TSTP Solution File: SEU160+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n026.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 10:57:50 EDT 2023
% Result : Theorem 10.85s 3.55s
% Output : CNFRefutation 11.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 64
% Syntax : Number of formulae : 155 ( 63 unt; 49 typ; 0 def)
% Number of atoms : 157 ( 83 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 89 ( 38 ~; 40 |; 1 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 96 ( 42 >; 54 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 44 ( 44 usr; 7 con; 0-4 aty)
% Number of variables : 89 (; 88 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > ordered_pair > cartesian_product2 > #nlpp > union > singleton > powerset > empty_set > #skF_13 > #skF_24 > #skF_17 > #skF_6 > #skF_31 > #skF_25 > #skF_18 > #skF_20 > #skF_22 > #skF_12 > #skF_34 > #skF_15 > #skF_26 > #skF_23 > #skF_19 > #skF_33 > #skF_11 > #skF_32 > #skF_7 > #skF_9 > #skF_28 > #skF_30 > #skF_3 > #skF_29 > #skF_2 > #skF_8 > #skF_27 > #skF_14 > #skF_1 > #skF_16 > #skF_21 > #skF_5 > #skF_4 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff(union,type,
union: $i > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_33',type,
'#skF_33': ( $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_225,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_220,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_313,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( ( A = empty_set )
| ( A = singleton(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
tff(f_178,lemma,
! [A,B] :
( in(A,B)
=> ( set_union2(singleton(A),B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
tff(f_378,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_267,lemma,
! [A,B] :
( subset(A,B)
=> ( set_intersection2(A,B) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
tff(f_40,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_42,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_244,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
tff(f_306,lemma,
! [A,B] : ( set_union2(A,set_difference(B,A)) = set_union2(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
tff(f_343,lemma,
! [A,B] :
( subset(A,B)
=> ( B = set_union2(A,set_difference(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
tff(f_61,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_114,axiom,
! [A,B,C] :
( ( C = set_intersection2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
tff(f_55,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_278,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
tff(c_248,plain,
! [A_149] : subset(A_149,A_149),
inference(cnfTransformation,[status(thm)],[f_225]) ).
tff(c_244,plain,
empty('#skF_25'),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_306,plain,
( ~ subset('#skF_29',singleton('#skF_30'))
| ( singleton('#skF_32') != '#skF_31' ) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_421,plain,
singleton('#skF_32') != '#skF_31',
inference(splitLeft,[status(thm)],[c_306]) ).
tff(c_3922,plain,
! [A_486,B_487] :
( ( set_union2(singleton(A_486),B_487) = B_487 )
| ~ in(A_486,B_487) ),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_385,plain,
! [A_247] :
( ( empty_set = A_247 )
| ~ empty(A_247) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_392,plain,
empty_set = '#skF_25',
inference(resolution,[status(thm)],[c_244,c_385]) ).
tff(c_316,plain,
( ( singleton('#skF_30') = '#skF_29' )
| ( empty_set = '#skF_29' )
| subset('#skF_31',singleton('#skF_32')) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_783,plain,
( ( singleton('#skF_30') = '#skF_29' )
| ( '#skF_25' = '#skF_29' )
| subset('#skF_31',singleton('#skF_32')) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_316]) ).
tff(c_784,plain,
subset('#skF_31',singleton('#skF_32')),
inference(splitLeft,[status(thm)],[c_783]) ).
tff(c_1671,plain,
! [A_355,B_356] :
( ( set_intersection2(A_355,B_356) = A_355 )
| ~ subset(A_355,B_356) ),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_1705,plain,
set_intersection2('#skF_31',singleton('#skF_32')) = '#skF_31',
inference(resolution,[status(thm)],[c_784,c_1671]) ).
tff(c_8,plain,
! [B_8,A_7] : ( set_union2(B_8,A_7) = set_union2(A_7,B_8) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_10,plain,
! [B_10,A_9] : ( set_intersection2(B_10,A_9) = set_intersection2(A_9,B_10) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_256,plain,
! [A_159,B_160] : subset(set_intersection2(A_159,B_160),A_159),
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_304,plain,
! [A_194,B_195] : ( set_union2(A_194,set_difference(B_195,A_194)) = set_union2(A_194,B_195) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_330,plain,
! [A_205,B_206] :
( ( set_union2(A_205,set_difference(B_206,A_205)) = B_206 )
| ~ subset(A_205,B_206) ),
inference(cnfTransformation,[status(thm)],[f_343]) ).
tff(c_1222,plain,
! [A_334,B_335] :
( ( set_union2(A_334,B_335) = B_335 )
| ~ subset(A_334,B_335) ),
inference(demodulation,[status(thm),theory(equality)],[c_304,c_330]) ).
tff(c_1322,plain,
! [A_338,B_339] : ( set_union2(set_intersection2(A_338,B_339),A_338) = A_338 ),
inference(resolution,[status(thm)],[c_256,c_1222]) ).
tff(c_1522,plain,
! [A_344,B_345] : ( set_union2(set_intersection2(A_344,B_345),B_345) = B_345 ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_1322]) ).
tff(c_1939,plain,
! [A_363,A_364] : ( set_union2(A_363,set_intersection2(A_364,A_363)) = A_363 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1522]) ).
tff(c_1986,plain,
set_union2(singleton('#skF_32'),'#skF_31') = singleton('#skF_32'),
inference(superposition,[status(thm),theory(equality)],[c_1705,c_1939]) ).
tff(c_3960,plain,
( ( singleton('#skF_32') = '#skF_31' )
| ~ in('#skF_32','#skF_31') ),
inference(superposition,[status(thm),theory(equality)],[c_3922,c_1986]) ).
tff(c_4051,plain,
~ in('#skF_32','#skF_31'),
inference(negUnitSimplification,[status(thm)],[c_421,c_3960]) ).
tff(c_310,plain,
( ~ subset('#skF_29',singleton('#skF_30'))
| ( empty_set != '#skF_31' ) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_384,plain,
empty_set != '#skF_31',
inference(splitLeft,[status(thm)],[c_310]) ).
tff(c_396,plain,
'#skF_31' != '#skF_25',
inference(demodulation,[status(thm),theory(equality)],[c_392,c_384]) ).
tff(c_32,plain,
! [A_18] :
( ( empty_set = A_18 )
| in('#skF_3'(A_18),A_18) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_634,plain,
! [A_18] :
( ( A_18 = '#skF_25' )
| in('#skF_3'(A_18),A_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_32]) ).
tff(c_5127,plain,
! [D_529,B_530,A_531] :
( in(D_529,B_530)
| ~ in(D_529,set_intersection2(A_531,B_530)) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_6131,plain,
! [D_547] :
( in(D_547,singleton('#skF_32'))
| ~ in(D_547,'#skF_31') ),
inference(superposition,[status(thm),theory(equality)],[c_1705,c_5127]) ).
tff(c_18,plain,
! [C_17,A_13] :
( ( C_17 = A_13 )
| ~ in(C_17,singleton(A_13)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_6192,plain,
! [D_548] :
( ( D_548 = '#skF_32' )
| ~ in(D_548,'#skF_31') ),
inference(resolution,[status(thm)],[c_6131,c_18]) ).
tff(c_6208,plain,
( ( '#skF_3'('#skF_31') = '#skF_32' )
| ( '#skF_31' = '#skF_25' ) ),
inference(resolution,[status(thm)],[c_634,c_6192]) ).
tff(c_6214,plain,
'#skF_3'('#skF_31') = '#skF_32',
inference(negUnitSimplification,[status(thm)],[c_396,c_6208]) ).
tff(c_6221,plain,
( ( '#skF_31' = '#skF_25' )
| in('#skF_32','#skF_31') ),
inference(superposition,[status(thm),theory(equality)],[c_6214,c_634]) ).
tff(c_6226,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4051,c_396,c_6221]) ).
tff(c_6227,plain,
( ( '#skF_25' = '#skF_29' )
| ( singleton('#skF_30') = '#skF_29' ) ),
inference(splitRight,[status(thm)],[c_783]) ).
tff(c_6318,plain,
singleton('#skF_30') = '#skF_29',
inference(splitLeft,[status(thm)],[c_6227]) ).
tff(c_314,plain,
( ~ subset('#skF_29',singleton('#skF_30'))
| subset('#skF_31',singleton('#skF_32')) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_665,plain,
~ subset('#skF_29',singleton('#skF_30')),
inference(splitLeft,[status(thm)],[c_314]) ).
tff(c_6320,plain,
~ subset('#skF_29','#skF_29'),
inference(demodulation,[status(thm),theory(equality)],[c_6318,c_665]) ).
tff(c_6323,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_248,c_6320]) ).
tff(c_6324,plain,
'#skF_25' = '#skF_29',
inference(splitRight,[status(thm)],[c_6227]) ).
tff(c_280,plain,
! [A_177] : subset(empty_set,A_177),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_398,plain,
! [A_177] : subset('#skF_25',A_177),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_280]) ).
tff(c_6343,plain,
! [A_177] : subset('#skF_29',A_177),
inference(demodulation,[status(thm),theory(equality)],[c_6324,c_398]) ).
tff(c_6358,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6343,c_665]) ).
tff(c_6359,plain,
subset('#skF_31',singleton('#skF_32')),
inference(splitRight,[status(thm)],[c_314]) ).
tff(c_6973,plain,
! [A_619,B_620] :
( ( set_intersection2(A_619,B_620) = A_619 )
| ~ subset(A_619,B_620) ),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_7016,plain,
set_intersection2('#skF_31',singleton('#skF_32')) = '#skF_31',
inference(resolution,[status(thm)],[c_6359,c_6973]) ).
tff(c_7969,plain,
! [A_678,B_679] :
( ( set_union2(A_678,B_679) = B_679 )
| ~ subset(A_678,B_679) ),
inference(demodulation,[status(thm),theory(equality)],[c_304,c_330]) ).
tff(c_8145,plain,
! [A_682,B_683] : ( set_union2(set_intersection2(A_682,B_683),A_682) = A_682 ),
inference(resolution,[status(thm)],[c_256,c_7969]) ).
tff(c_8460,plain,
! [A_686,B_687] : ( set_union2(set_intersection2(A_686,B_687),B_687) = B_687 ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_8145]) ).
tff(c_11274,plain,
! [B_801,A_802] : ( set_union2(B_801,set_intersection2(A_802,B_801)) = B_801 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_8460]) ).
tff(c_11396,plain,
set_union2(singleton('#skF_32'),'#skF_31') = singleton('#skF_32'),
inference(superposition,[status(thm),theory(equality)],[c_7016,c_11274]) ).
tff(c_214,plain,
! [A_128,B_129] :
( ( set_union2(singleton(A_128),B_129) = B_129 )
| ~ in(A_128,B_129) ),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_11441,plain,
( ( singleton('#skF_32') = '#skF_31' )
| ~ in('#skF_32','#skF_31') ),
inference(superposition,[status(thm),theory(equality)],[c_11396,c_214]) ).
tff(c_11506,plain,
~ in('#skF_32','#skF_31'),
inference(negUnitSimplification,[status(thm)],[c_421,c_11441]) ).
tff(c_11537,plain,
! [D_805,B_806,A_807] :
( in(D_805,B_806)
| ~ in(D_805,set_intersection2(A_807,B_806)) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_11640,plain,
! [D_810] :
( in(D_810,singleton('#skF_32'))
| ~ in(D_810,'#skF_31') ),
inference(superposition,[status(thm),theory(equality)],[c_7016,c_11537]) ).
tff(c_11696,plain,
! [D_811] :
( ( D_811 = '#skF_32' )
| ~ in(D_811,'#skF_31') ),
inference(resolution,[status(thm)],[c_11640,c_18]) ).
tff(c_11716,plain,
( ( '#skF_3'('#skF_31') = '#skF_32' )
| ( '#skF_31' = '#skF_25' ) ),
inference(resolution,[status(thm)],[c_634,c_11696]) ).
tff(c_11723,plain,
'#skF_3'('#skF_31') = '#skF_32',
inference(negUnitSimplification,[status(thm)],[c_396,c_11716]) ).
tff(c_11730,plain,
( ( '#skF_31' = '#skF_25' )
| in('#skF_32','#skF_31') ),
inference(superposition,[status(thm),theory(equality)],[c_11723,c_634]) ).
tff(c_11735,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11506,c_396,c_11730]) ).
tff(c_11737,plain,
singleton('#skF_32') = '#skF_31',
inference(splitRight,[status(thm)],[c_306]) ).
tff(c_308,plain,
( ( singleton('#skF_30') = '#skF_29' )
| ( empty_set = '#skF_29' )
| ( singleton('#skF_32') != '#skF_31' ) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_11866,plain,
( ( singleton('#skF_30') = '#skF_29' )
| ( '#skF_25' = '#skF_29' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_11737,c_392,c_308]) ).
tff(c_11867,plain,
'#skF_25' = '#skF_29',
inference(splitLeft,[status(thm)],[c_11866]) ).
tff(c_11878,plain,
! [A_177] : subset('#skF_29',A_177),
inference(demodulation,[status(thm),theory(equality)],[c_11867,c_398]) ).
tff(c_11736,plain,
~ subset('#skF_29',singleton('#skF_30')),
inference(splitRight,[status(thm)],[c_306]) ).
tff(c_11897,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11878,c_11736]) ).
tff(c_11898,plain,
singleton('#skF_30') = '#skF_29',
inference(splitRight,[status(thm)],[c_11866]) ).
tff(c_11901,plain,
~ subset('#skF_29','#skF_29'),
inference(demodulation,[status(thm),theory(equality)],[c_11898,c_11736]) ).
tff(c_11904,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_248,c_11901]) ).
tff(c_11906,plain,
empty_set = '#skF_31',
inference(splitRight,[status(thm)],[c_310]) ).
tff(c_346,plain,
! [A_221] :
( ( empty_set = A_221 )
| ~ empty(A_221) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_11992,plain,
! [A_838] :
( ( A_838 = '#skF_31' )
| ~ empty(A_838) ),
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_346]) ).
tff(c_12001,plain,
'#skF_31' = '#skF_25',
inference(resolution,[status(thm)],[c_244,c_11992]) ).
tff(c_12012,plain,
empty_set = '#skF_25',
inference(demodulation,[status(thm),theory(equality)],[c_12001,c_11906]) ).
tff(c_312,plain,
( ( singleton('#skF_30') = '#skF_29' )
| ( empty_set = '#skF_29' )
| ( empty_set != '#skF_31' ) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_12023,plain,
( ( singleton('#skF_30') = '#skF_29' )
| ( '#skF_25' = '#skF_29' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12012,c_12001,c_12012,c_312]) ).
tff(c_12024,plain,
'#skF_25' = '#skF_29',
inference(splitLeft,[status(thm)],[c_12023]) ).
tff(c_11908,plain,
! [A_177] : subset('#skF_31',A_177),
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_280]) ).
tff(c_12010,plain,
! [A_177] : subset('#skF_25',A_177),
inference(demodulation,[status(thm),theory(equality)],[c_12001,c_11908]) ).
tff(c_12053,plain,
! [A_177] : subset('#skF_29',A_177),
inference(demodulation,[status(thm),theory(equality)],[c_12024,c_12010]) ).
tff(c_11905,plain,
~ subset('#skF_29',singleton('#skF_30')),
inference(splitRight,[status(thm)],[c_310]) ).
tff(c_12061,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12053,c_11905]) ).
tff(c_12062,plain,
singleton('#skF_30') = '#skF_29',
inference(splitRight,[status(thm)],[c_12023]) ).
tff(c_12090,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_248,c_12062,c_11905]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % 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 : n026.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 : Thu Aug 3 11:54:01 EDT 2023
% 0.12/0.34 % CPUTime :
% 10.85/3.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.85/3.56
% 10.85/3.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.17/3.60
% 11.17/3.60 Inference rules
% 11.17/3.60 ----------------------
% 11.17/3.60 #Ref : 6
% 11.17/3.60 #Sup : 2865
% 11.17/3.60 #Fact : 0
% 11.17/3.60 #Define : 0
% 11.17/3.60 #Split : 11
% 11.17/3.60 #Chain : 0
% 11.17/3.60 #Close : 0
% 11.17/3.60
% 11.17/3.60 Ordering : KBO
% 11.17/3.60
% 11.17/3.60 Simplification rules
% 11.17/3.60 ----------------------
% 11.17/3.60 #Subsume : 832
% 11.17/3.60 #Demod : 1029
% 11.17/3.60 #Tautology : 1299
% 11.17/3.60 #SimpNegUnit : 63
% 11.17/3.60 #BackRed : 72
% 11.17/3.60
% 11.17/3.60 #Partial instantiations: 0
% 11.17/3.60 #Strategies tried : 1
% 11.17/3.60
% 11.17/3.60 Timing (in seconds)
% 11.17/3.60 ----------------------
% 11.17/3.61 Preprocessing : 0.75
% 11.17/3.61 Parsing : 0.35
% 11.17/3.61 CNF conversion : 0.08
% 11.17/3.61 Main loop : 1.78
% 11.17/3.61 Inferencing : 0.56
% 11.17/3.61 Reduction : 0.67
% 11.17/3.61 Demodulation : 0.47
% 11.17/3.61 BG Simplification : 0.07
% 11.17/3.61 Subsumption : 0.34
% 11.17/3.61 Abstraction : 0.05
% 11.17/3.61 MUC search : 0.00
% 11.17/3.61 Cooper : 0.00
% 11.17/3.61 Total : 2.59
% 11.17/3.61 Index Insertion : 0.00
% 11.17/3.61 Index Deletion : 0.00
% 11.17/3.61 Index Matching : 0.00
% 11.17/3.61 BG Taut test : 0.00
%------------------------------------------------------------------------------