%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU664^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.DRk2p4Q2Wc true
% Computer : n002.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 Oct 2 04:55:37 PM UTC 2025
% Result : Theorem 5.26s 1.27s
% Output : Refutation 5.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of formulae : 70 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 779 ( 115 equ; 0 cnn)
% Maximal formula atoms : 202 ( 11 avg)
% Number of connectives : 1344 ( 31 ~; 26 |; 8 &; 668 @)
% ( 0 <=>; 611 =>; 0 <=; 0 <~>)
% Maximal formula depth : 190 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 198 ( 196 usr; 184 con; 0-3 aty)
% Number of variables : 284 ( 4 ^; 272 !; 8 ?; 284 :)
% 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(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(binintersectSubset5_type,type,
binintersectSubset5: $o ).
thf(upairinpowunion_type,type,
upairinpowunion: $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(emptyset__Cong_type,type,
emptyset__Cong: $o ).
thf(cartprodpairmemER_type,type,
cartprodpairmemER: $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(ksnd_type,type,
ksnd: $i > $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(cartprodfstpairEq_type,type,
cartprodfstpairEq: $o ).
thf(quantDeMorgan1_type,type,
quantDeMorgan1: $o ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(symdiffI2_type,type,
symdiffI2: $o ).
thf(upairset2IR_type,type,
upairset2IR: $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(kfst_type,type,
kfst: $i > $i ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(singletonprop_type,type,
singletonprop: $o ).
thf(binintersectSubset4_type,type,
binintersectSubset4: $o ).
thf('#_fresh_sk3_type',type,
'#_fresh_sk3': $i > $i ).
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(setminusER_type,type,
setminusER: $o ).
thf(exuE2_type,type,
exuE2: $o ).
thf(powersetsubset_type,type,
powersetsubset: $o ).
thf(setukpairinjR1_type,type,
setukpairinjR1: $o ).
thf(subPowSU_type,type,
subPowSU: $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('#_fresh_sk10_type',type,
'#_fresh_sk10': $i > $i ).
thf(setunionE_type,type,
setunionE: $o ).
thf(setminusSubset1_type,type,
setminusSubset1: $o ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(sk__49_type,type,
sk__49: $i > $i > $i > $i ).
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(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(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(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(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(sk__52_type,type,
sk__52: $i ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(iskpair_type,type,
iskpair: $i > $o ).
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(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(sk__50_type,type,
sk__50: $i > $i > $i > $i ).
thf(sk__53_type,type,
sk__53: $i ).
thf(cartprodpairin_type,type,
cartprodpairin: $o ).
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(singleton_type,type,
singleton: $i > $o ).
thf(symdiffI1_type,type,
symdiffI1: $o ).
thf(subsetI2_type,type,
subsetI2: $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(disjointsetsI1_type,type,
disjointsetsI1: $o ).
thf(exuE3u_type,type,
exuE3u: $o ).
thf(setminusEL_type,type,
setminusEL: $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(notdallE_type,type,
notdallE: $o ).
thf(binintersectER_type,type,
binintersectER: $o ).
thf(ksndsingleton_type,type,
ksndsingleton: $o ).
thf(kfstsingleton_type,type,
kfstsingleton: $o ).
thf(dsetconstrI_type,type,
dsetconstrI: $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(sk__51_type,type,
sk__51: $i ).
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(cartprod_type,type,
cartprod: $i > $i > $i ).
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(cartprodsndpairEq,axiom,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ) ) ).
thf('0',plain,
( cartprodsndpairEq
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( ( ksnd @ ( kpair @ X8 @ X10 ) )
= X10 ) ) ) ) ),
define([status(thm)]) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ) ).
thf('1',plain,
( cartprodfstpairEq
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( ( kfst @ ( kpair @ X8 @ X10 ) )
= X8 ) ) ) ) ),
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('2',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(cartprodpairmemER,axiom,
( cartprodpairmemER
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) ) ).
thf('3',plain,
( cartprodpairmemER
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) )
=> ( in @ X10 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ) ).
thf('4',plain,
( cartprodpairmemEL
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) )
=> ( in @ X8 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(cartprodsndin,axiom,
( cartprodsndin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
thf('5',plain,
( cartprodsndin
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ( in @ ( ksnd @ X8 ) @ X6 ) ) ) ),
define([status(thm)]) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ) ).
thf('6',plain,
( kpairsurjEq
= ( ! [X4: $i] :
( ( iskpair @ X4 )
=> ( ( kpair @ ( kfst @ X4 ) @ ( ksnd @ X4 ) )
= X4 ) ) ) ),
define([status(thm)]) ).
thf(ksndpairEq,axiom,
( ksndpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ).
thf('7',plain,
( ksndpairEq
= ( ! [X4: $i,X6: $i] :
( ( ksnd @ ( kpair @ X4 @ X6 ) )
= X6 ) ) ),
define([status(thm)]) ).
thf(ksndsingleton,axiom,
( ksndsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
thf('8',plain,
( ksndsingleton
= ( ! [X4: $i] :
( ( iskpair @ X4 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X4 )
@ ^ [V_1: $i] :
( X4
= ( kpair @ ( kfst @ X4 ) @ V_1 ) ) ) ) ) ) ),
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(cartprodfstin,axiom,
( cartprodfstin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
thf('11',plain,
( cartprodfstin
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ( in @ ( kfst @ X8 ) @ X4 ) ) ) ),
define([status(thm)]) ).
thf(kfstpairEq,axiom,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ).
thf('12',plain,
( kfstpairEq
= ( ! [X4: $i,X6: $i] :
( ( kfst @ ( kpair @ X4 @ X6 ) )
= X4 ) ) ),
define([status(thm)]) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ? [Xy: $i] :
( ( Xu
= ( kpair @ Xx @ Xy ) )
& ( in @ Xy @ B ) )
& ( in @ Xx @ A ) ) ) ) ) ).
thf('13',plain,
( cartprodmempair1
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ? [X10: $i] :
( ? [X12: $i] :
( ( X8
= ( kpair @ X10 @ X12 ) )
& ( in @ X12 @ X6 ) )
& ( in @ X10 @ X4 ) ) ) ) ),
define([status(thm)]) ).
thf(cartprodpairin,axiom,
( cartprodpairin
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
thf('14',plain,
( cartprodpairin
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) ) ) ) ) ),
define([status(thm)]) ).
thf(cartprodpairsurjEq,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
=> ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) ) ) )
=> ( ! [X12: $i,X14: $i,X16: $i] :
( ( in @ X16 @ ( cartprod @ X12 @ X14 ) )
=> ? [X18: $i] :
( ? [X20: $i] :
( ( X16
= ( kpair @ X18 @ X20 ) )
& ( in @ X20 @ X14 ) )
& ( in @ X18 @ X12 ) ) )
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( ! [X22: $i,X24: $i] :
( ( kfst @ ( kpair @ X22 @ X24 ) )
= X22 )
=> ( ! [X26: $i,X28: $i,X30: $i] :
( ( in @ X30 @ ( cartprod @ X26 @ X28 ) )
=> ( in @ ( kfst @ X30 ) @ X26 ) )
=> ( setukpairinjL2
=> ( ! [X32: $i,X34: $i,X36: $i,X38: $i] :
( ( ( kpair @ X32 @ X34 )
= ( kpair @ X36 @ X38 ) )
=> ( X32 = X36 ) )
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( ! [X40: $i,X42: $i,X44: $i,X46: $i] :
( ( ( kpair @ X40 @ X42 )
= ( kpair @ X44 @ X46 ) )
=> ( X42 = X46 ) )
=> ( ! [X48: $i] :
( ( iskpair @ X48 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X48 )
@ ^ [V_1: $i] :
( X48
= ( kpair @ ( kfst @ X48 ) @ V_1 ) ) ) ) )
=> ( ! [X50: $i,X52: $i] :
( ( ksnd @ ( kpair @ X50 @ X52 ) )
= X52 )
=> ( ! [X54: $i] :
( ( iskpair @ X54 )
=> ( ( kpair @ ( kfst @ X54 ) @ ( ksnd @ X54 ) )
= X54 ) )
=> ( ! [X56: $i,X58: $i,X60: $i] :
( ( in @ X60 @ ( cartprod @ X56 @ X58 ) )
=> ( in @ ( ksnd @ X60 ) @ X58 ) )
=> ( ! [X62: $i,X64: $i,X66: $i,X68: $i] :
( ( in @ ( kpair @ X66 @ X68 ) @ ( cartprod @ X62 @ X64 ) )
=> ( in @ X66 @ X62 ) )
=> ( ! [X70: $i,X72: $i,X74: $i,X76: $i] :
( ( in @ ( kpair @ X74 @ X76 ) @ ( cartprod @ X70 @ X72 ) )
=> ( in @ X76 @ X72 ) )
=> ( ! [X78: $i,X80: $i,X82: $i] :
( ( in @ X82 @ X78 )
=> ! [X84: $i] :
( ( in @ X84 @ X80 )
=> ( ( kpair @ X82 @ X84 )
= ( kpair @ X82 @ X84 ) ) ) )
=> ( ! [X86: $i,X88: $i,X90: $i] :
( ( in @ X90 @ X86 )
=> ! [X92: $i] :
( ( in @ X92 @ X88 )
=> ( ( kfst @ ( kpair @ X90 @ X92 ) )
= X90 ) ) )
=> ( ! [X94: $i,X96: $i,X98: $i] :
( ( in @ X98 @ X94 )
=> ! [X100: $i] :
( ( in @ X100 @ X96 )
=> ( ( ksnd @ ( kpair @ X98 @ X100 ) )
= X100 ) ) )
=> ! [X102: $i,X104: $i,X106: $i] :
( ( in @ X106 @ ( cartprod @ X102 @ X104 ) )
=> ( ( kpair @ ( kfst @ X106 ) @ ( ksnd @ X106 ) )
= X106 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) ) ) )
=> ( ! [X12: $i,X14: $i,X16: $i] :
( ( in @ X16 @ ( cartprod @ X12 @ X14 ) )
=> ? [X18: $i] :
( ? [X20: $i] :
( ( X16
= ( kpair @ X18 @ X20 ) )
& ( in @ X20 @ X14 ) )
& ( in @ X18 @ X12 ) ) )
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( ! [X22: $i,X24: $i] :
( ( kfst @ ( kpair @ X22 @ X24 ) )
= X22 )
=> ( ! [X26: $i,X28: $i,X30: $i] :
( ( in @ X30 @ ( cartprod @ X26 @ X28 ) )
=> ( in @ ( kfst @ X30 ) @ X26 ) )
=> ( setukpairinjL2
=> ( ! [X32: $i,X34: $i,X36: $i,X38: $i] :
( ( ( kpair @ X32 @ X34 )
= ( kpair @ X36 @ X38 ) )
=> ( X32 = X36 ) )
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( ! [X40: $i,X42: $i,X44: $i,X46: $i] :
( ( ( kpair @ X40 @ X42 )
= ( kpair @ X44 @ X46 ) )
=> ( X42 = X46 ) )
=> ( ! [X48: $i] :
( ( iskpair @ X48 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X48 )
@ ^ [V_1: $i] :
( X48
= ( kpair @ ( kfst @ X48 ) @ V_1 ) ) ) ) )
=> ( ! [X50: $i,X52: $i] :
( ( ksnd @ ( kpair @ X50 @ X52 ) )
= X52 )
=> ( ! [X54: $i] :
( ( iskpair @ X54 )
=> ( ( kpair @ ( kfst @ X54 ) @ ( ksnd @ X54 ) )
= X54 ) )
=> ( ! [X56: $i,X58: $i,X60: $i] :
( ( in @ X60 @ ( cartprod @ X56 @ X58 ) )
=> ( in @ ( ksnd @ X60 ) @ X58 ) )
=> ( ! [X62: $i,X64: $i,X66: $i,X68: $i] :
( ( in @ ( kpair @ X66 @ X68 ) @ ( cartprod @ X62 @ X64 ) )
=> ( in @ X66 @ X62 ) )
=> ( ! [X70: $i,X72: $i,X74: $i,X76: $i] :
( ( in @ ( kpair @ X74 @ X76 ) @ ( cartprod @ X70 @ X72 ) )
=> ( in @ X76 @ X72 ) )
=> ( ! [X78: $i,X80: $i,X82: $i] :
( ( in @ X82 @ X78 )
=> ! [X84: $i] :
( ( in @ X84 @ X80 )
=> ( ( kpair @ X82 @ X84 )
= ( kpair @ X82 @ X84 ) ) ) )
=> ( ! [X86: $i,X88: $i,X90: $i] :
( ( in @ X90 @ X86 )
=> ! [X92: $i] :
( ( in @ X92 @ X88 )
=> ( ( kfst @ ( kpair @ X90 @ X92 ) )
= X90 ) ) )
=> ( ! [X94: $i,X96: $i,X98: $i] :
( ( in @ X98 @ X94 )
=> ! [X100: $i] :
( ( in @ X100 @ X96 )
=> ( ( ksnd @ ( kpair @ X98 @ X100 ) )
= X100 ) ) )
=> ! [X102: $i,X104: $i,X106: $i] :
( ( in @ X106 @ ( cartprod @ X102 @ X104 ) )
=> ( ( kpair @ ( kfst @ X106 ) @ ( ksnd @ X106 ) )
= X106 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl91,plain,
in @ sk__53 @ ( cartprod @ sk__51 @ sk__52 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl109,plain,
! [X44: $i,X45: $i,X46: $i] :
( ( X44
= ( kpair @ ( sk__49 @ X44 @ X45 @ X46 ) @ ( sk__50 @ X44 @ X45 @ X46 ) ) )
| ~ ( in @ X44 @ ( cartprod @ X46 @ X45 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl85,plain,
! [X11: $i,X12: $i,X13: $i,X14: $i] :
( ( X12 = X11 )
| ( ( kpair @ X14 @ X12 )
!= ( kpair @ X13 @ X11 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl281,plain,
! [X12: $i,X14: $i] :
( ( '#_fresh_sk10' @ ( kpair @ X14 @ X12 ) )
= X12 ),
inference(inj_rec,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl647,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( '#_fresh_sk10' @ X0 )
= ( sk__50 @ X0 @ X2 @ X1 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl109,zip_derived_cl281]) ).
thf(zip_derived_cl91_001,plain,
in @ sk__53 @ ( cartprod @ sk__51 @ sk__52 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl109_002,plain,
! [X44: $i,X45: $i,X46: $i] :
( ( X44
= ( kpair @ ( sk__49 @ X44 @ X45 @ X46 ) @ ( sk__50 @ X44 @ X45 @ X46 ) ) )
| ~ ( in @ X44 @ ( cartprod @ X46 @ X45 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl82,plain,
! [X7: $i,X8: $i,X9: $i,X10: $i] :
( ( X8 = X7 )
| ( ( kpair @ X8 @ X10 )
!= ( kpair @ X7 @ X9 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl205,plain,
! [X8: $i,X10: $i] :
( ( '#_fresh_sk3' @ ( kpair @ X8 @ X10 ) )
= X8 ),
inference(inj_rec,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl650,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( '#_fresh_sk3' @ X0 )
= ( sk__49 @ X0 @ X2 @ X1 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl109,zip_derived_cl205]) ).
thf(zip_derived_cl109_003,plain,
! [X44: $i,X45: $i,X46: $i] :
( ( X44
= ( kpair @ ( sk__49 @ X44 @ X45 @ X46 ) @ ( sk__50 @ X44 @ X45 @ X46 ) ) )
| ~ ( in @ X44 @ ( cartprod @ X46 @ X45 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl101,plain,
! [X42: $i,X43: $i] :
( ( kfst @ ( kpair @ X42 @ X43 ) )
= X42 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl643,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( kfst @ X0 )
= ( sk__49 @ X0 @ X2 @ X1 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl109,zip_derived_cl101]) ).
thf(zip_derived_cl855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( kfst @ X0 )
= ( '#_fresh_sk3' @ X0 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl650,zip_derived_cl643]) ).
thf(zip_derived_cl861,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( ( kfst @ X0 )
= ( '#_fresh_sk3' @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl855]) ).
thf(zip_derived_cl885,plain,
( ( kfst @ sk__53 )
= ( '#_fresh_sk3' @ sk__53 ) ),
inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl861]) ).
thf(zip_derived_cl643_004,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( kfst @ X0 )
= ( sk__49 @ X0 @ X2 @ X1 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl109,zip_derived_cl101]) ).
thf(zip_derived_cl109_005,plain,
! [X44: $i,X45: $i,X46: $i] :
( ( X44
= ( kpair @ ( sk__49 @ X44 @ X45 @ X46 ) @ ( sk__50 @ X44 @ X45 @ X46 ) ) )
| ~ ( in @ X44 @ ( cartprod @ X46 @ X45 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl698,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0
= ( kpair @ ( kfst @ X0 ) @ ( sk__50 @ X0 @ X2 @ X1 ) ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl643,zip_derived_cl109]) ).
thf(zip_derived_cl702,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( X0
= ( kpair @ ( kfst @ X0 ) @ ( sk__50 @ X0 @ X2 @ X1 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl698]) ).
thf(zip_derived_cl994,plain,
! [X0: $i,X1: $i] :
( ( sk__53
= ( kpair @ ( '#_fresh_sk3' @ sk__53 ) @ ( sk__50 @ sk__53 @ X1 @ X0 ) ) )
| ~ ( in @ sk__53 @ ( cartprod @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl885,zip_derived_cl702]) ).
thf(zip_derived_cl1154,plain,
! [X0: $i,X1: $i] :
( ( sk__53
= ( kpair @ ( '#_fresh_sk3' @ sk__53 ) @ ( '#_fresh_sk10' @ sk__53 ) ) )
| ~ ( in @ sk__53 @ ( cartprod @ X0 @ X1 ) )
| ~ ( in @ sk__53 @ ( cartprod @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl647,zip_derived_cl994]) ).
thf(zip_derived_cl1182,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ sk__53 @ ( cartprod @ X0 @ X1 ) )
| ( sk__53
= ( kpair @ ( '#_fresh_sk3' @ sk__53 ) @ ( '#_fresh_sk10' @ sk__53 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1154]) ).
thf(zip_derived_cl90,plain,
( ( kpair @ ( kfst @ sk__53 ) @ ( ksnd @ sk__53 ) )
!= sk__53 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl91_006,plain,
in @ sk__53 @ ( cartprod @ sk__51 @ sk__52 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl647_007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( '#_fresh_sk10' @ X0 )
= ( sk__50 @ X0 @ X2 @ X1 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl109,zip_derived_cl281]) ).
thf(zip_derived_cl109_008,plain,
! [X44: $i,X45: $i,X46: $i] :
( ( X44
= ( kpair @ ( sk__49 @ X44 @ X45 @ X46 ) @ ( sk__50 @ X44 @ X45 @ X46 ) ) )
| ~ ( in @ X44 @ ( cartprod @ X46 @ X45 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl86,plain,
! [X15: $i,X16: $i] :
( ( ksnd @ ( kpair @ X16 @ X15 ) )
= X15 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl646,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( ksnd @ X0 )
= ( sk__50 @ X0 @ X2 @ X1 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl109,zip_derived_cl86]) ).
thf(zip_derived_cl713,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( ksnd @ X0 )
= ( '#_fresh_sk10' @ X0 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl647,zip_derived_cl646]) ).
thf(zip_derived_cl719,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( ( ksnd @ X0 )
= ( '#_fresh_sk10' @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl713]) ).
thf(zip_derived_cl729,plain,
( ( ksnd @ sk__53 )
= ( '#_fresh_sk10' @ sk__53 ) ),
inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl719]) ).
thf(zip_derived_cl739,plain,
( ( kpair @ ( kfst @ sk__53 ) @ ( '#_fresh_sk10' @ sk__53 ) )
!= sk__53 ),
inference(demod,[status(thm)],[zip_derived_cl90,zip_derived_cl729]) ).
thf(zip_derived_cl885_009,plain,
( ( kfst @ sk__53 )
= ( '#_fresh_sk3' @ sk__53 ) ),
inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl861]) ).
thf(zip_derived_cl898,plain,
( ( kpair @ ( '#_fresh_sk3' @ sk__53 ) @ ( '#_fresh_sk10' @ sk__53 ) )
!= sk__53 ),
inference(demod,[status(thm)],[zip_derived_cl739,zip_derived_cl885]) ).
thf(zip_derived_cl1183,plain,
! [X0: $i,X1: $i] :
~ ( in @ sk__53 @ ( cartprod @ X0 @ X1 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1182,zip_derived_cl898]) ).
thf(zip_derived_cl1204,plain,
$false,
inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl1183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU664^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.DRk2p4Q2Wc true
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Wed Oct 1 16:05:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.48/0.61 % Total configuration time : 828
% 0.48/0.61 % Estimated wc time : 1656
% 0.48/0.61 % Estimated cpu time (8 cpus) : 207.0
% 0.51/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.51/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 5.26/1.27 % Solved by lams/40_c_ic.sh.
% 5.26/1.27 % done 276 iterations in 0.516s
% 5.26/1.27 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 5.26/1.27 % SZS output start Refutation
% See solution above
% 5.26/1.28
% 5.26/1.28
% 5.26/1.28 % Terminating...
% 5.26/1.34 % Runner terminated.
% 5.26/1.35 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------