%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUN080+1 : 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 : n015.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 08:21:00 PM UTC 2025
% Result : Theorem 11.84s 4.49s
% Output : CNFRefutation 11.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 150 ( 68 ~; 61 |; 21 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-2 aty)
% Number of variables : 136 ( 116 !; 20 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ r4 > r3 > r2 > id > 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(id,type,
id: ( $i * $i ) > $o ).
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_231,axiom,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
tff(f_114,axiom,
! [X23,X24,X25] :
( ~ id(X23,X24)
| id(X23,X25)
| ~ id(X24,X25) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
tff(f_106,axiom,
! [X21,X22] :
( ~ id(X21,X22)
| id(X22,X21) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
tff(f_196,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( id(Y5,Y4)
& ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) ) )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).
tff(f_101,axiom,
! [X20] : id(X20,X20),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
tff(f_75,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( id(X12,Y21)
& r2(X11,X12) )
| ( ~ r2(X11,X12)
& ~ id(X12,Y21) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
tff(f_278,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( id(Y3,Y2)
& ? [Y4] :
( r3(Y1,Y4,Y3)
& ? [Y5] :
( r2(Y5,Y4)
& ? [Y6] :
( r1(Y6)
& r2(Y6,Y5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xplustwoidy) ).
tff(f_242,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( id(Y8,Y18)
& r1(Y18) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
tff(f_127,axiom,
! [X26,X27] :
( ~ id(X26,X27)
| ( ~ r1(X26)
& ~ r1(X27) )
| ( r1(X26)
& r1(X27) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
tff(f_63,axiom,
? [Y24] :
! [X19] :
( ( id(X19,Y24)
& r1(X19) )
| ( ~ r1(X19)
& ~ id(X19,Y24) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
tff(f_252,axiom,
! [X6] :
( ? [Y19] :
( id(X6,Y19)
& r1(Y19) )
| ? [Y1,Y11] :
( id(X6,Y11)
& r2(Y1,Y11) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6a) ).
tff(f_262,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ id(Y20,Y10)
| ~ r1(Y20) )
| ~ r2(X7,Y10) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
tff(c_98,plain,
! [X4_87] : id('#skF_13'(X4_87),X4_87),
inference(cnfTransformation,[status(thm)],[f_231]) ).
tff(c_1053,plain,
! [X24_310,X25_311,X23_312] :
( ~ id(X24_310,X25_311)
| id(X23_312,X25_311)
| ~ id(X23_312,X24_310) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_1117,plain,
! [X23_313,X4_314] :
( id(X23_313,X4_314)
| ~ id(X23_313,'#skF_13'(X4_314)) ),
inference(resolution,[status(thm)],[c_98,c_1053]) ).
tff(c_1159,plain,
! [X4_315] : id('#skF_13'('#skF_13'(X4_315)),X4_315),
inference(resolution,[status(thm)],[c_98,c_1117]) ).
tff(c_1115,plain,
! [X23_312,X4_87] :
( id(X23_312,X4_87)
| ~ id(X23_312,'#skF_13'(X4_87)) ),
inference(resolution,[status(thm)],[c_98,c_1053]) ).
tff(c_1353,plain,
! [X4_329] : id('#skF_13'('#skF_13'('#skF_13'(X4_329))),X4_329),
inference(resolution,[status(thm)],[c_1159,c_1115]) ).
tff(c_36,plain,
! [X22_25,X21_24] :
( id(X22_25,X21_24)
| ~ id(X21_24,X22_25) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_1416,plain,
! [X4_329] : id(X4_329,'#skF_13'('#skF_13'('#skF_13'(X4_329)))),
inference(resolution,[status(thm)],[c_1353,c_36]) ).
tff(c_76,plain,
! [X1_47,X8_48] : r3(X1_47,'#skF_7'(X1_47,X8_48),'#skF_6'(X1_47,X8_48)),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_78,plain,
! [X8_48,X1_47] : r2(X8_48,'#skF_7'(X1_47,X8_48)),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_34,plain,
! [X20_23] : id(X20_23,X20_23),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_330,plain,
! [X11_181,X12_182] :
( r2(X11_181,X12_182)
| ~ id(X12_182,'#skF_2'(X11_181)) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_350,plain,
! [X11_183] : r2(X11_183,'#skF_2'(X11_183)),
inference(resolution,[status(thm)],[c_34,c_330]) ).
tff(c_118,plain,
! [Y3_110,Y5_122,Y2_109,Y6_124,Y1_108,Y4_118] :
( ~ r2(Y6_124,Y5_122)
| ~ r1(Y6_124)
| ~ r2(Y5_122,Y4_118)
| ~ r3(Y1_108,Y4_118,Y3_110)
| ~ id(Y3_110,Y2_109) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_414,plain,
! [Y3_194,Y1_193,X11_191,Y4_190,Y2_192] :
( ~ r1(X11_191)
| ~ r2('#skF_2'(X11_191),Y4_190)
| ~ r3(Y1_193,Y4_190,Y3_194)
| ~ id(Y3_194,Y2_192) ),
inference(resolution,[status(thm)],[c_350,c_118]) ).
tff(c_1970,plain,
! [X11_381,Y2_382,Y1_379,X1_380,Y3_383] :
( ~ r1(X11_381)
| ~ r3(Y1_379,'#skF_7'(X1_380,'#skF_2'(X11_381)),Y3_383)
| ~ id(Y3_383,Y2_382) ),
inference(resolution,[status(thm)],[c_78,c_414]) ).
tff(c_20000,plain,
! [X11_1112,X1_1113,Y2_1114] :
( ~ r1(X11_1112)
| ~ id('#skF_6'(X1_1113,'#skF_2'(X11_1112)),Y2_1114) ),
inference(resolution,[status(thm)],[c_76,c_1970]) ).
tff(c_20140,plain,
! [X11_1112] : ~ r1(X11_1112),
inference(resolution,[status(thm)],[c_1416,c_20000]) ).
tff(c_1206,plain,
! [X4_87] : id('#skF_13'('#skF_13'('#skF_13'(X4_87))),X4_87),
inference(resolution,[status(thm)],[c_1159,c_1115]) ).
tff(c_38,plain,
! [X24_27,X25_28,X23_26] :
( ~ id(X24_27,X25_28)
| id(X23_26,X25_28)
| ~ id(X23_26,X24_27) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_16389,plain,
! [X23_991,X4_992] :
( id(X23_991,X4_992)
| ~ id(X23_991,'#skF_13'('#skF_13'(X4_992))) ),
inference(resolution,[status(thm)],[c_1159,c_38]) ).
tff(c_16850,plain,
! [X4_1003] : id('#skF_13'('#skF_13'('#skF_13'('#skF_13'('#skF_13'(X4_1003))))),X4_1003),
inference(resolution,[status(thm)],[c_1206,c_16389]) ).
tff(c_100,plain,
! [X5_92] : r1('#skF_17'(X5_92)),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_102,plain,
! [X5_92] : id('#skF_15'(X5_92),'#skF_17'(X5_92)),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_151,plain,
! [X22_144,X21_145] :
( id(X22_144,X21_145)
| ~ id(X21_145,X22_144) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_160,plain,
! [X5_92] : id('#skF_17'(X5_92),'#skF_15'(X5_92)),
inference(resolution,[status(thm)],[c_102,c_151]) ).
tff(c_198,plain,
! [X26_160,X27_161] :
( ~ r1(X26_160)
| r1(X27_161)
| ~ id(X26_160,X27_161) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_201,plain,
! [X5_92] :
( ~ r1('#skF_17'(X5_92))
| r1('#skF_15'(X5_92)) ),
inference(resolution,[status(thm)],[c_160,c_198]) ).
tff(c_222,plain,
! [X5_92] : r1('#skF_15'(X5_92)),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_201]) ).
tff(c_8,plain,
! [X19_2] :
( id(X19_2,'#skF_1')
| ~ r1(X19_2) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_161,plain,
! [X19_2] :
( id('#skF_1',X19_2)
| ~ r1(X19_2) ),
inference(resolution,[status(thm)],[c_8,c_151]) ).
tff(c_2831,plain,
! [X23_472,X5_473] :
( id(X23_472,'#skF_17'(X5_473))
| ~ id(X23_472,'#skF_15'(X5_473)) ),
inference(resolution,[status(thm)],[c_102,c_1053]) ).
tff(c_2870,plain,
! [X5_473] :
( id('#skF_1','#skF_17'(X5_473))
| ~ r1('#skF_15'(X5_473)) ),
inference(resolution,[status(thm)],[c_161,c_2831]) ).
tff(c_2895,plain,
! [X5_474] : id('#skF_1','#skF_17'(X5_474)),
inference(demodulation,[status(thm),theory(equality)],[c_222,c_2870]) ).
tff(c_3582,plain,
! [X23_510,X5_511] :
( id(X23_510,'#skF_17'(X5_511))
| ~ id(X23_510,'#skF_1') ),
inference(resolution,[status(thm)],[c_2895,c_38]) ).
tff(c_3616,plain,
! [X5_511,X23_510] :
( id('#skF_17'(X5_511),X23_510)
| ~ id(X23_510,'#skF_1') ),
inference(resolution,[status(thm)],[c_3582,c_36]) ).
tff(c_162,plain,
! [X4_87] : id(X4_87,'#skF_13'(X4_87)),
inference(resolution,[status(thm)],[c_98,c_151]) ).
tff(c_1673,plain,
! [X23_356,X4_357] :
( id(X23_356,'#skF_13'(X4_357))
| ~ id(X23_356,X4_357) ),
inference(resolution,[status(thm)],[c_162,c_1053]) ).
tff(c_1696,plain,
! [X4_357,X23_356] :
( id('#skF_13'(X4_357),X23_356)
| ~ id(X23_356,X4_357) ),
inference(resolution,[status(thm)],[c_1673,c_36]) ).
tff(c_5607,plain,
! [X23_630,X5_631] :
( id(X23_630,'#skF_15'(X5_631))
| ~ id(X23_630,'#skF_17'(X5_631)) ),
inference(resolution,[status(thm)],[c_160,c_1053]) ).
tff(c_44,plain,
! [X27_30,X26_29] :
( ~ r1(X27_30)
| r1(X26_29)
| ~ id(X26_29,X27_30) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_5630,plain,
! [X5_631,X23_630] :
( ~ r1('#skF_15'(X5_631))
| r1(X23_630)
| ~ id(X23_630,'#skF_17'(X5_631)) ),
inference(resolution,[status(thm)],[c_5607,c_44]) ).
tff(c_5666,plain,
! [X23_634,X5_635] :
( r1(X23_634)
| ~ id(X23_634,'#skF_17'(X5_635)) ),
inference(demodulation,[status(thm),theory(equality)],[c_222,c_5630]) ).
tff(c_5782,plain,
! [X4_636,X5_637] :
( r1('#skF_13'(X4_636))
| ~ id('#skF_17'(X5_637),X4_636) ),
inference(resolution,[status(thm)],[c_1696,c_5666]) ).
tff(c_5883,plain,
! [X23_510] :
( r1('#skF_13'(X23_510))
| ~ id(X23_510,'#skF_1') ),
inference(resolution,[status(thm)],[c_3616,c_5782]) ).
tff(c_1156,plain,
! [X4_314] : id('#skF_13'('#skF_13'(X4_314)),X4_314),
inference(resolution,[status(thm)],[c_98,c_1117]) ).
tff(c_112,plain,
! [X6_100] :
( r1('#skF_18'(X6_100))
| id(X6_100,'#skF_20'(X6_100)) ),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_5535,plain,
! [X23_617,X6_618] :
( id(X23_617,'#skF_20'(X6_618))
| ~ id(X23_617,X6_618)
| r1('#skF_18'(X6_618)) ),
inference(resolution,[status(thm)],[c_112,c_1053]) ).
tff(c_108,plain,
! [X6_100] :
( r1('#skF_18'(X6_100))
| r2('#skF_19'(X6_100),'#skF_20'(X6_100)) ),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_497,plain,
! [X7_204,Y10_205,Y20_206] :
( ~ r2(X7_204,Y10_205)
| ~ r1(Y20_206)
| ~ id(Y20_206,Y10_205) ),
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_510,plain,
! [Y20_206,X6_100] :
( ~ r1(Y20_206)
| ~ id(Y20_206,'#skF_20'(X6_100))
| r1('#skF_18'(X6_100)) ),
inference(resolution,[status(thm)],[c_108,c_497]) ).
tff(c_6663,plain,
! [X23_680,X6_681] :
( ~ r1(X23_680)
| ~ id(X23_680,X6_681)
| r1('#skF_18'(X6_681)) ),
inference(resolution,[status(thm)],[c_5535,c_510]) ).
tff(c_6990,plain,
! [X4_711] :
( ~ r1('#skF_13'('#skF_13'(X4_711)))
| r1('#skF_18'(X4_711)) ),
inference(resolution,[status(thm)],[c_1156,c_6663]) ).
tff(c_7032,plain,
! [X4_711] :
( r1('#skF_18'(X4_711))
| ~ id('#skF_13'(X4_711),'#skF_1') ),
inference(resolution,[status(thm)],[c_5883,c_6990]) ).
tff(c_17025,plain,
r1('#skF_18'('#skF_13'('#skF_13'('#skF_13'('#skF_13'('#skF_1')))))),
inference(resolution,[status(thm)],[c_16850,c_7032]) ).
tff(c_20255,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20140,c_17025]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN080+1 : TPTP v9.0.0. 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
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 16:11:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 11.84/4.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.98/4.50
% 11.98/4.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------