%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUN070+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 : n031.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 08:20:58 PM UTC 2025
% Result : Theorem 4.90s 2.17s
% Output : CNFRefutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 72 ( 32 ~; 22 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 65 ( 50 !; 15 ?; 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_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_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_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_202,negated_conjecture,
~ ? [Y1] :
( ? [Y2] :
( ? [Y4] :
( r1(Y4)
& r3(Y2,Y4,Y1) )
& ? [Y5] :
( r1(Y5)
& r2(Y5,Y2) ) )
& ? [Y3] :
( ( Y1 = Y3 )
& ? [Y6] :
( r1(Y6)
& r2(Y6,Y3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',onepluszeroeqone) ).
tff(c_7,plain,
r1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_64,plain,
! [X4_63] : r1('#skF_14'(X4_63)),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_111,plain,
! [X19_107] :
( ~ r1(X19_107)
| ( X19_107 = '#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_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_443,plain,
! [X13_178,X14_179,X15_180] :
( ~ r3(X13_178,X14_179,X15_180)
| ( X15_180 = '#skF_3'(X13_178,X14_179) ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_497,plain,
! [X1_184,X8_185] : ( '#skF_3'(X1_184,X8_185) = '#skF_8'(X1_184,X8_185) ),
inference(resolution,[status(thm)],[c_38,c_443]) ).
tff(c_468,plain,
! [X4_63] : ( '#skF_3'(X4_63,'#skF_1') = X4_63 ),
inference(resolution,[status(thm)],[c_202,c_443]) ).
tff(c_523,plain,
! [X1_191] : ( '#skF_8'(X1_191,'#skF_1') = X1_191 ),
inference(superposition,[status(thm),theory(equality)],[c_497,c_468]) ).
tff(c_325,plain,
! [X1_160,X8_161] : r2('#skF_8'(X1_160,X8_161),'#skF_5'(X1_160,X8_161)),
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_339,plain,
! [X1_160,X8_161] : ( '#skF_2'('#skF_8'(X1_160,X8_161)) = '#skF_5'(X1_160,X8_161) ),
inference(resolution,[status(thm)],[c_325,c_14]) ).
tff(c_529,plain,
! [X1_191] : ( '#skF_2'(X1_191) = '#skF_5'(X1_191,'#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_523,c_339]) ).
tff(c_16,plain,
! [X11_3] : r2(X11_3,'#skF_2'(X11_3)),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_138,plain,
! [Y4_109,Y2_110,Y3_111,Y6_112,Y5_113] :
( ~ r2(Y6_112,Y3_111)
| ~ r1(Y6_112)
| ~ r2(Y5_113,Y2_110)
| ~ r1(Y5_113)
| ~ r3(Y2_110,Y4_109,Y3_111)
| ~ r1(Y4_109) ),
inference(cnfTransformation,[status(thm)],[f_202]) ).
tff(c_192,plain,
! [X11_128,Y5_129,Y2_130,Y4_131] :
( ~ r1(X11_128)
| ~ r2(Y5_129,Y2_130)
| ~ r1(Y5_129)
| ~ r3(Y2_130,Y4_131,'#skF_2'(X11_128))
| ~ r1(Y4_131) ),
inference(resolution,[status(thm)],[c_16,c_138]) ).
tff(c_201,plain,
! [X11_128,X11_3,Y4_131] :
( ~ r1(X11_128)
| ~ r1(X11_3)
| ~ r3('#skF_2'(X11_3),Y4_131,'#skF_2'(X11_128))
| ~ r1(Y4_131) ),
inference(resolution,[status(thm)],[c_16,c_192]) ).
tff(c_1200,plain,
! [X11_254,X11_255,Y4_256] :
( ~ r1(X11_254)
| ~ r1(X11_255)
| ~ r3('#skF_5'(X11_255,'#skF_1'),Y4_256,'#skF_5'(X11_254,'#skF_1'))
| ~ r1(Y4_256) ),
inference(demodulation,[status(thm),theory(equality)],[c_529,c_529,c_201]) ).
tff(c_1204,plain,
! [X11_255] :
( ~ r1(X11_255)
| ~ r1('#skF_1') ),
inference(resolution,[status(thm)],[c_202,c_1200]) ).
tff(c_1207,plain,
! [X11_255] : ~ r1(X11_255),
inference(demodulation,[status(thm),theory(equality)],[c_7,c_1204]) ).
tff(c_1215,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1207,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUN070+2 : TPTP v9.0.0. Released v7.3.0.
% 0.04/0.14 % 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
% 0.14/0.36 % Computer : n031.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 8 16:10:07 EDT 2025
% 0.14/0.36 % CPUTime :
% 4.90/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.90/2.18
% 4.90/2.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------