TSTP Solution File: COM142+1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : COM142+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.CdLw9jBLtN true
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 18:49:28 EDT 2023
% Result : Theorem 68.05s 10.33s
% Output : Refutation 68.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 65
% Syntax : Number of formulae : 164 ( 42 unt; 30 typ; 0 def)
% Number of atoms : 373 ( 230 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 2894 ( 96 ~; 200 |; 22 &;2559 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 8 con; 0-7 aty)
% Number of variables : 413 ( 0 ^; 397 !; 16 ?; 413 :)
% Comments :
%------------------------------------------------------------------------------
thf(vabs_type,type,
vabs: $i > $i > $i > $i ).
thf(zip_tseitin_18_type,type,
zip_tseitin_18: $i > $i > $i > $i > $o ).
thf(sk__71_type,type,
sk__71: $i > $i > $i > $i ).
thf(vsubst_type,type,
vsubst: $i > $i > $i > $i ).
thf(zip_tseitin_17_type,type,
zip_tseitin_17: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(sk__73_type,type,
sk__73: $i > $i > $i > $i ).
thf(vsomeType_type,type,
vsomeType: $i > $i ).
thf(sk__70_type,type,
sk__70: $i > $i > $i > $i ).
thf(sk__69_type,type,
sk__69: $i > $i > $i > $i ).
thf(vbind_type,type,
vbind: $i > $i > $i > $i ).
thf(vvar_type,type,
vvar: $i > $i ).
thf(varrow_type,type,
varrow: $i > $i > $i ).
thf(vnoType_type,type,
vnoType: $i ).
thf(vlookup_type,type,
vlookup: $i > $i > $i ).
thf(sk__67_type,type,
sk__67: $i > $i > $i > $i ).
thf(sk__76_type,type,
sk__76: $i ).
thf(ve2app_type,type,
ve2app: $i ).
thf(sk__75_type,type,
sk__75: $i ).
thf(vtcheck_type,type,
vtcheck: $i > $i > $i > $o ).
thf(sk__66_type,type,
sk__66: $i > $i > $i > $i ).
thf(sk__68_type,type,
sk__68: $i > $i > $i > $i ).
thf(sk__72_type,type,
sk__72: $i > $i > $i > $i ).
thf(zip_tseitin_16_type,type,
zip_tseitin_16: $i > $i > $i > $i > $i > $i > $o ).
thf(sk__77_type,type,
sk__77: $i ).
thf(sk__74_type,type,
sk__74: $i ).
thf(vapp_type,type,
vapp: $i > $i > $i ).
thf(ve1app_type,type,
ve1app: $i ).
thf('T-Weak-app',conjecture,
! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vapp @ ve1app @ ve2app ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vapp @ ve1app @ ve2app ) @ VT ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vapp @ ve1app @ ve2app ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vapp @ ve1app @ ve2app ) @ VT ) ),
inference('cnf.neg',[status(esa)],[T-Weak-app]) ).
thf(zip_derived_cl153,plain,
~ ( vtcheck @ ( vbind @ sk__74 @ sk__75 @ sk__76 ) @ ( vapp @ ve1app @ ve2app ) @ sk__77 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl154,plain,
vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('T-inv',axiom,
! [Ve: $i,VT: $i,VC: $i] :
( ( vtcheck @ VC @ Ve @ VT )
=> ( ? [Ve1: $i,Ve2: $i,VS: $i] :
( ( Ve
= ( vapp @ Ve1 @ Ve2 ) )
& ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) )
& ( vtcheck @ VC @ Ve2 @ VS ) )
| ? [Vx: $i,Ve2: $i,VT1: $i,VT2: $i] :
( ( Ve
= ( vabs @ Vx @ VT1 @ Ve2 ) )
& ( VT
= ( varrow @ VT1 @ VT2 ) )
& ( vtcheck @ ( vbind @ Vx @ VT1 @ VC ) @ Ve2 @ VT2 ) )
| ? [Vx: $i] :
( ( Ve
= ( vvar @ Vx ) )
& ( ( vlookup @ Vx @ VC )
= ( vsomeType @ VT ) ) ) ) ) ).
thf(zf_stmt_1,type,
zip_tseitin_18: $i > $i > $i > $i > $o ).
thf(zf_stmt_2,axiom,
! [Vx: $i,VC: $i,VT: $i,Ve: $i] :
( ( zip_tseitin_18 @ Vx @ VC @ VT @ Ve )
=> ( ( ( vlookup @ Vx @ VC )
= ( vsomeType @ VT ) )
& ( Ve
= ( vvar @ Vx ) ) ) ) ).
thf(zf_stmt_3,type,
zip_tseitin_17: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(zf_stmt_4,axiom,
! [VT2: $i,VT1: $i,Ve2: $i,Vx: $i,VC: $i,VT: $i,Ve: $i] :
( ( zip_tseitin_17 @ VT2 @ VT1 @ Ve2 @ Vx @ VC @ VT @ Ve )
=> ( ( vtcheck @ ( vbind @ Vx @ VT1 @ VC ) @ Ve2 @ VT2 )
& ( VT
= ( varrow @ VT1 @ VT2 ) )
& ( Ve
= ( vabs @ Vx @ VT1 @ Ve2 ) ) ) ) ).
thf(zf_stmt_5,type,
zip_tseitin_16: $i > $i > $i > $i > $i > $i > $o ).
thf(zf_stmt_6,axiom,
! [VS: $i,Ve2: $i,Ve1: $i,VC: $i,VT: $i,Ve: $i] :
( ( zip_tseitin_16 @ VS @ Ve2 @ Ve1 @ VC @ VT @ Ve )
=> ( ( vtcheck @ VC @ Ve2 @ VS )
& ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) )
& ( Ve
= ( vapp @ Ve1 @ Ve2 ) ) ) ) ).
thf(zf_stmt_7,axiom,
! [Ve: $i,VT: $i,VC: $i] :
( ( vtcheck @ VC @ Ve @ VT )
=> ( ? [Vx: $i] : ( zip_tseitin_18 @ Vx @ VC @ VT @ Ve )
| ? [Vx: $i,Ve2: $i,VT1: $i,VT2: $i] : ( zip_tseitin_17 @ VT2 @ VT1 @ Ve2 @ Vx @ VC @ VT @ Ve )
| ? [Ve1: $i,Ve2: $i,VS: $i] : ( zip_tseitin_16 @ VS @ Ve2 @ Ve1 @ VC @ VT @ Ve ) ) ) ).
thf(zip_derived_cl150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zip_tseitin_16 @ ( sk__68 @ X0 @ X1 @ X2 ) @ ( sk__67 @ X0 @ X1 @ X2 ) @ ( sk__66 @ X0 @ X1 @ X2 ) @ X0 @ X1 @ X2 )
| ( zip_tseitin_17 @ ( sk__72 @ X0 @ X1 @ X2 ) @ ( sk__71 @ X0 @ X1 @ X2 ) @ ( sk__70 @ X0 @ X1 @ X2 ) @ ( sk__69 @ X0 @ X1 @ X2 ) @ X0 @ X1 @ X2 )
| ( zip_tseitin_18 @ ( sk__73 @ X0 @ X1 @ X2 ) @ X0 @ X1 @ X2 )
| ~ ( vtcheck @ X0 @ X2 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_7]) ).
thf(zip_derived_cl149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1
= ( vvar @ X0 ) )
| ~ ( zip_tseitin_18 @ X0 @ X2 @ X3 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl474,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( zip_tseitin_17 @ ( sk__72 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) @ ( sk__69 @ X2 @ X1 @ X0 ) @ X2 @ X1 @ X0 )
| ( zip_tseitin_16 @ ( sk__68 @ X2 @ X1 @ X0 ) @ ( sk__67 @ X2 @ X1 @ X0 ) @ ( sk__66 @ X2 @ X1 @ X0 ) @ X2 @ X1 @ X0 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl150,zip_derived_cl149]) ).
thf(zip_derived_cl143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( vtcheck @ X0 @ X1 @ ( varrow @ X2 @ X3 ) )
| ~ ( zip_tseitin_16 @ X2 @ X4 @ X1 @ X0 @ X3 @ X5 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl488,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1
= ( vvar @ ( sk__73 @ X2 @ X0 @ X1 ) ) )
| ( zip_tseitin_17 @ ( sk__72 @ X2 @ X0 @ X1 ) @ ( sk__71 @ X2 @ X0 @ X1 ) @ ( sk__70 @ X2 @ X0 @ X1 ) @ ( sk__69 @ X2 @ X0 @ X1 ) @ X2 @ X0 @ X1 )
| ~ ( vtcheck @ X2 @ X1 @ X0 )
| ( vtcheck @ X2 @ ( sk__66 @ X2 @ X0 @ X1 ) @ ( varrow @ ( sk__68 @ X2 @ X0 @ X1 ) @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl474,zip_derived_cl143]) ).
thf(zip_derived_cl147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X3
= ( vabs @ X0 @ X1 @ X2 ) )
| ~ ( zip_tseitin_17 @ X4 @ X1 @ X2 @ X0 @ X5 @ X6 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl548,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vtcheck @ X2 @ ( sk__66 @ X2 @ X1 @ X0 ) @ ( varrow @ ( sk__68 @ X2 @ X1 @ X0 ) @ X1 ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl488,zip_derived_cl147]) ).
thf(subst1,axiom,
! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vvar @ Vy ) ) ) ) ) ).
thf(zip_derived_cl55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X3
!= ( vsubst @ X0 @ X1 @ X2 ) )
| ( X1 != X4 )
| ( X0 != X5 )
| ( X2
!= ( vvar @ X6 ) )
| ( X3
= ( vvar @ X6 ) )
| ( X5 = X6 ) ),
inference(cnf,[status(esa)],[subst1]) ).
thf(zip_derived_cl1547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X0 = X1 )
| ( X2
= ( vvar @ X1 ) )
| ( X3
!= ( vvar @ X1 ) )
| ( X4 != X0 )
| ( X2
!= ( vsubst @ X4 @ X5 @ X3 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl1551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0
!= ( vsubst @ X3 @ X2 @ X1 ) )
| ( X1
!= ( vvar @ X4 ) )
| ( X0
= ( vvar @ X4 ) )
| ( X3 = X4 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1547]) ).
thf(zip_derived_cl1558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ( ( vsubst @ X0 @ X3 @ X2 )
= ( vvar @ X1 ) )
| ( X2
!= ( vvar @ X1 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1551]) ).
thf(zip_derived_cl1559,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( vsubst @ X2 @ X1 @ ( vvar @ X0 ) )
= ( vvar @ X0 ) )
| ( X2 = X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1558]) ).
thf(zip_derived_cl1735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( vsubst @ X4 @ X3 @ X0 )
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( vtcheck @ X2 @ ( sk__66 @ X2 @ X1 @ X0 ) @ ( varrow @ ( sk__68 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( X4
= ( sk__73 @ X2 @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl548,zip_derived_cl1559]) ).
thf(zip_derived_cl24855,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl154,zip_derived_cl1735]) ).
thf(zip_derived_cl154_001,plain,
vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl474_002,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( zip_tseitin_17 @ ( sk__72 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) @ ( sk__69 @ X2 @ X1 @ X0 ) @ X2 @ X1 @ X0 )
| ( zip_tseitin_16 @ ( sk__68 @ X2 @ X1 @ X0 ) @ ( sk__67 @ X2 @ X1 @ X0 ) @ ( sk__66 @ X2 @ X1 @ X0 ) @ X2 @ X1 @ X0 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl150,zip_derived_cl149]) ).
thf(zip_derived_cl144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X2
= ( vapp @ X0 @ X1 ) )
| ~ ( zip_tseitin_16 @ X3 @ X1 @ X0 @ X4 @ X5 @ X2 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl489,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1
= ( vvar @ ( sk__73 @ X2 @ X0 @ X1 ) ) )
| ( zip_tseitin_17 @ ( sk__72 @ X2 @ X0 @ X1 ) @ ( sk__71 @ X2 @ X0 @ X1 ) @ ( sk__70 @ X2 @ X0 @ X1 ) @ ( sk__69 @ X2 @ X0 @ X1 ) @ X2 @ X0 @ X1 )
| ~ ( vtcheck @ X2 @ X1 @ X0 )
| ( X1
= ( vapp @ ( sk__66 @ X2 @ X0 @ X1 ) @ ( sk__67 @ X2 @ X0 @ X1 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl474,zip_derived_cl144]) ).
thf(zip_derived_cl147_003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X3
= ( vabs @ X0 @ X1 @ X2 ) )
| ~ ( zip_tseitin_17 @ X4 @ X1 @ X2 @ X0 @ X5 @ X6 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl551,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0
= ( vapp @ ( sk__66 @ X2 @ X1 @ X0 ) @ ( sk__67 @ X2 @ X1 @ X0 ) ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl489,zip_derived_cl147]) ).
thf(zip_derived_cl1559_004,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( vsubst @ X2 @ X1 @ ( vvar @ X0 ) )
= ( vvar @ X0 ) )
| ( X2 = X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1558]) ).
thf(zip_derived_cl1698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( vsubst @ X4 @ X3 @ X0 )
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( X0
= ( vapp @ ( sk__66 @ X2 @ X1 @ X0 ) @ ( sk__67 @ X2 @ X1 @ X0 ) ) )
| ( X4
= ( sk__73 @ X2 @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl551,zip_derived_cl1559]) ).
thf(zip_derived_cl13863,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl154,zip_derived_cl1698]) ).
thf('DIFF-abs-app',axiom,
! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( vabs @ X2 @ X3 @ X4 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-abs-app]) ).
thf(zip_derived_cl13885,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl13863,zip_derived_cl11]) ).
thf(subst2,axiom,
! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve1: $i,Vx: $i,Ve: $i,Ve2: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vapp @ ( vsubst @ Vx @ Ve @ Ve1 ) @ ( vsubst @ Vx @ Ve @ Ve2 ) ) ) ) ) ).
thf(zip_derived_cl56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X3
!= ( vsubst @ X0 @ X1 @ X2 ) )
| ( X1 != X4 )
| ( X0 != X5 )
| ( X2
!= ( vapp @ X6 @ X7 ) )
| ( X3
= ( vapp @ ( vsubst @ X5 @ X4 @ X6 ) @ ( vsubst @ X5 @ X4 @ X7 ) ) ) ),
inference(cnf,[status(esa)],[subst2]) ).
thf(zip_derived_cl1567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X0
= ( vapp @ ( vsubst @ X3 @ X2 @ X4 ) @ ( vsubst @ X3 @ X2 @ X1 ) ) )
| ( X5
!= ( vapp @ X4 @ X1 ) )
| ( X6 != X3 )
| ( X0
!= ( vsubst @ X6 @ X2 @ X5 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl2125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X0
!= ( vsubst @ X3 @ X2 @ X1 ) )
| ( X1
!= ( vapp @ X5 @ X4 ) )
| ( X0
= ( vapp @ ( vsubst @ X3 @ X2 @ X5 ) @ ( vsubst @ X3 @ X2 @ X4 ) ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1567]) ).
thf(zip_derived_cl2198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( vsubst @ X2 @ X1 @ X0 )
= ( vapp @ ( vsubst @ X2 @ X1 @ X4 ) @ ( vsubst @ X2 @ X1 @ X3 ) ) )
| ( X0
!= ( vapp @ X4 @ X3 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl2125]) ).
thf(zip_derived_cl2200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( vsubst @ X3 @ X2 @ ( vapp @ X1 @ X0 ) )
= ( vapp @ ( vsubst @ X3 @ X2 @ X1 ) @ ( vsubst @ X3 @ X2 @ X0 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl2198]) ).
thf(zip_derived_cl20385,plain,
! [X0: $i,X1: $i] :
( ( ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
= ( vapp @ ( vsubst @ X1 @ X0 @ ve1app ) @ ( vsubst @ X1 @ X0 @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( X1
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl13885,zip_derived_cl2200]) ).
thf('DIFF-var-app',axiom,
! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vvar @ X2 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-var-app]) ).
thf(zip_derived_cl20790,plain,
! [X1: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( X1
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl20385,zip_derived_cl10]) ).
thf(zip_derived_cl551_005,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0
= ( vapp @ ( sk__66 @ X2 @ X1 @ X0 ) @ ( sk__67 @ X2 @ X1 @ X0 ) ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl489,zip_derived_cl147]) ).
thf(zip_derived_cl20799,plain,
! [X0: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ~ ( vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77 )
| ( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl20790,zip_derived_cl551]) ).
thf(zip_derived_cl154_006,plain,
vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl23426,plain,
! [X0: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl20799,zip_derived_cl154]) ).
thf(zip_derived_cl23427,plain,
! [X0: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl23426]) ).
thf(zip_derived_cl10_007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vvar @ X2 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-var-app]) ).
thf(zip_derived_cl11_008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( vabs @ X2 @ X3 @ X4 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-abs-app]) ).
thf(zip_derived_cl23428,plain,
( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl23427,zip_derived_cl10,zip_derived_cl11]) ).
thf('EQ-app',axiom,
! [VExp0: $i,VExp1: $i,VExp2: $i,VExp3: $i] :
( ( ( ( VExp0 = VExp2 )
& ( VExp1 = VExp3 ) )
=> ( ( vapp @ VExp0 @ VExp1 )
= ( vapp @ VExp2 @ VExp3 ) ) )
& ( ( ( vapp @ VExp0 @ VExp1 )
= ( vapp @ VExp2 @ VExp3 ) )
=> ( ( VExp0 = VExp2 )
& ( VExp1 = VExp3 ) ) ) ) ).
thf(zip_derived_cl6,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X0 )
| ( ( vapp @ X1 @ X3 )
!= ( vapp @ X0 @ X2 ) ) ),
inference(cnf,[status(esa)],[EQ-app]) ).
thf(zip_derived_cl23496,plain,
! [X0: $i,X1: $i] :
( ( ( vapp @ X1 @ X0 )
!= ( vapp @ ve1app @ ve2app ) )
| ( X1
= ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl23428,zip_derived_cl6]) ).
thf(zip_derived_cl23757,plain,
( ve1app
= ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl23496]) ).
thf(zip_derived_cl24875,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ve1app @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl24855,zip_derived_cl23757]) ).
thf(zip_derived_cl11_009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( vabs @ X2 @ X3 @ X4 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-abs-app]) ).
thf(zip_derived_cl24876,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ve1app @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl24875,zip_derived_cl11]) ).
thf(zip_derived_cl2200_010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( vsubst @ X3 @ X2 @ ( vapp @ X1 @ X0 ) )
= ( vapp @ ( vsubst @ X3 @ X2 @ X1 ) @ ( vsubst @ X3 @ X2 @ X0 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl2198]) ).
thf(zip_derived_cl27701,plain,
! [X0: $i,X1: $i] :
( ( ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
= ( vapp @ ( vsubst @ X1 @ X0 @ ve1app ) @ ( vsubst @ X1 @ X0 @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ve1app @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) )
| ( X1
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl24876,zip_derived_cl2200]) ).
thf(zip_derived_cl10_011,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vvar @ X2 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-var-app]) ).
thf(zip_derived_cl28118,plain,
! [X1: $i] :
( ( vtcheck @ sk__76 @ ve1app @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) )
| ( X1
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl27701,zip_derived_cl10]) ).
thf(zip_derived_cl548_012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vtcheck @ X2 @ ( sk__66 @ X2 @ X1 @ X0 ) @ ( varrow @ ( sk__68 @ X2 @ X1 @ X0 ) @ X1 ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl488,zip_derived_cl147]) ).
thf(zip_derived_cl28124,plain,
! [X0: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) )
| ( vtcheck @ sk__76 @ ve1app @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ~ ( vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77 )
| ( vtcheck @ sk__76 @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl28118,zip_derived_cl548]) ).
thf(zip_derived_cl154_013,plain,
vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl23757_014,plain,
( ve1app
= ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl23496]) ).
thf(zip_derived_cl30822,plain,
! [X0: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) )
| ( vtcheck @ sk__76 @ ve1app @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( vtcheck @ sk__76 @ ve1app @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl28124,zip_derived_cl154,zip_derived_cl23757]) ).
thf(zip_derived_cl30823,plain,
! [X0: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( vtcheck @ sk__76 @ ve1app @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl30822]) ).
thf(zip_derived_cl10_015,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vvar @ X2 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-var-app]) ).
thf(zip_derived_cl11_016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( vabs @ X2 @ X3 @ X4 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-abs-app]) ).
thf(zip_derived_cl30824,plain,
vtcheck @ sk__76 @ ve1app @ ( varrow @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ sk__77 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl30823,zip_derived_cl10,zip_derived_cl11]) ).
thf('T-Weak-app-IH2',axiom,
! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ve2app @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ve2app @ VT ) ) ).
thf(zip_derived_cl152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( vlookup @ X0 @ X1 )
!= vnoType )
| ~ ( vtcheck @ X1 @ ve2app @ X2 )
| ( vtcheck @ ( vbind @ X0 @ X3 @ X1 ) @ ve2app @ X2 ) ),
inference(cnf,[status(esa)],[T-Weak-app-IH2]) ).
thf('T-Weak-app-IH1',axiom,
! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ve1app @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ve1app @ VT ) ) ).
thf(zip_derived_cl151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( vlookup @ X0 @ X1 )
!= vnoType )
| ~ ( vtcheck @ X1 @ ve1app @ X2 )
| ( vtcheck @ ( vbind @ X0 @ X3 @ X1 ) @ ve1app @ X2 ) ),
inference(cnf,[status(esa)],[T-Weak-app-IH1]) ).
thf('T-app',axiom,
! [VS: $i,VC: $i,Ve1: $i,Ve2: $i,VT: $i] :
( ( ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) )
& ( vtcheck @ VC @ Ve2 @ VS ) )
=> ( vtcheck @ VC @ ( vapp @ Ve1 @ Ve2 ) @ VT ) ) ).
thf(zip_derived_cl141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( vtcheck @ X0 @ X1 @ X2 )
| ~ ( vtcheck @ X0 @ X3 @ ( varrow @ X2 @ X4 ) )
| ( vtcheck @ X0 @ ( vapp @ X3 @ X1 ) @ X4 ) ),
inference(cnf,[status(esa)],[T-app]) ).
thf(zip_derived_cl1578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( vtcheck @ X2 @ ve1app @ ( varrow @ X1 @ X0 ) )
| ( ( vlookup @ X4 @ X2 )
!= vnoType )
| ( vtcheck @ ( vbind @ X4 @ X3 @ X2 ) @ ( vapp @ ve1app @ X5 ) @ X0 )
| ~ ( vtcheck @ ( vbind @ X4 @ X3 @ X2 ) @ X5 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl151,zip_derived_cl141]) ).
thf(zip_derived_cl2746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( vtcheck @ X1 @ ve2app @ X0 )
| ( ( vlookup @ X3 @ X1 )
!= vnoType )
| ( vtcheck @ ( vbind @ X3 @ X2 @ X1 ) @ ( vapp @ ve1app @ ve2app ) @ X4 )
| ( ( vlookup @ X3 @ X1 )
!= vnoType )
| ~ ( vtcheck @ X1 @ ve1app @ ( varrow @ X0 @ X4 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl152,zip_derived_cl1578]) ).
thf(zip_derived_cl2748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( vtcheck @ X1 @ ve1app @ ( varrow @ X0 @ X4 ) )
| ( vtcheck @ ( vbind @ X3 @ X2 @ X1 ) @ ( vapp @ ve1app @ ve2app ) @ X4 )
| ( ( vlookup @ X3 @ X1 )
!= vnoType )
| ~ ( vtcheck @ X1 @ ve2app @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2746]) ).
thf(zip_derived_cl30912,plain,
! [X0: $i,X1: $i] :
( ~ ( vtcheck @ sk__76 @ ve2app @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vlookup @ X0 @ sk__76 )
!= vnoType )
| ( vtcheck @ ( vbind @ X0 @ X1 @ sk__76 ) @ ( vapp @ ve1app @ ve2app ) @ sk__77 ) ),
inference('sup-',[status(thm)],[zip_derived_cl30824,zip_derived_cl2748]) ).
thf(zip_derived_cl154_017,plain,
vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl474_018,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( zip_tseitin_17 @ ( sk__72 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) @ ( sk__69 @ X2 @ X1 @ X0 ) @ X2 @ X1 @ X0 )
| ( zip_tseitin_16 @ ( sk__68 @ X2 @ X1 @ X0 ) @ ( sk__67 @ X2 @ X1 @ X0 ) @ ( sk__66 @ X2 @ X1 @ X0 ) @ X2 @ X1 @ X0 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl150,zip_derived_cl149]) ).
thf(zip_derived_cl142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( vtcheck @ X0 @ X1 @ X2 )
| ~ ( zip_tseitin_16 @ X2 @ X1 @ X3 @ X0 @ X4 @ X5 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl487,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1
= ( vvar @ ( sk__73 @ X2 @ X0 @ X1 ) ) )
| ( zip_tseitin_17 @ ( sk__72 @ X2 @ X0 @ X1 ) @ ( sk__71 @ X2 @ X0 @ X1 ) @ ( sk__70 @ X2 @ X0 @ X1 ) @ ( sk__69 @ X2 @ X0 @ X1 ) @ X2 @ X0 @ X1 )
| ~ ( vtcheck @ X2 @ X1 @ X0 )
| ( vtcheck @ X2 @ ( sk__67 @ X2 @ X0 @ X1 ) @ ( sk__68 @ X2 @ X0 @ X1 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl474,zip_derived_cl142]) ).
thf(zip_derived_cl147_019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X3
= ( vabs @ X0 @ X1 @ X2 ) )
| ~ ( zip_tseitin_17 @ X4 @ X1 @ X2 @ X0 @ X5 @ X6 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl545,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vtcheck @ X2 @ ( sk__67 @ X2 @ X1 @ X0 ) @ ( sk__68 @ X2 @ X1 @ X0 ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl487,zip_derived_cl147]) ).
thf(zip_derived_cl1559_020,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( vsubst @ X2 @ X1 @ ( vvar @ X0 ) )
= ( vvar @ X0 ) )
| ( X2 = X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1558]) ).
thf(zip_derived_cl1686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( vsubst @ X4 @ X3 @ X0 )
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( vtcheck @ X2 @ ( sk__67 @ X2 @ X1 @ X0 ) @ ( sk__68 @ X2 @ X1 @ X0 ) )
| ( X4
= ( sk__73 @ X2 @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl545,zip_derived_cl1559]) ).
thf(zip_derived_cl10092,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl154,zip_derived_cl1686]) ).
thf(zip_derived_cl11_021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( vabs @ X2 @ X3 @ X4 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-abs-app]) ).
thf(zip_derived_cl10111,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl10092,zip_derived_cl11]) ).
thf(zip_derived_cl545_022,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vtcheck @ X2 @ ( sk__67 @ X2 @ X1 @ X0 ) @ ( sk__68 @ X2 @ X1 @ X0 ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl487,zip_derived_cl147]) ).
thf(zip_derived_cl12539,plain,
! [X0: $i,X1: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vsubst @ X1 @ X0 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( X1
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ~ ( vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77 )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10111,zip_derived_cl545]) ).
thf(zip_derived_cl154_023,plain,
vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12722,plain,
! [X0: $i,X1: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vsubst @ X1 @ X0 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( X1
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl12539,zip_derived_cl154]) ).
thf(zip_derived_cl12723,plain,
! [X0: $i,X1: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( X1
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vsubst @ X1 @ X0 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl12722]) ).
thf(zip_derived_cl11_024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( vabs @ X2 @ X3 @ X4 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-abs-app]) ).
thf(zip_derived_cl12724,plain,
! [X0: $i,X1: $i] :
( ( X1
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vsubst @ X1 @ X0 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl12723,zip_derived_cl11]) ).
thf(zip_derived_cl10111_025,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl10092,zip_derived_cl11]) ).
thf(zip_derived_cl545_026,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vtcheck @ X2 @ ( sk__67 @ X2 @ X1 @ X0 ) @ ( sk__68 @ X2 @ X1 @ X0 ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl487,zip_derived_cl147]) ).
thf(zip_derived_cl10173,plain,
! [X0: $i,X1: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ~ ( vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77 )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10111,zip_derived_cl545]) ).
thf(zip_derived_cl154_027,plain,
vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12571,plain,
! [X0: $i,X1: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl10173,zip_derived_cl154]) ).
thf(zip_derived_cl12572,plain,
! [X0: $i,X1: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl12571]) ).
thf(zip_derived_cl10_028,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vvar @ X2 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-var-app]) ).
thf(zip_derived_cl11_029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( vabs @ X2 @ X3 @ X4 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-abs-app]) ).
thf(zip_derived_cl12573,plain,
! [X0: $i,X1: $i] :
( ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vsubst @ X0 @ X1 @ ( vapp @ ve1app @ ve2app ) )
= ( vvar @ ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl12572,zip_derived_cl10,zip_derived_cl11]) ).
thf(zip_derived_cl10_030,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vvar @ X2 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-var-app]) ).
thf(zip_derived_cl12951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( vsubst @ X1 @ X0 @ ( vapp @ ve1app @ ve2app ) )
!= ( vapp @ X3 @ X2 ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl12573,zip_derived_cl10]) ).
thf(zip_derived_cl14230,plain,
! [X1: $i] :
( ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( X1
= ( sk__73 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl12724,zip_derived_cl12951]) ).
thf(zip_derived_cl545_031,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vtcheck @ X2 @ ( sk__67 @ X2 @ X1 @ X0 ) @ ( sk__68 @ X2 @ X1 @ X0 ) )
| ~ ( vtcheck @ X2 @ X0 @ X1 )
| ( X0
= ( vvar @ ( sk__73 @ X2 @ X1 @ X0 ) ) )
| ( X0
= ( vabs @ ( sk__69 @ X2 @ X1 @ X0 ) @ ( sk__71 @ X2 @ X1 @ X0 ) @ ( sk__70 @ X2 @ X1 @ X0 ) ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl487,zip_derived_cl147]) ).
thf(zip_derived_cl14233,plain,
! [X0: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ~ ( vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77 )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl14230,zip_derived_cl545]) ).
thf(zip_derived_cl154_032,plain,
vtcheck @ sk__76 @ ( vapp @ ve1app @ ve2app ) @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16910,plain,
! [X0: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl14233,zip_derived_cl154]) ).
thf(zip_derived_cl16911,plain,
! [X0: $i] :
( ( ( vapp @ ve1app @ ve2app )
= ( vabs @ ( sk__69 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__71 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__70 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) )
| ( vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) )
| ( ( vapp @ ve1app @ ve2app )
= ( vvar @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl16910]) ).
thf(zip_derived_cl10_033,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vvar @ X2 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-var-app]) ).
thf(zip_derived_cl11_034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( vabs @ X2 @ X3 @ X4 )
!= ( vapp @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[DIFF-abs-app]) ).
thf(zip_derived_cl16912,plain,
vtcheck @ sk__76 @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl16911,zip_derived_cl10,zip_derived_cl11]) ).
thf(zip_derived_cl23428_035,plain,
( ( vapp @ ve1app @ ve2app )
= ( vapp @ ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl23427,zip_derived_cl10,zip_derived_cl11]) ).
thf(zip_derived_cl23757_036,plain,
( ve1app
= ( sk__66 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl23496]) ).
thf(zip_derived_cl23768,plain,
( ( vapp @ ve1app @ ve2app )
= ( vapp @ ve1app @ ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl23428,zip_derived_cl23757]) ).
thf(zip_derived_cl7,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X0 )
| ( ( vapp @ X3 @ X1 )
!= ( vapp @ X2 @ X0 ) ) ),
inference(cnf,[status(esa)],[EQ-app]) ).
thf(zip_derived_cl23781,plain,
! [X0: $i,X1: $i] :
( ( ( vapp @ X1 @ X0 )
!= ( vapp @ ve1app @ ve2app ) )
| ( X0
= ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl23768,zip_derived_cl7]) ).
thf(zip_derived_cl24185,plain,
( ve2app
= ( sk__67 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl23781]) ).
thf(zip_derived_cl24256,plain,
vtcheck @ sk__76 @ ve2app @ ( sk__68 @ sk__76 @ sk__77 @ ( vapp @ ve1app @ ve2app ) ),
inference(demod,[status(thm)],[zip_derived_cl16912,zip_derived_cl24185]) ).
thf(zip_derived_cl30919,plain,
! [X0: $i,X1: $i] :
( ( ( vlookup @ X0 @ sk__76 )
!= vnoType )
| ( vtcheck @ ( vbind @ X0 @ X1 @ sk__76 ) @ ( vapp @ ve1app @ ve2app ) @ sk__77 ) ),
inference(demod,[status(thm)],[zip_derived_cl30912,zip_derived_cl24256]) ).
thf(zip_derived_cl30932,plain,
( ( vlookup @ sk__74 @ sk__76 )
!= vnoType ),
inference('sup+',[status(thm)],[zip_derived_cl153,zip_derived_cl30919]) ).
thf(zip_derived_cl155,plain,
( ( vlookup @ sk__74 @ sk__76 )
= vnoType ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl30933,plain,
vnoType != vnoType,
inference(demod,[status(thm)],[zip_derived_cl30932,zip_derived_cl155]) ).
thf(zip_derived_cl30934,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl30933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COM142+1 : TPTP v8.1.2. Released v6.4.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.CdLw9jBLtN true
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 13:49:46 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.54/0.64 % Total configuration time : 435
% 0.54/0.64 % Estimated wc time : 1092
% 0.54/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 68.05/10.33 % Solved by fo/fo3_bce.sh.
% 68.05/10.33 % BCE start: 156
% 68.05/10.33 % BCE eliminated: 0
% 68.05/10.33 % PE start: 156
% 68.05/10.33 logic: eq
% 68.05/10.33 % PE eliminated: -34
% 68.05/10.33 % done 1687 iterations in 9.572s
% 68.05/10.33 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 68.05/10.33 % SZS output start Refutation
% See solution above
% 68.05/10.33
% 68.05/10.33
% 68.05/10.33 % Terminating...
% 68.05/10.39 % Runner terminated.
% 68.05/10.41 % Zipperpin 1.5 exiting
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