TSTP Solution File: NUN068+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUN068+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 : n010.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 10:53:22 EDT 2023
% Result : Theorem 9.42s 3.44s
% Output : CNFRefutation 9.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 35
% Syntax : Number of formulae : 92 ( 21 unt; 27 typ; 0 def)
% Number of atoms : 135 ( 73 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 105 ( 35 ~; 57 |; 13 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 26 >; 15 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 1 con; 0-2 aty)
% Number of variables : 101 (; 91 !; 10 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ r4 > r3 > r2 > r1 > #nlpp > #skF_11 > #skF_21 > #skF_16 > #skF_6 > #skF_2 > #skF_18 > #skF_19 > #skF_22 > #skF_3 > #skF_15 > #skF_12 > #skF_10 > #skF_1 > #skF_8 > #skF_23 > #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_21',type,
'#skF_21': $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_22',type,
'#skF_22': $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_23',type,
'#skF_23': $i > $i ).
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_201,negated_conjecture,
~ ? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y2) )
| ( Y1 != Y2 ) )
& ! [Y4] :
( ~ r1(Y4)
| ( Y1 != Y4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerosnononesexist) ).
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_141,axiom,
! [X3,X10] :
( ! [Y12] :
( ! [Y13] :
( ~ r2(X3,Y13)
| ( Y13 != Y12 ) )
| ~ r2(X10,Y12) )
| ( X3 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
tff(f_180,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| ( Y20 != Y10 ) )
| ~ r2(X7,Y10) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
tff(c_7,plain,
r1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_205,plain,
! [Y1_117] :
( r1('#skF_22'(Y1_117))
| r1('#skF_23'(Y1_117)) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_5,plain,
! [X19_2] :
( ~ r1(X19_2)
| ( X19_2 = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_324,plain,
! [Y1_139] :
( ( '#skF_22'(Y1_139) = '#skF_1' )
| r1('#skF_23'(Y1_139)) ),
inference(resolution,[status(thm)],[c_205,c_5]) ).
tff(c_328,plain,
! [Y1_139] :
( ( '#skF_23'(Y1_139) = '#skF_1' )
| ( '#skF_22'(Y1_139) = '#skF_1' ) ),
inference(resolution,[status(thm)],[c_324,c_5]) ).
tff(c_149,plain,
! [Y1_98] :
( ( '#skF_21'(Y1_98) = Y1_98 )
| r1('#skF_23'(Y1_98)) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_153,plain,
! [Y1_98] :
( ( '#skF_23'(Y1_98) = '#skF_1' )
| ( '#skF_21'(Y1_98) = Y1_98 ) ),
inference(resolution,[status(thm)],[c_149,c_5]) ).
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_539,plain,
! [X13_157,X14_158,X15_159] :
( ~ r3(X13_157,X14_158,X15_159)
| ( X15_159 = '#skF_3'(X13_157,X14_158) ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_569,plain,
! [X1_161,X8_162] : ( '#skF_3'(X1_161,X8_162) = '#skF_8'(X1_161,X8_162) ),
inference(resolution,[status(thm)],[c_38,c_539]) ).
tff(c_64,plain,
! [X4_63] : r1('#skF_14'(X4_63)),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_121,plain,
! [X19_96] :
( ~ r1(X19_96)
| ( X19_96 = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_135,plain,
! [X4_63] : ( '#skF_14'(X4_63) = '#skF_1' ),
inference(resolution,[status(thm)],[c_64,c_121]) ).
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_96,plain,
! [X4_63] : r3(X4_63,'#skF_14'(X4_63),X4_63),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_62]) ).
tff(c_189,plain,
! [X4_63] : r3(X4_63,'#skF_1',X4_63),
inference(demodulation,[status(thm),theory(equality)],[c_135,c_96]) ).
tff(c_552,plain,
! [X4_63] : ( '#skF_3'(X4_63,'#skF_1') = X4_63 ),
inference(resolution,[status(thm)],[c_189,c_539]) ).
tff(c_576,plain,
! [X1_161] : ( '#skF_8'(X1_161,'#skF_1') = X1_161 ),
inference(superposition,[status(thm),theory(equality)],[c_569,c_552]) ).
tff(c_585,plain,
! [X1_163] : ( '#skF_8'(X1_163,'#skF_1') = X1_163 ),
inference(superposition,[status(thm),theory(equality)],[c_569,c_552]) ).
tff(c_472,plain,
! [X1_149,X8_150] : r2('#skF_8'(X1_149,X8_150),'#skF_5'(X1_149,X8_150)),
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_479,plain,
! [X1_149,X8_150] : ( '#skF_2'('#skF_8'(X1_149,X8_150)) = '#skF_5'(X1_149,X8_150) ),
inference(resolution,[status(thm)],[c_472,c_14]) ).
tff(c_591,plain,
! [X1_163] : ( '#skF_2'(X1_163) = '#skF_5'(X1_163,'#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_585,c_479]) ).
tff(c_92,plain,
! [Y1_84] :
( r2('#skF_22'(Y1_84),'#skF_21'(Y1_84))
| r1('#skF_23'(Y1_84)) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_266,plain,
! [X11_131,X12_132] :
( ~ r2(X11_131,X12_132)
| ( X12_132 = '#skF_2'(X11_131) ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_534,plain,
! [Y1_156] :
( ( '#skF_2'('#skF_22'(Y1_156)) = '#skF_21'(Y1_156) )
| r1('#skF_23'(Y1_156)) ),
inference(resolution,[status(thm)],[c_92,c_266]) ).
tff(c_538,plain,
! [Y1_156] :
( ( '#skF_23'(Y1_156) = '#skF_1' )
| ( '#skF_2'('#skF_22'(Y1_156)) = '#skF_21'(Y1_156) ) ),
inference(resolution,[status(thm)],[c_534,c_5]) ).
tff(c_2115,plain,
! [Y1_242] :
( ( '#skF_23'(Y1_242) = '#skF_1' )
| ( '#skF_5'('#skF_22'(Y1_242),'#skF_1') = '#skF_21'(Y1_242) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_538]) ).
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_2147,plain,
! [Y1_242] :
( r2('#skF_8'('#skF_22'(Y1_242),'#skF_1'),'#skF_21'(Y1_242))
| ( '#skF_23'(Y1_242) = '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_2115,c_40]) ).
tff(c_2864,plain,
! [Y1_259] :
( r2('#skF_22'(Y1_259),'#skF_21'(Y1_259))
| ( '#skF_23'(Y1_259) = '#skF_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_576,c_2147]) ).
tff(c_11377,plain,
! [Y1_386] :
( r2('#skF_22'(Y1_386),Y1_386)
| ( '#skF_23'(Y1_386) = '#skF_1' )
| ( '#skF_23'(Y1_386) = '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_2864]) ).
tff(c_617,plain,
! [X11_3,X12_8] :
( ~ r2(X11_3,X12_8)
| ( X12_8 = '#skF_5'(X11_3,'#skF_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_14]) ).
tff(c_11476,plain,
! [Y1_387] :
( ( '#skF_5'('#skF_22'(Y1_387),'#skF_1') = Y1_387 )
| ( '#skF_23'(Y1_387) = '#skF_1' ) ),
inference(resolution,[status(thm)],[c_11377,c_617]) ).
tff(c_594,plain,
! [X1_163] : r2(X1_163,'#skF_5'(X1_163,'#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_585,c_40]) ).
tff(c_11626,plain,
! [Y1_388] :
( r2('#skF_22'(Y1_388),Y1_388)
| ( '#skF_23'(Y1_388) = '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_11476,c_594]) ).
tff(c_12180,plain,
! [Y1_395] :
( r2('#skF_1',Y1_395)
| ( '#skF_23'(Y1_395) = '#skF_1' )
| ( '#skF_23'(Y1_395) = '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_328,c_11626]) ).
tff(c_711,plain,
! [X3_175,X10_176,Y13_177] :
( ( X3_175 = X10_176 )
| ~ r2(X10_176,Y13_177)
| ~ r2(X3_175,Y13_177) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_722,plain,
! [X3_175,X1_163] :
( ( X3_175 = X1_163 )
| ~ r2(X3_175,'#skF_5'(X1_163,'#skF_1')) ),
inference(resolution,[status(thm)],[c_594,c_711]) ).
tff(c_12252,plain,
! [X1_396] :
( ( X1_396 = '#skF_1' )
| ( '#skF_23'('#skF_5'(X1_396,'#skF_1')) = '#skF_1' ) ),
inference(resolution,[status(thm)],[c_12180,c_722]) ).
tff(c_198,plain,
! [Y1_112] :
( r1('#skF_22'(Y1_112))
| ( '#skF_23'(Y1_112) = Y1_112 ) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_202,plain,
! [Y1_112] :
( ( '#skF_22'(Y1_112) = '#skF_1' )
| ( '#skF_23'(Y1_112) = Y1_112 ) ),
inference(resolution,[status(thm)],[c_198,c_5]) ).
tff(c_84,plain,
! [Y1_84] :
( ( '#skF_21'(Y1_84) = Y1_84 )
| ( '#skF_23'(Y1_84) = Y1_84 ) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_370,plain,
! [Y1_142] :
( r2('#skF_22'(Y1_142),'#skF_21'(Y1_142))
| ( '#skF_23'(Y1_142) = Y1_142 ) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_1449,plain,
! [Y1_226] :
( r2('#skF_22'(Y1_226),Y1_226)
| ( '#skF_23'(Y1_226) = Y1_226 )
| ( '#skF_23'(Y1_226) = Y1_226 ) ),
inference(superposition,[status(thm),theory(equality)],[c_84,c_370]) ).
tff(c_4995,plain,
! [Y1_302] :
( r2('#skF_1',Y1_302)
| ( '#skF_23'(Y1_302) = Y1_302 )
| ( '#skF_23'(Y1_302) = Y1_302 )
| ( '#skF_23'(Y1_302) = Y1_302 ) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_1449]) ).
tff(c_58,plain,
! [X3_55,X10_56,Y13_62] :
( ( X3_55 = X10_56 )
| ~ r2(X10_56,Y13_62)
| ~ r2(X3_55,Y13_62) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_5225,plain,
! [X3_304,Y1_305] :
( ( X3_304 = '#skF_1' )
| ~ r2(X3_304,Y1_305)
| ( '#skF_23'(Y1_305) = Y1_305 ) ),
inference(resolution,[status(thm)],[c_4995,c_58]) ).
tff(c_5302,plain,
! [X1_163] :
( ( X1_163 = '#skF_1' )
| ( '#skF_23'('#skF_5'(X1_163,'#skF_1')) = '#skF_5'(X1_163,'#skF_1') ) ),
inference(resolution,[status(thm)],[c_594,c_5225]) ).
tff(c_12802,plain,
! [X1_400] :
( ( X1_400 = '#skF_1' )
| ( '#skF_5'(X1_400,'#skF_1') = '#skF_1' )
| ( X1_400 = '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_12252,c_5302]) ).
tff(c_82,plain,
! [X7_80,Y20_83] :
( ~ r2(X7_80,Y20_83)
| ~ r1(Y20_83) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_480,plain,
! [X1_149,X8_150] : ~ r1('#skF_5'(X1_149,X8_150)),
inference(resolution,[status(thm)],[c_472,c_82]) ).
tff(c_12963,plain,
! [X1_400] :
( ~ r1('#skF_1')
| ( X1_400 = '#skF_1' )
| ( X1_400 = '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_12802,c_480]) ).
tff(c_13054,plain,
! [X1_401] : ( X1_401 = '#skF_1' ),
inference(demodulation,[status(thm),theory(equality)],[c_7,c_12963]) ).
tff(c_13382,plain,
~ r1('#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_13054,c_480]) ).
tff(c_13456,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7,c_13382]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN068+2 : TPTP v8.1.2. Released v7.3.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 18:28:14 EDT 2023
% 0.13/0.34 % CPUTime :
% 9.42/3.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.42/3.45
% 9.42/3.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.42/3.48
% 9.42/3.48 Inference rules
% 9.42/3.48 ----------------------
% 9.42/3.48 #Ref : 0
% 9.42/3.48 #Sup : 3705
% 9.42/3.48 #Fact : 0
% 9.42/3.48 #Define : 0
% 9.42/3.48 #Split : 0
% 9.42/3.48 #Chain : 0
% 9.42/3.48 #Close : 0
% 9.42/3.48
% 9.42/3.48 Ordering : KBO
% 9.42/3.48
% 9.42/3.48 Simplification rules
% 9.42/3.48 ----------------------
% 9.42/3.48 #Subsume : 1351
% 9.42/3.48 #Demod : 965
% 9.42/3.48 #Tautology : 1134
% 9.42/3.48 #SimpNegUnit : 23
% 9.42/3.48 #BackRed : 18
% 9.42/3.48
% 9.42/3.48 #Partial instantiations: 0
% 9.42/3.48 #Strategies tried : 1
% 9.42/3.48
% 9.42/3.48 Timing (in seconds)
% 9.42/3.48 ----------------------
% 9.42/3.49 Preprocessing : 0.61
% 9.42/3.49 Parsing : 0.31
% 9.42/3.49 CNF conversion : 0.05
% 9.42/3.49 Main loop : 1.75
% 9.42/3.49 Inferencing : 0.56
% 9.42/3.49 Reduction : 0.59
% 9.42/3.49 Demodulation : 0.44
% 9.42/3.49 BG Simplification : 0.06
% 9.42/3.49 Subsumption : 0.44
% 9.42/3.49 Abstraction : 0.07
% 9.42/3.49 MUC search : 0.00
% 9.42/3.49 Cooper : 0.00
% 9.42/3.49 Total : 2.42
% 9.42/3.49 Index Insertion : 0.00
% 9.42/3.49 Index Deletion : 0.00
% 9.42/3.49 Index Matching : 0.00
% 9.42/3.49 BG Taut test : 0.00
%------------------------------------------------------------------------------