%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUN071+2 : TPTP v9.0.0. 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 : n028.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 : Wed Apr 9 08:20:59 PM UTC 2025
% Result : Theorem 6.84s 2.62s
% Output : CNFRefutation 6.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 43 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 75 ( 29 ~; 20 |; 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 : 0 ( 0 >; 0 *; 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 : 144 ( 122 !; 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_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_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_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_199,negated_conjecture,
~ ? [Y1] :
( ? [Y2] :
( r4(Y2,Y2,Y1)
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) )
& ? [Y3] :
( ( Y1 = Y3 )
& ? [Y5] :
( r1(Y5)
& r2(Y5,Y3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',onetimesoneeqone) ).
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_626,plain,
! [X13_198,X14_199,X15_200] :
( ~ r3(X13_198,X14_199,X15_200)
| ( X15_200 = '#skF_3'(X13_198,X14_199) ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_664,plain,
! [X1_202,X8_203] : ( '#skF_3'(X1_202,X8_203) = '#skF_8'(X1_202,X8_203) ),
inference(resolution,[status(thm)],[c_38,c_626]) ).
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_202,plain,
! [X4_63] : r3(X4_63,'#skF_1',X4_63),
inference(demodulation,[status(thm),theory(equality)],[c_125,c_86]) ).
tff(c_647,plain,
! [X4_63] : ( '#skF_3'(X4_63,'#skF_1') = X4_63 ),
inference(resolution,[status(thm)],[c_202,c_626]) ).
tff(c_671,plain,
! [X1_202] : ( '#skF_8'(X1_202,'#skF_1') = X1_202 ),
inference(superposition,[status(thm),theory(equality)],[c_664,c_647]) ).
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_213,plain,
! [X5_68] : r4(X5_68,'#skF_1','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_124,c_85]) ).
tff(c_453,plain,
! [X16_172,X17_173,X18_174] :
( ~ r4(X16_172,X17_173,X18_174)
| ( X18_174 = '#skF_4'(X16_172,X17_173) ) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_466,plain,
! [X5_68] : ( '#skF_4'(X5_68,'#skF_1') = '#skF_1' ),
inference(resolution,[status(thm)],[c_213,c_453]) ).
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_463,plain,
! [X2_39,X9_40] : ( '#skF_12'(X2_39,X9_40) = '#skF_4'(X2_39,X9_40) ),
inference(resolution,[status(thm)],[c_48,c_453]) ).
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_882,plain,
! [X2_227,X9_228] : r3('#skF_4'(X2_227,X9_228),X2_227,'#skF_9'(X2_227,X9_228)),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_50]) ).
tff(c_890,plain,
! [X5_229] : r3('#skF_1',X5_229,'#skF_9'(X5_229,'#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_466,c_882]) ).
tff(c_644,plain,
! [X1_23,X8_24] : ( '#skF_3'(X1_23,X8_24) = '#skF_8'(X1_23,X8_24) ),
inference(resolution,[status(thm)],[c_38,c_626]) ).
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_661,plain,
! [X13_9,X14_10,X15_15] :
( ~ r3(X13_9,X14_10,X15_15)
| ( X15_15 = '#skF_8'(X13_9,X14_10) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_644,c_23]) ).
tff(c_895,plain,
! [X5_230] : ( '#skF_8'('#skF_1',X5_230) = '#skF_9'(X5_230,'#skF_1') ),
inference(resolution,[status(thm)],[c_890,c_661]) ).
tff(c_680,plain,
! [X1_204] : ( '#skF_8'(X1_204,'#skF_1') = X1_204 ),
inference(superposition,[status(thm),theory(equality)],[c_664,c_647]) ).
tff(c_319,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_330,plain,
! [X1_149,X8_150] : ( '#skF_2'('#skF_8'(X1_149,X8_150)) = '#skF_5'(X1_149,X8_150) ),
inference(resolution,[status(thm)],[c_319,c_14]) ).
tff(c_686,plain,
! [X1_204] : ( '#skF_2'(X1_204) = '#skF_5'(X1_204,'#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_680,c_330]) ).
tff(c_46,plain,
! [X8_24,X1_23] : r2(X8_24,'#skF_7'(X1_23,X8_24)),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_216,plain,
! [X11_132,X12_133] :
( ~ r2(X11_132,X12_133)
| ( X12_133 = '#skF_2'(X11_132) ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_226,plain,
! [X1_23,X8_24] : ( '#skF_7'(X1_23,X8_24) = '#skF_2'(X8_24) ),
inference(resolution,[status(thm)],[c_46,c_216]) ).
tff(c_42,plain,
! [X1_23,X8_24] : ( '#skF_6'(X1_23,X8_24) = '#skF_5'(X1_23,X8_24) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_44,plain,
! [X1_23,X8_24] : r3(X1_23,'#skF_7'(X1_23,X8_24),'#skF_6'(X1_23,X8_24)),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_537,plain,
! [X1_185,X8_186] : r3(X1_185,'#skF_7'(X1_185,X8_186),'#skF_5'(X1_185,X8_186)),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_44]) ).
tff(c_546,plain,
! [X1_23,X8_24] : r3(X1_23,'#skF_2'(X8_24),'#skF_5'(X1_23,X8_24)),
inference(superposition,[status(thm),theory(equality)],[c_226,c_537]) ).
tff(c_642,plain,
! [X1_23,X8_24] : ( '#skF_3'(X1_23,'#skF_2'(X8_24)) = '#skF_5'(X1_23,X8_24) ),
inference(resolution,[status(thm)],[c_546,c_626]) ).
tff(c_806,plain,
! [X1_23,X8_24] : ( '#skF_8'(X1_23,'#skF_5'(X8_24,'#skF_1')) = '#skF_5'(X1_23,X8_24) ),
inference(demodulation,[status(thm),theory(equality)],[c_644,c_686,c_642]) ).
tff(c_1527,plain,
! [X8_265] : ( '#skF_9'('#skF_5'(X8_265,'#skF_1'),'#skF_1') = '#skF_5'('#skF_1',X8_265) ),
inference(superposition,[status(thm),theory(equality)],[c_895,c_806]) ).
tff(c_724,plain,
! [X1_23,X8_24] : ( '#skF_7'(X1_23,X8_24) = '#skF_5'(X8_24,'#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_686,c_226]) ).
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_227,plain,
! [X2_39,X9_40] : ( '#skF_11'(X2_39,X9_40) = '#skF_2'(X9_40) ),
inference(resolution,[status(thm)],[c_56,c_216]) ).
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_555,plain,
! [X2_189,X9_190] : r4(X2_189,'#skF_2'(X9_190),'#skF_9'(X2_189,X9_190)),
inference(demodulation,[status(thm),theory(equality)],[c_227,c_87]) ).
tff(c_564,plain,
! [X2_189,X1_23,X8_24] : r4(X2_189,'#skF_7'(X1_23,X8_24),'#skF_9'(X2_189,X8_24)),
inference(superposition,[status(thm),theory(equality)],[c_226,c_555]) ).
tff(c_1140,plain,
! [X2_189,X8_24] : r4(X2_189,'#skF_5'(X8_24,'#skF_1'),'#skF_9'(X2_189,X8_24)),
inference(demodulation,[status(thm),theory(equality)],[c_724,c_564]) ).
tff(c_5715,plain,
! [X8_383] : r4('#skF_5'(X8_383,'#skF_1'),'#skF_5'('#skF_1','#skF_1'),'#skF_5'('#skF_1',X8_383)),
inference(superposition,[status(thm),theory(equality)],[c_1527,c_1140]) ).
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_84,plain,
! [Y5_96,Y3_94,Y4_93,Y2_91] :
( ~ r2(Y5_96,Y3_94)
| ~ r1(Y5_96)
| ~ r2(Y4_93,Y2_91)
| ~ r1(Y4_93)
| ~ r4(Y2_91,Y2_91,Y3_94) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_490,plain,
! [X1_178,X8_179,Y4_180,Y2_181] :
( ~ r1('#skF_8'(X1_178,X8_179))
| ~ r2(Y4_180,Y2_181)
| ~ r1(Y4_180)
| ~ r4(Y2_181,Y2_181,'#skF_5'(X1_178,X8_179)) ),
inference(resolution,[status(thm)],[c_319,c_84]) ).
tff(c_497,plain,
! [X1_178,X8_179,X1_23,X8_24] :
( ~ r1('#skF_8'(X1_178,X8_179))
| ~ r1('#skF_8'(X1_23,X8_24))
| ~ r4('#skF_5'(X1_23,X8_24),'#skF_5'(X1_23,X8_24),'#skF_5'(X1_178,X8_179)) ),
inference(resolution,[status(thm)],[c_40,c_490]) ).
tff(c_5719,plain,
~ r1('#skF_8'('#skF_1','#skF_1')),
inference(resolution,[status(thm)],[c_5715,c_497]) ).
tff(c_5768,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7,c_671,c_5719]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN071+2 : TPTP v9.0.0. Released v7.3.0.
% 0.03/0.13 % 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 : n028.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 : Tue Apr 8 16:09:50 EDT 2025
% 0.13/0.34 % CPUTime :
% 6.84/2.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.84/2.63
% 6.84/2.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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