%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC183-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 03:08:23 PM UTC 2026
% Result : Unsatisfiable 96.88s 16.80s
% Output : CNFRefutation 66.15s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f252ERROR: Could not build tree for root c_390420ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause50) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
fof(f72,axiom,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
fof(f83,axiom,
! [X0] :
( frontsegP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause83) ).
fof(f84,axiom,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause84) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f96,axiom,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
fof(f97,axiom,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
fof(f107,axiom,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
fof(f112,axiom,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
fof(f119,axiom,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
fof(f121,axiom,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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(f138,axiom,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001-0.ax',clause131) ).
fof(f147,axiom,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SWC001-0.ax',clause151) ).
fof(f166,axiom,
! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause154) ).
fof(f169,axiom,
! [X2,X0,X1] :
( cons(X0,app(X1,X2)) = app(cons(X0,X1),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).
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/sandbox/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(f188,axiom,
! [X2,X3,X0,X1] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause174) ).
fof(f190,axiom,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause176) ).
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/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
sk1 = app(app(sk6,cons(sk5,nil)),sk7),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
( nil = sk3
| ssItem(sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f214,negated_conjecture,
( nil = sk4
| cons(sk8,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f215,plain,
( nil = sk4
| sk3 = cons(sk8,nil) ),
inference(reorient_equations,[],[f214]) ).
fof(f218,negated_conjecture,
( nil = sk3
| cons(sk8,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f219,plain,
( nil = sk3
| sk3 = cons(sk8,nil) ),
inference(reorient_equations,[],[f218]) ).
fof(f220,negated_conjecture,
( nil = sk3
| memberP(sk4,sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f224,plain,
sk3 = app(app(sk6,cons(sk5,nil)),sk7),
inference(definition_unfolding,[],[f210,f205]) ).
fof(f227,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f83]) ).
fof(f232,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f235,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f236,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
fof(f242,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_260,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_264,plain,
! [X0: $i] : ssItem(skaf83(X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_265,plain,
! [X0: $i] : ssList(skaf82(X0)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_299,plain,
! [X0: $i] : ssItem(skaf44(X0)),
inference(cnf_transformation,[],[f47]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_323,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_325,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_326,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_335,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_336,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_353,plain,
! [X0: $i] :
( ( cons(skaf44(X0),nil) = X0 )
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_356,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_361,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_368,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_383,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,X2: $i] :
( rearsegP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_389,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_390,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_392,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_393,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_395,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_402,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_403,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_406,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(X0,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_409,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cons(X2,app(X0,X1)) = app(cons(X2,X0),X1) )
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_413,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] :
( frontsegP(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_431,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,[],[f242]) ).
tcf(c_440,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_441,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_442,negated_conjecture,
ssItem(sk5),
inference(cnf_transformation,[],[f206]) ).
tcf(c_443,negated_conjecture,
ssList(sk6),
inference(cnf_transformation,[],[f207]) ).
tcf(c_444,negated_conjecture,
ssList(sk7),
inference(cnf_transformation,[],[f208]) ).
tcf(c_445,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk3,
inference(cnf_transformation,[],[f224]) ).
tcf(c_446,negated_conjecture,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_448,negated_conjecture,
( ssItem(sk8)
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_449,negated_conjecture,
( ( sk4 = nil )
| ( cons(sk8,nil) = sk3 ) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_452,negated_conjecture,
( ( sk3 = nil )
| ( cons(sk8,nil) = sk3 ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_453,negated_conjecture,
( memberP(sk4,sk8)
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_515,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(instantiation,[status(thm)],[c_336]) ).
tcf(c_840,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_395,c_337]) ).
tcf(c_841,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_396,c_337]) ).
tcf(c_6637,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_324]) ).
tcf(c_6638,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_324]) ).
tcf(c_6639,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_324]) ).
tcf(c_6640,definition,
iPr_def_12 = cons(sk5,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6641,definition,
iPr_def_13 = app(sk6,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6642,definition,
iPr_def_14 = app(iPr_def_13,sk7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_6643,definition,
iPr_def_15 = cons(sk8,nil),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_6644,negated_conjecture,
iPr_def_14 = sk3,
inference(demodulation,[status(thm)],[c_445,c_6640,c_6641,c_6642]) ).
tcf(c_6646,negated_conjecture,
( memberP(sk4,sk8)
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_453]) ).
tcf(c_6647,negated_conjecture,
( ( iPr_def_15 = sk3 )
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_452,c_6643]) ).
tcf(c_6650,negated_conjecture,
( ( iPr_def_15 = sk3 )
| ( sk4 = nil ) ),
inference(demodulation,[status(thm)],[c_449]) ).
tcf(c_6651,negated_conjecture,
( ssItem(sk8)
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_448]) ).
tcf(c_6653,negated_conjecture,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
inference(demodulation,[status(thm)],[c_446]) ).
tcf(c_6654,negated_conjecture,
ssList(sk7),
inference(demodulation,[status(thm)],[c_444]) ).
tcf(c_6655,negated_conjecture,
ssList(sk6),
inference(demodulation,[status(thm)],[c_443]) ).
tcf(c_6656,negated_conjecture,
ssItem(sk5),
inference(demodulation,[status(thm)],[c_442]) ).
tcf(c_6657,negated_conjecture,
ssList(sk4),
inference(demodulation,[status(thm)],[c_441]) ).
tcf(c_6658,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_440]) ).
tcf(c_6659,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_6661,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6663,plain,
! [X0: $i,X1: $i] :
( ssItem(X0)
| ~ ssItem(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X0,X2)
| ~ memberP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9264,plain,
( ssItem(sk8)
| ( nil = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6651,c_6644]) ).
tcf(c_9275,plain,
( memberP(sk4,sk8)
| ( nil = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6646,c_6644]) ).
tcf(c_9585,plain,
! [X0: $i,X1: $i] : app(skaf46(X0,X1),nil) = skaf46(X0,X1),
inference(superposition,[status(thm)],[c_302,c_325]) ).
tcf(c_9841,plain,
app(nil,sk4) = sk4,
inference(superposition,[status(thm)],[c_6657,c_326]) ).
tcf(c_9845,plain,
! [X0: $i] : app(nil,skaf82(X0)) = skaf82(X0),
inference(superposition,[status(thm)],[c_265,c_326]) ).
tcf(c_9928,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6641,c_337]) ).
tcf(c_9942,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9928,c_6655]) ).
tcf(c_10029,plain,
( ssList(iPr_def_12)
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6640,c_338]) ).
tcf(c_10038,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_10029,c_6656,c_260]) ).
tcf(c_10049,plain,
ssList(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_9942,c_10038]) ).
tcf(c_10079,plain,
app(iPr_def_12,nil) = iPr_def_12,
inference(superposition,[status(thm)],[c_10038,c_325]) ).
tcf(c_10380,plain,
( memberP(iPr_def_12,sk5)
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6640,c_390]) ).
tcf(c_10387,plain,
memberP(iPr_def_12,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_10380,c_6656,c_260]) ).
tcf(c_10425,plain,
( rearsegP(iPr_def_12,nil)
| ~ ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_10079,c_840]) ).
tcf(c_10433,plain,
rearsegP(iPr_def_12,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_10425,c_10038,c_260]) ).
tcf(c_10485,plain,
( ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(instantiation,[status(thm)],[c_323]) ).
tcf(c_10551,plain,
( frontsegP(iPr_def_12,iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_10079,c_841]) ).
tcf(c_10559,plain,
frontsegP(iPr_def_12,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_10551,c_10038,c_260]) ).
tcf(c_10669,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_338,c_368]) ).
tcf(c_10679,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10669,c_260]) ).
tcf(c_10694,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ iPr_def_10
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6637,c_348]) ).
tcf(c_10697,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(skaf83(X1),X0)) = X0 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_264,c_348]) ).
tcf(c_10825,plain,
! [X0: $i] :
( ( hd(cons(sk5,X0)) = sk5 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6656,c_349]) ).
tcf(c_10898,plain,
( ( hd(cons(sk5,nil)) = sk5 )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_10825]) ).
tcf(c_10919,plain,
! [X0: $i] :
( ssItem(X0)
| ~ ssItem(sk5)
| ( X0 != sk5 ) ),
inference(instantiation,[status(thm)],[c_6663]) ).
tcf(c_10961,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_6640,c_350]) ).
tcf(c_10968,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_10961,c_6656,c_260]) ).
tcf(c_11499,plain,
! [X0: $i,X1: $i] :
( ( skaf46(X0,X1) = nil )
| ( cons(hd(skaf46(X0,X1)),tl(skaf46(X0,X1))) = skaf46(X0,X1) ) ),
inference(superposition,[status(thm)],[c_302,c_356]) ).
tcf(c_11507,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_10049,c_356]) ).
tcf(c_11695,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_302,c_361]) ).
tcf(c_11858,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ iPr_def_10
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6637,c_372]) ).
tcf(c_12233,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk6,sk5)
| ( X1 != sk5 )
| ( X0 != sk6 ) ),
inference(instantiation,[status(thm)],[c_6666]) ).
tcf(c_12301,plain,
( ( nil = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ( nil != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6642,c_370]) ).
tcf(c_12338,plain,
( ( nil = iPr_def_13 )
| ( nil != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12301,c_10049,c_6654]) ).
tcf(c_12353,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6641,c_371]) ).
tcf(c_12394,plain,
nil != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_12353,c_10968,c_10038,c_6655]) ).
tcf(c_12484,plain,
nil != iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_12338,c_12338,c_12394]) ).
tcf(c_12496,plain,
memberP(sk4,sk8),
inference(backward_subsumption_resolution,[status(thm)],[c_9275,c_12484]) ).
tcf(c_12497,plain,
ssItem(sk8),
inference(backward_subsumption_resolution,[status(thm)],[c_9264,c_12484]) ).
tcf(c_13914,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_431]) ).
tcf(c_13915,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_13914]) ).
tcf(c_13961,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_6641,c_388]) ).
tcf(c_14014,plain,
! [X0: $i] :
( rearsegP(iPr_def_13,X0)
| ~ ssList(X0)
| ~ rearsegP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13961,c_10038,c_6655]) ).
tcf(c_14417,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_6642,c_392]) ).
tcf(c_14447,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14417,c_10049,c_6654]) ).
tcf(c_14483,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_6641,c_393]) ).
tcf(c_14518,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14483,c_10038,c_6655]) ).
tcf(c_15363,plain,
! [X0: $i] :
( ssItem(hd(cons(sk5,X0)))
| ~ ssItem(sk5)
| ( hd(cons(sk5,X0)) != sk5 ) ),
inference(instantiation,[status(thm)],[c_10919]) ).
tcf(c_15365,plain,
( ssItem(hd(cons(sk5,nil)))
| ~ ssItem(sk5)
| ( hd(cons(sk5,nil)) != sk5 ) ),
inference(instantiation,[status(thm)],[c_15363]) ).
tcf(c_15897,plain,
( rearsegP(iPr_def_13,nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_10433,c_14014]) ).
tcf(c_15898,plain,
rearsegP(iPr_def_13,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_15897,c_260]) ).
tcf(c_16443,plain,
( ( app(skaf46(iPr_def_13,nil),nil) = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_15898,c_383]) ).
tcf(c_16446,plain,
app(skaf46(iPr_def_13,nil),nil) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_16443,c_10049,c_260]) ).
tcf(c_16574,plain,
! [X0: $i,X1: $i] :
( ( cons(X1,app(X0,sk4)) = app(cons(X1,X0),sk4) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6657,c_409]) ).
tcf(c_16849,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk6 )
| ( sk6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_6661]) ).
tcf(c_16850,plain,
( ( nil = sk6 )
| ( nil != nil )
| ( sk6 != nil ) ),
inference(instantiation,[status(thm)],[c_16849]) ).
tcf(c_18009,plain,
( memberP(iPr_def_13,sk5)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm)],[c_10387,c_14518]) ).
tcf(c_18010,plain,
memberP(iPr_def_13,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_18009,c_6656]) ).
tcf(c_18011,plain,
( memberP(iPr_def_14,sk5)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm)],[c_18010,c_14447]) ).
tcf(c_18012,plain,
memberP(iPr_def_14,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_18011,c_6656]) ).
tcf(c_18580,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_337]) ).
tcf(c_18581,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_18580]) ).
tcf(c_20355,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk7,sk5)
| ( X1 != sk5 )
| ( X0 != sk7 ) ),
inference(instantiation,[status(thm)],[c_6666]) ).
tcf(c_20364,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,cons(sk5,X0)))
| ~ ssList(X1)
| ~ ssList(cons(sk5,X0)) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_20365,plain,
( ssList(app(nil,cons(sk5,nil)))
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil)) ),
inference(instantiation,[status(thm)],[c_20364]) ).
tcf(c_21141,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk5 )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(superposition,[status(thm)],[c_6640,c_428]) ).
tcf(c_21160,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk5 )
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21141,c_6656,c_260]) ).
tcf(c_25131,plain,
! [X0: $i] :
( frontsegP(skaf82(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf82(X0)) ),
inference(superposition,[status(thm)],[c_9845,c_841]) ).
tcf(c_25139,plain,
! [X0: $i] : frontsegP(skaf82(X0),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_25131,c_260,c_265]) ).
tcf(c_25181,plain,
! [X0: $i] :
( ( skaf82(X0) = nil )
| ~ ssList(nil)
| ~ ssList(skaf82(X0))
| ~ frontsegP(nil,skaf82(X0)) ),
inference(superposition,[status(thm)],[c_25139,c_381]) ).
tcf(c_25182,plain,
! [X0: $i] :
( ( skaf82(X0) = nil )
| ~ frontsegP(nil,skaf82(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25181,c_260,c_265]) ).
tcf(c_27601,plain,
( singletonP(iPr_def_12)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm)],[c_6640,c_10679]) ).
tcf(c_27605,plain,
singletonP(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_27601,c_6656]) ).
tcf(c_27666,plain,
( ( cons(skaf44(iPr_def_12),nil) = iPr_def_12 )
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_27605,c_353]) ).
tcf(c_27667,plain,
cons(skaf44(iPr_def_12),nil) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_27666,c_10038]) ).
tcf(c_29226,plain,
( ( skaf44(iPr_def_12) = sk5 )
| ~ ssList(nil)
| ~ frontsegP(iPr_def_12,iPr_def_12)
| ~ ssItem(skaf44(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_27667,c_21160]) ).
tcf(c_29255,plain,
skaf44(iPr_def_12) = sk5,
inference(forward_subsumption_resolution,[status(thm)],[c_29226,c_260,c_10559,c_299]) ).
tcf(c_29398,plain,
cons(sk5,nil) = iPr_def_12,
inference(demodulation,[status(thm)],[c_27667,c_29255]) ).
tcf(c_31023,plain,
! [X0: $i] :
( memberP(X0,sk5)
| ~ memberP(sk6,sk5)
| ( sk5 != sk5 )
| ( X0 != sk6 ) ),
inference(instantiation,[status(thm)],[c_12233]) ).
tcf(c_31024,plain,
sk5 = sk5,
inference(instantiation,[status(thm)],[c_6659]) ).
tcf(c_31025,plain,
( memberP(nil,sk5)
| ~ memberP(sk6,sk5)
| ( nil != sk6 )
| ( sk5 != sk5 ) ),
inference(instantiation,[status(thm)],[c_31023]) ).
tcf(c_32331,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk7 )
| ( sk7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_6661]) ).
tcf(c_32332,plain,
( ( nil = sk7 )
| ( nil != nil )
| ( sk7 != nil ) ),
inference(instantiation,[status(thm)],[c_32331]) ).
tcf(c_32846,plain,
! [X0: $i] :
( ~ ssItem(hd(cons(sk5,X0)))
| ~ memberP(nil,hd(cons(sk5,X0))) ),
inference(instantiation,[status(thm)],[c_323]) ).
tcf(c_32847,plain,
( ~ ssItem(hd(cons(sk5,nil)))
| ~ memberP(nil,hd(cons(sk5,nil))) ),
inference(instantiation,[status(thm)],[c_32846]) ).
tcf(c_32916,plain,
! [X0: $i] :
( ssList(cons(sk5,X0))
| ~ ssItem(sk5)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_32917,plain,
( ssList(cons(sk5,nil))
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_32916]) ).
tcf(c_43723,plain,
! [X0: $i,X1: $i] :
( memberP(X1,hd(cons(sk5,X0)))
| ~ memberP(sk7,sk5)
| ( X1 != sk7 )
| ( hd(cons(sk5,X0)) != sk5 ) ),
inference(instantiation,[status(thm)],[c_20355]) ).
tcf(c_43724,plain,
( memberP(nil,hd(cons(sk5,nil)))
| ~ memberP(sk7,sk5)
| ( nil != sk7 )
| ( hd(cons(sk5,nil)) != sk5 ) ),
inference(instantiation,[status(thm)],[c_43723]) ).
tcf(c_47430,plain,
skaf46(iPr_def_13,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_16446,c_9585]) ).
tcf(c_50682,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_6638]) ).
tcf(c_50683,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_50682]) ).
tcf(c_53108,plain,
! [X0: $i] :
( ( cons(sk5,app(X0,sk4)) = app(cons(sk5,X0),sk4) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6656,c_16574]) ).
tcf(c_53528,plain,
cons(sk5,app(nil,sk4)) = app(cons(sk5,nil),sk4),
inference(superposition,[status(thm)],[c_260,c_53108]) ).
tcf(c_53589,plain,
cons(sk5,sk4) = app(iPr_def_12,sk4),
inference(light_normalisation,[status(thm)],[c_53528,c_9841,c_29398]) ).
tcf(c_54364,plain,
( ssList(cons(sk5,sk4))
| ~ ssList(iPr_def_12)
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_53589,c_337]) ).
tcf(c_54380,plain,
ssList(cons(sk5,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_54364,c_10038,c_6657]) ).
tcf(c_54455,plain,
( duplicatefreeP(cons(sk5,sk4))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_54380,c_6638]) ).
tcf(c_56650,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_54455,c_442,c_260,c_13915,c_18581,c_20365,c_32917,c_50683]) ).
tcf(c_56652,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_6639,c_56650]) ).
tcf(c_56653,plain,
! [X0: $i] : ssItem(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_6637,c_56652]) ).
tcf(c_56681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X1,X3)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_426,c_56653]) ).
tcf(c_56684,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_390,c_56653]) ).
tcf(c_56686,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_413,c_56653]) ).
tcf(c_56696,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_393,c_56653]) ).
tcf(c_56697,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_392,c_56653]) ).
tcf(c_56718,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_338,c_56653]) ).
tcf(c_73259,plain,
( ( skaf46(iPr_def_13,nil) = nil )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_47430,c_11499]) ).
tcf(c_73264,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_73259,c_47430]) ).
tcf(c_73265,plain,
cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_73264,c_12394]) ).
tcf(c_73498,plain,
( memberP(iPr_def_13,hd(iPr_def_13))
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_73265,c_56684]) ).
tcf(c_100104,plain,
! [X0: $i] : ~ memberP(nil,X0),
inference(global_subsumption_just,[status(thm)],[c_323,c_442,c_260,c_323,c_6637,c_6639,c_13915,c_18581,c_20365,c_32917,c_50683]) ).
tcf(c_100108,negated_conjecture,
memberP(sk4,sk8),
inference(global_subsumption_just,[status(thm)],[c_6646,c_12496]) ).
tcf(c_100135,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( sk4 = nil ) ),
inference(light_normalisation,[status(thm)],[c_6650,c_6644]) ).
tcf(c_100142,plain,
( memberP(nil,sk8)
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_100135,c_100108]) ).
tcf(c_100144,plain,
iPr_def_14 = iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_100142,c_100104]) ).
tcf(c_100281,plain,
cons(sk8,nil) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6643,c_100144]) ).
tcf(c_100411,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6641,c_337]) ).
tcf(c_100426,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100411,c_6655]) ).
tcf(c_100458,plain,
ssList(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_100426,c_10049]) ).
tcf(c_100617,plain,
( frontsegP(iPr_def_14,iPr_def_13)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_6642,c_841]) ).
tcf(c_100664,plain,
frontsegP(iPr_def_14,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_100617,c_100458,c_6654]) ).
tcf(c_100971,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_100458,c_356]) ).
tcf(c_101993,plain,
cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_100971,c_11507,c_12394]) ).
tcf(c_108807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X1,X3)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_426,c_56681]) ).
tcf(c_108823,plain,
! [X0: $i,X1: $i] :
( frontsegP(nil,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(iPr_def_14,cons(X0,X1)) ),
inference(superposition,[status(thm)],[c_100281,c_108807]) ).
tcf(c_108883,plain,
! [X0: $i,X1: $i] :
( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(iPr_def_14,cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108823,c_260]) ).
tcf(c_125971,plain,
( ( skaf46(iPr_def_13,nil) = nil )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_47430,c_11695]) ).
tcf(c_125982,plain,
( ( nil = iPr_def_13 )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_125971,c_47430]) ).
tcf(c_125983,plain,
cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_125982,c_12394]) ).
tcf(c_135068,plain,
! [X0: $i,X1: $i] : tl(cons(skaf83(X0),skaf82(X1))) = skaf82(X1),
inference(superposition,[status(thm)],[c_265,c_10697]) ).
tcf(c_135943,plain,
skaf82(iPr_def_13) = tl(iPr_def_13),
inference(superposition,[status(thm)],[c_125983,c_135068]) ).
tcf(c_136256,plain,
( ( skaf82(iPr_def_13) = nil )
| ~ frontsegP(nil,tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_135943,c_25182]) ).
tcf(c_136277,plain,
ssList(tl(iPr_def_13)),
inference(superposition,[status(thm)],[c_135943,c_265]) ).
tcf(c_136281,plain,
( ( tl(iPr_def_13) = nil )
| ~ frontsegP(nil,tl(iPr_def_13)) ),
inference(light_normalisation,[status(thm)],[c_136256,c_135943]) ).
tcf(c_180441,plain,
( frontsegP(nil,tl(iPr_def_13))
| ~ frontsegP(iPr_def_14,iPr_def_13)
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_101993,c_108883]) ).
tcf(c_180453,plain,
( frontsegP(nil,tl(iPr_def_13))
| ~ ssList(tl(iPr_def_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_180441,c_100664]) ).
tcf(c_237939,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk4,sk8)
| ( X1 != sk8 )
| ( X0 != sk4 ) ),
inference(instantiation,[status(thm)],[c_6666]) ).
tcf(c_238094,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk4 )
| ( sk4 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_6661]) ).
tcf(c_238095,plain,
( ( nil = sk4 )
| ( nil != nil )
| ( sk4 != nil ) ),
inference(instantiation,[status(thm)],[c_238094]) ).
tcf(c_238950,plain,
! [X0: $i] :
( memberP(X0,sk8)
| ~ memberP(sk4,sk8)
| ( sk8 != sk8 )
| ( X0 != sk4 ) ),
inference(instantiation,[status(thm)],[c_237939]) ).
tcf(c_238951,plain,
sk8 = sk8,
inference(instantiation,[status(thm)],[c_6659]) ).
tcf(c_238952,plain,
( memberP(nil,sk8)
| ~ memberP(sk4,sk8)
| ( sk8 != sk8 )
| ( nil != sk4 ) ),
inference(instantiation,[status(thm)],[c_238950]) ).
tcf(c_248763,plain,
( ~ ssItem(sk8)
| ~ memberP(nil,sk8) ),
inference(instantiation,[status(thm)],[c_323]) ).
tcf(c_260129,plain,
ssList(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_6658,c_6644]) ).
tcf(c_260140,negated_conjecture,
iPr_def_15 = sk3,
inference(global_subsumption_just,[status(thm)],[c_6647,c_260,c_335,c_515,c_6650,c_12497,c_12496,c_238095,c_238952,c_238951,c_248763]) ).
tcf(c_260142,plain,
iPr_def_14 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_260140,c_6644]) ).
tcf(c_260158,plain,
cons(sk8,nil) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6643,c_260142]) ).
tcf(c_260251,plain,
! [X0: $i] : ~ memberP(nil,X0),
inference(global_subsumption_just,[status(thm)],[c_323,c_442,c_260,c_323,c_6637,c_6639,c_13915,c_18581,c_20365,c_32917,c_50683]) ).
tcf(c_260314,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6641,c_337]) ).
tcf(c_260331,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_260314,c_6655]) ).
tcf(c_260340,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_338,c_56718]) ).
tcf(c_260346,plain,
( ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6640,c_260340]) ).
tcf(c_260350,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_260346,c_260]) ).
tcf(c_260355,plain,
app(nil,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_260350,c_326]) ).
tcf(c_260357,plain,
ssList(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_260331,c_10049]) ).
tcf(c_260360,plain,
app(iPr_def_13,nil) = iPr_def_13,
inference(superposition,[status(thm)],[c_260357,c_325]) ).
tcf(c_260473,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_390,c_56684]) ).
tcf(c_260502,plain,
( rearsegP(iPr_def_14,sk7)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_6642,c_840]) ).
tcf(c_260576,plain,
rearsegP(iPr_def_14,sk7),
inference(forward_subsumption_resolution,[status(thm)],[c_260502,c_260357,c_6654]) ).
tcf(c_260635,plain,
( frontsegP(iPr_def_14,iPr_def_13)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_6642,c_841]) ).
tcf(c_260709,plain,
frontsegP(iPr_def_14,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_260635,c_260357,c_6654]) ).
tcf(c_260775,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_348,c_442,c_260,c_6639,c_10694,c_13915,c_18581,c_20365,c_32917,c_50683]) ).
tcf(c_260785,plain,
! [X0: $i,X1: $i] : tl(cons(X0,skaf82(X1))) = skaf82(X1),
inference(superposition,[status(thm)],[c_265,c_260775]) ).
tcf(c_261110,plain,
! [X0: $i,X1: $i] :
( ( skaf46(X0,X1) = nil )
| ( cons(hd(skaf46(X0,X1)),tl(skaf46(X0,X1))) = skaf46(X0,X1) ) ),
inference(superposition,[status(thm)],[c_302,c_356]) ).
tcf(c_261260,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_302,c_361]) ).
tcf(c_261371,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_372,c_442,c_260,c_6639,c_11858,c_13915,c_18581,c_20365,c_32917,c_50683]) ).
tcf(c_261378,plain,
! [X0: $i] : app(cons(X0,nil),sk6) = cons(X0,sk6),
inference(superposition,[status(thm)],[c_6655,c_261371]) ).
tcf(c_261490,plain,
( ( sk6 = nil )
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6641,c_370]) ).
tcf(c_261557,plain,
( ( sk6 = nil )
| ( nil != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_261490,c_260350,c_6655]) ).
tcf(c_261560,plain,
nil != iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_261557,c_12394]) ).
tcf(c_261594,plain,
cons(sk5,sk6) = app(iPr_def_12,sk6),
inference(superposition,[status(thm)],[c_6640,c_261378]) ).
tcf(c_262730,plain,
( ( app(skaf46(iPr_def_14,sk7),sk7) = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_260576,c_383]) ).
tcf(c_262776,plain,
app(skaf46(iPr_def_14,sk7),sk7) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_262730,c_260129,c_6654]) ).
tcf(c_263714,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_392,c_56697]) ).
tcf(c_263715,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(renaming,[status(thm)],[c_263714]) ).
tcf(c_263726,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_6642,c_263715]) ).
tcf(c_263797,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_263726,c_260357,c_6654]) ).
tcf(c_263924,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_393,c_56696]) ).
tcf(c_263925,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(renaming,[status(thm)],[c_263924]) ).
tcf(c_263936,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ memberP(sk7,X0) ),
inference(superposition,[status(thm)],[c_6642,c_263925]) ).
tcf(c_264009,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_263936,c_260357,c_6654]) ).
tcf(c_264378,plain,
( memberP(iPr_def_14,sk5)
| memberP(sk6,sk5) ),
inference(superposition,[status(thm)],[c_6653,c_264009]) ).
tcf(c_264381,plain,
memberP(iPr_def_14,sk5),
inference(global_subsumption_just,[status(thm)],[c_264378,c_18012]) ).
tcf(c_266477,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_6642,c_402]) ).
tcf(c_266608,plain,
! [X0: $i] :
( ( X0 = sk7 )
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_266477,c_260357,c_6654]) ).
tcf(c_267039,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_6641,c_403]) ).
tcf(c_267040,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_6642,c_403]) ).
tcf(c_267171,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ~ ssList(X0)
| ( app(X0,sk7) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_267040,c_260357,c_6654]) ).
tcf(c_267175,plain,
! [X0: $i] :
( ( X0 = sk6 )
| ~ ssList(X0)
| ( app(X0,iPr_def_12) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_267039,c_260350,c_6655]) ).
tcf(c_268032,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_413,c_56686]) ).
tcf(c_268045,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sk8 )
| ~ ssList(nil)
| ~ memberP(iPr_def_14,X0) ),
inference(superposition,[status(thm)],[c_260158,c_268032]) ).
tcf(c_268052,plain,
! [X0: $i] :
( ( X0 = sk8 )
| ~ memberP(iPr_def_14,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_268045,c_260251,c_260]) ).
tcf(c_272248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X1,X3)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_426,c_56681]) ).
tcf(c_277883,plain,
( ( sk7 = nil )
| ~ ssList(nil)
| ( iPr_def_13 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_260360,c_266608]) ).
tcf(c_277884,plain,
( ( sk7 = nil )
| ( iPr_def_13 != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_277883,c_260]) ).
tcf(c_278204,plain,
( ( skaf46(iPr_def_14,sk7) = iPr_def_13 )
| ~ ssList(skaf46(iPr_def_14,sk7)) ),
inference(superposition,[status(thm)],[c_262776,c_267171]) ).
tcf(c_278206,plain,
skaf46(iPr_def_14,sk7) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_278204,c_302]) ).
tcf(c_278222,plain,
( ( sk6 = nil )
| ~ ssList(nil)
| ( iPr_def_12 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_260355,c_267175]) ).
tcf(c_278223,plain,
( ( sk6 = nil )
| ( iPr_def_12 != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_278222,c_260]) ).
tcf(c_286793,plain,
! [X0: $i] :
( frontsegP(cons(sk5,sk6),X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_261594,c_389]) ).
tcf(c_286805,plain,
! [X0: $i] :
( frontsegP(cons(sk5,sk6),X0)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_286793,c_260350,c_6655]) ).
tcf(c_288399,plain,
! [X0: $i,X1: $i] :
( frontsegP(sk6,X1)
| ~ ssList(sk6)
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(superposition,[status(thm)],[c_286805,c_272248]) ).
tcf(c_288411,plain,
! [X0: $i,X1: $i] :
( frontsegP(sk6,X1)
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_288399,c_6655]) ).
tcf(c_292211,plain,
sk5 = sk8,
inference(superposition,[status(thm)],[c_264381,c_268052]) ).
tcf(c_292266,plain,
cons(sk8,nil) = iPr_def_12,
inference(demodulation,[status(thm)],[c_6640,c_292211]) ).
tcf(c_292270,plain,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_260158,c_292266]) ).
tcf(c_292271,plain,
! [X0: $i] :
( ( X0 = sk8 )
| ~ memberP(iPr_def_12,X0) ),
inference(demodulation,[status(thm)],[c_268052,c_292270]) ).
tcf(c_292304,plain,
skaf46(iPr_def_12,sk7) = iPr_def_13,
inference(demodulation,[status(thm)],[c_278206,c_292270]) ).
tcf(c_292349,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ memberP(iPr_def_13,X0) ),
inference(demodulation,[status(thm)],[c_263797,c_292270]) ).
tcf(c_292355,plain,
frontsegP(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_260709,c_292270]) ).
tcf(c_311669,plain,
( ( skaf46(iPr_def_12,sk7) = nil )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_292304,c_261110]) ).
tcf(c_311704,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_311669,c_292304]) ).
tcf(c_311705,plain,
cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_311704,c_261560]) ).
tcf(c_313450,plain,
( memberP(iPr_def_13,hd(iPr_def_13))
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_311705,c_260473]) ).
tcf(c_313851,plain,
memberP(iPr_def_13,hd(iPr_def_13)),
inference(global_subsumption_just,[status(thm)],[c_313450,c_73498,c_136277]) ).
tcf(c_313854,plain,
memberP(iPr_def_12,hd(iPr_def_13)),
inference(superposition,[status(thm)],[c_313851,c_292349]) ).
tcf(c_315086,plain,
hd(iPr_def_13) = sk8,
inference(superposition,[status(thm)],[c_313854,c_292271]) ).
tcf(c_315092,plain,
cons(sk8,tl(iPr_def_13)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_311705,c_315086]) ).
tcf(c_319449,plain,
( ( sk7 = nil )
| ( iPr_def_12 != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_277884,c_292270]) ).
tcf(c_339372,plain,
( ( skaf46(iPr_def_12,sk7) = nil )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_292304,c_261260]) ).
tcf(c_339409,plain,
( ( nil = iPr_def_13 )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_339372,c_292304]) ).
tcf(c_339410,plain,
cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_339409,c_261560]) ).
tcf(c_342058,plain,
skaf82(iPr_def_13) = tl(iPr_def_13),
inference(superposition,[status(thm)],[c_339410,c_260785]) ).
tcf(c_344470,plain,
ssList(tl(iPr_def_13)),
inference(superposition,[status(thm)],[c_342058,c_265]) ).
tcf(c_385618,plain,
! [X0: $i,X1: $i] :
( frontsegP(sk6,X1)
| ~ ssList(X1)
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_288411,c_260340]) ).
tcf(c_385688,plain,
( frontsegP(sk6,tl(iPr_def_13))
| ~ frontsegP(iPr_def_12,iPr_def_13)
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_315092,c_385618]) ).
tcf(c_385689,plain,
frontsegP(sk6,tl(iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_385688,c_292355,c_344470]) ).
tcf(c_388349,plain,
! [X0: $i] :
( frontsegP(X0,tl(iPr_def_13))
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssList(tl(iPr_def_13))
| ~ frontsegP(X0,sk6) ),
inference(superposition,[status(thm)],[c_385689,c_406]) ).
tcf(c_388358,plain,
! [X0: $i] :
( frontsegP(X0,tl(iPr_def_13))
| ~ ssList(X0)
| ~ frontsegP(X0,sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_388349,c_6655,c_344470]) ).
tcf(c_388645,plain,
( ( tl(iPr_def_13) = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,sk6)
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_388358,c_336]) ).
tcf(c_388657,plain,
( ( tl(iPr_def_13) = nil )
| ~ frontsegP(nil,sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_388645,c_260,c_344470]) ).
tcf(c_388951,plain,
tl(iPr_def_13) = nil,
inference(global_subsumption_just,[status(thm)],[c_388657,c_136277,c_136281,c_180453]) ).
tcf(c_388992,plain,
cons(sk8,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_315092,c_388951]) ).
tcf(c_388996,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_388992,c_292266]) ).
tcf(c_389005,plain,
sk7 = nil,
inference(backward_subsumption_resolution,[status(thm)],[c_319449,c_388996]) ).
tcf(c_389006,plain,
sk6 = nil,
inference(backward_subsumption_resolution,[status(thm)],[c_278223,c_388996]) ).
tcf(c_390420,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_389005,c_389006,c_43724,c_32847,c_32332,c_31024,c_31025,c_16850,c_15365,c_10898,c_10485,c_515,c_335,c_446,c_260,c_442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC183-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.37 % Computer : n011.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Thu Sep 24 16:50:57 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 96.88/16.80 % SZS status Started for theBenchmark.p
% 96.88/16.80 % SZS status Unsatisfiable for theBenchmark.p
% 96.88/16.80
% 96.88/16.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 96.88/16.80
% 96.88/16.80 % ------ iProver source info
% 96.88/16.80
% 96.88/16.80 % git: date: 2026-07-19 20:42:38 +0200
% 96.88/16.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 96.88/16.80 % git: non_committed_changes: false
% 96.88/16.80
% 96.88/16.80 % ------ Parsing...% successful
% 96.88/16.80
% 96.88/16.80
% 96.88/16.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 96.88/16.80
% 96.88/16.80 % ------ 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 %
% 96.88/16.80
% 96.88/16.80 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 96.88/16.80
% 96.88/16.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 96.88/16.80 % ------ Proving...
% 96.88/16.80 % ------ Problem Properties
% 96.88/16.80
% 96.88/16.80 %
% 96.88/16.80 % clauses 196
% 96.88/16.80 % conjectures 15
% 96.88/16.80 % EPR 67
% 96.88/16.80 % Horn 159
% 96.88/16.80 % unary 68
% 96.88/16.80 % binary 28
% 96.88/16.80 % lits 575
% 96.88/16.80 % lits eq 86
% 96.88/16.80 % fd_pure 0
% 96.88/16.80 % fd_pseudo 0
% 96.88/16.80 % fd_cond 17
% 96.88/16.80 % fd_pseudo_cond 14
% 96.88/16.80 % AC symbols 0
% 96.88/16.80
% 96.88/16.80 % ------ Schedule dynamic 5 is on
% 96.88/16.80
% 96.88/16.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 96.88/16.80
% 96.88/16.80
% 96.88/16.80 % ------
% 96.88/16.80 % Current options:
% 96.88/16.80 % ------
% 96.88/16.80
% 96.88/16.80
% 96.88/16.80 %
% 96.88/16.80
% 96.88/16.80 % ------ Proving...
% 96.88/16.80 % Proof_search_loop: time out after: 8932 full_loop iterations
% 96.88/16.80
% 96.88/16.80 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 96.88/16.80
% 96.88/16.80
% 96.88/16.80 % ------
% 96.88/16.80 % Current options:
% 96.88/16.80 % ------
% 96.88/16.80
% 96.88/16.80
% 96.88/16.80 %
% 96.88/16.80
% 96.88/16.80 % ------ Proving...
% 96.88/16.80 %
% 96.88/16.80
% 96.88/16.80 % SZS status Unsatisfiable for theBenchmark.p
% 96.88/16.80
% 96.88/16.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 66.15/16.81
% 66.15/16.81
%------------------------------------------------------------------------------