TSTP Solution File: SEU170+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU170+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/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 : Tue Aug 22 10:57:53 EDT 2023
% Result : Theorem 123.05s 104.71s
% Output : CNFRefutation 123.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 79
% Syntax : Number of formulae : 155 ( 46 unt; 57 typ; 0 def)
% Number of atoms : 169 ( 50 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 125 ( 54 ~; 37 |; 11 &)
% ( 13 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 109 ( 51 >; 58 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 50 ( 50 usr; 6 con; 0-4 aty)
% Number of variables : 132 (; 129 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > element > disjoint > are_equipotent > empty > unordered_pair > subset_complement > set_union2 > set_intersection2 > set_difference > ordered_pair > cartesian_product2 > #nlpp > union > singleton > powerset > empty_set > #skF_13 > #skF_25 > #skF_24 > #skF_37 > #skF_17 > #skF_6 > #skF_18 > #skF_20 > #skF_32 > #skF_36 > #skF_22 > #skF_12 > #skF_31 > #skF_15 > #skF_23 > #skF_19 > #skF_28 > #skF_33 > #skF_38 > #skF_11 > #skF_7 > #skF_9 > #skF_26 > #skF_3 > #skF_29 > #skF_2 > #skF_35 > #skF_27 > #skF_8 > #skF_14 > #skF_1 > #skF_16 > #skF_21 > #skF_5 > #skF_30 > #skF_4 > #skF_10 > #skF_34 > #skF_39
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff(are_equipotent,type,
are_equipotent: ( $i * $i ) > $o ).
tff('#skF_25',type,
'#skF_25': $i > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff('#skF_37',type,
'#skF_37': ( $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(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_32',type,
'#skF_32': ( $i * $i ) > $i ).
tff('#skF_36',type,
'#skF_36': $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_31',type,
'#skF_31': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i * $i ) > $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('#skF_28',type,
'#skF_28': $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('#skF_38',type,
'#skF_38': $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_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_26',type,
'#skF_26': $i > $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('#skF_35',type,
'#skF_35': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $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_30',type,
'#skF_30': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i ) > $i ).
tff(f_267,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_491,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_389,lemma,
! [A,B] :
( ( set_difference(A,B) = empty_set )
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
tff(f_443,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
tff(f_157,axiom,
! [A,B] :
( disjoint(A,B)
<=> ( set_intersection2(A,B) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
tff(f_42,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_175,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
tff(f_81,axiom,
! [A,B] :
( ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) )
& ( empty(A)
=> ( element(B,A)
<=> empty(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
tff(f_68,axiom,
! [A,B] :
( ( B = powerset(A) )
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
tff(f_362,lemma,
! [A,B] :
( subset(A,B)
=> ( set_intersection2(A,B) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
tff(f_453,lemma,
! [A,B] : ( set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
tff(f_151,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( subset_complement(A,B) = set_difference(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
tff(f_427,lemma,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ~ ( ? [C] :
( in(C,A)
& in(C,B) )
& disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
tff(f_127,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_147,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_61,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_469,lemma,
! [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_506,lemma,
! [A,B] :
( disjoint(A,B)
<=> ( set_difference(A,B) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
tff(f_377,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
tff(f_199,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( subset_complement(A,subset_complement(A,B)) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
tff(f_169,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
tff(f_339,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
tff(c_270,plain,
empty('#skF_27'),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_464,plain,
! [A_348] :
( ( empty_set = A_348 )
| ~ empty(A_348) ),
inference(cnfTransformation,[status(thm)],[f_491]) ).
tff(c_477,plain,
empty_set = '#skF_27',
inference(resolution,[status(thm)],[c_270,c_464]) ).
tff(c_340,plain,
! [A_235,B_236] :
( subset(A_235,B_236)
| ( set_difference(A_235,B_236) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_389]) ).
tff(c_308704,plain,
! [A_235,B_236] :
( subset(A_235,B_236)
| ( set_difference(A_235,B_236) != '#skF_27' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_477,c_340]) ).
tff(c_384,plain,
( disjoint('#skF_35','#skF_36')
| subset('#skF_35',subset_complement('#skF_34','#skF_36')) ),
inference(cnfTransformation,[status(thm)],[f_443]) ).
tff(c_566,plain,
subset('#skF_35',subset_complement('#skF_34','#skF_36')),
inference(splitLeft,[status(thm)],[c_384]) ).
tff(c_180,plain,
! [A_115,B_116] :
( disjoint(A_115,B_116)
| ( set_intersection2(A_115,B_116) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_1478,plain,
! [A_465,B_466] :
( disjoint(A_465,B_466)
| ( set_intersection2(A_465,B_466) != '#skF_27' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_477,c_180]) ).
tff(c_378,plain,
( ~ subset('#skF_35',subset_complement('#skF_34','#skF_36'))
| ~ disjoint('#skF_35','#skF_36') ),
inference(cnfTransformation,[status(thm)],[f_443]) ).
tff(c_636,plain,
~ disjoint('#skF_35','#skF_36'),
inference(splitLeft,[status(thm)],[c_378]) ).
tff(c_1485,plain,
set_intersection2('#skF_35','#skF_36') != '#skF_27',
inference(resolution,[status(thm)],[c_1478,c_636]) ).
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_374,plain,
element('#skF_36',powerset('#skF_34')),
inference(cnfTransformation,[status(thm)],[f_443]) ).
tff(c_214,plain,
! [A_123] : ~ empty(powerset(A_123)),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_5467,plain,
! [B_649,A_650] :
( in(B_649,A_650)
| ~ element(B_649,A_650)
| empty(A_650) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_34,plain,
! [C_26,A_22] :
( subset(C_26,A_22)
| ~ in(C_26,powerset(A_22)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_5529,plain,
! [B_649,A_22] :
( subset(B_649,A_22)
| ~ element(B_649,powerset(A_22))
| empty(powerset(A_22)) ),
inference(resolution,[status(thm)],[c_5467,c_34]) ).
tff(c_13425,plain,
! [B_936,A_937] :
( subset(B_936,A_937)
| ~ element(B_936,powerset(A_937)) ),
inference(negUnitSimplification,[status(thm)],[c_214,c_5529]) ).
tff(c_13489,plain,
subset('#skF_36','#skF_34'),
inference(resolution,[status(thm)],[c_374,c_13425]) ).
tff(c_318,plain,
! [A_219,B_220] :
( ( set_intersection2(A_219,B_220) = A_219 )
| ~ subset(A_219,B_220) ),
inference(cnfTransformation,[status(thm)],[f_362]) ).
tff(c_13514,plain,
set_intersection2('#skF_36','#skF_34') = '#skF_36',
inference(resolution,[status(thm)],[c_13489,c_318]) ).
tff(c_14207,plain,
set_intersection2('#skF_34','#skF_36') = '#skF_36',
inference(superposition,[status(thm),theory(equality)],[c_10,c_13514]) ).
tff(c_390,plain,
! [A_260,B_261] : ( set_difference(A_260,set_difference(A_260,B_261)) = set_intersection2(A_260,B_261) ),
inference(cnfTransformation,[status(thm)],[f_453]) ).
tff(c_10608,plain,
! [A_834,B_835] :
( ( subset_complement(A_834,B_835) = set_difference(A_834,B_835) )
| ~ element(B_835,powerset(A_834)) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_10651,plain,
subset_complement('#skF_34','#skF_36') = set_difference('#skF_34','#skF_36'),
inference(resolution,[status(thm)],[c_374,c_10608]) ).
tff(c_2111,plain,
! [A_501,B_502] :
( ( set_intersection2(A_501,B_502) = A_501 )
| ~ subset(A_501,B_502) ),
inference(cnfTransformation,[status(thm)],[f_362]) ).
tff(c_2143,plain,
set_intersection2('#skF_35',subset_complement('#skF_34','#skF_36')) = '#skF_35',
inference(resolution,[status(thm)],[c_566,c_2111]) ).
tff(c_10732,plain,
set_intersection2('#skF_35',set_difference('#skF_34','#skF_36')) = '#skF_35',
inference(demodulation,[status(thm),theory(equality)],[c_10651,c_2143]) ).
tff(c_8947,plain,
! [A_753,B_754] :
( in('#skF_33'(A_753,B_754),B_754)
| disjoint(A_753,B_754) ),
inference(cnfTransformation,[status(thm)],[f_427]) ).
tff(c_122,plain,
! [D_85,B_81,A_80] :
( in(D_85,B_81)
| ~ in(D_85,set_intersection2(A_80,B_81)) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_230853,plain,
! [A_439037,A_439038,B_439039] :
( in('#skF_33'(A_439037,set_intersection2(A_439038,B_439039)),B_439039)
| disjoint(A_439037,set_intersection2(A_439038,B_439039)) ),
inference(resolution,[status(thm)],[c_8947,c_122]) ).
tff(c_6511,plain,
! [A_699,B_700] :
( in('#skF_33'(A_699,B_700),A_699)
| disjoint(A_699,B_700) ),
inference(cnfTransformation,[status(thm)],[f_427]) ).
tff(c_158,plain,
! [D_110,B_106,A_105] :
( ~ in(D_110,B_106)
| ~ in(D_110,set_difference(A_105,B_106)) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_6555,plain,
! [A_105,B_106,B_700] :
( ~ in('#skF_33'(set_difference(A_105,B_106),B_700),B_106)
| disjoint(set_difference(A_105,B_106),B_700) ),
inference(resolution,[status(thm)],[c_6511,c_158]) ).
tff(c_246998,plain,
! [A_451616,B_451617,A_451618] : disjoint(set_difference(A_451616,B_451617),set_intersection2(A_451618,B_451617)),
inference(resolution,[status(thm)],[c_230853,c_6555]) ).
tff(c_306388,plain,
! [A_742933] : disjoint(set_difference(A_742933,set_difference('#skF_34','#skF_36')),'#skF_35'),
inference(superposition,[status(thm),theory(equality)],[c_10732,c_246998]) ).
tff(c_306480,plain,
disjoint(set_intersection2('#skF_34','#skF_36'),'#skF_35'),
inference(superposition,[status(thm),theory(equality)],[c_390,c_306388]) ).
tff(c_306515,plain,
disjoint('#skF_36','#skF_35'),
inference(demodulation,[status(thm),theory(equality)],[c_14207,c_306480]) ).
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_1247,plain,
! [A_18] :
( ( A_18 = '#skF_27' )
| in('#skF_3'(A_18),A_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_477,c_32]) ).
tff(c_3445,plain,
! [A_558,B_559,C_560] :
( ~ disjoint(A_558,B_559)
| ~ in(C_560,set_intersection2(A_558,B_559)) ),
inference(cnfTransformation,[status(thm)],[f_469]) ).
tff(c_72739,plain,
! [B_201971,A_201972,C_201973] :
( ~ disjoint(B_201971,A_201972)
| ~ in(C_201973,set_intersection2(A_201972,B_201971)) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_3445]) ).
tff(c_73005,plain,
! [B_201971,A_201972] :
( ~ disjoint(B_201971,A_201972)
| ( set_intersection2(A_201972,B_201971) = '#skF_27' ) ),
inference(resolution,[status(thm)],[c_1247,c_72739]) ).
tff(c_306522,plain,
set_intersection2('#skF_35','#skF_36') = '#skF_27',
inference(resolution,[status(thm)],[c_306515,c_73005]) ).
tff(c_306538,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1485,c_306522]) ).
tff(c_306539,plain,
~ subset('#skF_35',subset_complement('#skF_34','#skF_36')),
inference(splitRight,[status(thm)],[c_378]) ).
tff(c_306658,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_566,c_306539]) ).
tff(c_306659,plain,
disjoint('#skF_35','#skF_36'),
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_307719,plain,
! [A_743630,B_743631] :
( ( set_difference(A_743630,B_743631) = A_743630 )
| ~ disjoint(A_743630,B_743631) ),
inference(cnfTransformation,[status(thm)],[f_506]) ).
tff(c_307727,plain,
set_difference('#skF_35','#skF_36') = '#skF_35',
inference(resolution,[status(thm)],[c_306659,c_307719]) ).
tff(c_317421,plain,
! [A_744006,C_744007,B_744008] :
( subset(set_difference(A_744006,C_744007),set_difference(B_744008,C_744007))
| ~ subset(A_744006,B_744008) ),
inference(cnfTransformation,[status(thm)],[f_377]) ).
tff(c_317515,plain,
! [B_744008] :
( subset('#skF_35',set_difference(B_744008,'#skF_36'))
| ~ subset('#skF_35',B_744008) ),
inference(superposition,[status(thm),theory(equality)],[c_307727,c_317421]) ).
tff(c_319104,plain,
! [A_744027,B_744028] :
( ( subset_complement(A_744027,B_744028) = set_difference(A_744027,B_744028) )
| ~ element(B_744028,powerset(A_744027)) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_319143,plain,
subset_complement('#skF_34','#skF_36') = set_difference('#skF_34','#skF_36'),
inference(resolution,[status(thm)],[c_374,c_319104]) ).
tff(c_306660,plain,
~ subset('#skF_35',subset_complement('#skF_34','#skF_36')),
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_319193,plain,
~ subset('#skF_35',set_difference('#skF_34','#skF_36')),
inference(demodulation,[status(thm),theory(equality)],[c_319143,c_306660]) ).
tff(c_319225,plain,
~ subset('#skF_35','#skF_34'),
inference(resolution,[status(thm)],[c_317515,c_319193]) ).
tff(c_319355,plain,
set_difference('#skF_35','#skF_34') != '#skF_27',
inference(resolution,[status(thm)],[c_308704,c_319225]) ).
tff(c_376,plain,
element('#skF_35',powerset('#skF_34')),
inference(cnfTransformation,[status(thm)],[f_443]) ).
tff(c_319144,plain,
subset_complement('#skF_34','#skF_35') = set_difference('#skF_34','#skF_35'),
inference(resolution,[status(thm)],[c_376,c_319104]) ).
tff(c_319383,plain,
! [A_744033,B_744034] :
( ( subset_complement(A_744033,subset_complement(A_744033,B_744034)) = B_744034 )
| ~ element(B_744034,powerset(A_744033)) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_319403,plain,
subset_complement('#skF_34',subset_complement('#skF_34','#skF_35')) = '#skF_35',
inference(resolution,[status(thm)],[c_376,c_319383]) ).
tff(c_319417,plain,
subset_complement('#skF_34',set_difference('#skF_34','#skF_35')) = '#skF_35',
inference(demodulation,[status(thm),theory(equality)],[c_319144,c_319403]) ).
tff(c_321645,plain,
! [A_744075,B_744076] :
( element(subset_complement(A_744075,B_744076),powerset(A_744075))
| ~ element(B_744076,powerset(A_744075)) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_321669,plain,
( element(set_difference('#skF_34','#skF_35'),powerset('#skF_34'))
| ~ element('#skF_35',powerset('#skF_34')) ),
inference(superposition,[status(thm),theory(equality)],[c_319144,c_321645]) ).
tff(c_321684,plain,
element(set_difference('#skF_34','#skF_35'),powerset('#skF_34')),
inference(demodulation,[status(thm),theory(equality)],[c_376,c_321669]) ).
tff(c_174,plain,
! [A_111,B_112] :
( ( subset_complement(A_111,B_112) = set_difference(A_111,B_112) )
| ~ element(B_112,powerset(A_111)) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_321713,plain,
subset_complement('#skF_34',set_difference('#skF_34','#skF_35')) = set_difference('#skF_34',set_difference('#skF_34','#skF_35')),
inference(resolution,[status(thm)],[c_321684,c_174]) ).
tff(c_321729,plain,
set_intersection2('#skF_34','#skF_35') = '#skF_35',
inference(demodulation,[status(thm),theory(equality)],[c_319417,c_390,c_321713]) ).
tff(c_306,plain,
! [A_207,B_208] : subset(set_intersection2(A_207,B_208),A_207),
inference(cnfTransformation,[status(thm)],[f_339]) ).
tff(c_342,plain,
! [A_235,B_236] :
( ( set_difference(A_235,B_236) = empty_set )
| ~ subset(A_235,B_236) ),
inference(cnfTransformation,[status(thm)],[f_389]) ).
tff(c_307968,plain,
! [A_743653,B_743654] :
( ( set_difference(A_743653,B_743654) = '#skF_27' )
| ~ subset(A_743653,B_743654) ),
inference(demodulation,[status(thm),theory(equality)],[c_477,c_342]) ).
tff(c_308002,plain,
! [A_207,B_208] : ( set_difference(set_intersection2(A_207,B_208),A_207) = '#skF_27' ),
inference(resolution,[status(thm)],[c_306,c_307968]) ).
tff(c_321819,plain,
set_difference('#skF_35','#skF_34') = '#skF_27',
inference(superposition,[status(thm),theory(equality)],[c_321729,c_308002]) ).
tff(c_321862,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_319355,c_321819]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU170+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/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 : Thu Aug 3 11:18:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 123.05/104.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 123.05/104.72
% 123.05/104.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 123.05/104.76
% 123.05/104.76 Inference rules
% 123.05/104.76 ----------------------
% 123.05/104.76 #Ref : 13
% 123.05/104.76 #Sup : 75027
% 123.05/104.76 #Fact : 6
% 123.05/104.76 #Define : 0
% 123.05/104.76 #Split : 35
% 123.05/104.76 #Chain : 0
% 123.05/104.76 #Close : 0
% 123.05/104.76
% 123.05/104.76 Ordering : KBO
% 123.05/104.76
% 123.05/104.76 Simplification rules
% 123.05/104.76 ----------------------
% 123.05/104.76 #Subsume : 29512
% 123.05/104.76 #Demod : 20697
% 123.05/104.76 #Tautology : 14970
% 123.05/104.76 #SimpNegUnit : 2610
% 123.05/104.76 #BackRed : 167
% 123.05/104.76
% 123.05/104.76 #Partial instantiations: 385200
% 123.05/104.76 #Strategies tried : 1
% 123.05/104.76
% 123.05/104.76 Timing (in seconds)
% 123.05/104.76 ----------------------
% 123.05/104.76 Preprocessing : 0.82
% 123.05/104.76 Parsing : 0.39
% 123.05/104.76 CNF conversion : 0.09
% 123.05/104.76 Main loop : 102.85
% 123.05/104.76 Inferencing : 10.59
% 123.05/104.76 Reduction : 52.16
% 123.05/104.76 Demodulation : 34.80
% 123.05/104.76 BG Simplification : 0.32
% 123.05/104.76 Subsumption : 32.96
% 123.05/104.76 Abstraction : 0.51
% 123.05/104.76 MUC search : 0.00
% 123.05/104.76 Cooper : 0.00
% 123.05/104.76 Total : 103.74
% 123.05/104.76 Index Insertion : 0.00
% 123.05/104.76 Index Deletion : 0.00
% 123.05/104.76 Index Matching : 0.00
% 123.05/104.76 BG Taut test : 0.00
%------------------------------------------------------------------------------