolution,[status(thm)],[c_56,c_233]) ).
tff(c_541,plain,
! [X2_39,X9_40] : ( '#skF_11'(X2_39,X9_40) = '#skF_5'(X9_40,'#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_526,c_244]) ).
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_628,plain,
! [X2_190,X9_191] : r4(X2_190,'#skF_11'(X2_190,X9_191),'#skF_9'(X2_190,X9_191)),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54]) ).
tff(c_84,plain,
! [Y5_96,Y4_95,Y2_91,Y3_94] :
( ~ r1(Y5_96)
| ~ r4(Y4_95,Y2_91,Y5_96)
| ~ r1(Y4_95)
| ~ r2(Y3_94,Y2_91)
| ~ r1(Y3_94) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_638,plain,
! [X2_190,X9_191,Y3_94] :
( ~ r1('#skF_9'(X2_190,X9_191))
| ~ r1(X2_190)
| ~ r2(Y3_94,'#skF_11'(X2_190,X9_191))
| ~ r1(Y3_94) ),
inference(resolution,[status(thm)],[c_628,c_84]) ).
tff(c_693,plain,
! [X2_197,X9_198,Y3_199] :
( ~ r1('#skF_9'(X2_197,X9_198))
| ~ r1(X2_197)
| ~ r2(Y3_199,'#skF_5'(X9_198,'#skF_1'))
| ~ r1(Y3_199) ),
inference(demodulation,[status(thm),theory(equality)],[c_541,c_638]) ).
tff(c_695,plain,
! [Y3_199] :
( ~ r1('#skF_1')
| ~ r1('#skF_1')
| ~ r2(Y3_199,'#skF_5'('#skF_1','#skF_1'))
| ~ r1(Y3_199) ),
inference(superposition,[status(thm),theory(equality)],[c_601,c_693]) ).
tff(c_794,plain,
! [Y3_209] :
( ~ r2(Y3_209,'#skF_5'('#skF_1','#skF_1'))
| ~ r1(Y3_209) ),
inference(demodulation,[status(thm),theory(equality)],[c_7,c_7,c_695]) ).
tff(c_798,plain,
~ r1('#skF_1'),
inference(resolution,[status(thm)],[c_529,c_794]) ).
tff(c_806,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7,c_798]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUN086+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.15 % 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
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 3 18:39:21 EDT 2023
% 0.16/0.37 % CPUTime :
% 3.94/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.94/2.00
% 3.94/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.94/2.04
% 3.94/2.04 Inference rules
% 3.94/2.04 ----------------------
% 3.94/2.04 #Ref : 0
% 3.94/2.04 #Sup : 167
% 3.94/2.04 #Fact : 0
% 3.94/2.04 #Define : 0
% 3.94/2.04 #Split : 1
% 3.94/2.04 #Chain : 0
% 3.94/2.04 #Close : 0
% 3.94/2.04
% 3.94/2.04 Ordering : KBO
% 3.94/2.04
% 3.94/2.04 Simplification rules
% 3.94/2.04 ----------------------
% 3.94/2.04 #Subsume : 24
% 3.94/2.04 #Demod : 71
% 3.94/2.04 #Tautology : 95
% 3.94/2.04 #SimpNegUnit : 0
% 3.94/2.04 #BackRed : 20
% 3.94/2.04
% 3.94/2.04 #Partial instantiations: 0
% 3.94/2.04 #Strategies tried : 1
% 3.94/2.04
% 3.94/2.04 Timing (in seconds)
% 3.94/2.04 ----------------------
% 3.94/2.04 Preprocessing : 0.54
% 3.94/2.04 Parsing : 0.26
% 3.94/2.04 CNF conversion : 0.05
% 3.94/2.04 Main loop : 0.43
% 3.94/2.04 Inferencing : 0.16
% 3.94/2.04 Reduction : 0.13
% 3.94/2.04 Demodulation : 0.10
% 3.94/2.04 BG Simplification : 0.03
% 3.94/2.04 Subsumption : 0.08
% 3.94/2.04 Abstraction : 0.02
% 4.28/2.04 MUC search : 0.00
% 4.28/2.04 Cooper : 0.00
% 4.28/2.04 Total : 1.02
% 4.28/2.04 Index Insertion : 0.00
% 4.28/2.05 Index Deletion : 0.00
% 4.28/2.05 Index Matching : 0.00
% 4.28/2.05 BG Taut test : 0.00
%------------------------------------------------------------------------------