%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU141+1 : TPTP v9.0.0. Released v3.3.0.
% 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 : 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 : Wed Apr 9 08:52:54 PM UTC 2025
% Result : Theorem 44.75s 30.70s
% Output : CNFRefutation 44.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 78 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 155 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 138 ( 61 ~; 65 |; 5 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 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; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 112 ( 110 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > disjoint > empty > set_intersection2 > set_difference > #nlpp > empty_set > #skF_11 > #skF_4 > #skF_7 > #skF_10 > #skF_6 > #skF_5 > #skF_2 > #skF_8 > #skF_9 > #skF_3 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_118,negated_conjecture,
~ ! [A,B] :
( disjoint(A,B)
<=> ( set_difference(A,B) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
tff(f_104,axiom,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ~ ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
tff(f_55,axiom,
! [A,B,C] :
( ( C = set_intersection2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
tff(f_65,axiom,
! [A,B,C] :
( ( C = set_difference(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
tff(f_75,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_108,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_69,axiom,
! [A,B] :
( disjoint(A,B)
<=> ( set_intersection2(A,B) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
tff(c_94,plain,
( ~ disjoint('#skF_9','#skF_10')
| disjoint('#skF_11','#skF_12') ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_154,plain,
~ disjoint('#skF_9','#skF_10'),
inference(splitLeft,[status(thm)],[c_94]) ).
tff(c_128548,plain,
! [A_1806,B_1807] :
( in('#skF_8'(A_1806,B_1807),set_intersection2(A_1806,B_1807))
| disjoint(A_1806,B_1807) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_22,plain,
! [D_17,A_12,B_13] :
( in(D_17,A_12)
| ~ in(D_17,set_intersection2(A_12,B_13)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_129303,plain,
! [A_1863,B_1864] :
( in('#skF_8'(A_1863,B_1864),A_1863)
| disjoint(A_1863,B_1864) ),
inference(resolution,[status(thm)],[c_128548,c_22]) ).
tff(c_20,plain,
! [D_17,B_13,A_12] :
( in(D_17,B_13)
| ~ in(D_17,set_intersection2(A_12,B_13)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_128821,plain,
! [A_1830,B_1831] :
( in('#skF_8'(A_1830,B_1831),B_1831)
| disjoint(A_1830,B_1831) ),
inference(resolution,[status(thm)],[c_128548,c_20]) ).
tff(c_127497,plain,
! [A_1709,B_1710] :
( in('#skF_8'(A_1709,B_1710),set_intersection2(A_1709,B_1710))
| disjoint(A_1709,B_1710) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_128239,plain,
! [A_1750,B_1751] :
( in('#skF_8'(A_1750,B_1751),A_1750)
| disjoint(A_1750,B_1751) ),
inference(resolution,[status(thm)],[c_127497,c_22]) ).
tff(c_127710,plain,
! [A_1721,B_1722] :
( in('#skF_8'(A_1721,B_1722),B_1722)
| disjoint(A_1721,B_1722) ),
inference(resolution,[status(thm)],[c_127497,c_20]) ).
tff(c_92,plain,
( ( set_difference('#skF_9','#skF_10') = '#skF_9' )
| ( set_difference('#skF_11','#skF_12') != '#skF_11' ) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_322,plain,
set_difference('#skF_11','#skF_12') != '#skF_11',
inference(splitLeft,[status(thm)],[c_92]) ).
tff(c_1895,plain,
! [A_204,B_205,C_206] :
( in('#skF_4'(A_204,B_205,C_206),A_204)
| in('#skF_5'(A_204,B_205,C_206),C_206)
| ( set_difference(A_204,B_205) = C_206 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_48,plain,
! [A_18,B_19,C_20] :
( ~ in('#skF_4'(A_18,B_19,C_20),C_20)
| in('#skF_5'(A_18,B_19,C_20),C_20)
| ( set_difference(A_18,B_19) = C_20 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_1983,plain,
! [A_204,B_205] :
( in('#skF_5'(A_204,B_205,A_204),A_204)
| ( set_difference(A_204,B_205) = A_204 ) ),
inference(resolution,[status(thm)],[c_1895,c_48]) ).
tff(c_3235,plain,
! [A_264,B_265,C_266] :
( in('#skF_4'(A_264,B_265,C_266),A_264)
| in('#skF_5'(A_264,B_265,C_266),B_265)
| ~ in('#skF_5'(A_264,B_265,C_266),A_264)
| ( set_difference(A_264,B_265) = C_266 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_42,plain,
! [A_18,B_19,C_20] :
( ~ in('#skF_4'(A_18,B_19,C_20),C_20)
| in('#skF_5'(A_18,B_19,C_20),B_19)
| ~ in('#skF_5'(A_18,B_19,C_20),A_18)
| ( set_difference(A_18,B_19) = C_20 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_17205,plain,
! [A_612,B_613] :
( in('#skF_5'(A_612,B_613,A_612),B_613)
| ~ in('#skF_5'(A_612,B_613,A_612),A_612)
| ( set_difference(A_612,B_613) = A_612 ) ),
inference(resolution,[status(thm)],[c_3235,c_42]) ).
tff(c_126824,plain,
! [A_1643,B_1644] :
( in('#skF_5'(A_1643,B_1644,A_1643),B_1644)
| ( set_difference(A_1643,B_1644) = A_1643 ) ),
inference(resolution,[status(thm)],[c_1983,c_17205]) ).
tff(c_4379,plain,
! [A_320,B_321] :
( in('#skF_5'(A_320,B_321,A_320),A_320)
| ( set_difference(A_320,B_321) = A_320 ) ),
inference(resolution,[status(thm)],[c_1895,c_48]) ).
tff(c_96,plain,
( ( set_difference('#skF_9','#skF_10') = '#skF_9' )
| disjoint('#skF_11','#skF_12') ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_297,plain,
disjoint('#skF_11','#skF_12'),
inference(splitLeft,[status(thm)],[c_96]) ).
tff(c_68,plain,
empty('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_135,plain,
! [A_49] :
( ( empty_set = A_49 )
| ~ empty(A_49) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_144,plain,
empty_set = '#skF_6',
inference(resolution,[status(thm)],[c_68,c_135]) ).
tff(c_54,plain,
! [A_24,B_25] :
( ( set_intersection2(A_24,B_25) = empty_set )
| ~ disjoint(A_24,B_25) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_324,plain,
! [A_67,B_68] :
( ( set_intersection2(A_67,B_68) = '#skF_6' )
| ~ disjoint(A_67,B_68) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_54]) ).
tff(c_336,plain,
set_intersection2('#skF_11','#skF_12') = '#skF_6',
inference(resolution,[status(thm)],[c_297,c_324]) ).
tff(c_361,plain,
! [A_69,B_70,C_71] :
( ~ disjoint(A_69,B_70)
| ~ in(C_71,set_intersection2(A_69,B_70)) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_364,plain,
! [C_71] :
( ~ disjoint('#skF_11','#skF_12')
| ~ in(C_71,'#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_336,c_361]) ).
tff(c_384,plain,
! [C_71] : ~ in(C_71,'#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_297,c_364]) ).
tff(c_794,plain,
! [D_128,A_129,B_130] :
( in(D_128,set_intersection2(A_129,B_130))
| ~ in(D_128,B_130)
| ~ in(D_128,A_129) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_823,plain,
! [D_128] :
( in(D_128,'#skF_6')
| ~ in(D_128,'#skF_12')
| ~ in(D_128,'#skF_11') ),
inference(superposition,[status(thm),theory(equality)],[c_336,c_794]) ).
tff(c_851,plain,
! [D_128] :
( ~ in(D_128,'#skF_12')
| ~ in(D_128,'#skF_11') ),
inference(negUnitSimplification,[status(thm)],[c_384,c_823]) ).
tff(c_4422,plain,
! [B_321] :
( ~ in('#skF_5'('#skF_11',B_321,'#skF_11'),'#skF_12')
| ( set_difference('#skF_11',B_321) = '#skF_11' ) ),
inference(resolution,[status(thm)],[c_4379,c_851]) ).
tff(c_127002,plain,
set_difference('#skF_11','#skF_12') = '#skF_11',
inference(resolution,[status(thm)],[c_126824,c_4422]) ).
tff(c_127107,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_322,c_322,c_127002]) ).
tff(c_127108,plain,
set_difference('#skF_9','#skF_10') = '#skF_9',
inference(splitRight,[status(thm)],[c_92]) ).
tff(c_127169,plain,
! [D_1649,B_1650,A_1651] :
( ~ in(D_1649,B_1650)
| ~ in(D_1649,set_difference(A_1651,B_1650)) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_127175,plain,
! [D_1649] :
( ~ in(D_1649,'#skF_10')
| ~ in(D_1649,'#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_127108,c_127169]) ).
tff(c_127766,plain,
! [A_1721] :
( ~ in('#skF_8'(A_1721,'#skF_10'),'#skF_9')
| disjoint(A_1721,'#skF_10') ),
inference(resolution,[status(thm)],[c_127710,c_127175]) ).
tff(c_128243,plain,
disjoint('#skF_9','#skF_10'),
inference(resolution,[status(thm)],[c_128239,c_127766]) ).
tff(c_128297,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_154,c_154,c_128243]) ).
tff(c_128298,plain,
set_difference('#skF_9','#skF_10') = '#skF_9',
inference(splitRight,[status(thm)],[c_96]) ).
tff(c_128381,plain,
! [D_1772,B_1773,A_1774] :
( ~ in(D_1772,B_1773)
| ~ in(D_1772,set_difference(A_1774,B_1773)) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_128384,plain,
! [D_1772] :
( ~ in(D_1772,'#skF_10')
| ~ in(D_1772,'#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_128298,c_128381]) ).
tff(c_128864,plain,
! [A_1830] :
( ~ in('#skF_8'(A_1830,'#skF_10'),'#skF_9')
| disjoint(A_1830,'#skF_10') ),
inference(resolution,[status(thm)],[c_128821,c_128384]) ).
tff(c_129311,plain,
disjoint('#skF_9','#skF_10'),
inference(resolution,[status(thm)],[c_129303,c_128864]) ).
tff(c_129354,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_154,c_154,c_129311]) ).
tff(c_129356,plain,
disjoint('#skF_9','#skF_10'),
inference(splitRight,[status(thm)],[c_94]) ).
tff(c_90,plain,
( ~ disjoint('#skF_9','#skF_10')
| ( set_difference('#skF_11','#skF_12') != '#skF_11' ) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_129518,plain,
set_difference('#skF_11','#skF_12') != '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_129356,c_90]) ).
tff(c_52,plain,
! [A_18,B_19,C_20] :
( in('#skF_4'(A_18,B_19,C_20),A_18)
| in('#skF_5'(A_18,B_19,C_20),C_20)
| ( set_difference(A_18,B_19) = C_20 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_130664,plain,
! [A_1977,B_1978,C_1979] :
( ~ in('#skF_4'(A_1977,B_1978,C_1979),C_1979)
| in('#skF_5'(A_1977,B_1978,C_1979),C_1979)
| ( set_difference(A_1977,B_1978) = C_1979 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_130677,plain,
! [A_18,B_19] :
( in('#skF_5'(A_18,B_19,A_18),A_18)
| ( set_difference(A_18,B_19) = A_18 ) ),
inference(resolution,[status(thm)],[c_52,c_130664]) ).
tff(c_132890,plain,
! [A_2098,B_2099,C_2100] :
( in('#skF_4'(A_2098,B_2099,C_2100),A_2098)
| in('#skF_5'(A_2098,B_2099,C_2100),B_2099)
| ~ in('#skF_5'(A_2098,B_2099,C_2100),A_2098)
| ( set_difference(A_2098,B_2099) = C_2100 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_144687,plain,
! [A_2383,B_2384] :
( in('#skF_5'(A_2383,B_2384,A_2383),B_2384)
| ~ in('#skF_5'(A_2383,B_2384,A_2383),A_2383)
| ( set_difference(A_2383,B_2384) = A_2383 ) ),
inference(resolution,[status(thm)],[c_132890,c_42]) ).
tff(c_249131,plain,
! [A_3338,B_3339] :
( in('#skF_5'(A_3338,B_3339,A_3338),B_3339)
| ( set_difference(A_3338,B_3339) = A_3338 ) ),
inference(resolution,[status(thm)],[c_130677,c_144687]) ).
tff(c_133473,plain,
! [A_2137,B_2138] :
( in('#skF_5'(A_2137,B_2138,A_2137),A_2137)
| ( set_difference(A_2137,B_2138) = A_2137 ) ),
inference(resolution,[status(thm)],[c_52,c_130664]) ).
tff(c_129355,plain,
disjoint('#skF_11','#skF_12'),
inference(splitRight,[status(thm)],[c_94]) ).
tff(c_129530,plain,
! [A_1882,B_1883] :
( ( set_intersection2(A_1882,B_1883) = '#skF_6' )
| ~ disjoint(A_1882,B_1883) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_54]) ).
tff(c_129550,plain,
set_intersection2('#skF_11','#skF_12') = '#skF_6',
inference(resolution,[status(thm)],[c_129355,c_129530]) ).
tff(c_129607,plain,
! [A_1886,B_1887,C_1888] :
( ~ disjoint(A_1886,B_1887)
| ~ in(C_1888,set_intersection2(A_1886,B_1887)) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_129613,plain,
! [C_1888] :
( ~ disjoint('#skF_11','#skF_12')
| ~ in(C_1888,'#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_129550,c_129607]) ).
tff(c_129638,plain,
! [C_1888] : ~ in(C_1888,'#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_129355,c_129613]) ).
tff(c_130080,plain,
! [D_1941,A_1942,B_1943] :
( in(D_1941,set_intersection2(A_1942,B_1943))
| ~ in(D_1941,B_1943)
| ~ in(D_1941,A_1942) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_130109,plain,
! [D_1941] :
( in(D_1941,'#skF_6')
| ~ in(D_1941,'#skF_12')
| ~ in(D_1941,'#skF_11') ),
inference(superposition,[status(thm),theory(equality)],[c_129550,c_130080]) ).
tff(c_130140,plain,
! [D_1941] :
( ~ in(D_1941,'#skF_12')
| ~ in(D_1941,'#skF_11') ),
inference(negUnitSimplification,[status(thm)],[c_129638,c_130109]) ).
tff(c_133521,plain,
! [B_2138] :
( ~ in('#skF_5'('#skF_11',B_2138,'#skF_11'),'#skF_12')
| ( set_difference('#skF_11',B_2138) = '#skF_11' ) ),
inference(resolution,[status(thm)],[c_133473,c_130140]) ).
tff(c_249324,plain,
set_difference('#skF_11','#skF_12') = '#skF_11',
inference(resolution,[status(thm)],[c_249131,c_133521]) ).
tff(c_249435,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_129518,c_129518,c_249324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU141+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % 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
% 0.13/0.34 % 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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 22:07:48 EDT 2025
% 0.13/0.35 % CPUTime :
% 44.75/30.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.75/30.71
% 44.75/30.71 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------