TSTP Solution File: SWC128+1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWC128+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n032.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 : 600s
% DateTime : Tue Jul 19 20:52:30 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(ax95,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( gt(U,V)
& gt(V,W) )
=> gt(U,W) ) ) ) ),
input ).
fof(ax95_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( gt(U,V)
& gt(V,W) )
=> gt(U,W) ) ) ) ),
inference(orientation,[status(thm)],[ax95]) ).
fof(ax94,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( gt(U,V)
=> ~ gt(V,U) ) ) ),
input ).
fof(ax94_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ( gt(U,V)
=> ~ gt(V,U) ) ) ),
inference(orientation,[status(thm)],[ax94]) ).
fof(ax93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( U != V
& leq(U,V) ) ) ) ),
input ).
fof(ax93_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( U != V
& leq(U,V) ) ) ) ),
inference(orientation,[status(thm)],[ax93]) ).
fof(ax92,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( leq(U,V)
=> ( U = V
| lt(U,V) ) ) ) ),
input ).
fof(ax92_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ( leq(U,V)
=> ( U = V
| lt(U,V) ) ) ) ),
inference(orientation,[status(thm)],[ax92]) ).
fof(ax91,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(U,V)
& lt(V,W) )
=> lt(U,W) ) ) ) ),
input ).
fof(ax91_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(U,V)
& lt(V,W) )
=> lt(U,W) ) ) ) ),
inference(orientation,[status(thm)],[ax91]) ).
fof(ax90,axiom,
! [U] :
( ssItem(U)
=> ~ lt(U,U) ),
input ).
fof(ax90_0,plain,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(orientation,[status(thm)],[ax90]) ).
fof(ax89,axiom,
! [U] :
( ssItem(U)
=> geq(U,U) ),
input ).
fof(ax89_0,plain,
! [U] :
( ~ ssItem(U)
| geq(U,U) ),
inference(orientation,[status(thm)],[ax89]) ).
fof(ax88,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( geq(U,V)
& geq(V,W) )
=> geq(U,W) ) ) ) ),
input ).
fof(ax88_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( geq(U,V)
& geq(V,W) )
=> geq(U,W) ) ) ) ),
inference(orientation,[status(thm)],[ax88]) ).
fof(ax87,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( ( geq(U,V)
& geq(V,U) )
=> U = V ) ) ),
input ).
fof(ax87_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ( ( geq(U,V)
& geq(V,U) )
=> U = V ) ) ),
inference(orientation,[status(thm)],[ax87]) ).
fof(ax86,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> tl(app(U,V)) = app(tl(U),V) ) ) ),
input ).
fof(ax86_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( nil != U
=> tl(app(U,V)) = app(tl(U),V) ) ) ),
inference(orientation,[status(thm)],[ax86]) ).
fof(ax85,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
input ).
fof(ax85_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
inference(orientation,[status(thm)],[ax85]) ).
fof(ax84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
input ).
fof(ax84_0,plain,
! [U] :
( ~ ssList(U)
| app(U,nil) = U ),
inference(orientation,[status(thm)],[ax84]) ).
fof(ax83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = V
& nil = U ) ) ) ),
input ).
fof(ax83_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = V
& nil = U ) ) ) ),
inference(orientation,[status(thm)],[ax83]) ).
fof(ax82,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> app(app(U,V),W) = app(U,app(V,W)) ) ) ),
input ).
fof(ax82_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> app(app(U,V),W) = app(U,app(V,W)) ) ) ),
inference(orientation,[status(thm)],[ax82]) ).
fof(ax81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
input ).
fof(ax81_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
inference(orientation,[status(thm)],[ax81]) ).
fof(ax80,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
input ).
fof(ax80_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
inference(orientation,[status(thm)],[ax80]) ).
fof(ax79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
input ).
fof(ax79_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
inference(orientation,[status(thm)],[ax79]) ).
fof(ax78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
input ).
fof(ax78_0,plain,
! [U] :
( ~ ssList(U)
| ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
inference(orientation,[status(thm)],[ax78]) ).
fof(ax77,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( nil != V
& nil != U
& hd(V) = hd(U)
& tl(V) = tl(U) )
=> V = U ) ) ),
input ).
fof(ax77_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( ( nil != V
& nil != U
& hd(V) = hd(U)
& tl(V) = tl(U) )
=> V = U ) ) ),
inference(orientation,[status(thm)],[ax77]) ).
fof(ax76,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ? [V] :
( ssList(V)
& tl(U) = V ) ) ),
input ).
fof(ax76_0,plain,
! [U] :
( ~ ssList(U)
| ( nil != U
=> ? [V] :
( ssList(V)
& tl(U) = V ) ) ),
inference(orientation,[status(thm)],[ax76]) ).
fof(ax75,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ? [V] :
( ssItem(V)
& hd(U) = V ) ) ),
input ).
fof(ax75_0,plain,
! [U] :
( ~ ssList(U)
| ( nil != U
=> ? [V] :
( ssItem(V)
& hd(U) = V ) ) ),
inference(orientation,[status(thm)],[ax75]) ).
fof(ax74,axiom,
equalelemsP(nil),
input ).
fof(ax74_0,plain,
( equalelemsP(nil)
| $false ),
inference(orientation,[status(thm)],[ax74]) ).
fof(ax73,axiom,
! [U] :
( ssItem(U)
=> equalelemsP(cons(U,nil)) ),
input ).
fof(ax73_0,plain,
! [U] :
( ~ ssItem(U)
| equalelemsP(cons(U,nil)) ),
inference(orientation,[status(thm)],[ax73]) ).
fof(ax72,axiom,
duplicatefreeP(nil),
input ).
fof(ax72_0,plain,
( duplicatefreeP(nil)
| $false ),
inference(orientation,[status(thm)],[ax72]) ).
fof(ax71,axiom,
! [U] :
( ssItem(U)
=> duplicatefreeP(cons(U,nil)) ),
input ).
fof(ax71_0,plain,
! [U] :
( ~ ssItem(U)
| duplicatefreeP(cons(U,nil)) ),
inference(orientation,[status(thm)],[ax71]) ).
fof(ax70,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ( strictorderedP(cons(U,V))
<=> ( nil = V
| ( nil != V
& strictorderedP(V)
& lt(U,hd(V)) ) ) ) ) ),
input ).
fof(ax70_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssList(V)
=> ( strictorderedP(cons(U,V))
<=> ( nil = V
| ( nil != V
& strictorderedP(V)
& lt(U,hd(V)) ) ) ) ) ),
inference(orientation,[status(thm)],[ax70]) ).
fof(ax69,axiom,
strictorderedP(nil),
input ).
fof(ax69_0,plain,
( strictorderedP(nil)
| $false ),
inference(orientation,[status(thm)],[ax69]) ).
fof(ax68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
input ).
fof(ax68_0,plain,
! [U] :
( ~ ssItem(U)
| strictorderedP(cons(U,nil)) ),
inference(orientation,[status(thm)],[ax68]) ).
fof(ax67,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ( totalorderedP(cons(U,V))
<=> ( nil = V
| ( nil != V
& totalorderedP(V)
& leq(U,hd(V)) ) ) ) ) ),
input ).
fof(ax67_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssList(V)
=> ( totalorderedP(cons(U,V))
<=> ( nil = V
| ( nil != V
& totalorderedP(V)
& leq(U,hd(V)) ) ) ) ) ),
inference(orientation,[status(thm)],[ax67]) ).
fof(ax66,axiom,
totalorderedP(nil),
input ).
fof(ax66_0,plain,
( totalorderedP(nil)
| $false ),
inference(orientation,[status(thm)],[ax66]) ).
fof(ax65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
input ).
fof(ax65_0,plain,
! [U] :
( ~ ssItem(U)
| totalorderedP(cons(U,nil)) ),
inference(orientation,[status(thm)],[ax65]) ).
fof(ax64,axiom,
strictorderP(nil),
input ).
fof(ax64_0,plain,
( strictorderP(nil)
| $false ),
inference(orientation,[status(thm)],[ax64]) ).
fof(ax63,axiom,
! [U] :
( ssItem(U)
=> strictorderP(cons(U,nil)) ),
input ).
fof(ax63_0,plain,
! [U] :
( ~ ssItem(U)
| strictorderP(cons(U,nil)) ),
inference(orientation,[status(thm)],[ax63]) ).
fof(ax62,axiom,
totalorderP(nil),
input ).
fof(ax62_0,plain,
( totalorderP(nil)
| $false ),
inference(orientation,[status(thm)],[ax62]) ).
fof(ax61,axiom,
! [U] :
( ssItem(U)
=> totalorderP(cons(U,nil)) ),
input ).
fof(ax61_0,plain,
! [U] :
( ~ ssItem(U)
| totalorderP(cons(U,nil)) ),
inference(orientation,[status(thm)],[ax61]) ).
fof(ax60,axiom,
cyclefreeP(nil),
input ).
fof(ax60_0,plain,
( cyclefreeP(nil)
| $false ),
inference(orientation,[status(thm)],[ax60]) ).
fof(ax59,axiom,
! [U] :
( ssItem(U)
=> cyclefreeP(cons(U,nil)) ),
input ).
fof(ax59_0,plain,
! [U] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ),
inference(orientation,[status(thm)],[ax59]) ).
fof(ax58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
input ).
fof(ax58_0,plain,
! [U] :
( ~ ssList(U)
| ( segmentP(nil,U)
<=> nil = U ) ),
inference(orientation,[status(thm)],[ax58]) ).
fof(ax57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
input ).
fof(ax57_0,plain,
! [U] :
( ~ ssList(U)
| segmentP(U,nil) ),
inference(orientation,[status(thm)],[ax57]) ).
fof(ax56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
input ).
fof(ax56_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
inference(orientation,[status(thm)],[ax56]) ).
fof(ax55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
input ).
fof(ax55_0,plain,
! [U] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(orientation,[status(thm)],[ax55]) ).
fof(ax54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(U,V)
& segmentP(V,U) )
=> U = V ) ) ),
input ).
fof(ax54_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( ( segmentP(U,V)
& segmentP(V,U) )
=> U = V ) ) ),
inference(orientation,[status(thm)],[ax54]) ).
fof(ax53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(U,V)
& segmentP(V,W) )
=> segmentP(U,W) ) ) ) ),
input ).
fof(ax53_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(U,V)
& segmentP(V,W) )
=> segmentP(U,W) ) ) ) ),
inference(orientation,[status(thm)],[ax53]) ).
fof(ax52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
input ).
fof(ax52_0,plain,
! [U] :
( ~ ssList(U)
| ( rearsegP(nil,U)
<=> nil = U ) ),
inference(orientation,[status(thm)],[ax52]) ).
fof(ax51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
input ).
fof(ax51_0,plain,
! [U] :
( ~ ssList(U)
| rearsegP(U,nil) ),
inference(orientation,[status(thm)],[ax51]) ).
fof(ax50,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( rearsegP(U,V)
=> rearsegP(app(W,U),V) ) ) ) ),
input ).
fof(ax50_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( rearsegP(U,V)
=> rearsegP(app(W,U),V) ) ) ) ),
inference(orientation,[status(thm)],[ax50]) ).
fof(ax49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
input ).
fof(ax49_0,plain,
! [U] :
( ~ ssList(U)
| rearsegP(U,U) ),
inference(orientation,[status(thm)],[ax49]) ).
fof(ax48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(U,V)
& rearsegP(V,U) )
=> U = V ) ) ),
input ).
fof(ax48_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( ( rearsegP(U,V)
& rearsegP(V,U) )
=> U = V ) ) ),
inference(orientation,[status(thm)],[ax48]) ).
fof(ax47,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(U,V)
& rearsegP(V,W) )
=> rearsegP(U,W) ) ) ) ),
input ).
fof(ax47_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(U,V)
& rearsegP(V,W) )
=> rearsegP(U,W) ) ) ) ),
inference(orientation,[status(thm)],[ax47]) ).
fof(ax46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
input ).
fof(ax46_0,plain,
! [U] :
( ~ ssList(U)
| ( frontsegP(nil,U)
<=> nil = U ) ),
inference(orientation,[status(thm)],[ax46]) ).
fof(ax45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
input ).
fof(ax45_0,plain,
! [U] :
( ~ ssList(U)
| frontsegP(U,nil) ),
inference(orientation,[status(thm)],[ax45]) ).
fof(ax44,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( U = V
& frontsegP(W,X) ) ) ) ) ) ),
input ).
fof(ax44_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( U = V
& frontsegP(W,X) ) ) ) ) ) ),
inference(orientation,[status(thm)],[ax44]) ).
fof(ax43,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
input ).
fof(ax43_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
inference(orientation,[status(thm)],[ax43]) ).
fof(ax42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
input ).
fof(ax42_0,plain,
! [U] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(orientation,[status(thm)],[ax42]) ).
fof(ax41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(U,V)
& frontsegP(V,U) )
=> U = V ) ) ),
input ).
fof(ax41_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( ( frontsegP(U,V)
& frontsegP(V,U) )
=> U = V ) ) ),
inference(orientation,[status(thm)],[ax41]) ).
fof(ax40,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(U,V)
& frontsegP(V,W) )
=> frontsegP(U,W) ) ) ) ),
input ).
fof(ax40_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(U,V)
& frontsegP(V,W) )
=> frontsegP(U,W) ) ) ) ),
inference(orientation,[status(thm)],[ax40]) ).
fof(ax39,axiom,
~ singletonP(nil),
input ).
fof(ax39_0,plain,
( ~ singletonP(nil)
| $false ),
inference(orientation,[status(thm)],[ax39]) ).
fof(ax38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
input ).
fof(ax38_0,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(orientation,[status(thm)],[ax38]) ).
fof(ax37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( U = V
| memberP(W,U) ) ) ) ) ),
input ).
fof(ax37_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( U = V
| memberP(W,U) ) ) ) ) ),
inference(orientation,[status(thm)],[ax37]) ).
fof(ax36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(V,U)
| memberP(W,U) ) ) ) ) ),
input ).
fof(ax36_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(V,U)
| memberP(W,U) ) ) ) ) ),
inference(orientation,[status(thm)],[ax36]) ).
fof(ax35,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( gt(U,V)
<=> lt(V,U) ) ) ),
input ).
fof(ax35_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ( gt(U,V)
<=> lt(V,U) ) ) ),
inference(orientation,[status(thm)],[ax35]) ).
fof(ax34,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( lt(U,V)
& lt(V,W) )
=> lt(U,W) ) ) ) ),
input ).
fof(ax34_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( lt(U,V)
& lt(V,W) )
=> lt(U,W) ) ) ) ),
inference(orientation,[status(thm)],[ax34]) ).
fof(ax33,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
=> ~ lt(V,U) ) ) ),
input ).
fof(ax33_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ( lt(U,V)
=> ~ lt(V,U) ) ) ),
inference(orientation,[status(thm)],[ax33]) ).
fof(ax32,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( geq(U,V)
<=> leq(V,U) ) ) ),
input ).
fof(ax32_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ( geq(U,V)
<=> leq(V,U) ) ) ),
inference(orientation,[status(thm)],[ax32]) ).
fof(ax31,axiom,
! [U] :
( ssItem(U)
=> leq(U,U) ),
input ).
fof(ax31_0,plain,
! [U] :
( ~ ssItem(U)
| leq(U,U) ),
inference(orientation,[status(thm)],[ax31]) ).
fof(ax30,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(U,V)
& leq(V,W) )
=> leq(U,W) ) ) ) ),
input ).
fof(ax30_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(U,V)
& leq(V,W) )
=> leq(U,W) ) ) ) ),
inference(orientation,[status(thm)],[ax30]) ).
fof(ax29,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( ( leq(U,V)
& leq(V,U) )
=> U = V ) ) ),
input ).
fof(ax29_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ( ( leq(U,V)
& leq(V,U) )
=> U = V ) ) ),
inference(orientation,[status(thm)],[ax29]) ).
fof(ax28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
input ).
fof(ax28_0,plain,
! [U] :
( ~ ssList(U)
| app(nil,U) = U ),
inference(orientation,[status(thm)],[ax28]) ).
fof(ax27,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> cons(W,app(V,U)) = app(cons(W,V),U) ) ) ),
input ).
fof(ax27_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> cons(W,app(V,U)) = app(cons(W,V),U) ) ) ),
inference(orientation,[status(thm)],[ax27]) ).
fof(ax26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
input ).
fof(ax26_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
inference(orientation,[status(thm)],[ax26]) ).
fof(ax25,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
input ).
fof(ax25_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
inference(orientation,[status(thm)],[ax25]) ).
fof(ax24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
input ).
fof(ax24_0,plain,
! [U] :
( ~ ssList(U)
| ( nil != U
=> ssList(tl(U)) ) ),
inference(orientation,[status(thm)],[ax24]) ).
fof(ax23,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
input ).
fof(ax23_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
inference(orientation,[status(thm)],[ax23]) ).
fof(ax22,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssItem(hd(U)) ) ),
input ).
fof(ax22_0,plain,
! [U] :
( ~ ssList(U)
| ( nil != U
=> ssItem(hd(U)) ) ),
inference(orientation,[status(thm)],[ax22]) ).
fof(ax21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
input ).
fof(ax21_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
inference(orientation,[status(thm)],[ax21]) ).
fof(ax20,axiom,
! [U] :
( ssList(U)
=> ( nil = U
| ? [V] :
( ssList(V)
& ? [W] :
( ssItem(W)
& cons(W,V) = U ) ) ) ),
input ).
fof(ax20_0,plain,
! [U] :
( ~ ssList(U)
| nil = U
| ? [V] :
( ssList(V)
& ? [W] :
( ssItem(W)
& cons(W,V) = U ) ) ),
inference(orientation,[status(thm)],[ax20]) ).
fof(ax19,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( W = X
& V = U ) ) ) ) ) ),
input ).
fof(ax19_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( W = X
& V = U ) ) ) ) ) ),
inference(orientation,[status(thm)],[ax19]) ).
fof(ax18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
input ).
fof(ax18_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
inference(orientation,[status(thm)],[ax18]) ).
fof(ax17,axiom,
ssList(nil),
input ).
fof(ax17_0,plain,
( ssList(nil)
| $false ),
inference(orientation,[status(thm)],[ax17]) ).
fof(ax16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
input ).
fof(ax16_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
inference(orientation,[status(thm)],[ax16]) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
input ).
fof(ax15_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
inference(orientation,[status(thm)],[ax15]) ).
fof(ax14,axiom,
! [U] :
( ssList(U)
=> ( equalelemsP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ( app(X,cons(V,cons(W,Y))) = U
=> V = W ) ) ) ) ) ) ),
input ).
fof(ax14_0,plain,
! [U] :
( ~ ssList(U)
| ( equalelemsP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ( app(X,cons(V,cons(W,Y))) = U
=> V = W ) ) ) ) ) ) ),
inference(orientation,[status(thm)],[ax14]) ).
fof(ax13,axiom,
! [U] :
( ssList(U)
=> ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
input ).
fof(ax13_0,plain,
! [U] :
( ~ ssList(U)
| ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
inference(orientation,[status(thm)],[ax13]) ).
fof(ax12,axiom,
! [U] :
( ssList(U)
=> ( strictorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> lt(V,W) ) ) ) ) ) ) ) ),
input ).
fof(ax12_0,plain,
! [U] :
( ~ ssList(U)
| ( strictorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> lt(V,W) ) ) ) ) ) ) ) ),
inference(orientation,[status(thm)],[ax12]) ).
fof(ax11,axiom,
! [U] :
( ssList(U)
=> ( totalorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> leq(V,W) ) ) ) ) ) ) ) ),
input ).
fof(ax11_0,plain,
! [U] :
( ~ ssList(U)
| ( totalorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> leq(V,W) ) ) ) ) ) ) ) ),
inference(orientation,[status(thm)],[ax11]) ).
fof(ax10,axiom,
! [U] :
( ssList(U)
=> ( strictorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( lt(V,W)
| lt(W,V) ) ) ) ) ) ) ) ) ),
input ).
fof(ax10_0,plain,
! [U] :
( ~ ssList(U)
| ( strictorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( lt(V,W)
| lt(W,V) ) ) ) ) ) ) ) ) ),
inference(orientation,[status(thm)],[ax10]) ).
fof(ax9,axiom,
! [U] :
( ssList(U)
=> ( totalorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( leq(V,W)
| leq(W,V) ) ) ) ) ) ) ) ) ),
input ).
fof(ax9_0,plain,
! [U] :
( ~ ssList(U)
| ( totalorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( leq(V,W)
| leq(W,V) ) ) ) ) ) ) ) ) ),
inference(orientation,[status(thm)],[ax9]) ).
fof(ax8,axiom,
! [U] :
( ssList(U)
=> ( cyclefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ~ ( leq(V,W)
& leq(W,V) ) ) ) ) ) ) ) ) ),
input ).
fof(ax8_0,plain,
! [U] :
( ~ ssList(U)
| ( cyclefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ~ ( leq(V,W)
& leq(W,V) ) ) ) ) ) ) ) ) ),
inference(orientation,[status(thm)],[ax8]) ).
fof(ax7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(app(W,V),X) = U ) ) ) ) ),
input ).
fof(ax7_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(app(W,V),X) = U ) ) ) ) ),
inference(orientation,[status(thm)],[ax7]) ).
fof(ax6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( ssList(W)
& app(W,V) = U ) ) ) ),
input ).
fof(ax6_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( ssList(W)
& app(W,V) = U ) ) ) ),
inference(orientation,[status(thm)],[ax6]) ).
fof(ax5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( ssList(W)
& app(V,W) = U ) ) ) ),
input ).
fof(ax5_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( ssList(W)
& app(V,W) = U ) ) ) ),
inference(orientation,[status(thm)],[ax5]) ).
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
input ).
fof(ax4_0,plain,
! [U] :
( ~ ssList(U)
| ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
inference(orientation,[status(thm)],[ax4]) ).
fof(ax3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(W,cons(V,X)) = U ) ) ) ) ),
input ).
fof(ax3_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(W,cons(V,X)) = U ) ) ) ) ),
inference(orientation,[status(thm)],[ax3]) ).
fof(ax1,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
input ).
fof(ax1_0,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
inference(orientation,[status(thm)],[ax1]) ).
fof(def_lhs_atom1,axiom,
! [U] :
( lhs_atom1(U)
<=> ~ ssItem(U) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
inference(fold_definition,[status(thm)],[ax1_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [U] :
( lhs_atom2(U)
<=> ~ ssList(U) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(W,cons(V,X)) = U ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax3_0,def_lhs_atom2]) ).
fof(to_be_clausified_2,plain,
! [U] :
( lhs_atom2(U)
| ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
inference(fold_definition,[status(thm)],[ax4_0,def_lhs_atom2]) ).
fof(to_be_clausified_3,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( ssList(W)
& app(V,W) = U ) ) ) ),
inference(fold_definition,[status(thm)],[ax5_0,def_lhs_atom2]) ).
fof(to_be_clausified_4,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( ssList(W)
& app(W,V) = U ) ) ) ),
inference(fold_definition,[status(thm)],[ax6_0,def_lhs_atom2]) ).
fof(to_be_clausified_5,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(app(W,V),X) = U ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax7_0,def_lhs_atom2]) ).
fof(to_be_clausified_6,plain,
! [U] :
( lhs_atom2(U)
| ( cyclefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ~ ( leq(V,W)
& leq(W,V) ) ) ) ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax8_0,def_lhs_atom2]) ).
fof(to_be_clausified_7,plain,
! [U] :
( lhs_atom2(U)
| ( totalorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( leq(V,W)
| leq(W,V) ) ) ) ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax9_0,def_lhs_atom2]) ).
fof(to_be_clausified_8,plain,
! [U] :
( lhs_atom2(U)
| ( strictorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( lt(V,W)
| lt(W,V) ) ) ) ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax10_0,def_lhs_atom2]) ).
fof(to_be_clausified_9,plain,
! [U] :
( lhs_atom2(U)
| ( totalorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> leq(V,W) ) ) ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax11_0,def_lhs_atom2]) ).
fof(to_be_clausified_10,plain,
! [U] :
( lhs_atom2(U)
| ( strictorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> lt(V,W) ) ) ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax12_0,def_lhs_atom2]) ).
fof(to_be_clausified_11,plain,
! [U] :
( lhs_atom2(U)
| ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax13_0,def_lhs_atom2]) ).
fof(to_be_clausified_12,plain,
! [U] :
( lhs_atom2(U)
| ( equalelemsP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ( app(X,cons(V,cons(W,Y))) = U
=> V = W ) ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax14_0,def_lhs_atom2]) ).
fof(to_be_clausified_13,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
inference(fold_definition,[status(thm)],[ax15_0,def_lhs_atom2]) ).
fof(to_be_clausified_14,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
inference(fold_definition,[status(thm)],[ax16_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
( lhs_atom3
<=> ssList(nil) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
( lhs_atom3
| $false ),
inference(fold_definition,[status(thm)],[ax17_0,def_lhs_atom3]) ).
fof(to_be_clausified_16,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
inference(fold_definition,[status(thm)],[ax18_0,def_lhs_atom2]) ).
fof(to_be_clausified_17,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( W = X
& V = U ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax19_0,def_lhs_atom2]) ).
fof(to_be_clausified_18,plain,
! [U] :
( lhs_atom2(U)
| nil = U
| ? [V] :
( ssList(V)
& ? [W] :
( ssItem(W)
& cons(W,V) = U ) ) ),
inference(fold_definition,[status(thm)],[ax20_0,def_lhs_atom2]) ).
fof(to_be_clausified_19,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
inference(fold_definition,[status(thm)],[ax21_0,def_lhs_atom2]) ).
fof(to_be_clausified_20,plain,
! [U] :
( lhs_atom2(U)
| ( nil != U
=> ssItem(hd(U)) ) ),
inference(fold_definition,[status(thm)],[ax22_0,def_lhs_atom2]) ).
fof(to_be_clausified_21,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
inference(fold_definition,[status(thm)],[ax23_0,def_lhs_atom2]) ).
fof(to_be_clausified_22,plain,
! [U] :
( lhs_atom2(U)
| ( nil != U
=> ssList(tl(U)) ) ),
inference(fold_definition,[status(thm)],[ax24_0,def_lhs_atom2]) ).
fof(to_be_clausified_23,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
inference(fold_definition,[status(thm)],[ax25_0,def_lhs_atom2]) ).
fof(to_be_clausified_24,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
inference(fold_definition,[status(thm)],[ax26_0,def_lhs_atom2]) ).
fof(to_be_clausified_25,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> cons(W,app(V,U)) = app(cons(W,V),U) ) ) ),
inference(fold_definition,[status(thm)],[ax27_0,def_lhs_atom2]) ).
fof(to_be_clausified_26,plain,
! [U] :
( lhs_atom2(U)
| app(nil,U) = U ),
inference(fold_definition,[status(thm)],[ax28_0,def_lhs_atom2]) ).
fof(to_be_clausified_27,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ( ( leq(U,V)
& leq(V,U) )
=> U = V ) ) ),
inference(fold_definition,[status(thm)],[ax29_0,def_lhs_atom1]) ).
fof(to_be_clausified_28,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(U,V)
& leq(V,W) )
=> leq(U,W) ) ) ) ),
inference(fold_definition,[status(thm)],[ax30_0,def_lhs_atom1]) ).
fof(to_be_clausified_29,plain,
! [U] :
( lhs_atom1(U)
| leq(U,U) ),
inference(fold_definition,[status(thm)],[ax31_0,def_lhs_atom1]) ).
fof(to_be_clausified_30,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ( geq(U,V)
<=> leq(V,U) ) ) ),
inference(fold_definition,[status(thm)],[ax32_0,def_lhs_atom1]) ).
fof(to_be_clausified_31,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ( lt(U,V)
=> ~ lt(V,U) ) ) ),
inference(fold_definition,[status(thm)],[ax33_0,def_lhs_atom1]) ).
fof(to_be_clausified_32,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( lt(U,V)
& lt(V,W) )
=> lt(U,W) ) ) ) ),
inference(fold_definition,[status(thm)],[ax34_0,def_lhs_atom1]) ).
fof(to_be_clausified_33,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ( gt(U,V)
<=> lt(V,U) ) ) ),
inference(fold_definition,[status(thm)],[ax35_0,def_lhs_atom1]) ).
fof(to_be_clausified_34,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(V,U)
| memberP(W,U) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax36_0,def_lhs_atom1]) ).
fof(to_be_clausified_35,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( U = V
| memberP(W,U) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax37_0,def_lhs_atom1]) ).
fof(to_be_clausified_36,plain,
! [U] :
( lhs_atom1(U)
| ~ memberP(nil,U) ),
inference(fold_definition,[status(thm)],[ax38_0,def_lhs_atom1]) ).
fof(def_lhs_atom4,axiom,
( lhs_atom4
<=> ~ singletonP(nil) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
( lhs_atom4
| $false ),
inference(fold_definition,[status(thm)],[ax39_0,def_lhs_atom4]) ).
fof(to_be_clausified_38,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(U,V)
& frontsegP(V,W) )
=> frontsegP(U,W) ) ) ) ),
inference(fold_definition,[status(thm)],[ax40_0,def_lhs_atom2]) ).
fof(to_be_clausified_39,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( ( frontsegP(U,V)
& frontsegP(V,U) )
=> U = V ) ) ),
inference(fold_definition,[status(thm)],[ax41_0,def_lhs_atom2]) ).
fof(to_be_clausified_40,plain,
! [U] :
( lhs_atom2(U)
| frontsegP(U,U) ),
inference(fold_definition,[status(thm)],[ax42_0,def_lhs_atom2]) ).
fof(to_be_clausified_41,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
inference(fold_definition,[status(thm)],[ax43_0,def_lhs_atom2]) ).
fof(to_be_clausified_42,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( U = V
& frontsegP(W,X) ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax44_0,def_lhs_atom1]) ).
fof(to_be_clausified_43,plain,
! [U] :
( lhs_atom2(U)
| frontsegP(U,nil) ),
inference(fold_definition,[status(thm)],[ax45_0,def_lhs_atom2]) ).
fof(to_be_clausified_44,plain,
! [U] :
( lhs_atom2(U)
| ( frontsegP(nil,U)
<=> nil = U ) ),
inference(fold_definition,[status(thm)],[ax46_0,def_lhs_atom2]) ).
fof(to_be_clausified_45,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(U,V)
& rearsegP(V,W) )
=> rearsegP(U,W) ) ) ) ),
inference(fold_definition,[status(thm)],[ax47_0,def_lhs_atom2]) ).
fof(to_be_clausified_46,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( ( rearsegP(U,V)
& rearsegP(V,U) )
=> U = V ) ) ),
inference(fold_definition,[status(thm)],[ax48_0,def_lhs_atom2]) ).
fof(to_be_clausified_47,plain,
! [U] :
( lhs_atom2(U)
| rearsegP(U,U) ),
inference(fold_definition,[status(thm)],[ax49_0,def_lhs_atom2]) ).
fof(to_be_clausified_48,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( rearsegP(U,V)
=> rearsegP(app(W,U),V) ) ) ) ),
inference(fold_definition,[status(thm)],[ax50_0,def_lhs_atom2]) ).
fof(to_be_clausified_49,plain,
! [U] :
( lhs_atom2(U)
| rearsegP(U,nil) ),
inference(fold_definition,[status(thm)],[ax51_0,def_lhs_atom2]) ).
fof(to_be_clausified_50,plain,
! [U] :
( lhs_atom2(U)
| ( rearsegP(nil,U)
<=> nil = U ) ),
inference(fold_definition,[status(thm)],[ax52_0,def_lhs_atom2]) ).
fof(to_be_clausified_51,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(U,V)
& segmentP(V,W) )
=> segmentP(U,W) ) ) ) ),
inference(fold_definition,[status(thm)],[ax53_0,def_lhs_atom2]) ).
fof(to_be_clausified_52,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( ( segmentP(U,V)
& segmentP(V,U) )
=> U = V ) ) ),
inference(fold_definition,[status(thm)],[ax54_0,def_lhs_atom2]) ).
fof(to_be_clausified_53,plain,
! [U] :
( lhs_atom2(U)
| segmentP(U,U) ),
inference(fold_definition,[status(thm)],[ax55_0,def_lhs_atom2]) ).
fof(to_be_clausified_54,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax56_0,def_lhs_atom2]) ).
fof(to_be_clausified_55,plain,
! [U] :
( lhs_atom2(U)
| segmentP(U,nil) ),
inference(fold_definition,[status(thm)],[ax57_0,def_lhs_atom2]) ).
fof(to_be_clausified_56,plain,
! [U] :
( lhs_atom2(U)
| ( segmentP(nil,U)
<=> nil = U ) ),
inference(fold_definition,[status(thm)],[ax58_0,def_lhs_atom2]) ).
fof(to_be_clausified_57,plain,
! [U] :
( lhs_atom1(U)
| cyclefreeP(cons(U,nil)) ),
inference(fold_definition,[status(thm)],[ax59_0,def_lhs_atom1]) ).
fof(def_lhs_atom5,axiom,
( lhs_atom5
<=> cyclefreeP(nil) ),
inference(definition,[],]) ).
fof(to_be_clausified_58,plain,
( lhs_atom5
| $false ),
inference(fold_definition,[status(thm)],[ax60_0,def_lhs_atom5]) ).
fof(to_be_clausified_59,plain,
! [U] :
( lhs_atom1(U)
| totalorderP(cons(U,nil)) ),
inference(fold_definition,[status(thm)],[ax61_0,def_lhs_atom1]) ).
fof(def_lhs_atom6,axiom,
( lhs_atom6
<=> totalorderP(nil) ),
inference(definition,[],]) ).
fof(to_be_clausified_60,plain,
( lhs_atom6
| $false ),
inference(fold_definition,[status(thm)],[ax62_0,def_lhs_atom6]) ).
fof(to_be_clausified_61,plain,
! [U] :
( lhs_atom1(U)
| strictorderP(cons(U,nil)) ),
inference(fold_definition,[status(thm)],[ax63_0,def_lhs_atom1]) ).
fof(def_lhs_atom7,axiom,
( lhs_atom7
<=> strictorderP(nil) ),
inference(definition,[],]) ).
fof(to_be_clausified_62,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[ax64_0,def_lhs_atom7]) ).
fof(to_be_clausified_63,plain,
! [U] :
( lhs_atom1(U)
| totalorderedP(cons(U,nil)) ),
inference(fold_definition,[status(thm)],[ax65_0,def_lhs_atom1]) ).
fof(def_lhs_atom8,axiom,
( lhs_atom8
<=> totalorderedP(nil) ),
inference(definition,[],]) ).
fof(to_be_clausified_64,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[ax66_0,def_lhs_atom8]) ).
fof(to_be_clausified_65,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssList(V)
=> ( totalorderedP(cons(U,V))
<=> ( nil = V
| ( nil != V
& totalorderedP(V)
& leq(U,hd(V)) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax67_0,def_lhs_atom1]) ).
fof(to_be_clausified_66,plain,
! [U] :
( lhs_atom1(U)
| strictorderedP(cons(U,nil)) ),
inference(fold_definition,[status(thm)],[ax68_0,def_lhs_atom1]) ).
fof(def_lhs_atom9,axiom,
( lhs_atom9
<=> strictorderedP(nil) ),
inference(definition,[],]) ).
fof(to_be_clausified_67,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[ax69_0,def_lhs_atom9]) ).
fof(to_be_clausified_68,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssList(V)
=> ( strictorderedP(cons(U,V))
<=> ( nil = V
| ( nil != V
& strictorderedP(V)
& lt(U,hd(V)) ) ) ) ) ),
inference(fold_definition,[status(thm)],[ax70_0,def_lhs_atom1]) ).
fof(to_be_clausified_69,plain,
! [U] :
( lhs_atom1(U)
| duplicatefreeP(cons(U,nil)) ),
inference(fold_definition,[status(thm)],[ax71_0,def_lhs_atom1]) ).
fof(def_lhs_atom10,axiom,
( lhs_atom10
<=> duplicatefreeP(nil) ),
inference(definition,[],]) ).
fof(to_be_clausified_70,plain,
( lhs_atom10
| $false ),
inference(fold_definition,[status(thm)],[ax72_0,def_lhs_atom10]) ).
fof(to_be_clausified_71,plain,
! [U] :
( lhs_atom1(U)
| equalelemsP(cons(U,nil)) ),
inference(fold_definition,[status(thm)],[ax73_0,def_lhs_atom1]) ).
fof(def_lhs_atom11,axiom,
( lhs_atom11
<=> equalelemsP(nil) ),
inference(definition,[],]) ).
fof(to_be_clausified_72,plain,
( lhs_atom11
| $false ),
inference(fold_definition,[status(thm)],[ax74_0,def_lhs_atom11]) ).
fof(to_be_clausified_73,plain,
! [U] :
( lhs_atom2(U)
| ( nil != U
=> ? [V] :
( ssItem(V)
& hd(U) = V ) ) ),
inference(fold_definition,[status(thm)],[ax75_0,def_lhs_atom2]) ).
fof(to_be_clausified_74,plain,
! [U] :
( lhs_atom2(U)
| ( nil != U
=> ? [V] :
( ssList(V)
& tl(U) = V ) ) ),
inference(fold_definition,[status(thm)],[ax76_0,def_lhs_atom2]) ).
fof(to_be_clausified_75,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( ( nil != V
& nil != U
& hd(V) = hd(U)
& tl(V) = tl(U) )
=> V = U ) ) ),
inference(fold_definition,[status(thm)],[ax77_0,def_lhs_atom2]) ).
fof(to_be_clausified_76,plain,
! [U] :
( lhs_atom2(U)
| ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
inference(fold_definition,[status(thm)],[ax78_0,def_lhs_atom2]) ).
fof(to_be_clausified_77,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
inference(fold_definition,[status(thm)],[ax79_0,def_lhs_atom2]) ).
fof(to_be_clausified_78,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
inference(fold_definition,[status(thm)],[ax80_0,def_lhs_atom2]) ).
fof(to_be_clausified_79,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
inference(fold_definition,[status(thm)],[ax81_0,def_lhs_atom2]) ).
fof(to_be_clausified_80,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> app(app(U,V),W) = app(U,app(V,W)) ) ) ),
inference(fold_definition,[status(thm)],[ax82_0,def_lhs_atom2]) ).
fof(to_be_clausified_81,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = V
& nil = U ) ) ) ),
inference(fold_definition,[status(thm)],[ax83_0,def_lhs_atom2]) ).
fof(to_be_clausified_82,plain,
! [U] :
( lhs_atom2(U)
| app(U,nil) = U ),
inference(fold_definition,[status(thm)],[ax84_0,def_lhs_atom2]) ).
fof(to_be_clausified_83,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
inference(fold_definition,[status(thm)],[ax85_0,def_lhs_atom2]) ).
fof(to_be_clausified_84,plain,
! [U] :
( lhs_atom2(U)
| ! [V] :
( ssList(V)
=> ( nil != U
=> tl(app(U,V)) = app(tl(U),V) ) ) ),
inference(fold_definition,[status(thm)],[ax86_0,def_lhs_atom2]) ).
fof(to_be_clausified_85,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ( ( geq(U,V)
& geq(V,U) )
=> U = V ) ) ),
inference(fold_definition,[status(thm)],[ax87_0,def_lhs_atom1]) ).
fof(to_be_clausified_86,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( geq(U,V)
& geq(V,W) )
=> geq(U,W) ) ) ) ),
inference(fold_definition,[status(thm)],[ax88_0,def_lhs_atom1]) ).
fof(to_be_clausified_87,plain,
! [U] :
( lhs_atom1(U)
| geq(U,U) ),
inference(fold_definition,[status(thm)],[ax89_0,def_lhs_atom1]) ).
fof(to_be_clausified_88,plain,
! [U] :
( lhs_atom1(U)
| ~ lt(U,U) ),
inference(fold_definition,[status(thm)],[ax90_0,def_lhs_atom1]) ).
fof(to_be_clausified_89,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(U,V)
& lt(V,W) )
=> lt(U,W) ) ) ) ),
inference(fold_definition,[status(thm)],[ax91_0,def_lhs_atom1]) ).
fof(to_be_clausified_90,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ( leq(U,V)
=> ( U = V
| lt(U,V) ) ) ) ),
inference(fold_definition,[status(thm)],[ax92_0,def_lhs_atom1]) ).
fof(to_be_clausified_91,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( U != V
& leq(U,V) ) ) ) ),
inference(fold_definition,[status(thm)],[ax93_0,def_lhs_atom1]) ).
fof(to_be_clausified_92,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ( gt(U,V)
=> ~ gt(V,U) ) ) ),
inference(fold_definition,[status(thm)],[ax94_0,def_lhs_atom1]) ).
fof(to_be_clausified_93,plain,
! [U] :
( lhs_atom1(U)
| ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( gt(U,V)
& gt(V,W) )
=> gt(U,W) ) ) ) ),
inference(fold_definition,[status(thm)],[ax95_0,def_lhs_atom1]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X1] :
( lhs_atom2(X1)
| ( cyclefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ~ ( leq(X2,X3)
& leq(X3,X2) ) ) ) ) ) ) ) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_1,axiom,
! [X1] :
( lhs_atom2(X1)
| ( strictorderP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ( lt(X2,X3)
| lt(X3,X2) ) ) ) ) ) ) ) ) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_2,axiom,
! [X1] :
( lhs_atom2(X1)
| ( totalorderP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ( leq(X2,X3)
| leq(X3,X2) ) ) ) ) ) ) ) ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_3,axiom,
! [X1] :
( lhs_atom2(X1)
| ( strictorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> lt(X2,X3) ) ) ) ) ) ) ) ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_4,axiom,
! [X1] :
( lhs_atom2(X1)
| ( totalorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> leq(X2,X3) ) ) ) ) ) ) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_5,axiom,
! [X1] :
( lhs_atom2(X1)
| ( duplicatefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> X2 != X3 ) ) ) ) ) ) ) ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_6,axiom,
! [X1] :
( lhs_atom2(X1)
| ( equalelemsP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X4,cons(X2,cons(X3,X5))) = X1
=> X2 = X3 ) ) ) ) ) ) ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_7,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_8,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_9,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_10,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_11,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_12,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_13,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_14,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_15,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssList(X2)
=> ( strictorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& strictorderedP(X2)
& lt(X1,hd(X2)) ) ) ) ) ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_16,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssList(X2)
=> ( totalorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& totalorderedP(X2)
& leq(X1,hd(X2)) ) ) ) ) ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_17,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_18,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_19,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( gt(X1,X2)
& gt(X2,X3) )
=> gt(X1,X3) ) ) ) ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_20,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( leq(X1,X2)
& lt(X2,X3) )
=> lt(X1,X3) ) ) ) ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_21,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( geq(X1,X2)
& geq(X2,X3) )
=> geq(X1,X3) ) ) ) ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_22,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_23,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( rearsegP(X1,X2)
& rearsegP(X2,X3) )
=> rearsegP(X1,X3) ) ) ) ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_24,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X3) )
=> frontsegP(X1,X3) ) ) ) ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_25,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( lt(X1,X2)
& lt(X2,X3) )
=> lt(X1,X3) ) ) ) ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_26,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( leq(X1,X2)
& leq(X2,X3) )
=> leq(X1,X3) ) ) ) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_27,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_28,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_29,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_30,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_31,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_32,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_33,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_34,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X2,X1) )
=> X1 = X2 ) ) ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_35,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_36,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X2,X1) )
=> X1 = X2 ) ) ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_37,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X1) )
=> X1 = X2 ) ) ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_38,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X2,X1) )
=> X1 = X2 ) ) ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_39,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( gt(X1,X2)
=> ~ gt(X2,X1) ) ) ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_40,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_41,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( X1 != X2
& leq(X1,X2) ) ) ) ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_42,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( leq(X1,X2)
=> ( X1 = X2
| lt(X1,X2) ) ) ) ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_43,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( gt(X1,X2)
<=> lt(X2,X1) ) ) ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_44,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( geq(X1,X2)
<=> leq(X2,X1) ) ) ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_45,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_46,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( ( nil != X2
& nil != X1
& hd(X2) = hd(X1)
& tl(X2) = tl(X1) )
=> X2 = X1 ) ) ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_47,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_48,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_49,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_50,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_51,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_52,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_53,axiom,
! [X1] :
( lhs_atom2(X1)
| ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_54,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_55,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_56,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_57,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_58,axiom,
! [X1] :
( lhs_atom2(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_59,axiom,
! [X1] :
( lhs_atom1(X1)
| equalelemsP(cons(X1,nil)) ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_60,axiom,
! [X1] :
( lhs_atom1(X1)
| duplicatefreeP(cons(X1,nil)) ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_61,axiom,
! [X1] :
( lhs_atom1(X1)
| strictorderedP(cons(X1,nil)) ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_62,axiom,
! [X1] :
( lhs_atom1(X1)
| totalorderedP(cons(X1,nil)) ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_63,axiom,
! [X1] :
( lhs_atom1(X1)
| strictorderP(cons(X1,nil)) ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_64,axiom,
! [X1] :
( lhs_atom1(X1)
| totalorderP(cons(X1,nil)) ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_65,axiom,
! [X1] :
( lhs_atom1(X1)
| cyclefreeP(cons(X1,nil)) ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_66,axiom,
! [X1] :
( lhs_atom1(X1)
| ~ lt(X1,X1) ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_67,axiom,
! [X1] :
( lhs_atom2(X1)
| ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_68,axiom,
! [X1] :
( lhs_atom2(X1)
| ( rearsegP(nil,X1)
<=> nil = X1 ) ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_69,axiom,
! [X1] :
( lhs_atom2(X1)
| ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_70,axiom,
! [X1] :
( lhs_atom1(X1)
| ~ memberP(nil,X1) ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_71,axiom,
! [X1] :
( lhs_atom1(X1)
| geq(X1,X1) ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_72,axiom,
! [X1] :
( lhs_atom2(X1)
| segmentP(X1,X1) ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_73,axiom,
! [X1] :
( lhs_atom2(X1)
| rearsegP(X1,X1) ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_74,axiom,
! [X1] :
( lhs_atom2(X1)
| frontsegP(X1,X1) ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_75,axiom,
! [X1] :
( lhs_atom1(X1)
| leq(X1,X1) ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_76,axiom,
! [X1] :
( lhs_atom2(X1)
| app(X1,nil) = X1 ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_77,axiom,
! [X1] :
( lhs_atom2(X1)
| app(nil,X1) = X1 ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_78,axiom,
! [X1] :
( lhs_atom2(X1)
| segmentP(X1,nil) ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_79,axiom,
! [X1] :
( lhs_atom2(X1)
| rearsegP(X1,nil) ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_80,axiom,
! [X1] :
( lhs_atom2(X1)
| frontsegP(X1,nil) ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_81,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> ? [X2] :
( ssList(X2)
& tl(X1) = X2 ) ) ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_82,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> ? [X2] :
( ssItem(X2)
& hd(X1) = X2 ) ) ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_83,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> ssList(tl(X1)) ) ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_84,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> ssItem(hd(X1)) ) ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_85,axiom,
( lhs_atom11
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_86,axiom,
( lhs_atom10
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_87,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_88,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_89,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_90,axiom,
( lhs_atom6
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_91,axiom,
( lhs_atom5
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_92,axiom,
( lhs_atom4
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_93,axiom,
( lhs_atom3
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_94,axiom,
! [X1] :
( lhs_atom2(X1)
| ( cyclefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ~ ( leq(X2,X3)
& leq(X3,X2) ) ) ) ) ) ) ) ) ),
c_0_0 ).
fof(c_0_95,axiom,
! [X1] :
( lhs_atom2(X1)
| ( strictorderP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ( lt(X2,X3)
| lt(X3,X2) ) ) ) ) ) ) ) ) ),
c_0_1 ).
fof(c_0_96,axiom,
! [X1] :
( lhs_atom2(X1)
| ( totalorderP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ( leq(X2,X3)
| leq(X3,X2) ) ) ) ) ) ) ) ) ),
c_0_2 ).
fof(c_0_97,axiom,
! [X1] :
( lhs_atom2(X1)
| ( strictorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> lt(X2,X3) ) ) ) ) ) ) ) ),
c_0_3 ).
fof(c_0_98,axiom,
! [X1] :
( lhs_atom2(X1)
| ( totalorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> leq(X2,X3) ) ) ) ) ) ) ) ),
c_0_4 ).
fof(c_0_99,axiom,
! [X1] :
( lhs_atom2(X1)
| ( duplicatefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> X2 != X3 ) ) ) ) ) ) ) ),
c_0_5 ).
fof(c_0_100,axiom,
! [X1] :
( lhs_atom2(X1)
| ( equalelemsP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X4,cons(X2,cons(X3,X5))) = X1
=> X2 = X3 ) ) ) ) ) ) ),
c_0_6 ).
fof(c_0_101,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
c_0_7 ).
fof(c_0_102,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
c_0_8 ).
fof(c_0_103,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
c_0_9 ).
fof(c_0_104,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
c_0_10 ).
fof(c_0_105,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
c_0_11 ).
fof(c_0_106,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
c_0_12 ).
fof(c_0_107,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
c_0_13 ).
fof(c_0_108,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
c_0_14 ).
fof(c_0_109,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssList(X2)
=> ( strictorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& strictorderedP(X2)
& lt(X1,hd(X2)) ) ) ) ) ),
c_0_15 ).
fof(c_0_110,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssList(X2)
=> ( totalorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& totalorderedP(X2)
& leq(X1,hd(X2)) ) ) ) ) ),
c_0_16 ).
fof(c_0_111,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
c_0_17 ).
fof(c_0_112,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
c_0_18 ).
fof(c_0_113,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( gt(X1,X2)
& gt(X2,X3) )
=> gt(X1,X3) ) ) ) ),
c_0_19 ).
fof(c_0_114,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( leq(X1,X2)
& lt(X2,X3) )
=> lt(X1,X3) ) ) ) ),
c_0_20 ).
fof(c_0_115,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( geq(X1,X2)
& geq(X2,X3) )
=> geq(X1,X3) ) ) ) ),
c_0_21 ).
fof(c_0_116,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
c_0_22 ).
fof(c_0_117,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( rearsegP(X1,X2)
& rearsegP(X2,X3) )
=> rearsegP(X1,X3) ) ) ) ),
c_0_23 ).
fof(c_0_118,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X3) )
=> frontsegP(X1,X3) ) ) ) ),
c_0_24 ).
fof(c_0_119,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( lt(X1,X2)
& lt(X2,X3) )
=> lt(X1,X3) ) ) ) ),
c_0_25 ).
fof(c_0_120,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( leq(X1,X2)
& leq(X2,X3) )
=> leq(X1,X3) ) ) ) ),
c_0_26 ).
fof(c_0_121,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
c_0_27 ).
fof(c_0_122,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
c_0_28 ).
fof(c_0_123,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
c_0_29 ).
fof(c_0_124,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
c_0_30 ).
fof(c_0_125,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
c_0_31 ).
fof(c_0_126,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
c_0_32 ).
fof(c_0_127,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
c_0_33 ).
fof(c_0_128,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X2,X1) )
=> X1 = X2 ) ) ),
c_0_34 ).
fof(c_0_129,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
c_0_35 ).
fof(c_0_130,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X2,X1) )
=> X1 = X2 ) ) ),
c_0_36 ).
fof(c_0_131,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X1) )
=> X1 = X2 ) ) ),
c_0_37 ).
fof(c_0_132,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X2,X1) )
=> X1 = X2 ) ) ),
c_0_38 ).
fof(c_0_133,plain,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( gt(X1,X2)
=> ~ gt(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_134,plain,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_135,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( X1 != X2
& leq(X1,X2) ) ) ) ),
c_0_41 ).
fof(c_0_136,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( leq(X1,X2)
=> ( X1 = X2
| lt(X1,X2) ) ) ) ),
c_0_42 ).
fof(c_0_137,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( gt(X1,X2)
<=> lt(X2,X1) ) ) ),
c_0_43 ).
fof(c_0_138,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( geq(X1,X2)
<=> leq(X2,X1) ) ) ),
c_0_44 ).
fof(c_0_139,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
c_0_45 ).
fof(c_0_140,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( ( nil != X2
& nil != X1
& hd(X2) = hd(X1)
& tl(X2) = tl(X1) )
=> X2 = X1 ) ) ),
c_0_46 ).
fof(c_0_141,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
c_0_47 ).
fof(c_0_142,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
c_0_48 ).
fof(c_0_143,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
c_0_49 ).
fof(c_0_144,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
c_0_50 ).
fof(c_0_145,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
c_0_51 ).
fof(c_0_146,axiom,
! [X1] :
( lhs_atom1(X1)
| ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
c_0_52 ).
fof(c_0_147,axiom,
! [X1] :
( lhs_atom2(X1)
| ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
c_0_53 ).
fof(c_0_148,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
c_0_54 ).
fof(c_0_149,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
c_0_55 ).
fof(c_0_150,axiom,
! [X1] :
( lhs_atom2(X1)
| ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
c_0_56 ).
fof(c_0_151,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
c_0_57 ).
fof(c_0_152,axiom,
! [X1] :
( lhs_atom2(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
c_0_58 ).
fof(c_0_153,axiom,
! [X1] :
( lhs_atom1(X1)
| equalelemsP(cons(X1,nil)) ),
c_0_59 ).
fof(c_0_154,axiom,
! [X1] :
( lhs_atom1(X1)
| duplicatefreeP(cons(X1,nil)) ),
c_0_60 ).
fof(c_0_155,axiom,
! [X1] :
( lhs_atom1(X1)
| strictorderedP(cons(X1,nil)) ),
c_0_61 ).
fof(c_0_156,axiom,
! [X1] :
( lhs_atom1(X1)
| totalorderedP(cons(X1,nil)) ),
c_0_62 ).
fof(c_0_157,axiom,
! [X1] :
( lhs_atom1(X1)
| strictorderP(cons(X1,nil)) ),
c_0_63 ).
fof(c_0_158,axiom,
! [X1] :
( lhs_atom1(X1)
| totalorderP(cons(X1,nil)) ),
c_0_64 ).
fof(c_0_159,axiom,
! [X1] :
( lhs_atom1(X1)
| cyclefreeP(cons(X1,nil)) ),
c_0_65 ).
fof(c_0_160,plain,
! [X1] :
( lhs_atom1(X1)
| ~ lt(X1,X1) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_161,axiom,
! [X1] :
( lhs_atom2(X1)
| ( segmentP(nil,X1)
<=> nil = X1 ) ),
c_0_67 ).
fof(c_0_162,axiom,
! [X1] :
( lhs_atom2(X1)
| ( rearsegP(nil,X1)
<=> nil = X1 ) ),
c_0_68 ).
fof(c_0_163,axiom,
! [X1] :
( lhs_atom2(X1)
| ( frontsegP(nil,X1)
<=> nil = X1 ) ),
c_0_69 ).
fof(c_0_164,plain,
! [X1] :
( lhs_atom1(X1)
| ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_165,axiom,
! [X1] :
( lhs_atom1(X1)
| geq(X1,X1) ),
c_0_71 ).
fof(c_0_166,axiom,
! [X1] :
( lhs_atom2(X1)
| segmentP(X1,X1) ),
c_0_72 ).
fof(c_0_167,axiom,
! [X1] :
( lhs_atom2(X1)
| rearsegP(X1,X1) ),
c_0_73 ).
fof(c_0_168,axiom,
! [X1] :
( lhs_atom2(X1)
| frontsegP(X1,X1) ),
c_0_74 ).
fof(c_0_169,axiom,
! [X1] :
( lhs_atom1(X1)
| leq(X1,X1) ),
c_0_75 ).
fof(c_0_170,axiom,
! [X1] :
( lhs_atom2(X1)
| app(X1,nil) = X1 ),
c_0_76 ).
fof(c_0_171,axiom,
! [X1] :
( lhs_atom2(X1)
| app(nil,X1) = X1 ),
c_0_77 ).
fof(c_0_172,axiom,
! [X1] :
( lhs_atom2(X1)
| segmentP(X1,nil) ),
c_0_78 ).
fof(c_0_173,axiom,
! [X1] :
( lhs_atom2(X1)
| rearsegP(X1,nil) ),
c_0_79 ).
fof(c_0_174,axiom,
! [X1] :
( lhs_atom2(X1)
| frontsegP(X1,nil) ),
c_0_80 ).
fof(c_0_175,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> ? [X2] :
( ssList(X2)
& tl(X1) = X2 ) ) ),
c_0_81 ).
fof(c_0_176,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> ? [X2] :
( ssItem(X2)
& hd(X1) = X2 ) ) ),
c_0_82 ).
fof(c_0_177,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> ssList(tl(X1)) ) ),
c_0_83 ).
fof(c_0_178,axiom,
! [X1] :
( lhs_atom2(X1)
| ( nil != X1
=> ssItem(hd(X1)) ) ),
c_0_84 ).
fof(c_0_179,plain,
lhs_atom11,
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_180,plain,
lhs_atom10,
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_181,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_182,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_183,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_184,plain,
lhs_atom6,
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_185,plain,
lhs_atom5,
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_186,plain,
lhs_atom4,
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_187,plain,
lhs_atom3,
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_188,plain,
! [X7,X8,X9,X10,X11,X12] :
( ( ~ cyclefreeP(X7)
| ~ ssItem(X8)
| ~ ssItem(X9)
| ~ ssList(X10)
| ~ ssList(X11)
| ~ ssList(X12)
| app(app(X10,cons(X8,X11)),cons(X9,X12)) != X7
| ~ leq(X8,X9)
| ~ leq(X9,X8)
| lhs_atom2(X7) )
& ( ssItem(esk8_1(X7))
| cyclefreeP(X7)
| lhs_atom2(X7) )
& ( ssItem(esk9_1(X7))
| cyclefreeP(X7)
| lhs_atom2(X7) )
& ( ssList(esk10_1(X7))
| cyclefreeP(X7)
| lhs_atom2(X7) )
& ( ssList(esk11_1(X7))
| cyclefreeP(X7)
| lhs_atom2(X7) )
& ( ssList(esk12_1(X7))
| cyclefreeP(X7)
| lhs_atom2(X7) )
& ( app(app(esk10_1(X7),cons(esk8_1(X7),esk11_1(X7))),cons(esk9_1(X7),esk12_1(X7))) = X7
| cyclefreeP(X7)
| lhs_atom2(X7) )
& ( leq(esk8_1(X7),esk9_1(X7))
| cyclefreeP(X7)
| lhs_atom2(X7) )
& ( leq(esk9_1(X7),esk8_1(X7))
| cyclefreeP(X7)
| lhs_atom2(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])])])]) ).
fof(c_0_189,plain,
! [X7,X8,X9,X10,X11,X12] :
( ( ~ strictorderP(X7)
| ~ ssItem(X8)
| ~ ssItem(X9)
| ~ ssList(X10)
| ~ ssList(X11)
| ~ ssList(X12)
| app(app(X10,cons(X8,X11)),cons(X9,X12)) != X7
| lt(X8,X9)
| lt(X9,X8)
| lhs_atom2(X7) )
& ( ssItem(esk18_1(X7))
| strictorderP(X7)
| lhs_atom2(X7) )
& ( ssItem(esk19_1(X7))
| strictorderP(X7)
| lhs_atom2(X7) )
& ( ssList(esk20_1(X7))
| strictorderP(X7)
| lhs_atom2(X7) )
& ( ssList(esk21_1(X7))
| strictorderP(X7)
| lhs_atom2(X7) )
& ( ssList(esk22_1(X7))
| strictorderP(X7)
| lhs_atom2(X7) )
& ( app(app(esk20_1(X7),cons(esk18_1(X7),esk21_1(X7))),cons(esk19_1(X7),esk22_1(X7))) = X7
| strictorderP(X7)
| lhs_atom2(X7) )
& ( ~ lt(esk18_1(X7),esk19_1(X7))
| strictorderP(X7)
| lhs_atom2(X7) )
& ( ~ lt(esk19_1(X7),esk18_1(X7))
| strictorderP(X7)
| lhs_atom2(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])])])]) ).
fof(c_0_190,plain,
! [X7,X8,X9,X10,X11,X12] :
( ( ~ totalorderP(X7)
| ~ ssItem(X8)
| ~ ssItem(X9)
| ~ ssList(X10)
| ~ ssList(X11)
| ~ ssList(X12)
| app(app(X10,cons(X8,X11)),cons(X9,X12)) != X7
| leq(X8,X9)
| leq(X9,X8)
| lhs_atom2(X7) )
& ( ssItem(esk13_1(X7))
| totalorderP(X7)
| lhs_atom2(X7) )
& ( ssItem(esk14_1(X7))
| totalorderP(X7)
| lhs_atom2(X7) )
& ( ssList(esk15_1(X7))
| totalorderP(X7)
| lhs_atom2(X7) )
& ( ssList(esk16_1(X7))
| totalorderP(X7)
| lhs_atom2(X7) )
& ( ssList(esk17_1(X7))
| totalorderP(X7)
| lhs_atom2(X7) )
& ( app(app(esk15_1(X7),cons(esk13_1(X7),esk16_1(X7))),cons(esk14_1(X7),esk17_1(X7))) = X7
| totalorderP(X7)
| lhs_atom2(X7) )
& ( ~ leq(esk13_1(X7),esk14_1(X7))
| totalorderP(X7)
| lhs_atom2(X7) )
& ( ~ leq(esk14_1(X7),esk13_1(X7))
| totalorderP(X7)
| lhs_atom2(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])])])]) ).
fof(c_0_191,plain,
! [X7,X8,X9,X10,X11,X12] :
( ( ~ strictorderedP(X7)
| ~ ssItem(X8)
| ~ ssItem(X9)
| ~ ssList(X10)
| ~ ssList(X11)
| ~ ssList(X12)
| app(app(X10,cons(X8,X11)),cons(X9,X12)) != X7
| lt(X8,X9)
| lhs_atom2(X7) )
& ( ssItem(esk28_1(X7))
| strictorderedP(X7)
| lhs_atom2(X7) )
& ( ssItem(esk29_1(X7))
| strictorderedP(X7)
| lhs_atom2(X7) )
& ( ssList(esk30_1(X7))
| strictorderedP(X7)
| lhs_atom2(X7) )
& ( ssList(esk31_1(X7))
| strictorderedP(X7)
| lhs_atom2(X7) )
& ( ssList(esk32_1(X7))
| strictorderedP(X7)
| lhs_atom2(X7) )
& ( app(app(esk30_1(X7),cons(esk28_1(X7),esk31_1(X7))),cons(esk29_1(X7),esk32_1(X7))) = X7
| strictorderedP(X7)
| lhs_atom2(X7) )
& ( ~ lt(esk28_1(X7),esk29_1(X7))
| strictorderedP(X7)
| lhs_atom2(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])])])]) ).
fof(c_0_192,plain,
! [X7,X8,X9,X10,X11,X12] :
( ( ~ totalorderedP(X7)
| ~ ssItem(X8)
| ~ ssItem(X9)
| ~ ssList(X10)
| ~ ssList(X11)
| ~ ssList(X12)
| app(app(X10,cons(X8,X11)),cons(X9,X12)) != X7
| leq(X8,X9)
| lhs_atom2(X7) )
& ( ssItem(esk23_1(X7))
| totalorderedP(X7)
| lhs_atom2(X7) )
& ( ssItem(esk24_1(X7))
| totalorderedP(X7)
| lhs_atom2(X7) )
& ( ssList(esk25_1(X7))
| totalorderedP(X7)
| lhs_atom2(X7) )
& ( ssList(esk26_1(X7))
| totalorderedP(X7)
| lhs_atom2(X7) )
& ( ssList(esk27_1(X7))
| totalorderedP(X7)
| lhs_atom2(X7) )
& ( app(app(esk25_1(X7),cons(esk23_1(X7),esk26_1(X7))),cons(esk24_1(X7),esk27_1(X7))) = X7
| totalorderedP(X7)
| lhs_atom2(X7) )
& ( ~ leq(esk23_1(X7),esk24_1(X7))
| totalorderedP(X7)
| lhs_atom2(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])])])])]) ).
fof(c_0_193,plain,
! [X7,X8,X9,X10,X11,X12] :
( ( ~ duplicatefreeP(X7)
| ~ ssItem(X8)
| ~ ssItem(X9)
| ~ ssList(X10)
| ~ ssList(X11)
| ~ ssList(X12)
| app(app(X10,cons(X8,X11)),cons(X9,X12)) != X7
| X8 != X9
| lhs_atom2(X7) )
& ( ssItem(esk33_1(X7))
| duplicatefreeP(X7)
| lhs_atom2(X7) )
& ( ssItem(esk34_1(X7))
| duplicatefreeP(X7)
| lhs_atom2(X7) )
& ( ssList(esk35_1(X7))
| duplicatefreeP(X7)
| lhs_atom2(X7) )
& ( ssList(esk36_1(X7))
| duplicatefreeP(X7)
| lhs_atom2(X7) )
& ( ssList(esk37_1(X7))
| duplicatefreeP(X7)
| lhs_atom2(X7) )
& ( app(app(esk35_1(X7),cons(esk33_1(X7),esk36_1(X7))),cons(esk34_1(X7),esk37_1(X7))) = X7
| duplicatefreeP(X7)
| lhs_atom2(X7) )
& ( esk33_1(X7) = esk34_1(X7)
| duplicatefreeP(X7)
| lhs_atom2(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_99])])])])]) ).
fof(c_0_194,plain,
! [X6,X7,X8,X9,X10] :
( ( ~ equalelemsP(X6)
| ~ ssItem(X7)
| ~ ssItem(X8)
| ~ ssList(X9)
| ~ ssList(X10)
| app(X9,cons(X7,cons(X8,X10))) != X6
| X7 = X8
| lhs_atom2(X6) )
& ( ssItem(esk38_1(X6))
| equalelemsP(X6)
| lhs_atom2(X6) )
& ( ssItem(esk39_1(X6))
| equalelemsP(X6)
| lhs_atom2(X6) )
& ( ssList(esk40_1(X6))
| equalelemsP(X6)
| lhs_atom2(X6) )
& ( ssList(esk41_1(X6))
| equalelemsP(X6)
| lhs_atom2(X6) )
& ( app(esk40_1(X6),cons(esk38_1(X6),cons(esk39_1(X6),esk41_1(X6)))) = X6
| equalelemsP(X6)
| lhs_atom2(X6) )
& ( esk38_1(X6) != esk39_1(X6)
| equalelemsP(X6)
| lhs_atom2(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])])])]) ).
fof(c_0_195,plain,
! [X5,X6,X9,X10] :
( ( ssList(esk6_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| lhs_atom2(X5) )
& ( ssList(esk7_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| lhs_atom2(X5) )
& ( app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| lhs_atom2(X5) )
& ( ~ ssList(X9)
| ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| segmentP(X5,X6)
| ~ ssList(X6)
| lhs_atom2(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_101])])])])]) ).
fof(c_0_196,plain,
! [X5,X6,X9,X10] :
( ( ssList(esk1_2(X5,X6))
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| lhs_atom2(X5) )
& ( ssList(esk2_2(X5,X6))
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| lhs_atom2(X5) )
& ( app(esk1_2(X5,X6),cons(X6,esk2_2(X5,X6))) = X5
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| lhs_atom2(X5) )
& ( ~ ssList(X9)
| ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5
| memberP(X5,X6)
| ~ ssItem(X6)
| lhs_atom2(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_102])])])])]) ).
fof(c_0_197,plain,
! [X5,X6,X7,X8] :
( ( X5 = X6
| ~ frontsegP(cons(X5,X7),cons(X6,X8))
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| lhs_atom1(X5) )
& ( frontsegP(X7,X8)
| ~ frontsegP(cons(X5,X7),cons(X6,X8))
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| lhs_atom1(X5) )
& ( X5 != X6
| ~ frontsegP(X7,X8)
| frontsegP(cons(X5,X7),cons(X6,X8))
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| lhs_atom1(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_103])])])]) ).
fof(c_0_198,plain,
! [X5,X6,X7,X8] :
( lhs_atom2(X5)
| ~ ssList(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_104])])]) ).
fof(c_0_199,plain,
! [X4,X5,X6] :
( ( ~ memberP(app(X5,X6),X4)
| memberP(X5,X4)
| memberP(X6,X4)
| ~ ssList(X6)
| ~ ssList(X5)
| lhs_atom1(X4) )
& ( ~ memberP(X5,X4)
| memberP(app(X5,X6),X4)
| ~ ssList(X6)
| ~ ssList(X5)
| lhs_atom1(X4) )
& ( ~ memberP(X6,X4)
| memberP(app(X5,X6),X4)
| ~ ssList(X6)
| ~ ssList(X5)
| lhs_atom1(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_105])])])]) ).
fof(c_0_200,plain,
! [X4,X5,X6] :
( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| lhs_atom1(X4) )
& ( X4 != X5
| memberP(cons(X5,X6),X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| lhs_atom1(X4) )
& ( ~ memberP(X6,X4)
| memberP(cons(X5,X6),X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| lhs_atom1(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_106])])])]) ).
fof(c_0_201,plain,
! [X4,X5,X6] :
( lhs_atom2(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) = app(X4,app(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])])]) ).
fof(c_0_202,plain,
! [X4,X5,X6] :
( lhs_atom2(X4)
| ~ ssList(X5)
| ~ ssItem(X6)
| cons(X6,app(X5,X4)) = app(cons(X6,X5),X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])])]) ).
fof(c_0_203,plain,
! [X3,X4] :
( ( nil != X4
| nil = X4
| ~ strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) )
& ( strictorderedP(X4)
| nil = X4
| ~ strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) )
& ( lt(X3,hd(X4))
| nil = X4
| ~ strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) )
& ( nil != X4
| strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) )
& ( nil = X4
| ~ strictorderedP(X4)
| ~ lt(X3,hd(X4))
| strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_109])])])]) ).
fof(c_0_204,plain,
! [X3,X4] :
( ( nil != X4
| nil = X4
| ~ totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) )
& ( totalorderedP(X4)
| nil = X4
| ~ totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) )
& ( leq(X3,hd(X4))
| nil = X4
| ~ totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) )
& ( nil != X4
| totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) )
& ( nil = X4
| ~ totalorderedP(X4)
| ~ leq(X3,hd(X4))
| totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| lhs_atom1(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_110])])])]) ).
fof(c_0_205,plain,
! [X4,X5,X6] :
( lhs_atom2(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ rearsegP(X4,X5)
| rearsegP(app(X6,X4),X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_111])])]) ).
fof(c_0_206,plain,
! [X4,X5,X6] :
( lhs_atom2(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ frontsegP(X4,X5)
| frontsegP(app(X4,X6),X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_112])])]) ).
fof(c_0_207,plain,
! [X4,X5,X6] :
( lhs_atom1(X4)
| ~ ssItem(X5)
| ~ ssItem(X6)
| ~ gt(X4,X5)
| ~ gt(X5,X6)
| gt(X4,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_113])])]) ).
fof(c_0_208,plain,
! [X4,X5,X6] :
( lhs_atom1(X4)
| ~ ssItem(X5)
| ~ ssItem(X6)
| ~ leq(X4,X5)
| ~ lt(X5,X6)
| lt(X4,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_114])])]) ).
fof(c_0_209,plain,
! [X4,X5,X6] :
( lhs_atom1(X4)
| ~ ssItem(X5)
| ~ ssItem(X6)
| ~ geq(X4,X5)
| ~ geq(X5,X6)
| geq(X4,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_115])])]) ).
fof(c_0_210,plain,
! [X4,X5,X6] :
( lhs_atom2(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_116])])]) ).
fof(c_0_211,plain,
! [X4,X5,X6] :
( lhs_atom2(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ rearsegP(X4,X5)
| ~ rearsegP(X5,X6)
| rearsegP(X4,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_117])])]) ).
fof(c_0_212,plain,
! [X4,X5,X6] :
( lhs_atom2(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ frontsegP(X4,X5)
| ~ frontsegP(X5,X6)
| frontsegP(X4,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_118])])]) ).
fof(c_0_213,plain,
! [X4,X5,X6] :
( lhs_atom1(X4)
| ~ ssItem(X5)
| ~ ssItem(X6)
| ~ lt(X4,X5)
| ~ lt(X5,X6)
| lt(X4,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])]) ).
fof(c_0_214,plain,
! [X4,X5,X6] :
( lhs_atom1(X4)
| ~ ssItem(X5)
| ~ ssItem(X6)
| ~ leq(X4,X5)
| ~ leq(X5,X6)
| leq(X4,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])])]) ).
fof(c_0_215,plain,
! [X4,X5,X7] :
( ( ssList(esk5_2(X4,X5))
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| lhs_atom2(X4) )
& ( app(esk5_2(X4,X5),X5) = X4
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| lhs_atom2(X4) )
& ( ~ ssList(X7)
| app(X7,X5) != X4
| rearsegP(X4,X5)
| ~ ssList(X5)
| lhs_atom2(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_121])])])])]) ).
fof(c_0_216,plain,
! [X4,X5,X7] :
( ( ssList(esk4_2(X4,X5))
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| lhs_atom2(X4) )
& ( app(X5,esk4_2(X4,X5)) = X4
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| lhs_atom2(X4) )
& ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5)
| ~ ssList(X5)
| lhs_atom2(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_122])])])])]) ).
fof(c_0_217,plain,
! [X5,X6,X7,X8] :
( ( X7 = X8
| cons(X7,X5) != cons(X8,X6)
| ~ ssItem(X8)
| ~ ssItem(X7)
| ~ ssList(X6)
| lhs_atom2(X5) )
& ( X6 = X5
| cons(X7,X5) != cons(X8,X6)
| ~ ssItem(X8)
| ~ ssItem(X7)
| ~ ssList(X6)
| lhs_atom2(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_123])])])]) ).
fof(c_0_218,plain,
! [X4,X5,X6] :
( lhs_atom2(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(X5,X6) != app(X5,X4)
| X6 = X4 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_124])])]) ).
fof(c_0_219,plain,
! [X4,X5,X6] :
( lhs_atom2(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(X6,X5) != app(X4,X5)
| X6 = X4 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])])]) ).
fof(c_0_220,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssList(X4)
| nil = X3
| tl(app(X3,X4)) = app(tl(X3),X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])]) ).
fof(c_0_221,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])])]) ).
fof(c_0_222,plain,
! [X3,X4] :
( lhs_atom1(X3)
| ~ ssItem(X4)
| ~ geq(X3,X4)
| ~ geq(X4,X3)
| X3 = X4 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])])]) ).
fof(c_0_223,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssList(X4)
| ~ segmentP(X3,X4)
| ~ segmentP(X4,X3)
| X3 = X4 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])])]) ).
fof(c_0_224,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssList(X4)
| ~ rearsegP(X3,X4)
| ~ rearsegP(X4,X3)
| X3 = X4 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])])]) ).
fof(c_0_225,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssList(X4)
| ~ frontsegP(X3,X4)
| ~ frontsegP(X4,X3)
| X3 = X4 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])])]) ).
fof(c_0_226,plain,
! [X3,X4] :
( lhs_atom1(X3)
| ~ ssItem(X4)
| ~ leq(X3,X4)
| ~ leq(X4,X3)
| X3 = X4 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])])]) ).
fof(c_0_227,plain,
! [X3,X4] :
( lhs_atom1(X3)
| ~ ssItem(X4)
| ~ gt(X3,X4)
| ~ gt(X4,X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_133])])]) ).
fof(c_0_228,plain,
! [X3,X4] :
( lhs_atom1(X3)
| ~ ssItem(X4)
| ~ lt(X3,X4)
| ~ lt(X4,X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_134])])]) ).
fof(c_0_229,plain,
! [X3,X4] :
( ( X3 != X4
| ~ lt(X3,X4)
| ~ ssItem(X4)
| lhs_atom1(X3) )
& ( leq(X3,X4)
| ~ lt(X3,X4)
| ~ ssItem(X4)
| lhs_atom1(X3) )
& ( X3 = X4
| ~ leq(X3,X4)
| lt(X3,X4)
| ~ ssItem(X4)
| lhs_atom1(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])])])]) ).
fof(c_0_230,plain,
! [X3,X4] :
( lhs_atom1(X3)
| ~ ssItem(X4)
| ~ leq(X3,X4)
| X3 = X4
| lt(X3,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_136])])]) ).
fof(c_0_231,plain,
! [X3,X4] :
( ( ~ gt(X3,X4)
| lt(X4,X3)
| ~ ssItem(X4)
| lhs_atom1(X3) )
& ( ~ lt(X4,X3)
| gt(X3,X4)
| ~ ssItem(X4)
| lhs_atom1(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])])])]) ).
fof(c_0_232,plain,
! [X3,X4] :
( ( ~ geq(X3,X4)
| leq(X4,X3)
| ~ ssItem(X4)
| lhs_atom1(X3) )
& ( ~ leq(X4,X3)
| geq(X3,X4)
| ~ ssItem(X4)
| lhs_atom1(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_138])])])]) ).
fof(c_0_233,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssList(X4)
| nil = X3
| hd(app(X3,X4)) = hd(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_139])])]) ).
fof(c_0_234,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssList(X4)
| nil = X4
| nil = X3
| hd(X4) != hd(X3)
| tl(X4) != tl(X3)
| X4 = X3 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_140])])]) ).
fof(c_0_235,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssItem(X4)
| tl(cons(X4,X3)) = X3 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_141])])]) ).
fof(c_0_236,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssItem(X4)
| hd(cons(X4,X3)) = X4 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_142])])]) ).
fof(c_0_237,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssList(X4)
| ssList(app(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])])]) ).
fof(c_0_238,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssItem(X4)
| ssList(cons(X4,X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_144])])]) ).
fof(c_0_239,plain,
! [X3,X4] :
( ( ~ neq(X3,X4)
| X3 != X4
| ~ ssList(X4)
| lhs_atom2(X3) )
& ( X3 = X4
| neq(X3,X4)
| ~ ssList(X4)
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_145])])])]) ).
fof(c_0_240,plain,
! [X3,X4] :
( ( ~ neq(X3,X4)
| X3 != X4
| ~ ssItem(X4)
| lhs_atom1(X3) )
& ( X3 = X4
| neq(X3,X4)
| ~ ssItem(X4)
| lhs_atom1(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])])])]) ).
fof(c_0_241,plain,
! [X3,X5] :
( ( ssItem(esk3_1(X3))
| ~ singletonP(X3)
| lhs_atom2(X3) )
& ( cons(esk3_1(X3),nil) = X3
| ~ singletonP(X3)
| lhs_atom2(X3) )
& ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3)
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_147])])])])]) ).
fof(c_0_242,plain,
! [X3,X4] :
( ( nil = X4
| nil != app(X3,X4)
| ~ ssList(X4)
| lhs_atom2(X3) )
& ( nil = X3
| nil != app(X3,X4)
| ~ ssList(X4)
| lhs_atom2(X3) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4)
| ~ ssList(X4)
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_148])])])]) ).
fof(c_0_243,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssItem(X4)
| cons(X4,X3) != X3 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])]) ).
fof(c_0_244,plain,
! [X3,X4] :
( lhs_atom2(X3)
| ~ ssItem(X4)
| nil != cons(X4,X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_150])])]) ).
fof(c_0_245,plain,
! [X2] :
( lhs_atom2(X2)
| nil = X2
| cons(hd(X2),tl(X2)) = X2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_151])]) ).
fof(c_0_246,plain,
! [X4] :
( ( ssList(esk42_1(X4))
| nil = X4
| lhs_atom2(X4) )
& ( ssItem(esk43_1(X4))
| nil = X4
| lhs_atom2(X4) )
& ( cons(esk43_1(X4),esk42_1(X4)) = X4
| nil = X4
| lhs_atom2(X4) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_152])])]) ).
fof(c_0_247,plain,
! [X2] :
( lhs_atom1(X2)
| equalelemsP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[c_0_153]) ).
fof(c_0_248,plain,
! [X2] :
( lhs_atom1(X2)
| duplicatefreeP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[c_0_154]) ).
fof(c_0_249,plain,
! [X2] :
( lhs_atom1(X2)
| strictorderedP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[c_0_155]) ).
fof(c_0_250,plain,
! [X2] :
( lhs_atom1(X2)
| totalorderedP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[c_0_156]) ).
fof(c_0_251,plain,
! [X2] :
( lhs_atom1(X2)
| strictorderP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[c_0_157]) ).
fof(c_0_252,plain,
! [X2] :
( lhs_atom1(X2)
| totalorderP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[c_0_158]) ).
fof(c_0_253,plain,
! [X2] :
( lhs_atom1(X2)
| cyclefreeP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[c_0_159]) ).
fof(c_0_254,plain,
! [X2] :
( lhs_atom1(X2)
| ~ lt(X2,X2) ),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_255,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| lhs_atom2(X2) )
& ( nil != X2
| segmentP(nil,X2)
| lhs_atom2(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_161])])]) ).
fof(c_0_256,plain,
! [X2] :
( ( ~ rearsegP(nil,X2)
| nil = X2
| lhs_atom2(X2) )
& ( nil != X2
| rearsegP(nil,X2)
| lhs_atom2(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])])]) ).
fof(c_0_257,plain,
! [X2] :
( ( ~ frontsegP(nil,X2)
| nil = X2
| lhs_atom2(X2) )
& ( nil != X2
| frontsegP(nil,X2)
| lhs_atom2(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])])]) ).
fof(c_0_258,plain,
! [X2] :
( lhs_atom1(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[c_0_164]) ).
fof(c_0_259,plain,
! [X2] :
( lhs_atom1(X2)
| geq(X2,X2) ),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_260,plain,
! [X2] :
( lhs_atom2(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_261,plain,
! [X2] :
( lhs_atom2(X2)
| rearsegP(X2,X2) ),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_262,plain,
! [X2] :
( lhs_atom2(X2)
| frontsegP(X2,X2) ),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_263,plain,
! [X2] :
( lhs_atom1(X2)
| leq(X2,X2) ),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_264,plain,
! [X2] :
( lhs_atom2(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_265,plain,
! [X2] :
( lhs_atom2(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_266,plain,
! [X2] :
( lhs_atom2(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_267,plain,
! [X2] :
( lhs_atom2(X2)
| rearsegP(X2,nil) ),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_268,plain,
! [X2] :
( lhs_atom2(X2)
| frontsegP(X2,nil) ),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_269,plain,
! [X3] :
( ( ssList(esk45_1(X3))
| nil = X3
| lhs_atom2(X3) )
& ( tl(X3) = esk45_1(X3)
| nil = X3
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_175])])])]) ).
fof(c_0_270,plain,
! [X3] :
( ( ssItem(esk44_1(X3))
| nil = X3
| lhs_atom2(X3) )
& ( hd(X3) = esk44_1(X3)
| nil = X3
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_176])])])]) ).
fof(c_0_271,plain,
! [X2] :
( lhs_atom2(X2)
| nil = X2
| ssList(tl(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_177])]) ).
fof(c_0_272,plain,
! [X2] :
( lhs_atom2(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_178])]) ).
fof(c_0_273,plain,
lhs_atom11,
c_0_179 ).
fof(c_0_274,plain,
lhs_atom10,
c_0_180 ).
fof(c_0_275,plain,
lhs_atom9,
c_0_181 ).
fof(c_0_276,plain,
lhs_atom8,
c_0_182 ).
fof(c_0_277,plain,
lhs_atom7,
c_0_183 ).
fof(c_0_278,plain,
lhs_atom6,
c_0_184 ).
fof(c_0_279,plain,
lhs_atom5,
c_0_185 ).
fof(c_0_280,plain,
lhs_atom4,
c_0_186 ).
fof(c_0_281,plain,
lhs_atom3,
c_0_187 ).
cnf(c_0_282,plain,
( lhs_atom2(X1)
| ~ leq(X2,X3)
| ~ leq(X3,X2)
| app(app(X4,cons(X3,X5)),cons(X2,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ cyclefreeP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_283,plain,
( lhs_atom2(X1)
| lt(X2,X3)
| lt(X3,X2)
| app(app(X4,cons(X3,X5)),cons(X2,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ strictorderP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_284,plain,
( lhs_atom2(X1)
| leq(X2,X3)
| leq(X3,X2)
| app(app(X4,cons(X3,X5)),cons(X2,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ totalorderP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_285,plain,
( lhs_atom2(X1)
| lt(X2,X3)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ strictorderedP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_286,plain,
( lhs_atom2(X1)
| leq(X2,X3)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ totalorderedP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_287,plain,
( lhs_atom2(X1)
| X2 != X3
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ duplicatefreeP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_288,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| app(app(esk35_1(X1),cons(esk33_1(X1),esk36_1(X1))),cons(esk34_1(X1),esk37_1(X1))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_289,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| app(app(esk30_1(X1),cons(esk28_1(X1),esk31_1(X1))),cons(esk29_1(X1),esk32_1(X1))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_290,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| app(app(esk25_1(X1),cons(esk23_1(X1),esk26_1(X1))),cons(esk24_1(X1),esk27_1(X1))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_291,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| app(app(esk20_1(X1),cons(esk18_1(X1),esk21_1(X1))),cons(esk19_1(X1),esk22_1(X1))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_292,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| app(app(esk15_1(X1),cons(esk13_1(X1),esk16_1(X1))),cons(esk14_1(X1),esk17_1(X1))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_293,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| app(app(esk10_1(X1),cons(esk8_1(X1),esk11_1(X1))),cons(esk9_1(X1),esk12_1(X1))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_294,plain,
( lhs_atom2(X1)
| X2 = X3
| app(X4,cons(X2,cons(X3,X5))) != X1
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ equalelemsP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_295,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| app(esk40_1(X1),cons(esk38_1(X1),cons(esk39_1(X1),esk41_1(X1)))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_296,plain,
( lhs_atom2(X1)
| app(app(esk6_2(X1,X2),X2),esk7_2(X1,X2)) = X1
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_297,plain,
( lhs_atom2(X1)
| app(esk1_2(X1,X2),cons(X2,esk2_2(X1,X2))) = X1
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_298,plain,
( lhs_atom1(X1)
| frontsegP(X3,X4)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X3),cons(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_299,plain,
( segmentP(app(app(X1,X2),X3),X4)
| lhs_atom2(X2)
| ~ segmentP(X2,X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_198]) ).
cnf(c_0_300,plain,
( lhs_atom1(X1)
| X1 = X2
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X3),cons(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_301,plain,
( lhs_atom1(X1)
| frontsegP(cons(X1,X3),cons(X2,X4))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(X3,X4)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_302,plain,
( lhs_atom1(X1)
| memberP(X3,X1)
| memberP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(app(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_303,plain,
( lhs_atom2(X1)
| segmentP(X1,X2)
| ~ ssList(X2)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_304,plain,
( lhs_atom2(X1)
| memberP(X1,X2)
| ~ ssItem(X2)
| app(X3,cons(X2,X4)) != X1
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_305,plain,
( lhs_atom1(X1)
| memberP(X3,X1)
| X1 = X2
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
cnf(c_0_306,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| lhs_atom2(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
cnf(c_0_307,plain,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| lhs_atom2(X3)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
cnf(c_0_308,plain,
( lhs_atom1(X1)
| strictorderedP(cons(X1,X2))
| nil = X2
| ~ ssList(X2)
| ~ lt(X1,hd(X2))
| ~ strictorderedP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_309,plain,
( lhs_atom1(X1)
| totalorderedP(cons(X1,X2))
| nil = X2
| ~ ssList(X2)
| ~ leq(X1,hd(X2))
| ~ totalorderedP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_310,plain,
( rearsegP(app(X1,X2),X3)
| lhs_atom2(X2)
| ~ rearsegP(X2,X3)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_205]) ).
cnf(c_0_311,plain,
( frontsegP(app(X1,X2),X3)
| lhs_atom2(X1)
| ~ frontsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_206]) ).
cnf(c_0_312,plain,
( lhs_atom1(X1)
| memberP(cons(X2,X3),X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
cnf(c_0_313,plain,
( lhs_atom1(X1)
| memberP(app(X2,X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_314,plain,
( lhs_atom1(X1)
| memberP(app(X2,X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_315,plain,
( lhs_atom1(X1)
| nil = X2
| lt(X1,hd(X2))
| ~ ssList(X2)
| ~ strictorderedP(cons(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_316,plain,
( lhs_atom1(X1)
| nil = X2
| leq(X1,hd(X2))
| ~ ssList(X2)
| ~ totalorderedP(cons(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_317,plain,
( gt(X1,X2)
| lhs_atom1(X1)
| ~ gt(X3,X2)
| ~ gt(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
cnf(c_0_318,plain,
( lt(X1,X2)
| lhs_atom1(X1)
| ~ lt(X3,X2)
| ~ leq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
cnf(c_0_319,plain,
( geq(X1,X2)
| lhs_atom1(X1)
| ~ geq(X3,X2)
| ~ geq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_209]) ).
cnf(c_0_320,plain,
( segmentP(X1,X2)
| lhs_atom2(X1)
| ~ segmentP(X3,X2)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_210]) ).
cnf(c_0_321,plain,
( rearsegP(X1,X2)
| lhs_atom2(X1)
| ~ rearsegP(X3,X2)
| ~ rearsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_322,plain,
( frontsegP(X1,X2)
| lhs_atom2(X1)
| ~ frontsegP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_323,plain,
( lt(X1,X2)
| lhs_atom1(X1)
| ~ lt(X3,X2)
| ~ lt(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_324,plain,
( leq(X1,X2)
| lhs_atom1(X1)
| ~ leq(X3,X2)
| ~ leq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
cnf(c_0_325,plain,
( lhs_atom2(X1)
| app(esk5_2(X1,X2),X2) = X1
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_326,plain,
( lhs_atom2(X1)
| app(X2,esk4_2(X1,X2)) = X1
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_216]) ).
cnf(c_0_327,plain,
( lhs_atom2(X1)
| X3 = X4
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_328,plain,
( lhs_atom2(X1)
| X2 = X1
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_329,plain,
( lhs_atom1(X1)
| nil = X2
| strictorderedP(X2)
| ~ ssList(X2)
| ~ strictorderedP(cons(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_330,plain,
( lhs_atom1(X1)
| nil = X2
| totalorderedP(X2)
| ~ ssList(X2)
| ~ totalorderedP(cons(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_331,plain,
( X1 = X2
| lhs_atom2(X2)
| app(X3,X1) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
cnf(c_0_332,plain,
( X1 = X2
| lhs_atom2(X2)
| app(X1,X3) != app(X2,X3)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_219]) ).
cnf(c_0_333,plain,
( lhs_atom2(X1)
| ssList(esk6_2(X1,X2))
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_334,plain,
( lhs_atom2(X1)
| ssList(esk7_2(X1,X2))
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_335,plain,
( lhs_atom2(X1)
| ssList(esk5_2(X1,X2))
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_336,plain,
( lhs_atom2(X1)
| ssList(esk4_2(X1,X2))
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_216]) ).
cnf(c_0_337,plain,
( lhs_atom2(X1)
| ssList(esk1_2(X1,X2))
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_338,plain,
( lhs_atom2(X1)
| ssList(esk2_2(X1,X2))
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_339,plain,
( tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1
| lhs_atom2(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_220]) ).
cnf(c_0_340,plain,
( lhs_atom1(X1)
| nil = X2
| ~ ssList(X2)
| ~ strictorderedP(cons(X1,X2))
| nil != X2 ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_341,plain,
( lhs_atom1(X1)
| nil = X2
| ~ ssList(X2)
| ~ totalorderedP(cons(X1,X2))
| nil != X2 ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_342,plain,
( lhs_atom1(X1)
| memberP(cons(X2,X3),X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
cnf(c_0_343,plain,
( cons(X1,X2) = app(cons(X1,nil),X2)
| lhs_atom2(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_344,plain,
( X1 = X2
| lhs_atom1(X1)
| ~ geq(X2,X1)
| ~ geq(X1,X2)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_222]) ).
cnf(c_0_345,plain,
( X1 = X2
| lhs_atom2(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_223]) ).
cnf(c_0_346,plain,
( X1 = X2
| lhs_atom2(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(X1,X2)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_347,plain,
( X1 = X2
| lhs_atom2(X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
cnf(c_0_348,plain,
( X1 = X2
| lhs_atom1(X1)
| ~ leq(X2,X1)
| ~ leq(X1,X2)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_349,plain,
( lhs_atom2(X1)
| rearsegP(X1,X2)
| ~ ssList(X2)
| app(X3,X2) != X1
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_350,plain,
( lhs_atom2(X1)
| frontsegP(X1,X2)
| ~ ssList(X2)
| app(X2,X3) != X1
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_216]) ).
cnf(c_0_351,plain,
( lhs_atom1(X2)
| ~ gt(X1,X2)
| ~ gt(X2,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_352,plain,
( lhs_atom1(X2)
| ~ lt(X1,X2)
| ~ lt(X2,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_353,plain,
( lhs_atom1(X1)
| lt(X1,X2)
| X1 = X2
| ~ ssItem(X2)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_354,plain,
( lt(X1,X2)
| X1 = X2
| lhs_atom1(X1)
| ~ leq(X1,X2)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_355,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ~ lt(esk28_1(X1),esk29_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_356,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ~ leq(esk23_1(X1),esk24_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_357,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ~ lt(esk18_1(X1),esk19_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_358,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ~ lt(esk19_1(X1),esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_359,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ~ leq(esk13_1(X1),esk14_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_360,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ~ leq(esk14_1(X1),esk13_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_361,plain,
( lhs_atom1(X1)
| leq(X1,X2)
| ~ ssItem(X2)
| ~ lt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_362,plain,
( lhs_atom1(X1)
| lt(X2,X1)
| ~ ssItem(X2)
| ~ gt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_363,plain,
( lhs_atom1(X1)
| gt(X1,X2)
| ~ ssItem(X2)
| ~ lt(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_364,plain,
( lhs_atom1(X1)
| leq(X2,X1)
| ~ ssItem(X2)
| ~ geq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_365,plain,
( lhs_atom1(X1)
| geq(X1,X2)
| ~ ssItem(X2)
| ~ leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_366,plain,
( hd(app(X1,X2)) = hd(X1)
| nil = X1
| lhs_atom2(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_367,plain,
( lhs_atom1(X1)
| strictorderedP(cons(X1,X2))
| ~ ssList(X2)
| nil != X2 ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_368,plain,
( lhs_atom1(X1)
| totalorderedP(cons(X1,X2))
| ~ ssList(X2)
| nil != X2 ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_369,plain,
( X1 = X2
| nil = X2
| nil = X1
| lhs_atom2(X2)
| tl(X1) != tl(X2)
| hd(X1) != hd(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_370,plain,
( tl(cons(X1,X2)) = X2
| lhs_atom2(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_371,plain,
( hd(cons(X1,X2)) = X1
| lhs_atom2(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_372,plain,
( ssList(app(X1,X2))
| lhs_atom2(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_373,plain,
( ssList(cons(X1,X2))
| lhs_atom2(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_374,plain,
( lhs_atom1(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_375,plain,
( lhs_atom2(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_376,plain,
( lhs_atom1(X1)
| ~ ssItem(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_377,plain,
( lhs_atom2(X1)
| singletonP(X1)
| cons(X2,nil) != X1
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_378,plain,
( lhs_atom2(X1)
| nil = X2
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_379,plain,
( lhs_atom2(X1)
| nil = X1
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_380,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| leq(esk8_1(X1),esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_381,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| leq(esk9_1(X1),esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_382,plain,
( lhs_atom2(X2)
| cons(X1,X2) != X2
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_383,plain,
( lhs_atom2(X2)
| nil != cons(X1,X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_384,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_385,plain,
( lhs_atom2(X1)
| nil = X1
| cons(esk43_1(X1),esk42_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_386,plain,
( equalelemsP(cons(X1,nil))
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_387,plain,
( duplicatefreeP(cons(X1,nil))
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_388,plain,
( strictorderedP(cons(X1,nil))
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_389,plain,
( totalorderedP(cons(X1,nil))
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_390,plain,
( strictorderP(cons(X1,nil))
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_391,plain,
( totalorderP(cons(X1,nil))
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_392,plain,
( cyclefreeP(cons(X1,nil))
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_393,plain,
( lhs_atom2(X1)
| cons(esk3_1(X1),nil) = X1
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_394,plain,
( lhs_atom2(X1)
| nil = app(X1,X2)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_395,plain,
( lhs_atom2(X1)
| neq(X1,X2)
| X1 = X2
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_396,plain,
( lhs_atom1(X1)
| neq(X1,X2)
| X1 = X2
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_397,plain,
( lhs_atom1(X1)
| ~ lt(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_398,plain,
( lhs_atom2(X1)
| nil = X1
| ~ segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_399,plain,
( lhs_atom2(X1)
| nil = X1
| ~ rearsegP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_400,plain,
( lhs_atom2(X1)
| nil = X1
| ~ frontsegP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_401,plain,
( lhs_atom1(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_258]) ).
cnf(c_0_402,plain,
( lhs_atom2(X1)
| ssItem(esk3_1(X1))
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_403,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| esk38_1(X1) != esk39_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_404,plain,
( lhs_atom2(X1)
| segmentP(nil,X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_405,plain,
( lhs_atom2(X1)
| rearsegP(nil,X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_406,plain,
( lhs_atom2(X1)
| frontsegP(nil,X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_407,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| ssItem(esk38_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_408,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| ssItem(esk39_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_409,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| ssList(esk40_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_410,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| ssList(esk41_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_411,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssItem(esk33_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_412,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssItem(esk34_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_413,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssList(esk35_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_414,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssList(esk36_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_415,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssList(esk37_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_416,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssItem(esk28_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_417,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssItem(esk29_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_418,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssList(esk30_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_419,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssList(esk31_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_420,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssList(esk32_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_421,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssItem(esk23_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_422,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssItem(esk24_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_423,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssList(esk25_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_424,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssList(esk26_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_425,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssList(esk27_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_426,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssItem(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_427,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssItem(esk19_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_428,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssList(esk20_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_429,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssList(esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_430,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssList(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_431,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssItem(esk13_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_432,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssItem(esk14_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_433,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssList(esk15_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_434,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssList(esk16_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_435,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssList(esk17_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_436,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssItem(esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_437,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssItem(esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_438,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssList(esk10_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_439,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssList(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_440,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssList(esk12_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_441,plain,
( geq(X1,X1)
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_259]) ).
cnf(c_0_442,plain,
( segmentP(X1,X1)
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_443,plain,
( rearsegP(X1,X1)
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_444,plain,
( frontsegP(X1,X1)
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_445,plain,
( leq(X1,X1)
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_446,plain,
( app(X1,nil) = X1
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_447,plain,
( app(nil,X1) = X1
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_448,plain,
( segmentP(X1,nil)
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_449,plain,
( rearsegP(X1,nil)
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_450,plain,
( frontsegP(X1,nil)
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_451,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| esk33_1(X1) = esk34_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_452,plain,
( lhs_atom2(X1)
| nil = X1
| ssList(esk45_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_453,plain,
( lhs_atom2(X1)
| nil = X1
| ssItem(esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_454,plain,
( ssList(tl(X1))
| nil = X1
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_455,plain,
( ssItem(hd(X1))
| nil = X1
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_456,plain,
( lhs_atom2(X1)
| nil = X1
| ssList(esk42_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_457,plain,
( lhs_atom2(X1)
| nil = X1
| ssItem(esk43_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_458,plain,
( lhs_atom2(X1)
| nil = X1
| tl(X1) = esk45_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_459,plain,
( lhs_atom2(X1)
| nil = X1
| hd(X1) = esk44_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_460,plain,
lhs_atom11,
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_461,plain,
lhs_atom10,
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_462,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_463,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_464,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_465,plain,
lhs_atom6,
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_466,plain,
lhs_atom5,
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_467,plain,
lhs_atom4,
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_468,plain,
lhs_atom3,
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_469,plain,
( lhs_atom2(X1)
| ~ leq(X2,X3)
| ~ leq(X3,X2)
| app(app(X4,cons(X3,X5)),cons(X2,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ cyclefreeP(X1) ),
c_0_282,
[final] ).
cnf(c_0_470,plain,
( lhs_atom2(X1)
| lt(X2,X3)
| lt(X3,X2)
| app(app(X4,cons(X3,X5)),cons(X2,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ strictorderP(X1) ),
c_0_283,
[final] ).
cnf(c_0_471,plain,
( lhs_atom2(X1)
| leq(X2,X3)
| leq(X3,X2)
| app(app(X4,cons(X3,X5)),cons(X2,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ totalorderP(X1) ),
c_0_284,
[final] ).
cnf(c_0_472,plain,
( lhs_atom2(X1)
| lt(X2,X3)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ strictorderedP(X1) ),
c_0_285,
[final] ).
cnf(c_0_473,plain,
( lhs_atom2(X1)
| leq(X2,X3)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ totalorderedP(X1) ),
c_0_286,
[final] ).
cnf(c_0_474,plain,
( lhs_atom2(X1)
| X2 != X3
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ duplicatefreeP(X1) ),
c_0_287,
[final] ).
cnf(c_0_475,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| app(app(esk35_1(X1),cons(esk33_1(X1),esk36_1(X1))),cons(esk34_1(X1),esk37_1(X1))) = X1 ),
c_0_288,
[final] ).
cnf(c_0_476,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| app(app(esk30_1(X1),cons(esk28_1(X1),esk31_1(X1))),cons(esk29_1(X1),esk32_1(X1))) = X1 ),
c_0_289,
[final] ).
cnf(c_0_477,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| app(app(esk25_1(X1),cons(esk23_1(X1),esk26_1(X1))),cons(esk24_1(X1),esk27_1(X1))) = X1 ),
c_0_290,
[final] ).
cnf(c_0_478,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| app(app(esk20_1(X1),cons(esk18_1(X1),esk21_1(X1))),cons(esk19_1(X1),esk22_1(X1))) = X1 ),
c_0_291,
[final] ).
cnf(c_0_479,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| app(app(esk15_1(X1),cons(esk13_1(X1),esk16_1(X1))),cons(esk14_1(X1),esk17_1(X1))) = X1 ),
c_0_292,
[final] ).
cnf(c_0_480,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| app(app(esk10_1(X1),cons(esk8_1(X1),esk11_1(X1))),cons(esk9_1(X1),esk12_1(X1))) = X1 ),
c_0_293,
[final] ).
cnf(c_0_481,plain,
( lhs_atom2(X1)
| X2 = X3
| app(X4,cons(X2,cons(X3,X5))) != X1
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ equalelemsP(X1) ),
c_0_294,
[final] ).
cnf(c_0_482,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| app(esk40_1(X1),cons(esk38_1(X1),cons(esk39_1(X1),esk41_1(X1)))) = X1 ),
c_0_295,
[final] ).
cnf(c_0_483,plain,
( lhs_atom2(X1)
| app(app(esk6_2(X1,X2),X2),esk7_2(X1,X2)) = X1
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
c_0_296,
[final] ).
cnf(c_0_484,plain,
( lhs_atom2(X1)
| app(esk1_2(X1,X2),cons(X2,esk2_2(X1,X2))) = X1
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
c_0_297,
[final] ).
cnf(c_0_485,plain,
( lhs_atom1(X1)
| frontsegP(X3,X4)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X3),cons(X2,X4)) ),
c_0_298,
[final] ).
cnf(c_0_486,plain,
( segmentP(app(app(X1,X2),X3),X4)
| lhs_atom2(X2)
| ~ segmentP(X2,X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X4) ),
c_0_299,
[final] ).
cnf(c_0_487,plain,
( lhs_atom1(X1)
| X1 = X2
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X3),cons(X2,X4)) ),
c_0_300,
[final] ).
cnf(c_0_488,plain,
( lhs_atom1(X1)
| frontsegP(cons(X1,X3),cons(X2,X4))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(X3,X4)
| X1 != X2 ),
c_0_301,
[final] ).
cnf(c_0_489,plain,
( lhs_atom1(X1)
| memberP(X3,X1)
| memberP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(app(X2,X3),X1) ),
c_0_302,
[final] ).
cnf(c_0_490,plain,
( lhs_atom2(X1)
| segmentP(X1,X2)
| ~ ssList(X2)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4)
| ~ ssList(X3) ),
c_0_303,
[final] ).
cnf(c_0_491,plain,
( lhs_atom2(X1)
| memberP(X1,X2)
| ~ ssItem(X2)
| app(X3,cons(X2,X4)) != X1
| ~ ssList(X4)
| ~ ssList(X3) ),
c_0_304,
[final] ).
cnf(c_0_492,plain,
( lhs_atom1(X1)
| memberP(X3,X1)
| X1 = X2
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(cons(X2,X3),X1) ),
c_0_305,
[final] ).
cnf(c_0_493,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| lhs_atom2(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
c_0_306,
[final] ).
cnf(c_0_494,plain,
( app(cons(X1,X2),X3) = cons(X1,app(X2,X3))
| lhs_atom2(X3)
| ~ ssItem(X1)
| ~ ssList(X2) ),
c_0_307,
[final] ).
cnf(c_0_495,plain,
( lhs_atom1(X1)
| strictorderedP(cons(X1,X2))
| nil = X2
| ~ ssList(X2)
| ~ lt(X1,hd(X2))
| ~ strictorderedP(X2) ),
c_0_308,
[final] ).
cnf(c_0_496,plain,
( lhs_atom1(X1)
| totalorderedP(cons(X1,X2))
| nil = X2
| ~ ssList(X2)
| ~ leq(X1,hd(X2))
| ~ totalorderedP(X2) ),
c_0_309,
[final] ).
cnf(c_0_497,plain,
( rearsegP(app(X1,X2),X3)
| lhs_atom2(X2)
| ~ rearsegP(X2,X3)
| ~ ssList(X1)
| ~ ssList(X3) ),
c_0_310,
[final] ).
cnf(c_0_498,plain,
( frontsegP(app(X1,X2),X3)
| lhs_atom2(X1)
| ~ frontsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
c_0_311,
[final] ).
cnf(c_0_499,plain,
( lhs_atom1(X1)
| memberP(cons(X2,X3),X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
c_0_312,
[final] ).
cnf(c_0_500,plain,
( lhs_atom1(X1)
| memberP(app(X2,X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X2,X1) ),
c_0_313,
[final] ).
cnf(c_0_501,plain,
( lhs_atom1(X1)
| memberP(app(X2,X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
c_0_314,
[final] ).
cnf(c_0_502,plain,
( lhs_atom1(X1)
| nil = X2
| lt(X1,hd(X2))
| ~ ssList(X2)
| ~ strictorderedP(cons(X1,X2)) ),
c_0_315,
[final] ).
cnf(c_0_503,plain,
( lhs_atom1(X1)
| nil = X2
| leq(X1,hd(X2))
| ~ ssList(X2)
| ~ totalorderedP(cons(X1,X2)) ),
c_0_316,
[final] ).
cnf(c_0_504,plain,
( gt(X1,X2)
| lhs_atom1(X1)
| ~ gt(X3,X2)
| ~ gt(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
c_0_317,
[final] ).
cnf(c_0_505,plain,
( lt(X1,X2)
| lhs_atom1(X1)
| ~ lt(X3,X2)
| ~ leq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
c_0_318,
[final] ).
cnf(c_0_506,plain,
( geq(X1,X2)
| lhs_atom1(X1)
| ~ geq(X3,X2)
| ~ geq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
c_0_319,
[final] ).
cnf(c_0_507,plain,
( segmentP(X1,X2)
| lhs_atom2(X1)
| ~ segmentP(X3,X2)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
c_0_320,
[final] ).
cnf(c_0_508,plain,
( rearsegP(X1,X2)
| lhs_atom2(X1)
| ~ rearsegP(X3,X2)
| ~ rearsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
c_0_321,
[final] ).
cnf(c_0_509,plain,
( frontsegP(X1,X2)
| lhs_atom2(X1)
| ~ frontsegP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
c_0_322,
[final] ).
cnf(c_0_510,plain,
( lt(X1,X2)
| lhs_atom1(X1)
| ~ lt(X3,X2)
| ~ lt(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
c_0_323,
[final] ).
cnf(c_0_511,plain,
( leq(X1,X2)
| lhs_atom1(X1)
| ~ leq(X3,X2)
| ~ leq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
c_0_324,
[final] ).
cnf(c_0_512,plain,
( lhs_atom2(X1)
| app(esk5_2(X1,X2),X2) = X1
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
c_0_325,
[final] ).
cnf(c_0_513,plain,
( lhs_atom2(X1)
| app(X2,esk4_2(X1,X2)) = X1
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
c_0_326,
[final] ).
cnf(c_0_514,plain,
( lhs_atom2(X1)
| X3 = X4
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2) ),
c_0_327,
[final] ).
cnf(c_0_515,plain,
( lhs_atom2(X1)
| X2 = X1
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2) ),
c_0_328,
[final] ).
cnf(c_0_516,plain,
( lhs_atom1(X1)
| nil = X2
| strictorderedP(X2)
| ~ ssList(X2)
| ~ strictorderedP(cons(X1,X2)) ),
c_0_329,
[final] ).
cnf(c_0_517,plain,
( lhs_atom1(X1)
| nil = X2
| totalorderedP(X2)
| ~ ssList(X2)
| ~ totalorderedP(cons(X1,X2)) ),
c_0_330,
[final] ).
cnf(c_0_518,plain,
( X1 = X2
| lhs_atom2(X2)
| app(X3,X1) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
c_0_331,
[final] ).
cnf(c_0_519,plain,
( X1 = X2
| lhs_atom2(X2)
| app(X1,X3) != app(X2,X3)
| ~ ssList(X1)
| ~ ssList(X3) ),
c_0_332,
[final] ).
cnf(c_0_520,plain,
( lhs_atom2(X1)
| ssList(esk6_2(X1,X2))
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
c_0_333,
[final] ).
cnf(c_0_521,plain,
( lhs_atom2(X1)
| ssList(esk7_2(X1,X2))
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
c_0_334,
[final] ).
cnf(c_0_522,plain,
( lhs_atom2(X1)
| ssList(esk5_2(X1,X2))
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
c_0_335,
[final] ).
cnf(c_0_523,plain,
( lhs_atom2(X1)
| ssList(esk4_2(X1,X2))
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
c_0_336,
[final] ).
cnf(c_0_524,plain,
( lhs_atom2(X1)
| ssList(esk1_2(X1,X2))
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
c_0_337,
[final] ).
cnf(c_0_525,plain,
( lhs_atom2(X1)
| ssList(esk2_2(X1,X2))
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
c_0_338,
[final] ).
cnf(c_0_526,plain,
( tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1
| lhs_atom2(X1)
| ~ ssList(X2) ),
c_0_339,
[final] ).
cnf(c_0_527,plain,
( lhs_atom1(X1)
| nil = X2
| ~ ssList(X2)
| ~ strictorderedP(cons(X1,X2))
| nil != X2 ),
c_0_340,
[final] ).
cnf(c_0_528,plain,
( lhs_atom1(X1)
| nil = X2
| ~ ssList(X2)
| ~ totalorderedP(cons(X1,X2))
| nil != X2 ),
c_0_341,
[final] ).
cnf(c_0_529,plain,
( lhs_atom1(X1)
| memberP(cons(X2,X3),X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2 ),
c_0_342,
[final] ).
cnf(c_0_530,plain,
( app(cons(X1,nil),X2) = cons(X1,X2)
| lhs_atom2(X2)
| ~ ssItem(X1) ),
c_0_343,
[final] ).
cnf(c_0_531,plain,
( X1 = X2
| lhs_atom1(X1)
| ~ geq(X2,X1)
| ~ geq(X1,X2)
| ~ ssItem(X2) ),
c_0_344,
[final] ).
cnf(c_0_532,plain,
( X1 = X2
| lhs_atom2(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) ),
c_0_345,
[final] ).
cnf(c_0_533,plain,
( X1 = X2
| lhs_atom2(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(X1,X2)
| ~ ssList(X2) ),
c_0_346,
[final] ).
cnf(c_0_534,plain,
( X1 = X2
| lhs_atom2(X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X2) ),
c_0_347,
[final] ).
cnf(c_0_535,plain,
( X1 = X2
| lhs_atom1(X1)
| ~ leq(X2,X1)
| ~ leq(X1,X2)
| ~ ssItem(X2) ),
c_0_348,
[final] ).
cnf(c_0_536,plain,
( lhs_atom2(X1)
| rearsegP(X1,X2)
| ~ ssList(X2)
| app(X3,X2) != X1
| ~ ssList(X3) ),
c_0_349,
[final] ).
cnf(c_0_537,plain,
( lhs_atom2(X1)
| frontsegP(X1,X2)
| ~ ssList(X2)
| app(X2,X3) != X1
| ~ ssList(X3) ),
c_0_350,
[final] ).
cnf(c_0_538,plain,
( lhs_atom1(X2)
| ~ gt(X1,X2)
| ~ gt(X2,X1)
| ~ ssItem(X1) ),
c_0_351,
[final] ).
cnf(c_0_539,plain,
( lhs_atom1(X2)
| ~ lt(X1,X2)
| ~ lt(X2,X1)
| ~ ssItem(X1) ),
c_0_352,
[final] ).
cnf(c_0_540,plain,
( lhs_atom1(X1)
| lt(X1,X2)
| X1 = X2
| ~ ssItem(X2)
| ~ leq(X1,X2) ),
c_0_353,
[final] ).
cnf(c_0_541,plain,
( lt(X1,X2)
| X1 = X2
| lhs_atom1(X1)
| ~ leq(X1,X2)
| ~ ssItem(X2) ),
c_0_354,
[final] ).
cnf(c_0_542,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ~ lt(esk28_1(X1),esk29_1(X1)) ),
c_0_355,
[final] ).
cnf(c_0_543,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ~ leq(esk23_1(X1),esk24_1(X1)) ),
c_0_356,
[final] ).
cnf(c_0_544,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ~ lt(esk18_1(X1),esk19_1(X1)) ),
c_0_357,
[final] ).
cnf(c_0_545,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ~ lt(esk19_1(X1),esk18_1(X1)) ),
c_0_358,
[final] ).
cnf(c_0_546,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ~ leq(esk13_1(X1),esk14_1(X1)) ),
c_0_359,
[final] ).
cnf(c_0_547,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ~ leq(esk14_1(X1),esk13_1(X1)) ),
c_0_360,
[final] ).
cnf(c_0_548,plain,
( lhs_atom1(X1)
| leq(X1,X2)
| ~ ssItem(X2)
| ~ lt(X1,X2) ),
c_0_361,
[final] ).
cnf(c_0_549,plain,
( lhs_atom1(X1)
| lt(X2,X1)
| ~ ssItem(X2)
| ~ gt(X1,X2) ),
c_0_362,
[final] ).
cnf(c_0_550,plain,
( lhs_atom1(X1)
| gt(X1,X2)
| ~ ssItem(X2)
| ~ lt(X2,X1) ),
c_0_363,
[final] ).
cnf(c_0_551,plain,
( lhs_atom1(X1)
| leq(X2,X1)
| ~ ssItem(X2)
| ~ geq(X1,X2) ),
c_0_364,
[final] ).
cnf(c_0_552,plain,
( lhs_atom1(X1)
| geq(X1,X2)
| ~ ssItem(X2)
| ~ leq(X2,X1) ),
c_0_365,
[final] ).
cnf(c_0_553,plain,
( hd(app(X1,X2)) = hd(X1)
| nil = X1
| lhs_atom2(X1)
| ~ ssList(X2) ),
c_0_366,
[final] ).
cnf(c_0_554,plain,
( lhs_atom1(X1)
| strictorderedP(cons(X1,X2))
| ~ ssList(X2)
| nil != X2 ),
c_0_367,
[final] ).
cnf(c_0_555,plain,
( lhs_atom1(X1)
| totalorderedP(cons(X1,X2))
| ~ ssList(X2)
| nil != X2 ),
c_0_368,
[final] ).
cnf(c_0_556,plain,
( X1 = X2
| nil = X2
| nil = X1
| lhs_atom2(X2)
| tl(X1) != tl(X2)
| hd(X1) != hd(X2)
| ~ ssList(X1) ),
c_0_369,
[final] ).
cnf(c_0_557,plain,
( tl(cons(X1,X2)) = X2
| lhs_atom2(X2)
| ~ ssItem(X1) ),
c_0_370,
[final] ).
cnf(c_0_558,plain,
( hd(cons(X1,X2)) = X1
| lhs_atom2(X2)
| ~ ssItem(X1) ),
c_0_371,
[final] ).
cnf(c_0_559,plain,
( ssList(app(X1,X2))
| lhs_atom2(X1)
| ~ ssList(X2) ),
c_0_372,
[final] ).
cnf(c_0_560,plain,
( ssList(cons(X1,X2))
| lhs_atom2(X2)
| ~ ssItem(X1) ),
c_0_373,
[final] ).
cnf(c_0_561,plain,
( lhs_atom1(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| X1 != X2 ),
c_0_374,
[final] ).
cnf(c_0_562,plain,
( lhs_atom2(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
c_0_375,
[final] ).
cnf(c_0_563,plain,
( lhs_atom1(X1)
| ~ ssItem(X2)
| X1 != X2
| ~ neq(X1,X2) ),
c_0_376,
[final] ).
cnf(c_0_564,plain,
( lhs_atom2(X1)
| singletonP(X1)
| cons(X2,nil) != X1
| ~ ssItem(X2) ),
c_0_377,
[final] ).
cnf(c_0_565,plain,
( lhs_atom2(X1)
| nil = X2
| ~ ssList(X2)
| app(X1,X2) != nil ),
c_0_378,
[final] ).
cnf(c_0_566,plain,
( lhs_atom2(X1)
| nil = X1
| ~ ssList(X2)
| app(X1,X2) != nil ),
c_0_379,
[final] ).
cnf(c_0_567,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| leq(esk8_1(X1),esk9_1(X1)) ),
c_0_380,
[final] ).
cnf(c_0_568,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| leq(esk9_1(X1),esk8_1(X1)) ),
c_0_381,
[final] ).
cnf(c_0_569,plain,
( lhs_atom2(X2)
| cons(X1,X2) != X2
| ~ ssItem(X1) ),
c_0_382,
[final] ).
cnf(c_0_570,plain,
( lhs_atom2(X2)
| cons(X1,X2) != nil
| ~ ssItem(X1) ),
c_0_383,
[final] ).
cnf(c_0_571,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| lhs_atom2(X1) ),
c_0_384,
[final] ).
cnf(c_0_572,plain,
( lhs_atom2(X1)
| nil = X1
| cons(esk43_1(X1),esk42_1(X1)) = X1 ),
c_0_385,
[final] ).
cnf(c_0_573,plain,
( equalelemsP(cons(X1,nil))
| lhs_atom1(X1) ),
c_0_386,
[final] ).
cnf(c_0_574,plain,
( duplicatefreeP(cons(X1,nil))
| lhs_atom1(X1) ),
c_0_387,
[final] ).
cnf(c_0_575,plain,
( strictorderedP(cons(X1,nil))
| lhs_atom1(X1) ),
c_0_388,
[final] ).
cnf(c_0_576,plain,
( totalorderedP(cons(X1,nil))
| lhs_atom1(X1) ),
c_0_389,
[final] ).
cnf(c_0_577,plain,
( strictorderP(cons(X1,nil))
| lhs_atom1(X1) ),
c_0_390,
[final] ).
cnf(c_0_578,plain,
( totalorderP(cons(X1,nil))
| lhs_atom1(X1) ),
c_0_391,
[final] ).
cnf(c_0_579,plain,
( cyclefreeP(cons(X1,nil))
| lhs_atom1(X1) ),
c_0_392,
[final] ).
cnf(c_0_580,plain,
( lhs_atom2(X1)
| cons(esk3_1(X1),nil) = X1
| ~ singletonP(X1) ),
c_0_393,
[final] ).
cnf(c_0_581,plain,
( lhs_atom2(X1)
| app(X1,X2) = nil
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
c_0_394,
[final] ).
cnf(c_0_582,plain,
( lhs_atom2(X1)
| neq(X1,X2)
| X1 = X2
| ~ ssList(X2) ),
c_0_395,
[final] ).
cnf(c_0_583,plain,
( lhs_atom1(X1)
| neq(X1,X2)
| X1 = X2
| ~ ssItem(X2) ),
c_0_396,
[final] ).
cnf(c_0_584,plain,
( lhs_atom1(X1)
| ~ lt(X1,X1) ),
c_0_397,
[final] ).
cnf(c_0_585,plain,
( lhs_atom2(X1)
| nil = X1
| ~ segmentP(nil,X1) ),
c_0_398,
[final] ).
cnf(c_0_586,plain,
( lhs_atom2(X1)
| nil = X1
| ~ rearsegP(nil,X1) ),
c_0_399,
[final] ).
cnf(c_0_587,plain,
( lhs_atom2(X1)
| nil = X1
| ~ frontsegP(nil,X1) ),
c_0_400,
[final] ).
cnf(c_0_588,plain,
( lhs_atom1(X1)
| ~ memberP(nil,X1) ),
c_0_401,
[final] ).
cnf(c_0_589,plain,
( lhs_atom2(X1)
| ssItem(esk3_1(X1))
| ~ singletonP(X1) ),
c_0_402,
[final] ).
cnf(c_0_590,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| esk39_1(X1) != esk38_1(X1) ),
c_0_403,
[final] ).
cnf(c_0_591,plain,
( lhs_atom2(X1)
| segmentP(nil,X1)
| nil != X1 ),
c_0_404,
[final] ).
cnf(c_0_592,plain,
( lhs_atom2(X1)
| rearsegP(nil,X1)
| nil != X1 ),
c_0_405,
[final] ).
cnf(c_0_593,plain,
( lhs_atom2(X1)
| frontsegP(nil,X1)
| nil != X1 ),
c_0_406,
[final] ).
cnf(c_0_594,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| ssItem(esk38_1(X1)) ),
c_0_407,
[final] ).
cnf(c_0_595,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| ssItem(esk39_1(X1)) ),
c_0_408,
[final] ).
cnf(c_0_596,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| ssList(esk40_1(X1)) ),
c_0_409,
[final] ).
cnf(c_0_597,plain,
( lhs_atom2(X1)
| equalelemsP(X1)
| ssList(esk41_1(X1)) ),
c_0_410,
[final] ).
cnf(c_0_598,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssItem(esk33_1(X1)) ),
c_0_411,
[final] ).
cnf(c_0_599,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssItem(esk34_1(X1)) ),
c_0_412,
[final] ).
cnf(c_0_600,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssList(esk35_1(X1)) ),
c_0_413,
[final] ).
cnf(c_0_601,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssList(esk36_1(X1)) ),
c_0_414,
[final] ).
cnf(c_0_602,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| ssList(esk37_1(X1)) ),
c_0_415,
[final] ).
cnf(c_0_603,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssItem(esk28_1(X1)) ),
c_0_416,
[final] ).
cnf(c_0_604,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssItem(esk29_1(X1)) ),
c_0_417,
[final] ).
cnf(c_0_605,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssList(esk30_1(X1)) ),
c_0_418,
[final] ).
cnf(c_0_606,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssList(esk31_1(X1)) ),
c_0_419,
[final] ).
cnf(c_0_607,plain,
( lhs_atom2(X1)
| strictorderedP(X1)
| ssList(esk32_1(X1)) ),
c_0_420,
[final] ).
cnf(c_0_608,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssItem(esk23_1(X1)) ),
c_0_421,
[final] ).
cnf(c_0_609,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssItem(esk24_1(X1)) ),
c_0_422,
[final] ).
cnf(c_0_610,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssList(esk25_1(X1)) ),
c_0_423,
[final] ).
cnf(c_0_611,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssList(esk26_1(X1)) ),
c_0_424,
[final] ).
cnf(c_0_612,plain,
( lhs_atom2(X1)
| totalorderedP(X1)
| ssList(esk27_1(X1)) ),
c_0_425,
[final] ).
cnf(c_0_613,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssItem(esk18_1(X1)) ),
c_0_426,
[final] ).
cnf(c_0_614,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssItem(esk19_1(X1)) ),
c_0_427,
[final] ).
cnf(c_0_615,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssList(esk20_1(X1)) ),
c_0_428,
[final] ).
cnf(c_0_616,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssList(esk21_1(X1)) ),
c_0_429,
[final] ).
cnf(c_0_617,plain,
( lhs_atom2(X1)
| strictorderP(X1)
| ssList(esk22_1(X1)) ),
c_0_430,
[final] ).
cnf(c_0_618,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssItem(esk13_1(X1)) ),
c_0_431,
[final] ).
cnf(c_0_619,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssItem(esk14_1(X1)) ),
c_0_432,
[final] ).
cnf(c_0_620,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssList(esk15_1(X1)) ),
c_0_433,
[final] ).
cnf(c_0_621,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssList(esk16_1(X1)) ),
c_0_434,
[final] ).
cnf(c_0_622,plain,
( lhs_atom2(X1)
| totalorderP(X1)
| ssList(esk17_1(X1)) ),
c_0_435,
[final] ).
cnf(c_0_623,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssItem(esk8_1(X1)) ),
c_0_436,
[final] ).
cnf(c_0_624,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssItem(esk9_1(X1)) ),
c_0_437,
[final] ).
cnf(c_0_625,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssList(esk10_1(X1)) ),
c_0_438,
[final] ).
cnf(c_0_626,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssList(esk11_1(X1)) ),
c_0_439,
[final] ).
cnf(c_0_627,plain,
( lhs_atom2(X1)
| cyclefreeP(X1)
| ssList(esk12_1(X1)) ),
c_0_440,
[final] ).
cnf(c_0_628,plain,
( geq(X1,X1)
| lhs_atom1(X1) ),
c_0_441,
[final] ).
cnf(c_0_629,plain,
( segmentP(X1,X1)
| lhs_atom2(X1) ),
c_0_442,
[final] ).
cnf(c_0_630,plain,
( rearsegP(X1,X1)
| lhs_atom2(X1) ),
c_0_443,
[final] ).
cnf(c_0_631,plain,
( frontsegP(X1,X1)
| lhs_atom2(X1) ),
c_0_444,
[final] ).
cnf(c_0_632,plain,
( leq(X1,X1)
| lhs_atom1(X1) ),
c_0_445,
[final] ).
cnf(c_0_633,plain,
( app(X1,nil) = X1
| lhs_atom2(X1) ),
c_0_446,
[final] ).
cnf(c_0_634,plain,
( app(nil,X1) = X1
| lhs_atom2(X1) ),
c_0_447,
[final] ).
cnf(c_0_635,plain,
( segmentP(X1,nil)
| lhs_atom2(X1) ),
c_0_448,
[final] ).
cnf(c_0_636,plain,
( rearsegP(X1,nil)
| lhs_atom2(X1) ),
c_0_449,
[final] ).
cnf(c_0_637,plain,
( frontsegP(X1,nil)
| lhs_atom2(X1) ),
c_0_450,
[final] ).
cnf(c_0_638,plain,
( lhs_atom2(X1)
| duplicatefreeP(X1)
| esk34_1(X1) = esk33_1(X1) ),
c_0_451,
[final] ).
cnf(c_0_639,plain,
( lhs_atom2(X1)
| nil = X1
| ssList(esk45_1(X1)) ),
c_0_452,
[final] ).
cnf(c_0_640,plain,
( lhs_atom2(X1)
| nil = X1
| ssItem(esk44_1(X1)) ),
c_0_453,
[final] ).
cnf(c_0_641,plain,
( ssList(tl(X1))
| nil = X1
| lhs_atom2(X1) ),
c_0_454,
[final] ).
cnf(c_0_642,plain,
( ssItem(hd(X1))
| nil = X1
| lhs_atom2(X1) ),
c_0_455,
[final] ).
cnf(c_0_643,plain,
( lhs_atom2(X1)
| nil = X1
| ssList(esk42_1(X1)) ),
c_0_456,
[final] ).
cnf(c_0_644,plain,
( lhs_atom2(X1)
| nil = X1
| ssItem(esk43_1(X1)) ),
c_0_457,
[final] ).
cnf(c_0_645,plain,
( lhs_atom2(X1)
| nil = X1
| tl(X1) = esk45_1(X1) ),
c_0_458,
[final] ).
cnf(c_0_646,plain,
( lhs_atom2(X1)
| nil = X1
| esk44_1(X1) = hd(X1) ),
c_0_459,
[final] ).
cnf(c_0_647,plain,
lhs_atom11,
c_0_460,
[final] ).
cnf(c_0_648,plain,
lhs_atom10,
c_0_461,
[final] ).
cnf(c_0_649,plain,
lhs_atom9,
c_0_462,
[final] ).
cnf(c_0_650,plain,
lhs_atom8,
c_0_463,
[final] ).
cnf(c_0_651,plain,
lhs_atom7,
c_0_464,
[final] ).
cnf(c_0_652,plain,
lhs_atom6,
c_0_465,
[final] ).
cnf(c_0_653,plain,
lhs_atom5,
c_0_466,
[final] ).
cnf(c_0_654,plain,
lhs_atom4,
c_0_467,
[final] ).
cnf(c_0_655,plain,
lhs_atom3,
c_0_468,
[final] ).
% End CNF derivation
cnf(c_0_469_0,axiom,
( ~ ssList(X1)
| ~ leq(X2,X3)
| ~ leq(X3,X2)
| app(app(X4,cons(X3,X5)),cons(X2,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ cyclefreeP(X1) ),
inference(unfold_definition,[status(thm)],[c_0_469,def_lhs_atom2]) ).
cnf(c_0_470_0,axiom,
( ~ ssList(X1)
| lt(X2,X3)
| lt(X3,X2)
| app(app(X4,cons(X3,X5)),cons(X2,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ strictorderP(X1) ),
inference(unfold_definition,[status(thm)],[c_0_470,def_lhs_atom2]) ).
cnf(c_0_471_0,axiom,
( ~ ssList(X1)
| leq(X2,X3)
| leq(X3,X2)
| app(app(X4,cons(X3,X5)),cons(X2,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ totalorderP(X1) ),
inference(unfold_definition,[status(thm)],[c_0_471,def_lhs_atom2]) ).
cnf(c_0_472_0,axiom,
( ~ ssList(X1)
| lt(X2,X3)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ strictorderedP(X1) ),
inference(unfold_definition,[status(thm)],[c_0_472,def_lhs_atom2]) ).
cnf(c_0_473_0,axiom,
( ~ ssList(X1)
| leq(X2,X3)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ totalorderedP(X1) ),
inference(unfold_definition,[status(thm)],[c_0_473,def_lhs_atom2]) ).
cnf(c_0_474_0,axiom,
( ~ ssList(X1)
| X2 != X3
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ duplicatefreeP(X1) ),
inference(unfold_definition,[status(thm)],[c_0_474,def_lhs_atom2]) ).
cnf(c_0_475_0,axiom,
( ~ ssList(X1)
| duplicatefreeP(X1)
| app(app(sk1_esk35_1(X1),cons(sk1_esk33_1(X1),sk1_esk36_1(X1))),cons(sk1_esk34_1(X1),sk1_esk37_1(X1))) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_475,def_lhs_atom2]) ).
cnf(c_0_476_0,axiom,
( ~ ssList(X1)
| strictorderedP(X1)
| app(app(sk1_esk30_1(X1),cons(sk1_esk28_1(X1),sk1_esk31_1(X1))),cons(sk1_esk29_1(X1),sk1_esk32_1(X1))) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_476,def_lhs_atom2]) ).
cnf(c_0_477_0,axiom,
( ~ ssList(X1)
| totalorderedP(X1)
| app(app(sk1_esk25_1(X1),cons(sk1_esk23_1(X1),sk1_esk26_1(X1))),cons(sk1_esk24_1(X1),sk1_esk27_1(X1))) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_477,def_lhs_atom2]) ).
cnf(c_0_478_0,axiom,
( ~ ssList(X1)
| strictorderP(X1)
| app(app(sk1_esk20_1(X1),cons(sk1_esk18_1(X1),sk1_esk21_1(X1))),cons(sk1_esk19_1(X1),sk1_esk22_1(X1))) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_478,def_lhs_atom2]) ).
cnf(c_0_479_0,axiom,
( ~ ssList(X1)
| totalorderP(X1)
| app(app(sk1_esk15_1(X1),cons(sk1_esk13_1(X1),sk1_esk16_1(X1))),cons(sk1_esk14_1(X1),sk1_esk17_1(X1))) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_479,def_lhs_atom2]) ).
cnf(c_0_480_0,axiom,
( ~ ssList(X1)
| cyclefreeP(X1)
| app(app(sk1_esk10_1(X1),cons(sk1_esk8_1(X1),sk1_esk11_1(X1))),cons(sk1_esk9_1(X1),sk1_esk12_1(X1))) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_480,def_lhs_atom2]) ).
cnf(c_0_481_0,axiom,
( ~ ssList(X1)
| X2 = X3
| app(X4,cons(X2,cons(X3,X5))) != X1
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ equalelemsP(X1) ),
inference(unfold_definition,[status(thm)],[c_0_481,def_lhs_atom2]) ).
cnf(c_0_482_0,axiom,
( ~ ssList(X1)
| equalelemsP(X1)
| app(sk1_esk40_1(X1),cons(sk1_esk38_1(X1),cons(sk1_esk39_1(X1),sk1_esk41_1(X1)))) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_482,def_lhs_atom2]) ).
cnf(c_0_483_0,axiom,
( ~ ssList(X1)
| app(app(sk1_esk6_2(X1,X2),X2),sk1_esk7_2(X1,X2)) = X1
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_483,def_lhs_atom2]) ).
cnf(c_0_484_0,axiom,
( ~ ssList(X1)
| app(sk1_esk1_2(X1,X2),cons(X2,sk1_esk2_2(X1,X2))) = X1
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_484,def_lhs_atom2]) ).
cnf(c_0_485_0,axiom,
( ~ ssItem(X1)
| frontsegP(X3,X4)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X3),cons(X2,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_485,def_lhs_atom1]) ).
cnf(c_0_486_0,axiom,
( ~ ssList(X2)
| segmentP(app(app(X1,X2),X3),X4)
| ~ segmentP(X2,X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X4) ),
inference(unfold_definition,[status(thm)],[c_0_486,def_lhs_atom2]) ).
cnf(c_0_487_0,axiom,
( ~ ssItem(X1)
| X1 = X2
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X3),cons(X2,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_487,def_lhs_atom1]) ).
cnf(c_0_488_0,axiom,
( ~ ssItem(X1)
| frontsegP(cons(X1,X3),cons(X2,X4))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(X3,X4)
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_488,def_lhs_atom1]) ).
cnf(c_0_489_0,axiom,
( ~ ssItem(X1)
| memberP(X3,X1)
| memberP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(app(X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_489,def_lhs_atom1]) ).
cnf(c_0_490_0,axiom,
( ~ ssList(X1)
| segmentP(X1,X2)
| ~ ssList(X2)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_490,def_lhs_atom2]) ).
cnf(c_0_491_0,axiom,
( ~ ssList(X1)
| memberP(X1,X2)
| ~ ssItem(X2)
| app(X3,cons(X2,X4)) != X1
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_491,def_lhs_atom2]) ).
cnf(c_0_492_0,axiom,
( ~ ssItem(X1)
| memberP(X3,X1)
| X1 = X2
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(cons(X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_492,def_lhs_atom1]) ).
cnf(c_0_493_0,axiom,
( ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(unfold_definition,[status(thm)],[c_0_493,def_lhs_atom2]) ).
cnf(c_0_494_0,axiom,
( ~ ssList(X3)
| app(cons(X1,X2),X3) = cons(X1,app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(unfold_definition,[status(thm)],[c_0_494,def_lhs_atom2]) ).
cnf(c_0_495_0,axiom,
( ~ ssItem(X1)
| strictorderedP(cons(X1,X2))
| nil = X2
| ~ ssList(X2)
| ~ lt(X1,hd(X2))
| ~ strictorderedP(X2) ),
inference(unfold_definition,[status(thm)],[c_0_495,def_lhs_atom1]) ).
cnf(c_0_496_0,axiom,
( ~ ssItem(X1)
| totalorderedP(cons(X1,X2))
| nil = X2
| ~ ssList(X2)
| ~ leq(X1,hd(X2))
| ~ totalorderedP(X2) ),
inference(unfold_definition,[status(thm)],[c_0_496,def_lhs_atom1]) ).
cnf(c_0_497_0,axiom,
( ~ ssList(X2)
| rearsegP(app(X1,X2),X3)
| ~ rearsegP(X2,X3)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_497,def_lhs_atom2]) ).
cnf(c_0_498_0,axiom,
( ~ ssList(X1)
| frontsegP(app(X1,X2),X3)
| ~ frontsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_498,def_lhs_atom2]) ).
cnf(c_0_499_0,axiom,
( ~ ssItem(X1)
| memberP(cons(X2,X3),X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_499,def_lhs_atom1]) ).
cnf(c_0_500_0,axiom,
( ~ ssItem(X1)
| memberP(app(X2,X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_500,def_lhs_atom1]) ).
cnf(c_0_501_0,axiom,
( ~ ssItem(X1)
| memberP(app(X2,X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_501,def_lhs_atom1]) ).
cnf(c_0_502_0,axiom,
( ~ ssItem(X1)
| nil = X2
| lt(X1,hd(X2))
| ~ ssList(X2)
| ~ strictorderedP(cons(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_502,def_lhs_atom1]) ).
cnf(c_0_503_0,axiom,
( ~ ssItem(X1)
| nil = X2
| leq(X1,hd(X2))
| ~ ssList(X2)
| ~ totalorderedP(cons(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_503,def_lhs_atom1]) ).
cnf(c_0_504_0,axiom,
( ~ ssItem(X1)
| gt(X1,X2)
| ~ gt(X3,X2)
| ~ gt(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(unfold_definition,[status(thm)],[c_0_504,def_lhs_atom1]) ).
cnf(c_0_505_0,axiom,
( ~ ssItem(X1)
| lt(X1,X2)
| ~ lt(X3,X2)
| ~ leq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(unfold_definition,[status(thm)],[c_0_505,def_lhs_atom1]) ).
cnf(c_0_506_0,axiom,
( ~ ssItem(X1)
| geq(X1,X2)
| ~ geq(X3,X2)
| ~ geq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(unfold_definition,[status(thm)],[c_0_506,def_lhs_atom1]) ).
cnf(c_0_507_0,axiom,
( ~ ssList(X1)
| segmentP(X1,X2)
| ~ segmentP(X3,X2)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_507,def_lhs_atom2]) ).
cnf(c_0_508_0,axiom,
( ~ ssList(X1)
| rearsegP(X1,X2)
| ~ rearsegP(X3,X2)
| ~ rearsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_508,def_lhs_atom2]) ).
cnf(c_0_509_0,axiom,
( ~ ssList(X1)
| frontsegP(X1,X2)
| ~ frontsegP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_509,def_lhs_atom2]) ).
cnf(c_0_510_0,axiom,
( ~ ssItem(X1)
| lt(X1,X2)
| ~ lt(X3,X2)
| ~ lt(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(unfold_definition,[status(thm)],[c_0_510,def_lhs_atom1]) ).
cnf(c_0_511_0,axiom,
( ~ ssItem(X1)
| leq(X1,X2)
| ~ leq(X3,X2)
| ~ leq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(unfold_definition,[status(thm)],[c_0_511,def_lhs_atom1]) ).
cnf(c_0_512_0,axiom,
( ~ ssList(X1)
| app(sk1_esk5_2(X1,X2),X2) = X1
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_512,def_lhs_atom2]) ).
cnf(c_0_513_0,axiom,
( ~ ssList(X1)
| app(X2,sk1_esk4_2(X1,X2)) = X1
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_513,def_lhs_atom2]) ).
cnf(c_0_514_0,axiom,
( ~ ssList(X1)
| X3 = X4
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_514,def_lhs_atom2]) ).
cnf(c_0_515_0,axiom,
( ~ ssList(X1)
| X2 = X1
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_515,def_lhs_atom2]) ).
cnf(c_0_516_0,axiom,
( ~ ssItem(X1)
| nil = X2
| strictorderedP(X2)
| ~ ssList(X2)
| ~ strictorderedP(cons(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_516,def_lhs_atom1]) ).
cnf(c_0_517_0,axiom,
( ~ ssItem(X1)
| nil = X2
| totalorderedP(X2)
| ~ ssList(X2)
| ~ totalorderedP(cons(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_517,def_lhs_atom1]) ).
cnf(c_0_518_0,axiom,
( ~ ssList(X2)
| X1 = X2
| app(X3,X1) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_518,def_lhs_atom2]) ).
cnf(c_0_519_0,axiom,
( ~ ssList(X2)
| X1 = X2
| app(X1,X3) != app(X2,X3)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_519,def_lhs_atom2]) ).
cnf(c_0_520_0,axiom,
( ~ ssList(X1)
| ssList(sk1_esk6_2(X1,X2))
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_520,def_lhs_atom2]) ).
cnf(c_0_521_0,axiom,
( ~ ssList(X1)
| ssList(sk1_esk7_2(X1,X2))
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_521,def_lhs_atom2]) ).
cnf(c_0_522_0,axiom,
( ~ ssList(X1)
| ssList(sk1_esk5_2(X1,X2))
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_522,def_lhs_atom2]) ).
cnf(c_0_523_0,axiom,
( ~ ssList(X1)
| ssList(sk1_esk4_2(X1,X2))
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_523,def_lhs_atom2]) ).
cnf(c_0_524_0,axiom,
( ~ ssList(X1)
| ssList(sk1_esk1_2(X1,X2))
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_524,def_lhs_atom2]) ).
cnf(c_0_525_0,axiom,
( ~ ssList(X1)
| ssList(sk1_esk2_2(X1,X2))
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_525,def_lhs_atom2]) ).
cnf(c_0_526_0,axiom,
( ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1
| ~ ssList(X2) ),
inference(unfold_definition,[status(thm)],[c_0_526,def_lhs_atom2]) ).
cnf(c_0_527_0,axiom,
( ~ ssItem(X1)
| nil = X2
| ~ ssList(X2)
| ~ strictorderedP(cons(X1,X2))
| nil != X2 ),
inference(unfold_definition,[status(thm)],[c_0_527,def_lhs_atom1]) ).
cnf(c_0_528_0,axiom,
( ~ ssItem(X1)
| nil = X2
| ~ ssList(X2)
| ~ totalorderedP(cons(X1,X2))
| nil != X2 ),
inference(unfold_definition,[status(thm)],[c_0_528,def_lhs_atom1]) ).
cnf(c_0_529_0,axiom,
( ~ ssItem(X1)
| memberP(cons(X2,X3),X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_529,def_lhs_atom1]) ).
cnf(c_0_530_0,axiom,
( ~ ssList(X2)
| app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1) ),
inference(unfold_definition,[status(thm)],[c_0_530,def_lhs_atom2]) ).
cnf(c_0_531_0,axiom,
( ~ ssItem(X1)
| X1 = X2
| ~ geq(X2,X1)
| ~ geq(X1,X2)
| ~ ssItem(X2) ),
inference(unfold_definition,[status(thm)],[c_0_531,def_lhs_atom1]) ).
cnf(c_0_532_0,axiom,
( ~ ssList(X1)
| X1 = X2
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) ),
inference(unfold_definition,[status(thm)],[c_0_532,def_lhs_atom2]) ).
cnf(c_0_533_0,axiom,
( ~ ssList(X1)
| X1 = X2
| ~ rearsegP(X2,X1)
| ~ rearsegP(X1,X2)
| ~ ssList(X2) ),
inference(unfold_definition,[status(thm)],[c_0_533,def_lhs_atom2]) ).
cnf(c_0_534_0,axiom,
( ~ ssList(X1)
| X1 = X2
| ~ frontsegP(X2,X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X2) ),
inference(unfold_definition,[status(thm)],[c_0_534,def_lhs_atom2]) ).
cnf(c_0_535_0,axiom,
( ~ ssItem(X1)
| X1 = X2
| ~ leq(X2,X1)
| ~ leq(X1,X2)
| ~ ssItem(X2) ),
inference(unfold_definition,[status(thm)],[c_0_535,def_lhs_atom1]) ).
cnf(c_0_536_0,axiom,
( ~ ssList(X1)
| rearsegP(X1,X2)
| ~ ssList(X2)
| app(X3,X2) != X1
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_536,def_lhs_atom2]) ).
cnf(c_0_537_0,axiom,
( ~ ssList(X1)
| frontsegP(X1,X2)
| ~ ssList(X2)
| app(X2,X3) != X1
| ~ ssList(X3) ),
inference(unfold_definition,[status(thm)],[c_0_537,def_lhs_atom2]) ).
cnf(c_0_538_0,axiom,
( ~ ssItem(X2)
| ~ gt(X1,X2)
| ~ gt(X2,X1)
| ~ ssItem(X1) ),
inference(unfold_definition,[status(thm)],[c_0_538,def_lhs_atom1]) ).
cnf(c_0_539_0,axiom,
( ~ ssItem(X2)
| ~ lt(X1,X2)
| ~ lt(X2,X1)
| ~ ssItem(X1) ),
inference(unfold_definition,[status(thm)],[c_0_539,def_lhs_atom1]) ).
cnf(c_0_540_0,axiom,
( ~ ssItem(X1)
| lt(X1,X2)
| X1 = X2
| ~ ssItem(X2)
| ~ leq(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_540,def_lhs_atom1]) ).
cnf(c_0_541_0,axiom,
( ~ ssItem(X1)
| lt(X1,X2)
| X1 = X2
| ~ leq(X1,X2)
| ~ ssItem(X2) ),
inference(unfold_definition,[status(thm)],[c_0_541,def_lhs_atom1]) ).
cnf(c_0_542_0,axiom,
( ~ ssList(X1)
| strictorderedP(X1)
| ~ lt(sk1_esk28_1(X1),sk1_esk29_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_542,def_lhs_atom2]) ).
cnf(c_0_543_0,axiom,
( ~ ssList(X1)
| totalorderedP(X1)
| ~ leq(sk1_esk23_1(X1),sk1_esk24_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_543,def_lhs_atom2]) ).
cnf(c_0_544_0,axiom,
( ~ ssList(X1)
| strictorderP(X1)
| ~ lt(sk1_esk18_1(X1),sk1_esk19_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_544,def_lhs_atom2]) ).
cnf(c_0_545_0,axiom,
( ~ ssList(X1)
| strictorderP(X1)
| ~ lt(sk1_esk19_1(X1),sk1_esk18_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_545,def_lhs_atom2]) ).
cnf(c_0_546_0,axiom,
( ~ ssList(X1)
| totalorderP(X1)
| ~ leq(sk1_esk13_1(X1),sk1_esk14_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_546,def_lhs_atom2]) ).
cnf(c_0_547_0,axiom,
( ~ ssList(X1)
| totalorderP(X1)
| ~ leq(sk1_esk14_1(X1),sk1_esk13_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_547,def_lhs_atom2]) ).
cnf(c_0_548_0,axiom,
( ~ ssItem(X1)
| leq(X1,X2)
| ~ ssItem(X2)
| ~ lt(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_548,def_lhs_atom1]) ).
cnf(c_0_549_0,axiom,
( ~ ssItem(X1)
| lt(X2,X1)
| ~ ssItem(X2)
| ~ gt(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_549,def_lhs_atom1]) ).
cnf(c_0_550_0,axiom,
( ~ ssItem(X1)
| gt(X1,X2)
| ~ ssItem(X2)
| ~ lt(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_550,def_lhs_atom1]) ).
cnf(c_0_551_0,axiom,
( ~ ssItem(X1)
| leq(X2,X1)
| ~ ssItem(X2)
| ~ geq(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_551,def_lhs_atom1]) ).
cnf(c_0_552_0,axiom,
( ~ ssItem(X1)
| geq(X1,X2)
| ~ ssItem(X2)
| ~ leq(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_552,def_lhs_atom1]) ).
cnf(c_0_553_0,axiom,
( ~ ssList(X1)
| hd(app(X1,X2)) = hd(X1)
| nil = X1
| ~ ssList(X2) ),
inference(unfold_definition,[status(thm)],[c_0_553,def_lhs_atom2]) ).
cnf(c_0_554_0,axiom,
( ~ ssItem(X1)
| strictorderedP(cons(X1,X2))
| ~ ssList(X2)
| nil != X2 ),
inference(unfold_definition,[status(thm)],[c_0_554,def_lhs_atom1]) ).
cnf(c_0_555_0,axiom,
( ~ ssItem(X1)
| totalorderedP(cons(X1,X2))
| ~ ssList(X2)
| nil != X2 ),
inference(unfold_definition,[status(thm)],[c_0_555,def_lhs_atom1]) ).
cnf(c_0_556_0,axiom,
( ~ ssList(X2)
| X1 = X2
| nil = X2
| nil = X1
| tl(X1) != tl(X2)
| hd(X1) != hd(X2)
| ~ ssList(X1) ),
inference(unfold_definition,[status(thm)],[c_0_556,def_lhs_atom2]) ).
cnf(c_0_557_0,axiom,
( ~ ssList(X2)
| tl(cons(X1,X2)) = X2
| ~ ssItem(X1) ),
inference(unfold_definition,[status(thm)],[c_0_557,def_lhs_atom2]) ).
cnf(c_0_558_0,axiom,
( ~ ssList(X2)
| hd(cons(X1,X2)) = X1
| ~ ssItem(X1) ),
inference(unfold_definition,[status(thm)],[c_0_558,def_lhs_atom2]) ).
cnf(c_0_559_0,axiom,
( ~ ssList(X1)
| ssList(app(X1,X2))
| ~ ssList(X2) ),
inference(unfold_definition,[status(thm)],[c_0_559,def_lhs_atom2]) ).
cnf(c_0_560_0,axiom,
( ~ ssList(X2)
| ssList(cons(X1,X2))
| ~ ssItem(X1) ),
inference(unfold_definition,[status(thm)],[c_0_560,def_lhs_atom2]) ).
cnf(c_0_561_0,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_561,def_lhs_atom1]) ).
cnf(c_0_562_0,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_562,def_lhs_atom2]) ).
cnf(c_0_563_0,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_563,def_lhs_atom1]) ).
cnf(c_0_564_0,axiom,
( ~ ssList(X1)
| singletonP(X1)
| cons(X2,nil) != X1
| ~ ssItem(X2) ),
inference(unfold_definition,[status(thm)],[c_0_564,def_lhs_atom2]) ).
cnf(c_0_565_0,axiom,
( ~ ssList(X1)
| nil = X2
| ~ ssList(X2)
| app(X1,X2) != nil ),
inference(unfold_definition,[status(thm)],[c_0_565,def_lhs_atom2]) ).
cnf(c_0_566_0,axiom,
( ~ ssList(X1)
| nil = X1
| ~ ssList(X2)
| app(X1,X2) != nil ),
inference(unfold_definition,[status(thm)],[c_0_566,def_lhs_atom2]) ).
cnf(c_0_567_0,axiom,
( ~ ssList(X1)
| cyclefreeP(X1)
| leq(sk1_esk8_1(X1),sk1_esk9_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_567,def_lhs_atom2]) ).
cnf(c_0_568_0,axiom,
( ~ ssList(X1)
| cyclefreeP(X1)
| leq(sk1_esk9_1(X1),sk1_esk8_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_568,def_lhs_atom2]) ).
cnf(c_0_569_0,axiom,
( ~ ssList(X2)
| cons(X1,X2) != X2
| ~ ssItem(X1) ),
inference(unfold_definition,[status(thm)],[c_0_569,def_lhs_atom2]) ).
cnf(c_0_570_0,axiom,
( ~ ssList(X2)
| cons(X1,X2) != nil
| ~ ssItem(X1) ),
inference(unfold_definition,[status(thm)],[c_0_570,def_lhs_atom2]) ).
cnf(c_0_571_0,axiom,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(unfold_definition,[status(thm)],[c_0_571,def_lhs_atom2]) ).
cnf(c_0_572_0,axiom,
( ~ ssList(X1)
| nil = X1
| cons(sk1_esk43_1(X1),sk1_esk42_1(X1)) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_572,def_lhs_atom2]) ).
cnf(c_0_573_0,axiom,
( ~ ssItem(X1)
| equalelemsP(cons(X1,nil)) ),
inference(unfold_definition,[status(thm)],[c_0_573,def_lhs_atom1]) ).
cnf(c_0_574_0,axiom,
( ~ ssItem(X1)
| duplicatefreeP(cons(X1,nil)) ),
inference(unfold_definition,[status(thm)],[c_0_574,def_lhs_atom1]) ).
cnf(c_0_575_0,axiom,
( ~ ssItem(X1)
| strictorderedP(cons(X1,nil)) ),
inference(unfold_definition,[status(thm)],[c_0_575,def_lhs_atom1]) ).
cnf(c_0_576_0,axiom,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
inference(unfold_definition,[status(thm)],[c_0_576,def_lhs_atom1]) ).
cnf(c_0_577_0,axiom,
( ~ ssItem(X1)
| strictorderP(cons(X1,nil)) ),
inference(unfold_definition,[status(thm)],[c_0_577,def_lhs_atom1]) ).
cnf(c_0_578_0,axiom,
( ~ ssItem(X1)
| totalorderP(cons(X1,nil)) ),
inference(unfold_definition,[status(thm)],[c_0_578,def_lhs_atom1]) ).
cnf(c_0_579_0,axiom,
( ~ ssItem(X1)
| cyclefreeP(cons(X1,nil)) ),
inference(unfold_definition,[status(thm)],[c_0_579,def_lhs_atom1]) ).
cnf(c_0_580_0,axiom,
( ~ ssList(X1)
| cons(sk1_esk3_1(X1),nil) = X1
| ~ singletonP(X1) ),
inference(unfold_definition,[status(thm)],[c_0_580,def_lhs_atom2]) ).
cnf(c_0_581_0,axiom,
( ~ ssList(X1)
| app(X1,X2) = nil
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(unfold_definition,[status(thm)],[c_0_581,def_lhs_atom2]) ).
cnf(c_0_582_0,axiom,
( ~ ssList(X1)
| neq(X1,X2)
| X1 = X2
| ~ ssList(X2) ),
inference(unfold_definition,[status(thm)],[c_0_582,def_lhs_atom2]) ).
cnf(c_0_583_0,axiom,
( ~ ssItem(X1)
| neq(X1,X2)
| X1 = X2
| ~ ssItem(X2) ),
inference(unfold_definition,[status(thm)],[c_0_583,def_lhs_atom1]) ).
cnf(c_0_584_0,axiom,
( ~ ssItem(X1)
| ~ lt(X1,X1) ),
inference(unfold_definition,[status(thm)],[c_0_584,def_lhs_atom1]) ).
cnf(c_0_585_0,axiom,
( ~ ssList(X1)
| nil = X1
| ~ segmentP(nil,X1) ),
inference(unfold_definition,[status(thm)],[c_0_585,def_lhs_atom2]) ).
cnf(c_0_586_0,axiom,
( ~ ssList(X1)
| nil = X1
| ~ rearsegP(nil,X1) ),
inference(unfold_definition,[status(thm)],[c_0_586,def_lhs_atom2]) ).
cnf(c_0_587_0,axiom,
( ~ ssList(X1)
| nil = X1
| ~ frontsegP(nil,X1) ),
inference(unfold_definition,[status(thm)],[c_0_587,def_lhs_atom2]) ).
cnf(c_0_588_0,axiom,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(unfold_definition,[status(thm)],[c_0_588,def_lhs_atom1]) ).
cnf(c_0_589_0,axiom,
( ~ ssList(X1)
| ssItem(sk1_esk3_1(X1))
| ~ singletonP(X1) ),
inference(unfold_definition,[status(thm)],[c_0_589,def_lhs_atom2]) ).
cnf(c_0_590_0,axiom,
( ~ ssList(X1)
| equalelemsP(X1)
| sk1_esk39_1(X1) != sk1_esk38_1(X1) ),
inference(unfold_definition,[status(thm)],[c_0_590,def_lhs_atom2]) ).
cnf(c_0_591_0,axiom,
( ~ ssList(X1)
| segmentP(nil,X1)
| nil != X1 ),
inference(unfold_definition,[status(thm)],[c_0_591,def_lhs_atom2]) ).
cnf(c_0_592_0,axiom,
( ~ ssList(X1)
| rearsegP(nil,X1)
| nil != X1 ),
inference(unfold_definition,[status(thm)],[c_0_592,def_lhs_atom2]) ).
cnf(c_0_593_0,axiom,
( ~ ssList(X1)
| frontsegP(nil,X1)
| nil != X1 ),
inference(unfold_definition,[status(thm)],[c_0_593,def_lhs_atom2]) ).
cnf(c_0_594_0,axiom,
( ~ ssList(X1)
| equalelemsP(X1)
| ssItem(sk1_esk38_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_594,def_lhs_atom2]) ).
cnf(c_0_595_0,axiom,
( ~ ssList(X1)
| equalelemsP(X1)
| ssItem(sk1_esk39_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_595,def_lhs_atom2]) ).
cnf(c_0_596_0,axiom,
( ~ ssList(X1)
| equalelemsP(X1)
| ssList(sk1_esk40_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_596,def_lhs_atom2]) ).
cnf(c_0_597_0,axiom,
( ~ ssList(X1)
| equalelemsP(X1)
| ssList(sk1_esk41_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_597,def_lhs_atom2]) ).
cnf(c_0_598_0,axiom,
( ~ ssList(X1)
| duplicatefreeP(X1)
| ssItem(sk1_esk33_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_598,def_lhs_atom2]) ).
cnf(c_0_599_0,axiom,
( ~ ssList(X1)
| duplicatefreeP(X1)
| ssItem(sk1_esk34_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_599,def_lhs_atom2]) ).
cnf(c_0_600_0,axiom,
( ~ ssList(X1)
| duplicatefreeP(X1)
| ssList(sk1_esk35_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_600,def_lhs_atom2]) ).
cnf(c_0_601_0,axiom,
( ~ ssList(X1)
| duplicatefreeP(X1)
| ssList(sk1_esk36_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_601,def_lhs_atom2]) ).
cnf(c_0_602_0,axiom,
( ~ ssList(X1)
| duplicatefreeP(X1)
| ssList(sk1_esk37_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_602,def_lhs_atom2]) ).
cnf(c_0_603_0,axiom,
( ~ ssList(X1)
| strictorderedP(X1)
| ssItem(sk1_esk28_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_603,def_lhs_atom2]) ).
cnf(c_0_604_0,axiom,
( ~ ssList(X1)
| strictorderedP(X1)
| ssItem(sk1_esk29_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_604,def_lhs_atom2]) ).
cnf(c_0_605_0,axiom,
( ~ ssList(X1)
| strictorderedP(X1)
| ssList(sk1_esk30_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_605,def_lhs_atom2]) ).
cnf(c_0_606_0,axiom,
( ~ ssList(X1)
| strictorderedP(X1)
| ssList(sk1_esk31_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_606,def_lhs_atom2]) ).
cnf(c_0_607_0,axiom,
( ~ ssList(X1)
| strictorderedP(X1)
| ssList(sk1_esk32_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_607,def_lhs_atom2]) ).
cnf(c_0_608_0,axiom,
( ~ ssList(X1)
| totalorderedP(X1)
| ssItem(sk1_esk23_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_608,def_lhs_atom2]) ).
cnf(c_0_609_0,axiom,
( ~ ssList(X1)
| totalorderedP(X1)
| ssItem(sk1_esk24_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_609,def_lhs_atom2]) ).
cnf(c_0_610_0,axiom,
( ~ ssList(X1)
| totalorderedP(X1)
| ssList(sk1_esk25_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_610,def_lhs_atom2]) ).
cnf(c_0_611_0,axiom,
( ~ ssList(X1)
| totalorderedP(X1)
| ssList(sk1_esk26_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_611,def_lhs_atom2]) ).
cnf(c_0_612_0,axiom,
( ~ ssList(X1)
| totalorderedP(X1)
| ssList(sk1_esk27_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_612,def_lhs_atom2]) ).
cnf(c_0_613_0,axiom,
( ~ ssList(X1)
| strictorderP(X1)
| ssItem(sk1_esk18_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_613,def_lhs_atom2]) ).
cnf(c_0_614_0,axiom,
( ~ ssList(X1)
| strictorderP(X1)
| ssItem(sk1_esk19_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_614,def_lhs_atom2]) ).
cnf(c_0_615_0,axiom,
( ~ ssList(X1)
| strictorderP(X1)
| ssList(sk1_esk20_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_615,def_lhs_atom2]) ).
cnf(c_0_616_0,axiom,
( ~ ssList(X1)
| strictorderP(X1)
| ssList(sk1_esk21_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_616,def_lhs_atom2]) ).
cnf(c_0_617_0,axiom,
( ~ ssList(X1)
| strictorderP(X1)
| ssList(sk1_esk22_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_617,def_lhs_atom2]) ).
cnf(c_0_618_0,axiom,
( ~ ssList(X1)
| totalorderP(X1)
| ssItem(sk1_esk13_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_618,def_lhs_atom2]) ).
cnf(c_0_619_0,axiom,
( ~ ssList(X1)
| totalorderP(X1)
| ssItem(sk1_esk14_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_619,def_lhs_atom2]) ).
cnf(c_0_620_0,axiom,
( ~ ssList(X1)
| totalorderP(X1)
| ssList(sk1_esk15_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_620,def_lhs_atom2]) ).
cnf(c_0_621_0,axiom,
( ~ ssList(X1)
| totalorderP(X1)
| ssList(sk1_esk16_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_621,def_lhs_atom2]) ).
cnf(c_0_622_0,axiom,
( ~ ssList(X1)
| totalorderP(X1)
| ssList(sk1_esk17_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_622,def_lhs_atom2]) ).
cnf(c_0_623_0,axiom,
( ~ ssList(X1)
| cyclefreeP(X1)
| ssItem(sk1_esk8_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_623,def_lhs_atom2]) ).
cnf(c_0_624_0,axiom,
( ~ ssList(X1)
| cyclefreeP(X1)
| ssItem(sk1_esk9_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_624,def_lhs_atom2]) ).
cnf(c_0_625_0,axiom,
( ~ ssList(X1)
| cyclefreeP(X1)
| ssList(sk1_esk10_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_625,def_lhs_atom2]) ).
cnf(c_0_626_0,axiom,
( ~ ssList(X1)
| cyclefreeP(X1)
| ssList(sk1_esk11_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_626,def_lhs_atom2]) ).
cnf(c_0_627_0,axiom,
( ~ ssList(X1)
| cyclefreeP(X1)
| ssList(sk1_esk12_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_627,def_lhs_atom2]) ).
cnf(c_0_628_0,axiom,
( ~ ssItem(X1)
| geq(X1,X1) ),
inference(unfold_definition,[status(thm)],[c_0_628,def_lhs_atom1]) ).
cnf(c_0_629_0,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(unfold_definition,[status(thm)],[c_0_629,def_lhs_atom2]) ).
cnf(c_0_630_0,axiom,
( ~ ssList(X1)
| rearsegP(X1,X1) ),
inference(unfold_definition,[status(thm)],[c_0_630,def_lhs_atom2]) ).
cnf(c_0_631_0,axiom,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(unfold_definition,[status(thm)],[c_0_631,def_lhs_atom2]) ).
cnf(c_0_632_0,axiom,
( ~ ssItem(X1)
| leq(X1,X1) ),
inference(unfold_definition,[status(thm)],[c_0_632,def_lhs_atom1]) ).
cnf(c_0_633_0,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_633,def_lhs_atom2]) ).
cnf(c_0_634_0,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_634,def_lhs_atom2]) ).
cnf(c_0_635_0,axiom,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(unfold_definition,[status(thm)],[c_0_635,def_lhs_atom2]) ).
cnf(c_0_636_0,axiom,
( ~ ssList(X1)
| rearsegP(X1,nil) ),
inference(unfold_definition,[status(thm)],[c_0_636,def_lhs_atom2]) ).
cnf(c_0_637_0,axiom,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(unfold_definition,[status(thm)],[c_0_637,def_lhs_atom2]) ).
cnf(c_0_638_0,axiom,
( ~ ssList(X1)
| duplicatefreeP(X1)
| sk1_esk34_1(X1) = sk1_esk33_1(X1) ),
inference(unfold_definition,[status(thm)],[c_0_638,def_lhs_atom2]) ).
cnf(c_0_639_0,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(sk1_esk45_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_639,def_lhs_atom2]) ).
cnf(c_0_640_0,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(sk1_esk44_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_640,def_lhs_atom2]) ).
cnf(c_0_641_0,axiom,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(unfold_definition,[status(thm)],[c_0_641,def_lhs_atom2]) ).
cnf(c_0_642_0,axiom,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(unfold_definition,[status(thm)],[c_0_642,def_lhs_atom2]) ).
cnf(c_0_643_0,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(sk1_esk42_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_643,def_lhs_atom2]) ).
cnf(c_0_644_0,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(sk1_esk43_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_644,def_lhs_atom2]) ).
cnf(c_0_645_0,axiom,
( ~ ssList(X1)
| nil = X1
| tl(X1) = sk1_esk45_1(X1) ),
inference(unfold_definition,[status(thm)],[c_0_645,def_lhs_atom2]) ).
cnf(c_0_646_0,axiom,
( ~ ssList(X1)
| nil = X1
| sk1_esk44_1(X1) = hd(X1) ),
inference(unfold_definition,[status(thm)],[c_0_646,def_lhs_atom2]) ).
cnf(c_0_647_0,axiom,
equalelemsP(nil),
inference(unfold_definition,[status(thm)],[c_0_647,def_lhs_atom11]) ).
cnf(c_0_648_0,axiom,
duplicatefreeP(nil),
inference(unfold_definition,[status(thm)],[c_0_648,def_lhs_atom10]) ).
cnf(c_0_649_0,axiom,
strictorderedP(nil),
inference(unfold_definition,[status(thm)],[c_0_649,def_lhs_atom9]) ).
cnf(c_0_650_0,axiom,
totalorderedP(nil),
inference(unfold_definition,[status(thm)],[c_0_650,def_lhs_atom8]) ).
cnf(c_0_651_0,axiom,
strictorderP(nil),
inference(unfold_definition,[status(thm)],[c_0_651,def_lhs_atom7]) ).
cnf(c_0_652_0,axiom,
totalorderP(nil),
inference(unfold_definition,[status(thm)],[c_0_652,def_lhs_atom6]) ).
cnf(c_0_653_0,axiom,
cyclefreeP(nil),
inference(unfold_definition,[status(thm)],[c_0_653,def_lhs_atom5]) ).
cnf(c_0_654_0,axiom,
~ singletonP(nil),
inference(unfold_definition,[status(thm)],[c_0_654,def_lhs_atom4]) ).
cnf(c_0_655_0,axiom,
ssList(nil),
inference(unfold_definition,[status(thm)],[c_0_655,def_lhs_atom3]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
? [X1] :
( ssItem(X1)
& ? [X2] :
( ssItem(X2)
& X1 != X2 ) ),
file('<stdin>',ax2) ).
fof(c_0_1_002,axiom,
? [X1] :
( ssItem(X1)
& ? [X2] :
( ssItem(X2)
& X1 != X2 ) ),
c_0_0 ).
fof(c_0_2_003,plain,
( ssItem(esk1_0)
& ssItem(esk2_0)
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1])]) ).
cnf(c_0_3_004,plain,
ssItem(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,plain,
ssItem(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_006,plain,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6_007,plain,
ssItem(esk1_0),
c_0_3,
[final] ).
cnf(c_0_7_008,plain,
ssItem(esk2_0),
c_0_4,
[final] ).
cnf(c_0_8_009,plain,
esk1_0 != esk2_0,
c_0_5,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_8_0,axiom,
sk2_esk1_0 != sk2_esk2_0,
inference(literals_permutation,[status(thm)],[c_0_8]) ).
cnf(c_0_6_0,axiom,
ssItem(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_6]) ).
cnf(c_0_7_0,axiom,
ssItem(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_7]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_010,conjecture,
$true,
file('<stdin>',co1) ).
fof(c_0_1_011,negated_conjecture,
~ $true,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).
fof(c_0_2_012,negated_conjecture,
~ $true,
c_0_1 ).
cnf(c_0_3_013,negated_conjecture,
$false,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_014,negated_conjecture,
$false,
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_190,negated_conjecture,
$false,
file('/export/starexec/sandbox2/tmp/iprover_modulo_8e3e2e.p',c_0_4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWC128+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.09 % Command : iprover_modulo %s %d
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Sun Jun 12 17:18:26 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.09/0.29 % Running in mono-core mode
% 0.13/0.34 % Orienting using strategy Equiv(ClausalAll)
% 0.13/0.34 % FOF problem with conjecture
% 0.13/0.34 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_ce4389.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_8e3e2e.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_d4ac61 | grep -v "SZS"
% 0.13/0.35
% 0.13/0.35 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.13/0.35
% 0.13/0.35 %
% 0.13/0.35 % ------ iProver source info
% 0.13/0.35
% 0.13/0.35 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.13/0.35 % git: non_committed_changes: true
% 0.13/0.35 % git: last_make_outside_of_git: true
% 0.13/0.35
% 0.13/0.35 %
% 0.13/0.35 % ------ Input Options
% 0.13/0.35
% 0.13/0.35 % --out_options all
% 0.13/0.35 % --tptp_safe_out true
% 0.13/0.35 % --problem_path ""
% 0.13/0.35 % --include_path ""
% 0.13/0.35 % --clausifier .//eprover
% 0.13/0.35 % --clausifier_options --tstp-format
% 0.13/0.35 % --stdin false
% 0.13/0.35 % --dbg_backtrace false
% 0.13/0.35 % --dbg_dump_prop_clauses false
% 0.13/0.35 % --dbg_dump_prop_clauses_file -
% 0.13/0.35 % --dbg_out_stat false
% 0.13/0.35
% 0.13/0.35 % ------ General Options
% 0.13/0.35
% 0.13/0.35 % --fof false
% 0.13/0.35 % --time_out_real 150.
% 0.13/0.35 % --time_out_prep_mult 0.2
% 0.13/0.35 % --time_out_virtual -1.
% 0.13/0.35 % --schedule none
% 0.13/0.35 % --ground_splitting input
% 0.13/0.35 % --splitting_nvd 16
% 0.13/0.35 % --non_eq_to_eq false
% 0.13/0.35 % --prep_gs_sim true
% 0.13/0.35 % --prep_unflatten false
% 0.13/0.35 % --prep_res_sim true
% 0.13/0.35 % --prep_upred true
% 0.13/0.35 % --res_sim_input true
% 0.13/0.35 % --clause_weak_htbl true
% 0.13/0.35 % --gc_record_bc_elim false
% 0.13/0.35 % --symbol_type_check false
% 0.13/0.35 % --clausify_out false
% 0.13/0.35 % --large_theory_mode false
% 0.13/0.35 % --prep_sem_filter none
% 0.13/0.35 % --prep_sem_filter_out false
% 0.13/0.35 % --preprocessed_out false
% 0.13/0.35 % --sub_typing false
% 0.13/0.35 % --brand_transform false
% 0.13/0.35 % --pure_diseq_elim true
% 0.13/0.35 % --min_unsat_core false
% 0.13/0.35 % --pred_elim true
% 0.13/0.35 % --add_important_lit false
% 0.13/0.35 % --soft_assumptions false
% 0.13/0.36 % --reset_solvers false
% 0.13/0.36 % --bc_imp_inh []
% 0.13/0.36 % --conj_cone_tolerance 1.5
% 0.13/0.36 % --prolific_symb_bound 500
% 0.13/0.36 % --lt_threshold 2000
% 0.13/0.36
% 0.13/0.36 % ------ SAT Options
% 0.13/0.36
% 0.13/0.36 % --sat_mode false
% 0.13/0.36 % --sat_fm_restart_options ""
% 0.13/0.36 % --sat_gr_def false
% 0.13/0.36 % --sat_epr_types true
% 0.13/0.36 % --sat_non_cyclic_types false
% 0.13/0.36 % --sat_finite_models false
% 0.13/0.36 % --sat_fm_lemmas false
% 0.13/0.36 % --sat_fm_prep false
% 0.13/0.36 % --sat_fm_uc_incr true
% 0.13/0.36 % --sat_out_model small
% 0.13/0.36 % --sat_out_clauses false
% 0.13/0.36
% 0.13/0.36 % ------ QBF Options
% 0.13/0.36
% 0.13/0.36 % --qbf_mode false
% 0.13/0.36 % --qbf_elim_univ true
% 0.13/0.36 % --qbf_sk_in true
% 0.13/0.36 % --qbf_pred_elim true
% 0.13/0.36 % --qbf_split 32
% 0.13/0.36
% 0.13/0.36 % ------ BMC1 Options
% 0.13/0.36
% 0.13/0.36 % --bmc1_incremental false
% 0.13/0.36 % --bmc1_axioms reachable_all
% 0.13/0.36 % --bmc1_min_bound 0
% 0.13/0.36 % --bmc1_max_bound -1
% 0.13/0.36 % --bmc1_max_bound_default -1
% 0.13/0.36 % --bmc1_symbol_reachability true
% 0.13/0.36 % --bmc1_property_lemmas false
% 0.13/0.36 % --bmc1_k_induction false
% 0.13/0.36 % --bmc1_non_equiv_states false
% 0.13/0.36 % --bmc1_deadlock false
% 0.13/0.36 % --bmc1_ucm false
% 0.13/0.36 % --bmc1_add_unsat_core none
% 0.13/0.36 % --bmc1_unsat_core_children false
% 0.13/0.36 % --bmc1_unsat_core_extrapolate_axioms false
% 0.13/0.36 % --bmc1_out_stat full
% 0.13/0.36 % --bmc1_ground_init false
% 0.13/0.36 % --bmc1_pre_inst_next_state false
% 0.13/0.36 % --bmc1_pre_inst_state false
% 0.13/0.36 % --bmc1_pre_inst_reach_state false
% 0.13/0.36 % --bmc1_out_unsat_core false
% 0.13/0.36 % --bmc1_aig_witness_out false
% 0.13/0.36 % --bmc1_verbose false
% 0.13/0.36 % --bmc1_dump_clauses_tptp false
% 0.13/0.36 % --bmc1_dump_unsat_core_tptp false
% 0.13/0.36 % --bmc1_dump_file -
% 0.13/0.36 % --bmc1_ucm_expand_uc_limit 128
% 0.13/0.36 % --bmc1_ucm_n_expand_iterations 6
% 0.13/0.36 % --bmc1_ucm_extend_mode 1
% 0.13/0.36 % --bmc1_ucm_init_mode 2
% 0.13/0.36 % --bmc1_ucm_cone_mode none
% 0.13/0.36 % --bmc1_ucm_reduced_relation_type 0
% 0.13/0.36 % --bmc1_ucm_relax_model 4
% 0.13/0.36 % --bmc1_ucm_full_tr_after_sat true
% 0.13/0.36 % --bmc1_ucm_expand_neg_assumptions false
% 0.13/0.36 % --bmc1_ucm_layered_model none
% 0.13/0.36 % --bmc1_ucm_max_lemma_size 10
% 0.13/0.36
% 0.13/0.36 % ------ AIG Options
% 0.13/0.36
% 0.13/0.36 % --aig_mode false
% 0.13/0.36
% 0.13/0.36 % ------ Instantiation Options
% 0.13/0.36
% 0.13/0.36 % --instantiation_flag true
% 0.13/0.36 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.13/0.36 % --inst_solver_per_active 750
% 0.13/0.36 % --inst_solver_calls_frac 0.5
% 0.13/0.36 % --inst_passive_queue_type priority_queues
% 0.13/0.36 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.13/0.36 % --inst_passive_queues_freq [25;2]
% 0.13/0.36 % --inst_dismatching true
% 0.13/0.36 % --inst_eager_unprocessed_to_passive true
% 0.13/0.36 % --inst_prop_sim_given true
% 0.13/0.36 % --inst_prop_sim_new false
% 0.13/0.36 % --inst_orphan_elimination true
% 0.13/0.36 % --inst_learning_loop_flag true
% 0.13/0.36 % --inst_learning_start 3000
% 0.13/0.36 % --inst_learning_factor 2
% 0.13/0.36 % --inst_start_prop_sim_after_learn 3
% 0.13/0.36 % --inst_sel_renew solver
% 0.13/0.36 % --inst_lit_activity_flag true
% 0.13/0.36 % --inst_out_proof true
% 0.13/0.36
% 0.13/0.36 % ------ Resolution Options
% 0.13/0.36
% 0.13/0.36 % --resolution_flag true
% 0.13/0.36 % --res_lit_sel kbo_max
% 0.13/0.36 % --res_to_prop_solver none
% 0.13/0.36 % --res_prop_simpl_new false
% 0.13/0.36 % --res_prop_simpl_given false
% 0.13/0.36 % --res_passive_queue_type priority_queues
% 0.13/0.36 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.13/0.36 % --res_passive_queues_freq [15;5]
% 0.13/0.36 % --res_forward_subs full
% 0.13/0.36 % --res_backward_subs full
% 0.13/0.36 % --res_forward_subs_resolution true
% 0.13/0.36 % --res_backward_subs_resolution true
% 0.13/0.36 % --res_orphan_elimination false
% 0.13/0.36 % --res_time_limit 1000.
% 0.13/0.36 % --res_out_proof true
% 0.13/0.36 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_ce4389.s
% 0.13/0.36 % --modulo true
% 0.13/0.36
% 0.13/0.36 % ------ Combination Options
% 0.13/0.36
% 0.13/0.36 % --comb_res_mult 1000
% 0.13/0.36 % --comb_inst_mult 300
% 0.13/0.36 % ------
% 0.13/0.36
% 0.13/0.36 % ------ Parsing...%
% 0.13/0.36
% 0.13/0.36
% 0.13/0.36 % Resolution empty clause
% 0.13/0.36
% 0.13/0.36 % ------ Statistics
% 0.13/0.36
% 0.13/0.36 % ------ General
% 0.13/0.36
% 0.13/0.36 % num_of_input_clauses: 191
% 0.13/0.36 % num_of_input_neg_conjectures: 1
% 0.13/0.36 % num_of_splits: 0
% 0.13/0.36 % num_of_split_atoms: 0
% 0.13/0.36 % num_of_sem_filtered_clauses: 0
% 0.13/0.36 % num_of_subtypes: 0
% 0.13/0.36 % monotx_restored_types: 0
% 0.13/0.36 % sat_num_of_epr_types: 0
% 0.13/0.36 % sat_num_of_non_cyclic_types: 0
% 0.13/0.36 % sat_guarded_non_collapsed_types: 0
% 0.13/0.36 % is_epr: 0
% 0.13/0.36 % is_horn: 0
% 0.13/0.36 % has_eq: 0
% 0.13/0.36 % num_pure_diseq_elim: 0
% 0.13/0.36 % simp_replaced_by: 0
% 0.13/0.36 % res_preprocessed: 0
% 0.13/0.36 % prep_upred: 0
% 0.13/0.36 % prep_unflattend: 0
% 0.13/0.36 % pred_elim_cands: 0
% 0.13/0.36 % pred_elim: 0
% 0.13/0.36 % pred_elim_cl: 0
% 0.13/0.36 % pred_elim_cycles: 0
% 0.13/0.36 % forced_gc_time: 0
% 0.13/0.36 % gc_basic_clause_elim: 0
% 0.13/0.36 % parsing_time: 0.
% 0.13/0.36 % sem_filter_time: 0.
% 0.13/0.36 % pred_elim_time: 0.
% 0.13/0.36 % out_proof_time: 0.
% 0.13/0.36 % monotx_time: 0.
% 0.13/0.36 % subtype_inf_time: 0.
% 0.13/0.36 % unif_index_cands_time: 0.
% 0.13/0.36 % unif_index_add_time: 0.
% 0.13/0.36 % total_time: 0.017
% 0.13/0.36 % num_of_symbols: 96
% 0.13/0.36 % num_of_terms: 521
% 0.13/0.36
% 0.13/0.36 % ------ Propositional Solver
% 0.13/0.36
% 0.13/0.36 % prop_solver_calls: 0
% 0.13/0.36 % prop_fast_solver_calls: 0
% 0.13/0.36 % prop_num_of_clauses: 0
% 0.13/0.36 % prop_preprocess_simplified: 0
% 0.13/0.36 % prop_fo_subsumed: 0
% 0.13/0.36 % prop_solver_time: 0.
% 0.13/0.36 % prop_fast_solver_time: 0.
% 0.13/0.36 % prop_unsat_core_time: 0.
% 0.13/0.36
% 0.13/0.36 % ------ QBF
% 0.13/0.36
% 0.13/0.36 % qbf_q_res: 0
% 0.13/0.36 % qbf_num_tautologies: 0
% 0.13/0.36 % qbf_prep_cycles: 0
% 0.13/0.36
% 0.13/0.36 % ------ BMC1
% 0.13/0.36
% 0.13/0.36 % bmc1_current_bound: -1
% 0.13/0.36 % bmc1_last_solved_bound: -1
% 0.13/0.36 % bmc1_unsat_core_size: -1
% 0.13/0.36 % bmc1_unsat_core_parents_size: -1
% 0.13/0.36 % bmc1_merge_next_fun: 0
% 0.13/0.36 % bmc1_unsat_core_clauses_time: 0.
% 0.13/0.36
% 0.13/0.36 % ------ Instantiation
% 0.13/0.36
% 0.13/0.36 % inst_num_of_clauses: undef
% 0.13/0.36 % inst_num_in_passive: undef
% 0.13/0.36 % inst_num_in_active: 0
% 0.13/0.36 % inst_num_in_unprocessed: 0
% 0.13/0.36 % inst_num_of_loops: 0
% 0.13/0.36 % inst_num_of_learning_restarts: 0
% 0.13/0.36 % inst_num_moves_active_passive: 0
% 0.13/0.36 % inst_lit_activity: 0
% 0.13/0.36 % inst_lit_activity_moves: 0
% 0.13/0.36 % inst_num_tautologies: 0
% 0.13/0.36 % inst_num_prop_implied: 0
% 0.13/0.36 % inst_num_existing_simplified: 0
% 0.13/0.36 % inst_num_eq_res_simplified: 0
% 0.13/0.36 % inst_num_child_elim: 0
% 0.13/0.36 % inst_num_of_dismatching_blockings: 0
% 0.13/0.36 % inst_num_of_non_proper_insts: 0
% 0.13/0.36 % inst_num_of_duplicates: 0
% 0.13/0.36 % inst_inst_num_from_inst_to_res: 0
% 0.13/0.36 % inst_dismatching_checking_time: 0.
% 0.13/0.36
% 0.13/0.36 % ------ Resolution
% 0.13/0.36
% 0.13/0.36 % res_num_of_clauses: undef
% 0.13/0.36 % res_num_in_passive: undef
% 0.13/0.36 % res_num_in_active: 0
% 0.13/0.36 % res_num_of_loops: 0
% 0.13/0.36 % res_forward_subset_subsumed: 0
% 0.13/0.36 % res_backward_subset_subsumed: 0
% 0.13/0.36 % res_forward_subsumed: 0
% 0.13/0.36 % res_backward_subsumed: 0
% 0.13/0.36 % res_forward_subsumption_resolution: 0
% 0.13/0.36 % res_backward_subsumption_resolution: 0
% 0.13/0.36 % res_clause_to_clause_subsumption: 0
% 0.13/0.36 % res_orphan_elimination: 0
% 0.13/0.36 % res_tautology_del: 0
% 0.13/0.36 % res_num_eq_res_simplified: 0
% 0.13/0.36 % res_num_sel_changes: 0
% 0.13/0.36 % res_moves_from_active_to_pass: 0
% 0.13/0.36
% 0.13/0.36 % Status Unsatisfiable
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------