%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC295-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:09:12 PM UTC 2026
% Result : Unsatisfiable 147.96s 27.08s
% Output : CNFRefutation 147.96s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f256ERROR: Could not build tree for root c_467873ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
fof(f60,axiom,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
fof(f72,axiom,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
fof(f83,axiom,
! [X0] :
( frontsegP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause83) ).
fof(f84,axiom,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause84) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f96,axiom,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
fof(f99,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| nil != cons(X0,X1) ),
inference(reorient_equations,[],[f98]) ).
fof(f103,axiom,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
fof(f107,axiom,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
fof(f112,axiom,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
fof(f119,axiom,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
fof(f121,axiom,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1) ),
inference(reorient_equations,[],[f121]) ).
fof(f123,axiom,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1) ),
inference(reorient_equations,[],[f123]) ).
fof(f125,axiom,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f134,axiom,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause127) ).
fof(f135,plain,
! [X0,X1] :
( X0 = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(reorient_equations,[],[f134]) ).
fof(f138,axiom,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause129) ).
fof(f139,plain,
! [X0,X1] :
( X0 = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(reorient_equations,[],[f138]) ).
fof(f142,axiom,
! [X0,X1] :
( app(skaf46(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause131) ).
fof(f143,axiom,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
fof(f147,axiom,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause136) ).
fof(f148,axiom,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause137) ).
fof(f151,axiom,
! [X2,X0,X1] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
fof(f152,axiom,
! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
fof(f154,axiom,
! [X2,X0,X1] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause143) ).
fof(f155,axiom,
! [X2,X0,X1] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
fof(f162,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause150) ).
fof(f163,axiom,
! [X2,X0,X1] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause151) ).
fof(f173,axiom,
! [X2,X0,X1] :
( X2 = X0
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause161) ).
fof(f174,plain,
! [X2,X0,X1] :
( X0 = X2
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(reorient_equations,[],[f173]) ).
fof(f183,axiom,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause170) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
fof(f193,axiom,
! [X2,X3,X0,X1,X4] :
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
sk1 = app(app(sk6,cons(sk5,nil)),sk7),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
ssItem(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f217,negated_conjecture,
( nil = sk3
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f218,negated_conjecture,
( nil = sk4
| cons(sk9,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f219,plain,
( nil = sk4
| sk3 = cons(sk9,nil) ),
inference(reorient_equations,[],[f218]) ).
fof(f222,negated_conjecture,
( nil = sk3
| cons(sk9,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_21) ).
fof(f223,plain,
( nil = sk3
| sk3 = cons(sk9,nil) ),
inference(reorient_equations,[],[f222]) ).
fof(f224,negated_conjecture,
( nil = sk3
| memberP(sk4,sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_22) ).
fof(f228,plain,
sk3 = app(app(sk6,cons(sk5,nil)),sk7),
inference(definition_unfolding,[],[f210,f205]) ).
fof(f231,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f83]) ).
fof(f236,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f239,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f240,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
fof(f243,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f187]) ).
fof(f246,plain,
! [X2,X3,X0,X1] :
( ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(equality_resolution,[],[f193]) ).
tcf(c_264,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_268,plain,
! [X0: $i] : ssItem(skaf83(X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_269,plain,
! [X0: $i] : ssList(skaf82(X0)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_307,plain,
! [X0: $i,X1: $i] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_316,plain,
! [X0: $i] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_327,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_329,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_330,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_339,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_340,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_357,plain,
! [X0: $i] :
( ( cons(skaf44(X0),nil) = X0 )
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_360,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_365,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_372,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] :
( ( app(skaf46(X0,X1),X1) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( ( app(X1,skaf45(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i,X2: $i] :
( rearsegP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X0,X2) ) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X2,X1) ) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X3)
| ~ ssList(X1)
| ( cons(X0,X1) != cons(X2,X3) ) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3))) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_444,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_445,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_446,negated_conjecture,
ssItem(sk5),
inference(cnf_transformation,[],[f206]) ).
tcf(c_447,negated_conjecture,
ssList(sk6),
inference(cnf_transformation,[],[f207]) ).
tcf(c_448,negated_conjecture,
ssList(sk7),
inference(cnf_transformation,[],[f208]) ).
tcf(c_449,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk3,
inference(cnf_transformation,[],[f228]) ).
tcf(c_450,negated_conjecture,
ssItem(sk8),
inference(cnf_transformation,[],[f211]) ).
tcf(c_451,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_456,negated_conjecture,
( ssItem(sk9)
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_457,negated_conjecture,
( ( sk4 = nil )
| ( cons(sk9,nil) = sk3 ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_460,negated_conjecture,
( ( sk3 = nil )
| ( cons(sk9,nil) = sk3 ) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_461,negated_conjecture,
( memberP(sk4,sk9)
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_523,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_399,c_341]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_400,c_341]) ).
tcf(c_6697,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_328]) ).
tcf(c_6698,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_328]) ).
tcf(c_6699,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_328]) ).
tcf(c_6700,definition,
iPr_def_12 = cons(sk5,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6701,definition,
iPr_def_13 = app(sk6,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6702,definition,
iPr_def_14 = app(iPr_def_13,sk7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_6703,definition,
iPr_def_15 = cons(sk9,nil),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_6704,negated_conjecture,
iPr_def_14 = sk3,
inference(demodulation,[status(thm)],[c_449,c_6700,c_6701,c_6702]) ).
tcf(c_6706,negated_conjecture,
( memberP(sk4,sk9)
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_461]) ).
tcf(c_6707,negated_conjecture,
( ( iPr_def_15 = sk3 )
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_460,c_6703]) ).
tcf(c_6710,negated_conjecture,
( ( iPr_def_15 = sk3 )
| ( sk4 = nil ) ),
inference(demodulation,[status(thm)],[c_457]) ).
tcf(c_6711,negated_conjecture,
( ssItem(sk9)
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_456]) ).
tcf(c_6716,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
inference(demodulation,[status(thm)],[c_451]) ).
tcf(c_6717,negated_conjecture,
ssItem(sk8),
inference(demodulation,[status(thm)],[c_450]) ).
tcf(c_6718,negated_conjecture,
ssList(sk7),
inference(demodulation,[status(thm)],[c_448]) ).
tcf(c_6719,negated_conjecture,
ssList(sk6),
inference(demodulation,[status(thm)],[c_447]) ).
tcf(c_6720,negated_conjecture,
ssItem(sk5),
inference(demodulation,[status(thm)],[c_446]) ).
tcf(c_6721,negated_conjecture,
ssList(sk4),
inference(demodulation,[status(thm)],[c_445]) ).
tcf(c_6722,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_444]) ).
tcf(c_6725,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X0,X2)
| ~ memberP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9355,plain,
ssList(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_6722,c_6704]) ).
tcf(c_9356,plain,
( ssItem(sk9)
| ( nil = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6711,c_6704]) ).
tcf(c_9367,plain,
( memberP(sk4,sk9)
| ( nil = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6706,c_6704]) ).
tcf(c_9386,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( nil = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6707,c_6704]) ).
tcf(c_9659,plain,
! [X0: $i,X1: $i] : app(skaf46(X0,X1),nil) = skaf46(X0,X1),
inference(superposition,[status(thm)],[c_306,c_329]) ).
tcf(c_10009,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6701,c_341]) ).
tcf(c_10023,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10009,c_6719]) ).
tcf(c_10110,plain,
( ssList(iPr_def_12)
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6700,c_342]) ).
tcf(c_10119,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_10110,c_6720,c_264]) ).
tcf(c_10130,plain,
ssList(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_10023,c_10119]) ).
tcf(c_10159,plain,
app(nil,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_10119,c_330]) ).
tcf(c_10160,plain,
app(iPr_def_12,nil) = iPr_def_12,
inference(superposition,[status(thm)],[c_10119,c_329]) ).
tcf(c_10512,plain,
( rearsegP(iPr_def_12,nil)
| ~ ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_10160,c_862]) ).
tcf(c_10517,plain,
rearsegP(iPr_def_12,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_10512,c_10119,c_264]) ).
tcf(c_10565,plain,
( ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(instantiation,[status(thm)],[c_327]) ).
tcf(c_10606,plain,
( frontsegP(iPr_def_13,sk6)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6701,c_863]) ).
tcf(c_10647,plain,
frontsegP(iPr_def_13,sk6),
inference(forward_subsumption_resolution,[status(thm)],[c_10606,c_10119,c_6719]) ).
tcf(c_10771,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ iPr_def_10
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6697,c_352]) ).
tcf(c_10774,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(skaf83(X1),X0)) = X0 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_268,c_352]) ).
tcf(c_11009,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_6700,c_354]) ).
tcf(c_11016,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_11009,c_6720,c_264]) ).
tcf(c_11018,plain,
! [X0: $i] :
( ( cons(skaf44(cons(X0,nil)),nil) = cons(X0,nil) )
| ~ singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(instantiation,[status(thm)],[c_357]) ).
tcf(c_11690,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_10130,c_360]) ).
tcf(c_11885,plain,
! [X0: $i,X1: $i] :
( ( skaf46(X0,X1) = nil )
| ( cons(skaf83(skaf46(X0,X1)),skaf82(skaf46(X0,X1))) = skaf46(X0,X1) ) ),
inference(superposition,[status(thm)],[c_306,c_365]) ).
tcf(c_12062,plain,
! [X0: $i] :
( ( app(cons(sk8,nil),X0) = cons(sk8,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6717,c_376]) ).
tcf(c_12160,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk6,sk8)
| ( X1 != sk8 )
| ( X0 != sk6 ) ),
inference(instantiation,[status(thm)],[c_6730]) ).
tcf(c_12387,plain,
( ( nil = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ( nil != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6702,c_374]) ).
tcf(c_12421,plain,
( ( nil = iPr_def_13 )
| ( nil != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12387,c_10130,c_6718]) ).
tcf(c_12436,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6701,c_375]) ).
tcf(c_12474,plain,
nil != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_12436,c_11016,c_10119,c_6719]) ).
tcf(c_12537,plain,
nil != iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_12421,c_12421,c_12474]) ).
tcf(c_12548,plain,
iPr_def_14 = iPr_def_15,
inference(backward_subsumption_resolution,[status(thm)],[c_9386,c_12537]) ).
tcf(c_12549,plain,
memberP(sk4,sk9),
inference(backward_subsumption_resolution,[status(thm)],[c_9367,c_12537]) ).
tcf(c_12550,plain,
ssItem(sk9),
inference(backward_subsumption_resolution,[status(thm)],[c_9356,c_12537]) ).
tcf(c_12557,plain,
cons(sk9,nil) = iPr_def_14,
inference(demodulation,[status(thm)],[c_6703,c_12548]) ).
tcf(c_12929,plain,
app(cons(sk8,nil),sk4) = cons(sk8,sk4),
inference(superposition,[status(thm)],[c_6721,c_12062]) ).
tcf(c_13025,plain,
( ssList(cons(sk8,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(sk8,nil)) ),
inference(superposition,[status(thm)],[c_12929,c_341]) ).
tcf(c_13030,plain,
( ssList(cons(sk8,sk4))
| ~ ssList(cons(sk8,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13025,c_6721]) ).
tcf(c_13051,plain,
( ssList(cons(sk8,sk4))
| ~ ssItem(sk8)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_342,c_13030]) ).
tcf(c_13052,plain,
ssList(cons(sk8,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_13051,c_6717,c_264]) ).
tcf(c_13824,plain,
! [X0: $i] :
( rearsegP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ rearsegP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_6701,c_392]) ).
tcf(c_13879,plain,
! [X0: $i] :
( rearsegP(iPr_def_13,X0)
| ~ ssList(X0)
| ~ rearsegP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13824,c_10119,c_6719]) ).
tcf(c_13974,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(sk5)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sk5,X1)),cons(sk5,X2)))
| ~ ssList(app(app(X0,cons(sk5,X1)),cons(sk5,X2))) ),
inference(instantiation,[status(thm)],[c_435]) ).
tcf(c_13975,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ duplicatefreeP(app(app(nil,cons(sk5,nil)),cons(sk5,nil)))
| ~ ssList(app(app(nil,cons(sk5,nil)),cons(sk5,nil))) ),
inference(instantiation,[status(thm)],[c_13974]) ).
tcf(c_14024,plain,
! [X0: $i] :
( frontsegP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_6702,c_393]) ).
tcf(c_14074,plain,
! [X0: $i] :
( frontsegP(iPr_def_14,X0)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14024,c_10130,c_6718]) ).
tcf(c_14413,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(superposition,[status(thm)],[c_6702,c_397]) ).
tcf(c_14445,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14413,c_10130,c_6718]) ).
tcf(c_15922,plain,
( rearsegP(iPr_def_13,nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_10517,c_13879]) ).
tcf(c_15923,plain,
rearsegP(iPr_def_13,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_15922,c_264]) ).
tcf(c_16128,plain,
! [X0: $i] :
( frontsegP(cons(sk5,X0),iPr_def_12)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(superposition,[status(thm)],[c_6700,c_434]) ).
tcf(c_16138,plain,
! [X0: $i] :
( frontsegP(cons(sk5,X0),iPr_def_12)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16128,c_6720,c_264]) ).
tcf(c_16502,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sk8 )
| ~ ssItem(sk8)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ( cons(X0,X1) != cons(sk8,X2) ) ),
inference(instantiation,[status(thm)],[c_426]) ).
tcf(c_16517,plain,
( ( app(skaf46(iPr_def_13,nil),nil) = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_15923,c_387]) ).
tcf(c_16520,plain,
app(skaf46(iPr_def_13,nil),nil) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_16517,c_10130,c_264]) ).
tcf(c_16572,plain,
( frontsegP(iPr_def_14,sk6)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_10647,c_14074]) ).
tcf(c_16573,plain,
frontsegP(iPr_def_14,sk6),
inference(forward_subsumption_resolution,[status(thm)],[c_16572,c_6719]) ).
tcf(c_16575,plain,
( ( app(sk6,skaf45(iPr_def_14,sk6)) = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_16573,c_388]) ).
tcf(c_16580,plain,
app(sk6,skaf45(iPr_def_14,sk6)) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_16575,c_9355,c_6719]) ).
tcf(c_16632,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(sk6)
| ~ ssItem(X0)
| ~ memberP(sk6,X0)
| ~ ssList(skaf45(iPr_def_14,sk6)) ),
inference(superposition,[status(thm)],[c_16580,c_396]) ).
tcf(c_16639,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16632,c_6719,c_307]) ).
tcf(c_17578,plain,
! [X0: $i] :
( ( X0 = sk6 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ~ ssList(X0)
| ( app(X0,iPr_def_12) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6701,c_407]) ).
tcf(c_17670,plain,
! [X0: $i] :
( ( X0 = sk6 )
| ~ ssList(X0)
| ( app(X0,iPr_def_12) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17578,c_10119,c_6719]) ).
tcf(c_18182,plain,
( memberP(iPr_def_14,sk8)
| memberP(sk6,sk8)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm)],[c_6716,c_14445]) ).
tcf(c_18183,plain,
( memberP(iPr_def_14,sk8)
| memberP(sk6,sk8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18182,c_6717]) ).
tcf(c_18850,plain,
( memberP(iPr_def_14,sk8)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm)],[c_18183,c_16639]) ).
tcf(c_18851,plain,
memberP(iPr_def_14,sk8),
inference(forward_subsumption_resolution,[status(thm)],[c_18850,c_6717]) ).
tcf(c_19289,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk6 )
| ( sk6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_6725]) ).
tcf(c_19290,plain,
( ( nil = sk6 )
| ( nil != nil )
| ( sk6 != nil ) ),
inference(instantiation,[status(thm)],[c_19289]) ).
tcf(c_21148,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,cons(sk5,X0)))
| ~ ssList(X1)
| ~ ssList(cons(sk5,X0)) ),
inference(instantiation,[status(thm)],[c_341]) ).
tcf(c_21149,plain,
( ssList(app(nil,cons(sk5,nil)))
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil)) ),
inference(instantiation,[status(thm)],[c_21148]) ).
tcf(c_21738,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk5 )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_6700,c_426]) ).
tcf(c_21746,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk5 )
| ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21738,c_6720,c_264]) ).
tcf(c_23614,plain,
! [X0: $i] :
( frontsegP(cons(sk5,X0),iPr_def_12)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_16138,c_316,c_16138]) ).
tcf(c_27012,plain,
( ( sk6 = nil )
| ~ ssList(nil)
| ( iPr_def_12 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_10159,c_17670]) ).
tcf(c_27013,plain,
( ( sk6 = nil )
| ( iPr_def_12 != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27012,c_264]) ).
tcf(c_32452,plain,
! [X0: $i] :
( ssList(cons(sk5,X0))
| ~ ssItem(sk5)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_342]) ).
tcf(c_32453,plain,
( ssList(cons(sk5,nil))
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_32452]) ).
tcf(c_32508,plain,
! [X0: $i] :
( ssList(cons(sk8,X0))
| ~ ssItem(sk8)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_342]) ).
tcf(c_32509,plain,
( ssList(cons(sk8,nil))
| ~ ssItem(sk8)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_32508]) ).
tcf(c_32937,plain,
! [X0: $i] :
( ( app(cons(sk8,nil),X0) = cons(sk8,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6717,c_376]) ).
tcf(c_33913,plain,
( ( sk5 = sk9 )
| ~ ssItem(sk9)
| ~ ssList(nil)
| ( iPr_def_12 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_12557,c_21746]) ).
tcf(c_33921,plain,
( ( sk5 = sk9 )
| ( iPr_def_12 != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33913,c_12550,c_264]) ).
tcf(c_36427,plain,
app(cons(sk8,nil),sk4) = cons(sk8,sk4),
inference(superposition,[status(thm)],[c_6721,c_32937]) ).
tcf(c_37092,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(app(X0,cons(sk5,X1)),cons(sk5,X2)))
| ~ ssList(cons(sk5,X2))
| ~ ssList(app(X0,cons(sk5,X1))) ),
inference(instantiation,[status(thm)],[c_21148]) ).
tcf(c_37093,plain,
( ssList(app(app(nil,cons(sk5,nil)),cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(nil,cons(sk5,nil))) ),
inference(instantiation,[status(thm)],[c_37092]) ).
tcf(c_37468,plain,
( ssList(cons(sk8,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(sk8,nil)) ),
inference(superposition,[status(thm)],[c_36427,c_341]) ).
tcf(c_37473,plain,
( ssList(cons(sk8,sk4))
| ~ ssList(cons(sk8,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37468,c_6721]) ).
tcf(c_37595,plain,
ssList(cons(sk8,sk4)),
inference(global_subsumption_just,[status(thm)],[c_37473,c_13052]) ).
tcf(c_37607,plain,
( duplicatefreeP(cons(sk8,sk4))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_37595,c_6698]) ).
tcf(c_41486,plain,
skaf46(iPr_def_13,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_16520,c_9659]) ).
tcf(c_46872,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk7 )
| ( sk7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_6725]) ).
tcf(c_46873,plain,
( ( nil = sk7 )
| ( nil != nil )
| ( sk7 != nil ) ),
inference(instantiation,[status(thm)],[c_46872]) ).
tcf(c_70223,plain,
! [X0: $i] :
( memberP(X0,sk5)
| ~ memberP(sk6,sk8)
| ( sk5 != sk8 )
| ( X0 != sk6 ) ),
inference(instantiation,[status(thm)],[c_12160]) ).
tcf(c_70224,plain,
( memberP(nil,sk5)
| ~ memberP(sk6,sk8)
| ( nil != sk6 )
| ( sk5 != sk8 ) ),
inference(instantiation,[status(thm)],[c_70223]) ).
tcf(c_74539,plain,
! [X0: $i,X1: $i,X2: $i] :
( duplicatefreeP(app(app(X0,cons(sk5,X1)),cons(sk5,X2)))
| ~ iPr_def_11
| ~ ssList(app(app(X0,cons(sk5,X1)),cons(sk5,X2))) ),
inference(instantiation,[status(thm)],[c_6698]) ).
tcf(c_74540,plain,
( duplicatefreeP(app(app(nil,cons(sk5,nil)),cons(sk5,nil)))
| ~ iPr_def_11
| ~ ssList(app(app(nil,cons(sk5,nil)),cons(sk5,nil))) ),
inference(instantiation,[status(thm)],[c_74539]) ).
tcf(c_76071,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_37607,c_446,c_264,c_13975,c_21149,c_32453,c_37093,c_74540]) ).
tcf(c_76073,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_6699,c_76071]) ).
tcf(c_76074,plain,
! [X0: $i] : ssItem(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_6697,c_76073]) ).
tcf(c_76086,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_434,c_76074]) ).
tcf(c_76093,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_394,c_76074]) ).
tcf(c_76094,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_417,c_76074]) ).
tcf(c_76104,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_397,c_76074]) ).
tcf(c_76105,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_396,c_76074]) ).
tcf(c_76126,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_342,c_76074]) ).
tcf(c_94663,plain,
! [X0: $i] : ~ memberP(nil,X0),
inference(global_subsumption_just,[status(thm)],[c_327,c_446,c_264,c_327,c_6697,c_6699,c_13975,c_21149,c_32453,c_37093,c_74540]) ).
tcf(c_94973,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6701,c_341]) ).
tcf(c_94986,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94973,c_6719]) ).
tcf(c_95012,plain,
ssList(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_94986,c_10130]) ).
tcf(c_95080,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_394,c_76093]) ).
tcf(c_95551,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_95012,c_360]) ).
tcf(c_96190,plain,
cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_95551,c_11690,c_12474]) ).
tcf(c_96192,plain,
( memberP(iPr_def_13,hd(iPr_def_13))
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_96190,c_95080]) ).
tcf(c_116190,plain,
( singletonP(cons(sk8,nil))
| ~ ssItem(sk8)
| ~ ssList(cons(sk8,nil)) ),
inference(instantiation,[status(thm)],[c_372]) ).
tcf(c_133289,plain,
( ( skaf46(iPr_def_13,nil) = nil )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_41486,c_11885]) ).
tcf(c_133297,plain,
( ( nil = iPr_def_13 )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_133289,c_41486]) ).
tcf(c_133298,plain,
cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_133297,c_12474]) ).
tcf(c_170592,plain,
( ( cons(skaf44(cons(sk8,nil)),nil) = cons(sk8,nil) )
| ~ singletonP(cons(sk8,nil))
| ~ ssList(cons(sk8,nil)) ),
inference(instantiation,[status(thm)],[c_11018]) ).
tcf(c_170593,plain,
( ( skaf44(cons(sk8,nil)) = sk8 )
| ~ ssItem(sk8)
| ~ ssList(nil)
| ~ ssItem(skaf44(cons(sk8,nil)))
| ( cons(skaf44(cons(sk8,nil)),nil) != cons(sk8,nil) ) ),
inference(instantiation,[status(thm)],[c_16502]) ).
tcf(c_184674,plain,
! [X0: $i,X1: $i] : tl(cons(skaf83(X0),skaf82(X1))) = skaf82(X1),
inference(superposition,[status(thm)],[c_269,c_10774]) ).
tcf(c_187313,plain,
skaf82(iPr_def_13) = tl(iPr_def_13),
inference(superposition,[status(thm)],[c_133298,c_184674]) ).
tcf(c_188098,plain,
ssList(tl(iPr_def_13)),
inference(superposition,[status(thm)],[c_187313,c_269]) ).
tcf(c_192136,plain,
ssList(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_6722,c_6704]) ).
tcf(c_192143,negated_conjecture,
memberP(sk4,sk9),
inference(global_subsumption_just,[status(thm)],[c_6706,c_12549]) ).
tcf(c_192187,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( sk4 = nil ) ),
inference(light_normalisation,[status(thm)],[c_6710,c_6704]) ).
tcf(c_192194,plain,
( memberP(nil,sk9)
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_192187,c_192143]) ).
tcf(c_192222,plain,
iPr_def_14 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_192194,c_12548]) ).
tcf(c_192232,plain,
cons(sk9,nil) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6703,c_192222]) ).
tcf(c_192386,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6701,c_341]) ).
tcf(c_192405,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192386,c_6719]) ).
tcf(c_192414,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_342,c_76126]) ).
tcf(c_192420,plain,
( ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6700,c_192414]) ).
tcf(c_192424,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_192420,c_264]) ).
tcf(c_192437,plain,
ssList(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_192405,c_10130]) ).
tcf(c_192547,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_394,c_76093]) ).
tcf(c_192553,plain,
( memberP(iPr_def_12,sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6700,c_192547]) ).
tcf(c_192556,plain,
memberP(iPr_def_12,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_192553,c_264]) ).
tcf(c_192565,plain,
( rearsegP(iPr_def_14,sk7)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_6702,c_862]) ).
tcf(c_192630,plain,
rearsegP(iPr_def_14,sk7),
inference(forward_subsumption_resolution,[status(thm)],[c_192565,c_192437,c_6718]) ).
tcf(c_192683,plain,
( frontsegP(iPr_def_14,iPr_def_13)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_6702,c_863]) ).
tcf(c_192749,plain,
frontsegP(iPr_def_14,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_192683,c_192437,c_6718]) ).
tcf(c_192802,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_352,c_446,c_264,c_6699,c_10771,c_13975,c_21149,c_32453,c_37093,c_74540]) ).
tcf(c_192812,plain,
! [X0: $i,X1: $i] : tl(cons(X0,skaf82(X1))) = skaf82(X1),
inference(superposition,[status(thm)],[c_269,c_192802]) ).
tcf(c_193127,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_192437,c_360]) ).
tcf(c_193287,plain,
cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_193127,c_11690,c_12474]) ).
tcf(c_193289,plain,
( memberP(iPr_def_13,hd(iPr_def_13))
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_193287,c_192547]) ).
tcf(c_193373,plain,
! [X0: $i,X1: $i] :
( ( skaf46(X0,X1) = nil )
| ( cons(skaf83(skaf46(X0,X1)),skaf82(skaf46(X0,X1))) = skaf46(X0,X1) ) ),
inference(superposition,[status(thm)],[c_306,c_365]) ).
tcf(c_193534,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk8 )
| ( sk8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_6725]) ).
tcf(c_193595,plain,
( ( sk6 = nil )
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6701,c_374]) ).
tcf(c_193654,plain,
( ( sk6 = nil )
| ( nil != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_193595,c_192424,c_6719]) ).
tcf(c_193782,plain,
nil != iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_193654,c_12474]) ).
tcf(c_194610,plain,
( ( iPr_def_13 = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ frontsegP(iPr_def_13,iPr_def_14) ),
inference(superposition,[status(thm)],[c_192749,c_385]) ).
tcf(c_194636,plain,
( ( iPr_def_13 = iPr_def_14 )
| ~ frontsegP(iPr_def_13,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_194610,c_192136,c_192437]) ).
tcf(c_194750,plain,
( ( app(skaf46(iPr_def_14,sk7),sk7) = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_192630,c_387]) ).
tcf(c_194798,plain,
app(skaf46(iPr_def_14,sk7),sk7) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_194750,c_192136,c_6718]) ).
tcf(c_195754,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ memberP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(global_subsumption_just,[status(thm)],[c_396,c_76105]) ).
tcf(c_195755,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(renaming,[status(thm)],[c_195754]) ).
tcf(c_195766,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_6702,c_195755]) ).
tcf(c_195834,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_195766,c_192437,c_6718]) ).
tcf(c_195968,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ memberP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(global_subsumption_just,[status(thm)],[c_397,c_76104]) ).
tcf(c_195969,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(renaming,[status(thm)],[c_195968]) ).
tcf(c_195979,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_6701,c_195969]) ).
tcf(c_195980,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ memberP(sk7,X0) ),
inference(superposition,[status(thm)],[c_6702,c_195969]) ).
tcf(c_196048,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_195980,c_192437,c_6718]) ).
tcf(c_196051,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_195979,c_192424,c_6719]) ).
tcf(c_196197,plain,
( memberP(iPr_def_14,sk8)
| memberP(sk6,sk8) ),
inference(superposition,[status(thm)],[c_6716,c_196048]) ).
tcf(c_196203,plain,
memberP(iPr_def_14,sk8),
inference(global_subsumption_just,[status(thm)],[c_196197,c_18851]) ).
tcf(c_196209,plain,
memberP(iPr_def_13,sk5),
inference(superposition,[status(thm)],[c_192556,c_196051]) ).
tcf(c_196867,plain,
memberP(iPr_def_14,sk5),
inference(superposition,[status(thm)],[c_196209,c_195834]) ).
tcf(c_197622,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_434,c_76086]) ).
tcf(c_197623,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(renaming,[status(thm)],[c_197622]) ).
tcf(c_197642,plain,
! [X0: $i] :
( frontsegP(cons(sk5,X0),iPr_def_12)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(superposition,[status(thm)],[c_6700,c_197623]) ).
tcf(c_197659,plain,
! [X0: $i] :
( frontsegP(cons(sk5,X0),iPr_def_12)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197642,c_264]) ).
tcf(c_199543,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ ssList(X0)
| ( app(X0,sk7) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6702,c_407]) ).
tcf(c_199675,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ~ ssList(X0)
| ( app(X0,sk7) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_199543,c_192437,c_6718]) ).
tcf(c_200527,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_417,c_76094]) ).
tcf(c_200540,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sk9 )
| ~ ssList(nil)
| ~ memberP(iPr_def_14,X0) ),
inference(superposition,[status(thm)],[c_192232,c_200527]) ).
tcf(c_200549,plain,
! [X0: $i] :
( ( X0 = sk9 )
| ~ memberP(iPr_def_14,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_200540,c_94663,c_264]) ).
tcf(c_211584,plain,
( ( skaf46(iPr_def_14,sk7) = iPr_def_13 )
| ~ ssList(skaf46(iPr_def_14,sk7)) ),
inference(superposition,[status(thm)],[c_194798,c_199675]) ).
tcf(c_211586,plain,
skaf46(iPr_def_14,sk7) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_211584,c_306]) ).
tcf(c_216737,plain,
ssItem(skaf44(cons(sk8,nil))),
inference(instantiation,[status(thm)],[c_76074]) ).
tcf(c_219189,plain,
memberP(iPr_def_13,hd(iPr_def_13)),
inference(global_subsumption_just,[status(thm)],[c_193289,c_96192,c_188098]) ).
tcf(c_219193,plain,
memberP(iPr_def_14,hd(iPr_def_13)),
inference(superposition,[status(thm)],[c_219189,c_195834]) ).
tcf(c_223488,plain,
sk8 = sk9,
inference(superposition,[status(thm)],[c_196203,c_200549]) ).
tcf(c_223489,plain,
sk5 = sk9,
inference(superposition,[status(thm)],[c_196867,c_200549]) ).
tcf(c_223490,plain,
hd(iPr_def_13) = sk9,
inference(superposition,[status(thm)],[c_219193,c_200549]) ).
tcf(c_223553,plain,
cons(sk9,nil) = iPr_def_12,
inference(demodulation,[status(thm)],[c_6700,c_223489]) ).
tcf(c_223554,plain,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_192232,c_223553]) ).
tcf(c_223575,plain,
( ( iPr_def_12 = iPr_def_13 )
| ~ frontsegP(iPr_def_13,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_194636,c_223554]) ).
tcf(c_223589,plain,
skaf46(iPr_def_12,sk7) = iPr_def_13,
inference(demodulation,[status(thm)],[c_211586,c_223554]) ).
tcf(c_223763,plain,
cons(sk9,tl(iPr_def_13)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_193287,c_223490]) ).
tcf(c_237029,plain,
! [X0: $i] :
( ( X0 = sk8 )
| ( sk8 != sk9 )
| ( X0 != sk9 ) ),
inference(instantiation,[status(thm)],[c_193534]) ).
tcf(c_272732,plain,
( ( skaf46(iPr_def_12,sk7) = nil )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_223589,c_193373]) ).
tcf(c_272769,plain,
( ( nil = iPr_def_13 )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_272732,c_223589]) ).
tcf(c_272770,plain,
cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_272769,c_193782]) ).
tcf(c_273517,plain,
skaf82(iPr_def_13) = tl(iPr_def_13),
inference(superposition,[status(thm)],[c_272770,c_192812]) ).
tcf(c_273777,plain,
ssList(tl(iPr_def_13)),
inference(superposition,[status(thm)],[c_273517,c_269]) ).
tcf(c_297087,plain,
ssList(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_6722,c_6704]) ).
tcf(c_297338,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6701,c_341]) ).
tcf(c_297344,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_297338,c_6719]) ).
tcf(c_297353,plain,
ssList(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_297344,c_10130]) ).
tcf(c_297356,plain,
app(iPr_def_13,nil) = iPr_def_13,
inference(superposition,[status(thm)],[c_297353,c_329]) ).
tcf(c_297942,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_342,c_76126]) ).
tcf(c_297948,plain,
( ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6700,c_297942]) ).
tcf(c_297956,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_297948,c_264]) ).
tcf(c_298002,plain,
app(nil,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_297956,c_330]) ).
tcf(c_302692,plain,
! [X0: $i] :
( ( X0 = sk7 )
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6702,c_406]) ).
tcf(c_302773,plain,
! [X0: $i] :
( ( X0 = sk7 )
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_302692,c_297353,c_6718]) ).
tcf(c_303058,plain,
! [X0: $i] :
( ( X0 = sk6 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ~ ssList(X0)
| ( app(X0,iPr_def_12) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6701,c_407]) ).
tcf(c_303144,plain,
! [X0: $i] :
( ( X0 = sk6 )
| ~ ssList(X0)
| ( app(X0,iPr_def_12) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_303058,c_297956,c_6719]) ).
tcf(c_305426,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssList(app(app(sk6,iPr_def_12),X0)) ),
inference(superposition,[status(thm)],[c_6701,c_429]) ).
tcf(c_305533,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_13,X0)) ),
inference(light_normalisation,[status(thm)],[c_305426,c_6701]) ).
tcf(c_305534,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_12)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_13,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_305533,c_297956,c_6719]) ).
tcf(c_310029,plain,
( ( sk5 = sk8 )
| ( sk8 != sk9 )
| ( sk5 != sk9 ) ),
inference(instantiation,[status(thm)],[c_237029]) ).
tcf(c_361288,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk7,sk8)
| ( X1 != sk8 )
| ( X0 != sk7 ) ),
inference(instantiation,[status(thm)],[c_6730]) ).
tcf(c_366934,plain,
! [X0: $i] :
( memberP(X0,skaf44(cons(sk8,nil)))
| ~ memberP(sk7,sk8)
| ( X0 != sk7 )
| ( skaf44(cons(sk8,nil)) != sk8 ) ),
inference(instantiation,[status(thm)],[c_361288]) ).
tcf(c_366935,plain,
( memberP(nil,skaf44(cons(sk8,nil)))
| ~ memberP(sk7,sk8)
| ( nil != sk7 )
| ( skaf44(cons(sk8,nil)) != sk8 ) ),
inference(instantiation,[status(thm)],[c_366934]) ).
tcf(c_370278,plain,
~ memberP(nil,skaf44(cons(sk8,nil))),
inference(instantiation,[status(thm)],[c_94663]) ).
tcf(c_421041,plain,
( segmentP(iPr_def_14,iPr_def_12)
| ~ ssList(sk7)
| ~ ssList(app(iPr_def_13,sk7)) ),
inference(superposition,[status(thm)],[c_6702,c_305534]) ).
tcf(c_421050,plain,
( segmentP(iPr_def_14,iPr_def_12)
| ~ ssList(iPr_def_14)
| ~ ssList(sk7) ),
inference(light_normalisation,[status(thm)],[c_421041,c_6702]) ).
tcf(c_421051,plain,
segmentP(iPr_def_14,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_421050,c_297087,c_6718]) ).
tcf(c_421196,plain,
( ( iPr_def_12 = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_12)
| ~ segmentP(iPr_def_12,iPr_def_14) ),
inference(superposition,[status(thm)],[c_421051,c_383]) ).
tcf(c_421197,plain,
( ( iPr_def_12 = iPr_def_14 )
| ~ segmentP(iPr_def_12,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_421196,c_297087,c_297956]) ).
tcf(c_423167,plain,
iPr_def_12 = iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_421197,c_223554]) ).
tcf(c_424935,plain,
! [X0: $i] :
( ( X0 = sk7 )
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_302773,c_423167]) ).
tcf(c_424945,plain,
( ( sk7 = nil )
| ~ ssList(nil)
| ( iPr_def_12 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_297356,c_424935]) ).
tcf(c_424947,plain,
( ( sk7 = nil )
| ( iPr_def_12 != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_424945,c_264]) ).
tcf(c_430392,plain,
( ( sk6 = nil )
| ~ ssList(nil)
| ( iPr_def_12 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_298002,c_303144]) ).
tcf(c_430397,plain,
( ( sk6 = nil )
| ( iPr_def_12 != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_430392,c_264]) ).
tcf(c_432791,plain,
iPr_def_12 != iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_430397,c_450,c_446,c_264,c_451,c_339,c_523,c_10565,c_19290,c_27013,c_32509,c_33921,c_46873,c_70224,c_116190,c_170592,c_170593,c_216737,c_223554,c_223488,c_310029,c_366935,c_370278,c_424947]) ).
tcf(c_465109,plain,
! [X0: $i] :
( frontsegP(cons(sk5,X0),iPr_def_12)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_197659,c_23614]) ).
tcf(c_465111,plain,
! [X0: $i] :
( frontsegP(cons(sk9,X0),iPr_def_12)
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_465109,c_223489]) ).
tcf(c_465119,plain,
( frontsegP(iPr_def_13,iPr_def_12)
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_223763,c_465111]) ).
tcf(c_465126,plain,
frontsegP(iPr_def_13,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_465119,c_273777]) ).
tcf(c_467873,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_465126,c_432791,c_223575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC295-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/3.58 % Computer : n005.cluster.edu
% 0.09/3.58 % Model : x86_64 x86_64
% 0.09/3.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/3.58 % Memory : 8046.5625MB
% 0.09/3.58 % OS : Linux 6.8.0-71-generic
% 0.09/3.58 % CPULimit : 300
% 0.09/3.58 % WCLimit : 300
% 0.09/3.58 % DateTime : Thu Sep 24 17:28:21 UTC 2026
% 0.09/3.58 % CPUTime :
% 0.09/3.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/3.62 Running first-order theorem proving
% 0.14/3.62 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/3.63
% 0.14/3.63 % ======== iProver multi-core TPTP/SMT =========
% 0.14/3.63
% 0.14/3.63 % Detected problem language: tptp
% 0.14/3.65 % Proving...
% 147.96/27.08 % SZS status Started for theBenchmark.p
% 147.96/27.08 % SZS status Unsatisfiable for theBenchmark.p
% 147.96/27.08
% 147.96/27.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 147.96/27.08
% 147.96/27.08 % ------ iProver source info
% 147.96/27.08
% 147.96/27.08 % git: date: 2026-07-19 20:42:38 +0200
% 147.96/27.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 147.96/27.08 % git: non_committed_changes: false
% 147.96/27.08
% 147.96/27.08 % ------ Parsing...% successful
% 147.96/27.08
% 147.96/27.08
% 147.96/27.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 147.96/27.08
% 147.96/27.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 147.96/27.08
% 147.96/27.08 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 147.96/27.08
% 147.96/27.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 147.96/27.08 % ------ Proving...
% 147.96/27.08 % ------ Problem Properties
% 147.96/27.08
% 147.96/27.08 %
% 147.96/27.08 % clauses 200
% 147.96/27.08 % conjectures 19
% 147.96/27.08 % EPR 71
% 147.96/27.08 % Horn 163
% 147.96/27.08 % unary 69
% 147.96/27.08 % binary 31
% 147.96/27.08 % lits 582
% 147.96/27.08 % lits eq 86
% 147.96/27.08 % fd_pure 0
% 147.96/27.08 % fd_pseudo 0
% 147.96/27.08 % fd_cond 17
% 147.96/27.08 % fd_pseudo_cond 14
% 147.96/27.08 % AC symbols 0
% 147.96/27.08
% 147.96/27.08 % ------ Schedule dynamic 5 is on
% 147.96/27.08
% 147.96/27.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 147.96/27.08
% 147.96/27.08
% 147.96/27.08 % ------
% 147.96/27.08 % Current options:
% 147.96/27.08 % ------
% 147.96/27.08
% 147.96/27.08
% 147.96/27.08 %
% 147.96/27.08
% 147.96/27.08 % ------ Proving...
% 147.96/27.08 % Proof_search_loop: time out after: 6929 full_loop iterations
% 147.96/27.08
% 147.96/27.08 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 147.96/27.08
% 147.96/27.08
% 147.96/27.08 % ------
% 147.96/27.08 % Current options:
% 147.96/27.08 % ------
% 147.96/27.08
% 147.96/27.08
% 147.96/27.08 %
% 147.96/27.08
% 147.96/27.08 % ------ Proving...
% 147.96/27.08 %
% 147.96/27.08
% 147.96/27.08 % SZS status Unsatisfiable for theBenchmark.p
% 147.96/27.08
% 147.96/27.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 147.96/27.08
% 147.96/27.08
%------------------------------------------------------------------------------