%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU687^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Hac4oNq7lL true
% Computer : n029.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 : Thu Aug 31 19:16:13 EDT 2023
% Result : Theorem 50.52s 7.15s
% Output : Refutation 50.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 243
% Syntax : Number of formulae : 365 ( 58 unt; 221 typ; 0 def)
% Number of atoms : 1191 ( 106 equ; 0 cnn)
% Maximal formula atoms : 248 ( 8 avg)
% Number of connectives : 3092 ( 199 ~; 233 |; 15 &;1928 @)
% ( 0 <=>; 717 =>; 0 <=; 0 <~>)
% Maximal formula depth : 221 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 223 ( 221 usr; 210 con; 0-4 aty)
% Number of variables : 350 ( 49 ^; 301 !; 0 ?; 350 :)
% Comments :
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
setadjoinAx: $o ).
thf(cartprodmempaircEq_type,type,
cartprodmempaircEq: $o ).
thf(notdexE_type,type,
notdexE: $o ).
thf(setunionAx_type,type,
setunionAx: $o ).
thf(setminusELneg_type,type,
setminusELneg: $o ).
thf(kpairsurjEq_type,type,
kpairsurjEq: $o ).
thf(powersetE_type,type,
powersetE: $o ).
thf(omegaSAx_type,type,
omegaSAx: $o ).
thf(exuI1_type,type,
exuI1: $o ).
thf(exuI2_type,type,
exuI2: $o ).
thf(sk__44_type,type,
sk__44: $i ).
thf(notequalI2_type,type,
notequalI2: $o ).
thf(kpairiskpair_type,type,
kpairiskpair: $o ).
thf(upairsubunion_type,type,
upairsubunion: $o ).
thf(powerset__Cong_type,type,
powerset__Cong: $o ).
thf(setminusILneg_type,type,
setminusILneg: $o ).
thf(wellorderingAx_type,type,
wellorderingAx: $o ).
thf(setadjoinSub2_type,type,
setadjoinSub2: $o ).
thf(lam2p_type,type,
lam2p: $o ).
thf(binintersectSubset5_type,type,
binintersectSubset5: $o ).
thf(upairinpowunion_type,type,
upairinpowunion: $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(emptyset__Cong_type,type,
emptyset__Cong: $o ).
thf(cartprodpairmemER_type,type,
cartprodpairmemER: $o ).
thf(infuncsetfunc_type,type,
infuncsetfunc: $o ).
thf(dpsetconstrI_type,type,
dpsetconstrI: $o ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(dpsetconstrER_type,type,
dpsetconstrER: $o ).
thf(sepInPowerset_type,type,
sepInPowerset: $o ).
thf(setukpairIR_type,type,
setukpairIR: $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(binunionE_type,type,
binunionE: $o ).
thf(setext_type,type,
setext: $o ).
thf(emptyinPowerset_type,type,
emptyinPowerset: $o ).
thf(sk__41_type,type,
sk__41: $i ).
thf(ubforcartprodlem1_type,type,
ubforcartprodlem1: $o ).
thf(setukpairinjR12_type,type,
setukpairinjR12: $o ).
thf(descr__Cong_type,type,
descr__Cong: $o ).
thf(binintersectSubset1_type,type,
binintersectSubset1: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(dpsetconstrSub_type,type,
dpsetconstrSub: $o ).
thf(cartprodfstpairEq_type,type,
cartprodfstpairEq: $o ).
thf(quantDeMorgan1_type,type,
quantDeMorgan1: $o ).
thf(funcGraphProp1_type,type,
funcGraphProp1: $o ).
thf(brelnall1_type,type,
brelnall1: $o ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(funcGraphProp3_type,type,
funcGraphProp3: $o ).
thf(ap_type,type,
ap: $i > $i > $i > $i > $i ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(sk__42_type,type,
sk__42: $i ).
thf(sk__43_type,type,
sk__43: $i ).
thf(symdiffI2_type,type,
symdiffI2: $o ).
thf(upairset2IR_type,type,
upairset2IR: $o ).
thf(lamProp_type,type,
lamProp: $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(prop2set2propI_type,type,
prop2set2propI: $o ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(setbeta_type,type,
setbeta: $o ).
thf(eqinunit_type,type,
eqinunit: $o ).
thf(upairsetIL_type,type,
upairsetIL: $o ).
thf(powersetI1_type,type,
powersetI1: $o ).
thf(binintersectSubset3_type,type,
binintersectSubset3: $o ).
thf(setukpairinjR_type,type,
setukpairinjR: $o ).
thf(cartprodfstin_type,type,
cartprodfstin: $o ).
thf(setminusIRneg_type,type,
setminusIRneg: $o ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(singletonprop_type,type,
singletonprop: $o ).
thf(binintersectSubset4_type,type,
binintersectSubset4: $o ).
thf(brelnall2_type,type,
brelnall2: $o ).
thf(singletoninpowunion_type,type,
singletoninpowunion: $o ).
thf(powersetI_type,type,
powersetI: $o ).
thf(cartprodmempair_type,type,
cartprodmempair: $o ).
thf(upairsetIR_type,type,
upairsetIR: $o ).
thf(cartprodsndpairEq_type,type,
cartprodsndpairEq: $o ).
thf(inCongP_type,type,
inCongP: $o ).
thf(setukpairinjL_type,type,
setukpairinjL: $o ).
thf(setadjoinSub_type,type,
setadjoinSub: $o ).
thf(exuE3e_type,type,
exuE3e: $o ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(upairequniteq_type,type,
upairequniteq: $o ).
thf(binintersectSubset2_type,type,
binintersectSubset2: $o ).
thf(setunionI_type,type,
setunionI: $o ).
thf(setunion__Cong_type,type,
setunion__Cong: $o ).
thf(prop2setI_type,type,
prop2setI: $o ).
thf(nonemptyImpWitness_type,type,
nonemptyImpWitness: $o ).
thf(ap2p_type,type,
ap2p: $o ).
thf(setminusER_type,type,
setminusER: $o ).
thf(exuE2_type,type,
exuE2: $o ).
thf(powersetsubset_type,type,
powersetsubset: $o ).
thf(setukpairinjR1_type,type,
setukpairinjR1: $o ).
thf(dpsetconstrERa_type,type,
dpsetconstrERa: $o ).
thf(subPowSU_type,type,
subPowSU: $o ).
thf(ex1_type,type,
ex1: $i > ( $i > $o ) > $o ).
thf(notequalI1_type,type,
notequalI1: $o ).
thf(notinemptyset_type,type,
notinemptyset: $o ).
thf(nonemptyI1_type,type,
nonemptyI1: $o ).
thf(subsetTrans_type,type,
subsetTrans: $o ).
thf(setukpairinjR2_type,type,
setukpairinjR2: $o ).
thf(kpairp_type,type,
kpairp: $o ).
thf(setminusI_type,type,
setminusI: $o ).
thf(binunionIL_type,type,
binunionIL: $o ).
thf(setunionsingleton_type,type,
setunionsingleton: $o ).
thf(subsetE2_type,type,
subsetE2: $o ).
thf(singletonsswitch_type,type,
singletonsswitch: $o ).
thf(kfstpairEq_type,type,
kfstpairEq: $o ).
thf(ubforcartprodlem3_type,type,
ubforcartprodlem3: $o ).
thf(setextsub_type,type,
setextsub: $o ).
thf(binunionLsub_type,type,
binunionLsub: $o ).
thf(setunionsingleton1_type,type,
setunionsingleton1: $o ).
thf(emptysetsubset_type,type,
emptysetsubset: $o ).
thf(quantDeMorgan3_type,type,
quantDeMorgan3: $o ).
thf(setunionE_type,type,
setunionE: $o ).
thf(setminusSubset1_type,type,
setminusSubset1: $o ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(binunionIR_type,type,
binunionIR: $o ).
thf(setadjoinE_type,type,
setadjoinE: $o ).
thf(cartprodpairmemEL_type,type,
cartprodpairmemEL: $o ).
thf(singletonsuniq_type,type,
singletonsuniq: $o ).
thf(dpsetconstrEL2_type,type,
dpsetconstrEL2: $o ).
thf(setadjoinIL_type,type,
setadjoinIL: $o ).
thf(exuE1_type,type,
exuE1: $o ).
thf(ubforcartprodlem2_type,type,
ubforcartprodlem2: $o ).
thf(binintersectRsub_type,type,
binintersectRsub: $o ).
thf(setminusLsub_type,type,
setminusLsub: $o ).
thf(notinsingleton_type,type,
notinsingleton: $o ).
thf(dpsetconstrEL1_type,type,
dpsetconstrEL1: $o ).
thf(app_type,type,
app: $o ).
thf(eqimpsubset2_type,type,
eqimpsubset2: $o ).
thf(exuEu_type,type,
exuEu: $o ).
thf(emptysetimpfalse_type,type,
emptysetimpfalse: $o ).
thf(ex1I2_type,type,
ex1I2: $o ).
thf(upairsetE_type,type,
upairsetE: $o ).
thf(omega0Ax_type,type,
omega0Ax: $o ).
thf(funcImageSingleton_type,type,
funcImageSingleton: $o ).
thf(sk__40_type,type,
sk__40: $i ).
thf(notsubsetI_type,type,
notsubsetI: $o ).
thf(quantDeMorgan4_type,type,
quantDeMorgan4: $o ).
thf(setextAx_type,type,
setextAx: $o ).
thf(powersetE1_type,type,
powersetE1: $o ).
thf(bs114d_type,type,
bs114d: $o ).
thf(sk__47_type,type,
sk__47: $i > $i > $i > $i ).
thf(ex1E2_type,type,
ex1E2: $o ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(sk__46_type,type,
sk__46: $i > $i > $i > $i ).
thf(binintersectLsub_type,type,
binintersectLsub: $o ).
thf(subsetI1_type,type,
subsetI1: $o ).
thf(symdiffE_type,type,
symdiffE: $o ).
thf(descrp_type,type,
descrp: $o ).
thf(dsetconstr__Cong_type,type,
dsetconstr__Cong: $o ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(emptysetAx_type,type,
emptysetAx: $o ).
thf(emptyI_type,type,
emptyI: $o ).
thf(setadjoinOr_type,type,
setadjoinOr: $o ).
thf(binintersectEL_type,type,
binintersectEL: $o ).
thf(emptyE1_type,type,
emptyE1: $o ).
thf(emptyInPowerset_type,type,
emptyInPowerset: $o ).
thf(sk__39_type,type,
sk__39: $i ).
thf(vacuousDall_type,type,
vacuousDall: $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(binintersectI_type,type,
binintersectI: $o ).
thf(cartprodpairin_type,type,
cartprodpairin: $o ).
thf(sk__45_type,type,
sk__45: $i > $i > $i > $i ).
thf(ex1I_type,type,
ex1I: $o ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $o ).
thf(cartprodsndin_type,type,
cartprodsndin: $o ).
thf(setukpairinjR11_type,type,
setukpairinjR11: $o ).
thf(symdiffI1_type,type,
symdiffI1: $o ).
thf(subsetI2_type,type,
subsetI2: $o ).
thf(setOfPairsIsBReln_type,type,
setOfPairsIsBReln: $o ).
thf(symdiffIneg1_type,type,
symdiffIneg1: $o ).
thf(theprop_type,type,
theprop: $o ).
thf(setminusERneg_type,type,
setminusERneg: $o ).
thf(symdiffIneg2_type,type,
symdiffIneg2: $o ).
thf(omega__Cong_type,type,
omega__Cong: $o ).
thf(subsetRefl_type,type,
subsetRefl: $o ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(setminusSubset2_type,type,
setminusSubset2: $o ).
thf(prop2setE_type,type,
prop2setE: $o ).
thf(binunionEcases_type,type,
binunionEcases: $o ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(apProp_type,type,
apProp: $o ).
thf(disjointsetsI1_type,type,
disjointsetsI1: $o ).
thf(exuE3u_type,type,
exuE3u: $o ).
thf(setminusEL_type,type,
setminusEL: $o ).
thf(funcGraphProp2_type,type,
funcGraphProp2: $o ).
thf(setunionsingleton2_type,type,
setunionsingleton2: $o ).
thf(sepSubset_type,type,
sepSubset: $o ).
thf(upairset2E_type,type,
upairset2E: $o ).
thf(eqimpsubset1_type,type,
eqimpsubset1: $o ).
thf(exuI3_type,type,
exuI3: $o ).
thf(funcSet_type,type,
funcSet: $i > $i > $i ).
thf(notdallE_type,type,
notdallE: $o ).
thf(binintersectER_type,type,
binintersectER: $o ).
thf(ksndsingleton_type,type,
ksndsingleton: $o ).
thf(lamp_type,type,
lamp: $o ).
thf(kfstsingleton_type,type,
kfstsingleton: $o ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(cartprodpairsurjEq_type,type,
cartprodpairsurjEq: $o ).
thf(exu__Cong_type,type,
exu__Cong: $o ).
thf(ksndpairEq_type,type,
ksndpairEq: $o ).
thf(quantDeMorgan2_type,type,
quantDeMorgan2: $o ).
thf(ex1E1_type,type,
ex1E1: $o ).
thf(secondinupair_type,type,
secondinupair: $o ).
thf(singletonsubset_type,type,
singletonsubset: $o ).
thf(singletoninpowerset_type,type,
singletoninpowerset: $o ).
thf(subsetemptysetimpeq_type,type,
subsetemptysetimpeq: $o ).
thf(replAx_type,type,
replAx: $o ).
thf(nonemptyE1_type,type,
nonemptyE1: $o ).
thf(omegaIndAx_type,type,
omegaIndAx: $o ).
thf(setukpairIL_type,type,
setukpairIL: $o ).
thf(setunionE2_type,type,
setunionE2: $o ).
thf(inPowerset_type,type,
inPowerset: $o ).
thf(funcinfuncset_type,type,
funcinfuncset: $o ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(setukpairinjL2_type,type,
setukpairinjL2: $o ).
thf(binunionRsub_type,type,
binunionRsub: $o ).
thf(subset2powerset_type,type,
subset2powerset: $o ).
thf(setukpairinjL1_type,type,
setukpairinjL1: $o ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ) ).
thf('0',plain,
( funcGraphProp2
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X6 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X8 )
=> ( ( ap @ X4 @ X6 @ X8 @ X10 )
= X12 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
thf('1',plain,
( funcGraphProp3
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( funcSet @ X4 @ X6 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
thf('2',plain,
( funcGraphProp1
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(ap2p,axiom,
( ap2p
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
thf('3',plain,
( ap2p
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( funcSet @ X4 @ X6 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(app,axiom,
( app
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
thf('4',plain,
( app
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(apProp,axiom,
( apProp
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) ) ) ).
thf('5',plain,
( apProp
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X6
@ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) )
@ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(func,axiom,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
thf('6',plain,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[func]) ).
thf('7',plain,
( func
= ( ^ [V_1: $i,V_2: $i,V_3: $i] :
( ( breln @ V_1 @ V_2 @ V_3 )
& ! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ( ex1 @ V_2
@ ^ [V_4: $i] : ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ),
define([status(thm)]) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
thf('8',plain,
( cartprodmempaircEq
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( ( kpair @ X8 @ X10 )
= ( kpair @ X8 @ X10 ) ) ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjR,axiom,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ) ).
thf('9',plain,
( setukpairinjR
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( kpair @ X4 @ X6 )
= ( kpair @ X8 @ X10 ) )
=> ( X6 = X10 ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjL,axiom,
( setukpairinjL
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ) ) ).
thf('10',plain,
( setukpairinjL
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( kpair @ X4 @ X6 )
= ( kpair @ X8 @ X10 ) )
=> ( X4 = X8 ) ) ) ),
define([status(thm)]) ).
thf(funcextLem,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( kpair @ X4 @ X6 )
= ( kpair @ X8 @ X10 ) )
=> ( X4 = X8 ) )
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( ! [X12: $i,X14: $i,X16: $i,X18: $i] :
( ( ( kpair @ X12 @ X14 )
= ( kpair @ X16 @ X18 ) )
=> ( X14 = X18 ) )
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ X20 )
=> ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ( ( kpair @ X24 @ X26 )
= ( kpair @ X24 @ X26 ) ) ) )
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( ! [X28: $i,X30: $i,X32: $i] :
( ( ( breln @ X28 @ X30 @ X32 )
& ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ( ex1 @ X30
@ ^ [V_1: $i] : ( in @ ( kpair @ X34 @ V_1 ) @ X32 ) ) ) )
=> ! [X36: $i] :
( ( in @ X36 @ X28 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X30
@ ^ [V_2: $i] : ( in @ ( kpair @ X36 @ V_2 ) @ X32 ) ) )
@ X30 ) ) )
=> ( ! [X38: $i,X40: $i,X42: $i] :
( ( ( breln @ X38 @ X40 @ X42 )
& ! [X44: $i] :
( ( in @ X44 @ X38 )
=> ( ex1 @ X40
@ ^ [V_3: $i] : ( in @ ( kpair @ X44 @ V_3 ) @ X42 ) ) ) )
=> ! [X46: $i] :
( ( in @ X46 @ X38 )
=> ( in @ ( ap @ X38 @ X40 @ X42 @ X46 ) @ X40 ) ) )
=> ( infuncsetfunc
=> ( ! [X48: $i,X50: $i,X52: $i] :
( ( in @ X52 @ ( funcSet @ X48 @ X50 ) )
=> ! [X54: $i] :
( ( in @ X54 @ X48 )
=> ( in @ ( ap @ X48 @ X50 @ X52 @ X54 ) @ X50 ) ) )
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( ! [X56: $i,X58: $i,X60: $i] :
( ( ( breln @ X56 @ X58 @ X60 )
& ! [X62: $i] :
( ( in @ X62 @ X56 )
=> ( ex1 @ X58
@ ^ [V_4: $i] : ( in @ ( kpair @ X62 @ V_4 ) @ X60 ) ) ) )
=> ! [X64: $i] :
( ( in @ X64 @ X56 )
=> ( in @ ( kpair @ X64 @ ( ap @ X56 @ X58 @ X60 @ X64 ) ) @ X60 ) ) )
=> ( ! [X66: $i,X68: $i,X70: $i] :
( ( in @ X70 @ ( funcSet @ X66 @ X68 ) )
=> ! [X72: $i] :
( ( in @ X72 @ X66 )
=> ( in @ ( kpair @ X72 @ ( ap @ X66 @ X68 @ X70 @ X72 ) ) @ X70 ) ) )
=> ( ! [X74: $i,X76: $i,X78: $i] :
( ( ( breln @ X74 @ X76 @ X78 )
& ! [X80: $i] :
( ( in @ X80 @ X74 )
=> ( ex1 @ X76
@ ^ [V_5: $i] : ( in @ ( kpair @ X80 @ V_5 ) @ X78 ) ) ) )
=> ! [X82: $i] :
( ( in @ X82 @ X74 )
=> ! [X84: $i] :
( ( in @ X84 @ X76 )
=> ( ( in @ ( kpair @ X82 @ X84 ) @ X78 )
=> ( ( ap @ X74 @ X76 @ X78 @ X82 )
= X84 ) ) ) ) )
=> ! [X86: $i,X88: $i,X90: $i] :
( ( ( breln @ X86 @ X88 @ X90 )
& ! [X92: $i] :
( ( in @ X92 @ X86 )
=> ( ex1 @ X88
@ ^ [V_6: $i] : ( in @ ( kpair @ X92 @ V_6 ) @ X90 ) ) ) )
=> ! [X94: $i] :
( ( ( breln @ X86 @ X88 @ X94 )
& ! [X96: $i] :
( ( in @ X96 @ X86 )
=> ( ex1 @ X88
@ ^ [V_7: $i] : ( in @ ( kpair @ X96 @ V_7 ) @ X94 ) ) ) )
=> ( ! [X98: $i] :
( ( in @ X98 @ X86 )
=> ( ( ap @ X86 @ X88 @ X90 @ X98 )
= ( ap @ X86 @ X88 @ X94 @ X98 ) ) )
=> ! [X100: $i] :
( ( in @ X100 @ X86 )
=> ! [X102: $i] :
( ( in @ X102 @ X88 )
=> ( ( in @ ( kpair @ X100 @ X102 ) @ X94 )
=> ( in @ ( kpair @ X100 @ X102 ) @ X90 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( kpair @ X4 @ X6 )
= ( kpair @ X8 @ X10 ) )
=> ( X4 = X8 ) )
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( ! [X12: $i,X14: $i,X16: $i,X18: $i] :
( ( ( kpair @ X12 @ X14 )
= ( kpair @ X16 @ X18 ) )
=> ( X14 = X18 ) )
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ X20 )
=> ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ( ( kpair @ X24 @ X26 )
= ( kpair @ X24 @ X26 ) ) ) )
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( ! [X28: $i,X30: $i,X32: $i] :
( ( ( breln @ X28 @ X30 @ X32 )
& ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ( ex1 @ X30
@ ^ [V_1: $i] : ( in @ ( kpair @ X34 @ V_1 ) @ X32 ) ) ) )
=> ! [X36: $i] :
( ( in @ X36 @ X28 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X30
@ ^ [V_2: $i] : ( in @ ( kpair @ X36 @ V_2 ) @ X32 ) ) )
@ X30 ) ) )
=> ( ! [X38: $i,X40: $i,X42: $i] :
( ( ( breln @ X38 @ X40 @ X42 )
& ! [X44: $i] :
( ( in @ X44 @ X38 )
=> ( ex1 @ X40
@ ^ [V_3: $i] : ( in @ ( kpair @ X44 @ V_3 ) @ X42 ) ) ) )
=> ! [X46: $i] :
( ( in @ X46 @ X38 )
=> ( in @ ( ap @ X38 @ X40 @ X42 @ X46 ) @ X40 ) ) )
=> ( infuncsetfunc
=> ( ! [X48: $i,X50: $i,X52: $i] :
( ( in @ X52 @ ( funcSet @ X48 @ X50 ) )
=> ! [X54: $i] :
( ( in @ X54 @ X48 )
=> ( in @ ( ap @ X48 @ X50 @ X52 @ X54 ) @ X50 ) ) )
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( ! [X56: $i,X58: $i,X60: $i] :
( ( ( breln @ X56 @ X58 @ X60 )
& ! [X62: $i] :
( ( in @ X62 @ X56 )
=> ( ex1 @ X58
@ ^ [V_4: $i] : ( in @ ( kpair @ X62 @ V_4 ) @ X60 ) ) ) )
=> ! [X64: $i] :
( ( in @ X64 @ X56 )
=> ( in @ ( kpair @ X64 @ ( ap @ X56 @ X58 @ X60 @ X64 ) ) @ X60 ) ) )
=> ( ! [X66: $i,X68: $i,X70: $i] :
( ( in @ X70 @ ( funcSet @ X66 @ X68 ) )
=> ! [X72: $i] :
( ( in @ X72 @ X66 )
=> ( in @ ( kpair @ X72 @ ( ap @ X66 @ X68 @ X70 @ X72 ) ) @ X70 ) ) )
=> ( ! [X74: $i,X76: $i,X78: $i] :
( ( ( breln @ X74 @ X76 @ X78 )
& ! [X80: $i] :
( ( in @ X80 @ X74 )
=> ( ex1 @ X76
@ ^ [V_5: $i] : ( in @ ( kpair @ X80 @ V_5 ) @ X78 ) ) ) )
=> ! [X82: $i] :
( ( in @ X82 @ X74 )
=> ! [X84: $i] :
( ( in @ X84 @ X76 )
=> ( ( in @ ( kpair @ X82 @ X84 ) @ X78 )
=> ( ( ap @ X74 @ X76 @ X78 @ X82 )
= X84 ) ) ) ) )
=> ! [X86: $i,X88: $i,X90: $i] :
( ( ( breln @ X86 @ X88 @ X90 )
& ! [X92: $i] :
( ( in @ X92 @ X86 )
=> ( ex1 @ X88
@ ^ [V_6: $i] : ( in @ ( kpair @ X92 @ V_6 ) @ X90 ) ) ) )
=> ! [X94: $i] :
( ( ( breln @ X86 @ X88 @ X94 )
& ! [X96: $i] :
( ( in @ X96 @ X86 )
=> ( ex1 @ X88
@ ^ [V_7: $i] : ( in @ ( kpair @ X96 @ V_7 ) @ X94 ) ) ) )
=> ( ! [X98: $i] :
( ( in @ X98 @ X86 )
=> ( ( ap @ X86 @ X88 @ X90 @ X98 )
= ( ap @ X86 @ X88 @ X94 @ X98 ) ) )
=> ! [X100: $i] :
( ( in @ X100 @ X86 )
=> ! [X102: $i] :
( ( in @ X102 @ X88 )
=> ( ( in @ ( kpair @ X100 @ X102 ) @ X94 )
=> ( in @ ( kpair @ X100 @ X102 ) @ X90 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl103,plain,
! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i] :
( ~ ( in @ X20 @ X21 )
| ~ ( in @ ( kpair @ X20 @ X22 ) @ X23 )
| ( ( ap @ X21 @ X24 @ X23 @ X20 )
= X22 )
| ~ ( in @ X22 @ X24 )
| ~ ( ex1 @ X24
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__45 @ X23 @ X24 @ X21 ) @ Y0 ) @ X23 ) )
| ~ ( breln @ X21 @ X24 @ X23 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl106,plain,
! [X25: $i] :
( ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ X25 @ Y0 ) @ sk__42 ) )
| ~ ( in @ X25 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl245,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( breln @ X0 @ sk__40 @ sk__42 )
| ~ ( in @ X1 @ sk__40 )
| ( ( ap @ X0 @ sk__40 @ sk__42 @ X2 )
= X1 )
| ~ ( in @ ( kpair @ X2 @ X1 ) @ sk__42 )
| ~ ( in @ X2 @ X0 )
| ~ ( in @ ( sk__45 @ sk__42 @ sk__40 @ X0 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl103,zip_derived_cl106]) ).
thf(zip_derived_cl110,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl105,plain,
breln @ sk__39 @ sk__40 @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl104,plain,
! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i] :
( ~ ( in @ X20 @ X21 )
| ~ ( in @ ( kpair @ X20 @ X22 ) @ X23 )
| ( ( ap @ X21 @ X24 @ X23 @ X20 )
= X22 )
| ~ ( in @ X22 @ X24 )
| ( in @ ( sk__45 @ X23 @ X24 @ X21 ) @ X21 )
| ~ ( breln @ X21 @ X24 @ X23 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl725,plain,
! [X0: $i,X1: $i] :
( ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ X0 @ sk__40 )
| ( ( ap @ sk__39 @ sk__40 @ sk__42 @ X1 )
= X0 )
| ~ ( in @ ( kpair @ X1 @ X0 ) @ sk__42 )
| ~ ( in @ X1 @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl105,zip_derived_cl104]) ).
thf(zip_derived_cl3476,plain,
! [X0: $i] :
( ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ( ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 )
= X0 )
| ~ ( in @ X0 @ sk__40 )
| ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl110,zip_derived_cl725]) ).
thf(zip_derived_cl106_001,plain,
! [X25: $i] :
( ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ X25 @ Y0 ) @ sk__42 ) )
| ~ ( in @ X25 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl109,plain,
in @ ( kpair @ sk__43 @ sk__44 ) @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl107,plain,
in @ sk__44 @ sk__40,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl103_002,plain,
! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i] :
( ~ ( in @ X20 @ X21 )
| ~ ( in @ ( kpair @ X20 @ X22 ) @ X23 )
| ( ( ap @ X21 @ X24 @ X23 @ X20 )
= X22 )
| ~ ( in @ X22 @ X24 )
| ~ ( ex1 @ X24
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__45 @ X23 @ X24 @ X21 ) @ Y0 ) @ X23 ) )
| ~ ( breln @ X21 @ X24 @ X23 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl772,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( breln @ X1 @ sk__40 @ X0 )
| ~ ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__45 @ X0 @ sk__40 @ X1 ) @ Y0 ) @ X0 ) )
| ( ( ap @ X1 @ sk__40 @ X0 @ X2 )
= sk__44 )
| ~ ( in @ ( kpair @ X2 @ sk__44 ) @ X0 )
| ~ ( in @ X2 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl107,zip_derived_cl103]) ).
thf(zip_derived_cl898,plain,
! [X0: $i] :
( ~ ( in @ sk__43 @ X0 )
| ( ( ap @ X0 @ sk__40 @ sk__42 @ sk__43 )
= sk__44 )
| ~ ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__45 @ sk__42 @ sk__40 @ X0 ) @ Y0 ) @ sk__42 ) )
| ~ ( breln @ X0 @ sk__40 @ sk__42 ) ),
inference('sup-',[status(thm)],[zip_derived_cl109,zip_derived_cl772]) ).
thf(zip_derived_cl103_003,plain,
! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i] :
( ~ ( in @ X20 @ X21 )
| ~ ( in @ ( kpair @ X20 @ X22 ) @ X23 )
| ( ( ap @ X21 @ X24 @ X23 @ X20 )
= X22 )
| ~ ( in @ X22 @ X24 )
| ~ ( ex1 @ X24
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__45 @ X23 @ X24 @ X21 ) @ Y0 ) @ X23 ) )
| ~ ( breln @ X21 @ X24 @ X23 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1509,plain,
! [X0: $i,X1: $i] :
( ( sk__44 = X0 )
| ~ ( breln @ X1 @ sk__40 @ sk__42 )
| ~ ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__45 @ sk__42 @ sk__40 @ X1 ) @ Y0 ) @ sk__42 ) )
| ~ ( in @ sk__43 @ X1 )
| ~ ( breln @ X1 @ sk__40 @ sk__42 )
| ~ ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__45 @ sk__42 @ sk__40 @ X1 ) @ Y0 ) @ sk__42 ) )
| ~ ( in @ X0 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ~ ( in @ sk__43 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl898,zip_derived_cl103]) ).
thf(zip_derived_cl1540,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ~ ( in @ X0 @ sk__40 )
| ~ ( in @ sk__43 @ X1 )
| ~ ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__45 @ sk__42 @ sk__40 @ X1 ) @ Y0 ) @ sk__42 ) )
| ~ ( breln @ X1 @ sk__40 @ sk__42 )
| ( sk__44 = X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1509]) ).
thf(zip_derived_cl1558,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( sk__45 @ sk__42 @ sk__40 @ X0 ) @ sk__39 )
| ( sk__44 = X1 )
| ~ ( breln @ X0 @ sk__40 @ sk__42 )
| ~ ( in @ sk__43 @ X0 )
| ~ ( in @ X1 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 ) ),
inference('sup-',[status(thm)],[zip_derived_cl106,zip_derived_cl1540]) ).
thf(zip_derived_cl7346,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ sk__40 )
| ( ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 )
= X1 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ~ ( in @ X0 @ sk__40 )
| ~ ( in @ sk__43 @ sk__39 )
| ~ ( breln @ sk__39 @ sk__40 @ sk__42 )
| ( sk__44 = X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl3476,zip_derived_cl1558]) ).
thf(zip_derived_cl110_004,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl105_005,plain,
breln @ sk__39 @ sk__40 @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl7617,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ sk__40 )
| ( ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 )
= X1 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ~ ( in @ X0 @ sk__40 )
| ( sk__44 = X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl7346,zip_derived_cl110,zip_derived_cl105]) ).
thf(zip_derived_cl8043,plain,
! [X0: $i] :
( ( sk__44 = X0 )
| ~ ( in @ X0 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ( ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 )
= X0 )
| ~ ( in @ X0 @ sk__40 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl7617]) ).
thf(zip_derived_cl8044,plain,
! [X0: $i] :
( ( ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 )
= X0 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ~ ( in @ X0 @ sk__40 )
| ( sk__44 = X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl8043]) ).
thf(zip_derived_cl8244,plain,
! [X0: $i] :
( ( ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 )
!= sk__44 )
| ( sk__44 = X0 )
| ~ ( in @ X0 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl8044]) ).
thf(zip_derived_cl8393,plain,
! [X0: $i,X1: $i] :
( ( X0 != sk__44 )
| ~ ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ sk__43 @ sk__39 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ~ ( in @ X0 @ sk__40 )
| ~ ( breln @ sk__39 @ sk__40 @ sk__42 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 )
| ~ ( in @ X1 @ sk__40 )
| ( sk__44 = X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl245,zip_derived_cl8244]) ).
thf(zip_derived_cl110_006,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl105_007,plain,
breln @ sk__39 @ sk__40 @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl8463,plain,
! [X0: $i,X1: $i] :
( ( X0 != sk__44 )
| ~ ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ~ ( in @ X0 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 )
| ~ ( in @ X1 @ sk__40 )
| ( sk__44 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl8393,zip_derived_cl110,zip_derived_cl105]) ).
thf(zip_derived_cl8464,plain,
! [X1: $i] :
( ( sk__44 = X1 )
| ~ ( in @ X1 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 )
| ~ ( in @ sk__44 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ sk__44 ) @ sk__42 )
| ~ ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference(simplify,[status(thm)],[zip_derived_cl8463]) ).
thf(zip_derived_cl107_008,plain,
in @ sk__44 @ sk__40,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl109_009,plain,
in @ ( kpair @ sk__43 @ sk__44 ) @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl8465,plain,
! [X1: $i] :
( ~ ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 )
| ~ ( in @ X1 @ sk__40 )
| ( sk__44 = X1 ) ),
inference('simplify_reflect+',[status(thm)],[zip_derived_cl8464,zip_derived_cl107,zip_derived_cl109]) ).
thf(zip_derived_cl3476_010,plain,
! [X0: $i] :
( ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ( ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 )
= X0 )
| ~ ( in @ X0 @ sk__40 )
| ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl110,zip_derived_cl725]) ).
thf(zip_derived_cl8244_011,plain,
! [X0: $i] :
( ( ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 )
!= sk__44 )
| ( sk__44 = X0 )
| ~ ( in @ X0 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl8044]) ).
thf(zip_derived_cl8391,plain,
! [X0: $i,X1: $i] :
( ( X0 != sk__44 )
| ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ X0 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X0 ) @ sk__42 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 )
| ~ ( in @ X1 @ sk__40 )
| ( sk__44 = X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl3476,zip_derived_cl8244]) ).
thf(zip_derived_cl8460,plain,
! [X1: $i] :
( ( sk__44 = X1 )
| ~ ( in @ X1 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 )
| ~ ( in @ ( kpair @ sk__43 @ sk__44 ) @ sk__42 )
| ~ ( in @ sk__44 @ sk__40 )
| ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference(simplify,[status(thm)],[zip_derived_cl8391]) ).
thf(zip_derived_cl107_012,plain,
in @ sk__44 @ sk__40,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl109_013,plain,
in @ ( kpair @ sk__43 @ sk__44 ) @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl8461,plain,
! [X1: $i] :
( ( in @ ( sk__45 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 )
| ~ ( in @ X1 @ sk__40 )
| ( sk__44 = X1 ) ),
inference('simplify_reflect+',[status(thm)],[zip_derived_cl8460,zip_derived_cl107,zip_derived_cl109]) ).
thf(zip_derived_cl8777,plain,
! [X1: $i] :
( ( sk__44 = X1 )
| ~ ( in @ X1 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 ) ),
inference(clc,[status(thm)],[zip_derived_cl8465,zip_derived_cl8461]) ).
thf(zip_derived_cl110_014,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl111,plain,
! [X26: $i] :
( ( ( ap @ sk__39 @ sk__40 @ sk__41 @ X26 )
= ( ap @ sk__39 @ sk__40 @ sk__42 @ X26 ) )
| ~ ( in @ X26 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl95,plain,
! [X8: $i,X9: $i,X10: $i,X11: $i] :
( ~ ( in @ X8 @ X9 )
| ( in @ ( ap @ X9 @ X10 @ X11 @ X8 ) @ X10 )
| ~ ( ex1 @ X10
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__47 @ X11 @ X10 @ X9 ) @ Y0 ) @ X11 ) )
| ~ ( breln @ X9 @ X10 @ X11 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl986,plain,
! [X0: $i] :
( ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) @ sk__40 )
| ~ ( in @ X0 @ sk__39 )
| ~ ( breln @ sk__39 @ sk__40 @ sk__42 )
| ~ ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ Y0 ) @ sk__42 ) )
| ~ ( in @ X0 @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl111,zip_derived_cl95]) ).
thf(zip_derived_cl105_015,plain,
breln @ sk__39 @ sk__40 @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1014,plain,
! [X0: $i] :
( ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) @ sk__40 )
| ~ ( in @ X0 @ sk__39 )
| ~ ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ Y0 ) @ sk__42 ) )
| ~ ( in @ X0 @ sk__39 ) ),
inference(demod,[status(thm)],[zip_derived_cl986,zip_derived_cl105]) ).
thf(zip_derived_cl1015,plain,
! [X0: $i] :
( ~ ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ Y0 ) @ sk__42 ) )
| ~ ( in @ X0 @ sk__39 )
| ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) @ sk__40 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1014]) ).
thf(zip_derived_cl106_016,plain,
! [X25: $i] :
( ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ X25 @ Y0 ) @ sk__42 ) )
| ~ ( in @ X25 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1050,plain,
! [X0: $i] :
( ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) @ sk__40 )
| ~ ( in @ X0 @ sk__39 )
| ~ ( in @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1015,zip_derived_cl106]) ).
thf(zip_derived_cl8777_017,plain,
! [X1: $i] :
( ( sk__44 = X1 )
| ~ ( in @ X1 @ sk__40 )
| ~ ( in @ ( kpair @ sk__43 @ X1 ) @ sk__42 ) ),
inference(clc,[status(thm)],[zip_derived_cl8465,zip_derived_cl8461]) ).
thf(zip_derived_cl111_018,plain,
! [X26: $i] :
( ( ( ap @ sk__39 @ sk__40 @ sk__41 @ X26 )
= ( ap @ sk__39 @ sk__40 @ sk__42 @ X26 ) )
| ~ ( in @ X26 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl110_019,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl105_020,plain,
breln @ sk__39 @ sk__40 @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl102,plain,
! [X16: $i,X17: $i,X18: $i,X19: $i] :
( ~ ( in @ X16 @ X17 )
| ( in @ ( kpair @ X16 @ ( ap @ X17 @ X18 @ X19 @ X16 ) ) @ X19 )
| ( in @ ( sk__46 @ X19 @ X18 @ X17 ) @ X17 )
| ~ ( breln @ X17 @ X18 @ X19 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl726,plain,
! [X0: $i] :
( ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ( in @ ( kpair @ X0 @ ( ap @ sk__39 @ sk__40 @ sk__42 @ X0 ) ) @ sk__42 )
| ~ ( in @ X0 @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl105,zip_derived_cl102]) ).
thf(zip_derived_cl1630,plain,
( ( in @ ( kpair @ sk__43 @ ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 ) ) @ sk__42 )
| ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl110,zip_derived_cl726]) ).
thf(zip_derived_cl1673,plain,
( ( in @ ( kpair @ sk__43 @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) @ sk__42 )
| ~ ( in @ sk__43 @ sk__39 )
| ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl111,zip_derived_cl1630]) ).
thf(zip_derived_cl110_021,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1717,plain,
( ( in @ ( kpair @ sk__43 @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) @ sk__42 )
| ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference(demod,[status(thm)],[zip_derived_cl1673,zip_derived_cl110]) ).
thf(zip_derived_cl8779,plain,
( ~ ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) @ sk__40 )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) )
| ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl8777,zip_derived_cl1717]) ).
thf(zip_derived_cl8923,plain,
( ~ ( in @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ sk__43 @ sk__39 )
| ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1050,zip_derived_cl8779]) ).
thf(zip_derived_cl110_022,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl8951,plain,
( ~ ( in @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8923,zip_derived_cl110]) ).
thf(zip_derived_cl111_023,plain,
! [X26: $i] :
( ( ( ap @ sk__39 @ sk__40 @ sk__41 @ X26 )
= ( ap @ sk__39 @ sk__40 @ sk__42 @ X26 ) )
| ~ ( in @ X26 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl110_024,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl105_025,plain,
breln @ sk__39 @ sk__40 @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl96,plain,
! [X8: $i,X9: $i,X10: $i,X11: $i] :
( ~ ( in @ X8 @ X9 )
| ( in @ ( ap @ X9 @ X10 @ X11 @ X8 ) @ X10 )
| ( in @ ( sk__47 @ X11 @ X10 @ X9 ) @ X9 )
| ~ ( breln @ X9 @ X10 @ X11 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl727,plain,
! [X0: $i] :
( ( in @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ( in @ ( ap @ sk__39 @ sk__40 @ sk__42 @ X0 ) @ sk__40 )
| ~ ( in @ X0 @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl105,zip_derived_cl96]) ).
thf(zip_derived_cl1187,plain,
( ( in @ ( ap @ sk__39 @ sk__40 @ sk__42 @ sk__43 ) @ sk__40 )
| ( in @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl110,zip_derived_cl727]) ).
thf(zip_derived_cl1222,plain,
( ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) @ sk__40 )
| ~ ( in @ sk__43 @ sk__39 )
| ( in @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl111,zip_derived_cl1187]) ).
thf(zip_derived_cl110_026,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1258,plain,
( ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) @ sk__40 )
| ( in @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference(demod,[status(thm)],[zip_derived_cl1222,zip_derived_cl110]) ).
thf(zip_derived_cl8779_027,plain,
( ~ ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) @ sk__40 )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) )
| ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl8777,zip_derived_cl1717]) ).
thf(zip_derived_cl8922,plain,
( ( in @ ( sk__47 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1258,zip_derived_cl8779]) ).
thf(zip_derived_cl9581,plain,
( ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) )
| ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference(clc,[status(thm)],[zip_derived_cl8951,zip_derived_cl8922]) ).
thf(zip_derived_cl111_028,plain,
! [X26: $i] :
( ( ( ap @ sk__39 @ sk__40 @ sk__41 @ X26 )
= ( ap @ sk__39 @ sk__40 @ sk__42 @ X26 ) )
| ~ ( in @ X26 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl101,plain,
! [X16: $i,X17: $i,X18: $i,X19: $i] :
( ~ ( in @ X16 @ X17 )
| ( in @ ( kpair @ X16 @ ( ap @ X17 @ X18 @ X19 @ X16 ) ) @ X19 )
| ~ ( ex1 @ X18
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__46 @ X19 @ X18 @ X17 ) @ Y0 ) @ X19 ) )
| ~ ( breln @ X17 @ X18 @ X19 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl106_029,plain,
! [X25: $i] :
( ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ X25 @ Y0 ) @ sk__42 ) )
| ~ ( in @ X25 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl233,plain,
! [X0: $i,X1: $i] :
( ~ ( breln @ X0 @ sk__40 @ sk__42 )
| ( in @ ( kpair @ X1 @ ( ap @ X0 @ sk__40 @ sk__42 @ X1 ) ) @ sk__42 )
| ~ ( in @ X1 @ X0 )
| ~ ( in @ ( sk__46 @ sk__42 @ sk__40 @ X0 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl101,zip_derived_cl106]) ).
thf(zip_derived_cl2980,plain,
! [X0: $i] :
( ( in @ ( kpair @ X0 @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) ) @ sk__42 )
| ~ ( in @ X0 @ sk__39 )
| ~ ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ X0 @ sk__39 )
| ~ ( breln @ sk__39 @ sk__40 @ sk__42 ) ),
inference('sup+',[status(thm)],[zip_derived_cl111,zip_derived_cl233]) ).
thf(zip_derived_cl105_030,plain,
breln @ sk__39 @ sk__40 @ sk__42,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl3030,plain,
! [X0: $i] :
( ( in @ ( kpair @ X0 @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) ) @ sk__42 )
| ~ ( in @ X0 @ sk__39 )
| ~ ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ X0 @ sk__39 ) ),
inference(demod,[status(thm)],[zip_derived_cl2980,zip_derived_cl105]) ).
thf(zip_derived_cl3031,plain,
! [X0: $i] :
( ~ ( in @ ( sk__46 @ sk__42 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ X0 @ sk__39 )
| ( in @ ( kpair @ X0 @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) ) @ sk__42 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3030]) ).
thf(zip_derived_cl9582,plain,
! [X0: $i] :
( ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) )
| ( in @ ( kpair @ X0 @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) ) @ sk__42 )
| ~ ( in @ X0 @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl9581,zip_derived_cl3031]) ).
thf(zip_derived_cl9678,plain,
( ( in @ ( kpair @ sk__43 @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) @ sk__42 )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl110,zip_derived_cl9582]) ).
thf(zip_derived_cl9757,plain,
( ~ ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) @ sk__40 )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8777,zip_derived_cl9678]) ).
thf(zip_derived_cl9807,plain,
( ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) )
| ~ ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) @ sk__40 ) ),
inference(simplify,[status(thm)],[zip_derived_cl9757]) ).
thf(zip_derived_cl110_031,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl113,plain,
breln @ sk__39 @ sk__40 @ sk__41,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl96_032,plain,
! [X8: $i,X9: $i,X10: $i,X11: $i] :
( ~ ( in @ X8 @ X9 )
| ( in @ ( ap @ X9 @ X10 @ X11 @ X8 ) @ X10 )
| ( in @ ( sk__47 @ X11 @ X10 @ X9 ) @ X9 )
| ~ ( breln @ X9 @ X10 @ X11 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl959,plain,
! [X0: $i] :
( ( in @ ( sk__47 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39 )
| ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) @ sk__40 )
| ~ ( in @ X0 @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl113,zip_derived_cl96]) ).
thf(zip_derived_cl1332,plain,
( ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) @ sk__40 )
| ( in @ ( sk__47 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl110,zip_derived_cl959]) ).
thf(zip_derived_cl9819,plain,
( ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) )
| ( in @ ( sk__47 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl9807,zip_derived_cl1332]) ).
thf(zip_derived_cl95_033,plain,
! [X8: $i,X9: $i,X10: $i,X11: $i] :
( ~ ( in @ X8 @ X9 )
| ( in @ ( ap @ X9 @ X10 @ X11 @ X8 ) @ X10 )
| ~ ( ex1 @ X10
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__47 @ X11 @ X10 @ X9 ) @ Y0 ) @ X11 ) )
| ~ ( breln @ X9 @ X10 @ X11 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl112,plain,
! [X27: $i] :
( ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ X27 @ Y0 ) @ sk__41 ) )
| ~ ( in @ X27 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl218,plain,
! [X0: $i,X1: $i] :
( ~ ( breln @ X0 @ sk__40 @ sk__41 )
| ( in @ ( ap @ X0 @ sk__40 @ sk__41 @ X1 ) @ sk__40 )
| ~ ( in @ X1 @ X0 )
| ~ ( in @ ( sk__47 @ sk__41 @ sk__40 @ X0 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl95,zip_derived_cl112]) ).
thf(zip_derived_cl9807_034,plain,
( ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) )
| ~ ( in @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) @ sk__40 ) ),
inference(simplify,[status(thm)],[zip_derived_cl9757]) ).
thf(zip_derived_cl9865,plain,
( ~ ( in @ ( sk__47 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ sk__43 @ sk__39 )
| ~ ( breln @ sk__39 @ sk__40 @ sk__41 )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl218,zip_derived_cl9807]) ).
thf(zip_derived_cl110_035,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl113_036,plain,
breln @ sk__39 @ sk__40 @ sk__41,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl9896,plain,
( ~ ( in @ ( sk__47 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39 )
| ( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9865,zip_derived_cl110,zip_derived_cl113]) ).
thf(zip_derived_cl9976,plain,
( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ),
inference(clc,[status(thm)],[zip_derived_cl9819,zip_derived_cl9896]) ).
thf(zip_derived_cl101_037,plain,
! [X16: $i,X17: $i,X18: $i,X19: $i] :
( ~ ( in @ X16 @ X17 )
| ( in @ ( kpair @ X16 @ ( ap @ X17 @ X18 @ X19 @ X16 ) ) @ X19 )
| ~ ( ex1 @ X18
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__46 @ X19 @ X18 @ X17 ) @ Y0 ) @ X19 ) )
| ~ ( breln @ X17 @ X18 @ X19 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl112_038,plain,
! [X27: $i] :
( ( ex1 @ sk__40
@ ^ [Y0: $i] : ( in @ ( kpair @ X27 @ Y0 ) @ sk__41 ) )
| ~ ( in @ X27 @ sk__39 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl232,plain,
! [X0: $i,X1: $i] :
( ~ ( breln @ X0 @ sk__40 @ sk__41 )
| ( in @ ( kpair @ X1 @ ( ap @ X0 @ sk__40 @ sk__41 @ X1 ) ) @ sk__41 )
| ~ ( in @ X1 @ X0 )
| ~ ( in @ ( sk__46 @ sk__41 @ sk__40 @ X0 ) @ sk__39 ) ),
inference('sup+',[status(thm)],[zip_derived_cl101,zip_derived_cl112]) ).
thf(zip_derived_cl9996,plain,
( ( in @ ( kpair @ sk__43 @ sk__44 ) @ sk__41 )
| ~ ( in @ ( sk__46 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39 )
| ~ ( in @ sk__43 @ sk__39 )
| ~ ( breln @ sk__39 @ sk__40 @ sk__41 ) ),
inference('sup+',[status(thm)],[zip_derived_cl9976,zip_derived_cl232]) ).
thf(zip_derived_cl108,plain,
~ ( in @ ( kpair @ sk__43 @ sk__44 ) @ sk__41 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl110_039,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl113_040,plain,
breln @ sk__39 @ sk__40 @ sk__41,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl10047,plain,
~ ( in @ ( sk__46 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39 ),
inference(demod,[status(thm)],[zip_derived_cl9996,zip_derived_cl108,zip_derived_cl110,zip_derived_cl113]) ).
thf(zip_derived_cl110_041,plain,
in @ sk__43 @ sk__39,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl113_042,plain,
breln @ sk__39 @ sk__40 @ sk__41,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl102_043,plain,
! [X16: $i,X17: $i,X18: $i,X19: $i] :
( ~ ( in @ X16 @ X17 )
| ( in @ ( kpair @ X16 @ ( ap @ X17 @ X18 @ X19 @ X16 ) ) @ X19 )
| ( in @ ( sk__46 @ X19 @ X18 @ X17 ) @ X17 )
| ~ ( breln @ X17 @ X18 @ X19 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl958,plain,
! [X0: $i] :
( ( in @ ( sk__46 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39 )
| ( in @ ( kpair @ X0 @ ( ap @ sk__39 @ sk__40 @ sk__41 @ X0 ) ) @ sk__41 )
| ~ ( in @ X0 @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl113,zip_derived_cl102]) ).
thf(zip_derived_cl1995,plain,
( ( in @ ( kpair @ sk__43 @ ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ) @ sk__41 )
| ( in @ ( sk__46 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39 ) ),
inference('sup-',[status(thm)],[zip_derived_cl110,zip_derived_cl958]) ).
thf(zip_derived_cl9976_044,plain,
( sk__44
= ( ap @ sk__39 @ sk__40 @ sk__41 @ sk__43 ) ),
inference(clc,[status(thm)],[zip_derived_cl9819,zip_derived_cl9896]) ).
thf(zip_derived_cl108_045,plain,
~ ( in @ ( kpair @ sk__43 @ sk__44 ) @ sk__41 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl9986,plain,
in @ ( sk__46 @ sk__41 @ sk__40 @ sk__39 ) @ sk__39,
inference(demod,[status(thm)],[zip_derived_cl1995,zip_derived_cl9976,zip_derived_cl108]) ).
thf(zip_derived_cl10179,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl10047,zip_derived_cl9986]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU687^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Hac4oNq7lL true
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 14:43:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.20/0.63 % Total configuration time : 828
% 0.20/0.63 % Estimated wc time : 1656
% 0.20/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.82 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.42/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 50.52/7.15 % Solved by lams/40_c_ic.sh.
% 50.52/7.15 % done 690 iterations in 6.330s
% 50.52/7.15 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 50.52/7.15 % SZS output start Refutation
% See solution above
% 50.52/7.16
% 50.52/7.16
% 50.52/7.16 % Terminating...
% 51.70/7.36 % Runner terminated.
% 51.70/7.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------