%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC172-1 : 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 : n009.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 03:08:13 PM UTC 2026
% Result : Unsatisfiable 71.33s 17.92s
% Output : CNFRefutation 71.33s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f253ERROR: Could not build tree for root c_377288ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
fof(f14,axiom,
! [X0] : ssList(skaf81(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause14) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause50) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
fof(f57,axiom,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
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(f104,axiom,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause102) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f104]) ).
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(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(f134,axiom,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
file('/export/starexec/sandbox/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/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(f143,axiom,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox/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/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(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(f186,axiom,
! [X2,X3,X0,X1] :
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause172) ).
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/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).
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(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(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,
ssItem(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,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,plain,
sk1 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
~ neq(sk5,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f219,negated_conjecture,
( nil = sk3
| cons(sk9,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f220,plain,
( nil = sk3
| sk3 = cons(sk9,nil) ),
inference(reorient_equations,[],[f219]) ).
fof(f225,plain,
sk3 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(definition_unfolding,[],[f211,f205]) ).
fof(f228,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f83]) ).
fof(f236,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f237,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
fof(f240,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(f243,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_261,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_266,plain,
! [X0: $i] : ssList(skaf82(X0)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_267,plain,
! [X0: $i] : ssList(skaf81(X0)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_310,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_324,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_326,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_327,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_336,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_337,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_357,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_362,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i] :
( ( app(skaf46(X0,X1),X1) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i] :
( ( app(X1,skaf45(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_389,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_390,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_391,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_393,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_394,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_396,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_403,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_404,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_407,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_414,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_425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_426,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,[],[f240]) ).
tcf(c_427,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_432,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,[],[f243]) ).
tcf(c_441,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_443,negated_conjecture,
ssItem(sk5),
inference(cnf_transformation,[],[f206]) ).
tcf(c_444,negated_conjecture,
ssItem(sk6),
inference(cnf_transformation,[],[f207]) ).
tcf(c_445,negated_conjecture,
ssList(sk7),
inference(cnf_transformation,[],[f208]) ).
tcf(c_446,negated_conjecture,
ssList(sk8),
inference(cnf_transformation,[],[f209]) ).
tcf(c_447,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk3,
inference(cnf_transformation,[],[f225]) ).
tcf(c_448,negated_conjecture,
~ neq(sk5,sk6),
inference(cnf_transformation,[],[f212]) ).
tcf(c_454,negated_conjecture,
( ( sk3 = nil )
| ( cons(sk9,nil) = sk3 ) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_517,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_842,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_397,c_338]) ).
tcf(c_843,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_396,c_338]) ).
tcf(c_2817,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0)
| ( X1 != sk6 )
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_448,c_355]) ).
tcf(c_2818,plain,
( ( sk5 = sk6 )
| ~ ssItem(sk6)
| ~ ssItem(sk5) ),
inference(unflattening,[status(thm)],[c_2817]) ).
tcf(c_2819,plain,
sk5 = sk6,
inference(global_subsumption_just,[status(thm)],[c_2818,c_444,c_443,c_2818]) ).
tcf(c_5085,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)),sk8) = sk3,
inference(light_normalisation,[status(thm)],[c_447,c_2819]) ).
tcf(c_9628,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_325]) ).
tcf(c_9629,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_325]) ).
tcf(c_9630,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_325]) ).
tcf(c_9631,definition,
iPr_def_12 = cons(sk5,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_9632,definition,
iPr_def_13 = app(sk7,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_9633,definition,
iPr_def_14 = app(iPr_def_13,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_9634,definition,
iPr_def_15 = app(iPr_def_14,sk8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_9635,definition,
iPr_def_16 = cons(sk9,nil),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_9636,plain,
iPr_def_15 = sk3,
inference(demodulation,[status(thm)],[c_5085,c_9631,c_9632,c_9633,c_9634]) ).
tcf(c_9640,negated_conjecture,
( ( iPr_def_16 = sk3 )
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_454,c_9635]) ).
tcf(c_9646,negated_conjecture,
ssList(sk8),
inference(demodulation,[status(thm)],[c_446]) ).
tcf(c_9647,negated_conjecture,
ssList(sk7),
inference(demodulation,[status(thm)],[c_445]) ).
tcf(c_9648,negated_conjecture,
ssItem(sk5),
inference(demodulation,[status(thm)],[c_443]) ).
tcf(c_9650,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_441]) ).
tcf(c_9653,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_12543,plain,
app(sk7,nil) = sk7,
inference(superposition,[status(thm)],[c_9647,c_326]) ).
tcf(c_12569,plain,
! [X0: $i,X1: $i] : app(skaf46(X0,X1),nil) = skaf46(X0,X1),
inference(superposition,[status(thm)],[c_303,c_326]) ).
tcf(c_12905,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_9632,c_338]) ).
tcf(c_12906,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_9633,c_338]) ).
tcf(c_12923,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12905,c_9647]) ).
tcf(c_12926,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_12906,c_12923]) ).
tcf(c_13013,plain,
( ssList(iPr_def_12)
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_9631,c_339]) ).
tcf(c_13022,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_13013,c_9648,c_261]) ).
tcf(c_13033,plain,
ssList(iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_12926,c_13022]) ).
tcf(c_13034,plain,
ssList(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_12923,c_13022]) ).
tcf(c_13064,plain,
app(iPr_def_12,nil) = iPr_def_12,
inference(superposition,[status(thm)],[c_13022,c_326]) ).
tcf(c_13387,plain,
( frontsegP(iPr_def_13,sk7)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_9632,c_842]) ).
tcf(c_13388,plain,
( frontsegP(iPr_def_14,iPr_def_13)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_9633,c_842]) ).
tcf(c_13429,plain,
frontsegP(iPr_def_14,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_13388,c_13034,c_13022]) ).
tcf(c_13430,plain,
frontsegP(iPr_def_13,sk7),
inference(forward_subsumption_resolution,[status(thm)],[c_13387,c_13022,c_9647]) ).
tcf(c_13529,plain,
( rearsegP(iPr_def_12,nil)
| ~ ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_13064,c_843]) ).
tcf(c_13534,plain,
rearsegP(iPr_def_12,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_13529,c_13022,c_261]) ).
tcf(c_13671,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ iPr_def_10
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_9628,c_349]) ).
tcf(c_13805,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ iPr_def_10
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_9628,c_350]) ).
tcf(c_13938,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_9631,c_351]) ).
tcf(c_13945,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_13938,c_9648,c_261]) ).
tcf(c_14675,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_303,c_357]) ).
tcf(c_15025,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ iPr_def_10
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_9628,c_373]) ).
tcf(c_15291,plain,
( ( nil = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ( nil != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9633,c_371]) ).
tcf(c_15292,plain,
( ( nil = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(sk8)
| ( nil != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_9634,c_371]) ).
tcf(c_15326,plain,
( ( nil = iPr_def_14 )
| ( nil != iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15292,c_13033,c_9646]) ).
tcf(c_15329,plain,
( ( nil = iPr_def_13 )
| ( nil != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15291,c_13034,c_13022]) ).
tcf(c_15344,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_9632,c_372]) ).
tcf(c_15384,plain,
nil != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_15344,c_13945,c_13022,c_9647]) ).
tcf(c_16818,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_432]) ).
tcf(c_16819,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_16818]) ).
tcf(c_17000,plain,
! [X0: $i] :
( rearsegP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ rearsegP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_9632,c_389]) ).
tcf(c_17057,plain,
! [X0: $i] :
( rearsegP(iPr_def_13,X0)
| ~ ssList(X0)
| ~ rearsegP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17000,c_13022,c_9647]) ).
tcf(c_18846,plain,
! [X0: $i] :
( frontsegP(X0,sk7)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ frontsegP(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_13430,c_407]) ).
tcf(c_18874,plain,
! [X0: $i] :
( frontsegP(X0,sk7)
| ~ ssList(X0)
| ~ frontsegP(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18846,c_13034,c_9647]) ).
tcf(c_18974,plain,
( rearsegP(iPr_def_13,nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_13534,c_17057]) ).
tcf(c_18975,plain,
rearsegP(iPr_def_13,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_18974,c_261]) ).
tcf(c_19526,plain,
( ( app(skaf46(iPr_def_13,nil),nil) = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_18975,c_384]) ).
tcf(c_19529,plain,
app(skaf46(iPr_def_13,nil),nil) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_19526,c_13034,c_261]) ).
tcf(c_19614,plain,
( frontsegP(iPr_def_14,sk7)
| ~ ssList(iPr_def_14) ),
inference(superposition,[status(thm)],[c_13429,c_18874]) ).
tcf(c_19617,plain,
frontsegP(iPr_def_14,sk7),
inference(forward_subsumption_resolution,[status(thm)],[c_19614,c_13033]) ).
tcf(c_20140,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(X0)
| ( app(sk7,X0) != sk7 ) ),
inference(superposition,[status(thm)],[c_12543,c_403]) ).
tcf(c_20213,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ( app(sk7,X0) != sk7 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20140,c_261,c_9647]) ).
tcf(c_20482,plain,
! [X0: $i] :
( ( X0 = sk7 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ~ ssList(X0)
| ( app(X0,iPr_def_12) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_9632,c_404]) ).
tcf(c_20575,plain,
! [X0: $i] :
( ( X0 = sk7 )
| ~ ssList(X0)
| ( app(X0,iPr_def_12) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20482,c_13022,c_9647]) ).
tcf(c_20751,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_338]) ).
tcf(c_20752,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_20751]) ).
tcf(c_21059,plain,
( ( app(sk7,skaf45(iPr_def_14,sk7)) = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_19617,c_385]) ).
tcf(c_21065,plain,
app(sk7,skaf45(iPr_def_14,sk7)) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_21059,c_13033,c_9647]) ).
tcf(c_23875,plain,
! [X0: $i,X1: $i] :
( segmentP(app(iPr_def_14,X1),X0)
| ~ ssList(sk7)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf45(iPr_def_14,sk7))
| ~ segmentP(skaf45(iPr_def_14,sk7),X0) ),
inference(superposition,[status(thm)],[c_21065,c_425]) ).
tcf(c_24056,plain,
! [X0: $i,X1: $i] :
( segmentP(app(iPr_def_14,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(skaf45(iPr_def_14,sk7),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23875,c_9647,c_304]) ).
tcf(c_24630,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,cons(sk5,X0)))
| ~ ssList(X1)
| ~ ssList(cons(sk5,X0)) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_24631,plain,
( ssList(app(nil,cons(sk5,nil)))
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil)) ),
inference(instantiation,[status(thm)],[c_24630]) ).
tcf(c_25325,plain,
! [X0: $i,X1: $i] :
( frontsegP(nil,X1)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(superposition,[status(thm)],[c_9631,c_427]) ).
tcf(c_25348,plain,
! [X0: $i,X1: $i] :
( frontsegP(nil,X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25325,c_9648,c_261]) ).
tcf(c_29654,plain,
! [X0: $i] :
( ssList(cons(sk5,X0))
| ~ ssItem(sk5)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_339]) ).
tcf(c_29655,plain,
( ssList(cons(sk5,nil))
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_29654]) ).
tcf(c_30453,plain,
! [X0: $i] :
( duplicatefreeP(skaf81(X0))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_267,c_9629]) ).
tcf(c_31124,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_9629]) ).
tcf(c_31125,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_31124]) ).
tcf(c_31519,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_30453,c_443,c_261,c_16819,c_20752,c_24631,c_29655,c_31125]) ).
tcf(c_31521,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_9630,c_31519]) ).
tcf(c_31522,plain,
! [X0: $i] : ssItem(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_9628,c_31521]) ).
tcf(c_31546,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_427,c_31522]) ).
tcf(c_31550,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_391,c_31522]) ).
tcf(c_31551,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_414,c_31522]) ).
tcf(c_31561,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_394,c_31522]) ).
tcf(c_31562,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_393,c_31522]) ).
tcf(c_31583,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_339,c_31522]) ).
tcf(c_31848,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ( sk7 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_9632,c_20213]) ).
tcf(c_31853,plain,
sk7 != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_31848,c_13945,c_13022]) ).
tcf(c_32139,plain,
( ( sk7 = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ( iPr_def_13 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9633,c_20575]) ).
tcf(c_32144,plain,
( ( sk7 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32139,c_13034]) ).
tcf(c_33230,plain,
! [X0: $i,X1: $i] :
( frontsegP(nil,X1)
| ~ frontsegP(iPr_def_12,cons(X0,X1))
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_25348,c_443,c_261,c_9628,c_9630,c_16819,c_20752,c_24631,c_25348,c_29655,c_31125]) ).
tcf(c_33231,plain,
! [X0: $i,X1: $i] :
( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(renaming,[status(thm)],[c_33230]) ).
tcf(c_35216,plain,
! [X0: $i] :
( segmentP(app(iPr_def_14,X0),skaf45(iPr_def_14,sk7))
| ~ ssList(X0)
| ~ ssList(skaf45(iPr_def_14,sk7)) ),
inference(superposition,[status(thm)],[c_310,c_24056]) ).
tcf(c_35217,plain,
! [X0: $i] :
( segmentP(app(iPr_def_14,X0),skaf45(iPr_def_14,sk7))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35216,c_304]) ).
tcf(c_54453,plain,
skaf46(iPr_def_13,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_19529,c_12569]) ).
tcf(c_109414,plain,
! [X0: $i] : ~ memberP(nil,X0),
inference(global_subsumption_just,[status(thm)],[c_324,c_443,c_261,c_324,c_9628,c_9630,c_16819,c_20752,c_24631,c_29655,c_31125]) ).
tcf(c_149642,plain,
( ( skaf46(iPr_def_13,nil) = nil )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_54453,c_14675]) ).
tcf(c_149667,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_149642,c_54453]) ).
tcf(c_149668,plain,
cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_149667,c_15384]) ).
tcf(c_150365,plain,
( frontsegP(nil,tl(iPr_def_13))
| ~ frontsegP(iPr_def_12,iPr_def_13)
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_149668,c_33231]) ).
tcf(c_150884,plain,
! [X0: $i] :
( ( nil = iPr_def_15 )
| ( iPr_def_15 != X0 )
| ( nil != X0 ) ),
inference(instantiation,[status(thm)],[c_9653]) ).
tcf(c_151124,plain,
( ( nil = iPr_def_15 )
| ( iPr_def_15 != sk3 )
| ( nil != sk3 ) ),
inference(instantiation,[status(thm)],[c_150884]) ).
tcf(c_152725,plain,
! [X0: $i] :
( ( nil = sk3 )
| ( nil != X0 )
| ( sk3 != X0 ) ),
inference(instantiation,[status(thm)],[c_9653]) ).
tcf(c_152726,plain,
( ( nil = sk3 )
| ( nil != nil )
| ( sk3 != nil ) ),
inference(instantiation,[status(thm)],[c_152725]) ).
tcf(c_237592,plain,
ssList(iPr_def_15),
inference(light_normalisation,[status(thm)],[c_9650,c_9636]) ).
tcf(c_237601,negated_conjecture,
iPr_def_16 = sk3,
inference(global_subsumption_just,[status(thm)],[c_9640,c_261,c_336,c_517,c_9636,c_9640,c_15329,c_15326,c_15384,c_151124,c_152726]) ).
tcf(c_237603,plain,
iPr_def_15 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_237601,c_9636]) ).
tcf(c_237644,plain,
cons(sk9,nil) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_9635,c_237603]) ).
tcf(c_237680,plain,
! [X0: $i,X1: $i] : app(skaf46(X0,X1),nil) = skaf46(X0,X1),
inference(superposition,[status(thm)],[c_303,c_326]) ).
tcf(c_237719,plain,
! [X0: $i] : app(nil,skaf82(X0)) = skaf82(X0),
inference(superposition,[status(thm)],[c_266,c_327]) ).
tcf(c_237743,plain,
! [X0: $i,X1: $i] : app(nil,skaf45(X0,X1)) = skaf45(X0,X1),
inference(superposition,[status(thm)],[c_304,c_327]) ).
tcf(c_237770,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_9632,c_338]) ).
tcf(c_237771,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_9633,c_338]) ).
tcf(c_237790,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_237770,c_9647]) ).
tcf(c_237793,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_237771,c_237790]) ).
tcf(c_237802,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_339,c_31583]) ).
tcf(c_237808,plain,
( ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_9631,c_237802]) ).
tcf(c_237812,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_237808,c_261]) ).
tcf(c_237817,plain,
app(nil,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_237812,c_327]) ).
tcf(c_237819,plain,
ssList(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_237790,c_13034]) ).
tcf(c_237822,plain,
app(iPr_def_13,nil) = iPr_def_13,
inference(superposition,[status(thm)],[c_237819,c_326]) ).
tcf(c_237823,plain,
ssList(iPr_def_14),
inference(global_subsumption_just,[status(thm)],[c_237793,c_13033]) ).
tcf(c_237825,plain,
app(nil,iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_237823,c_327]) ).
tcf(c_237938,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_391,c_31550]) ).
tcf(c_237944,plain,
( memberP(iPr_def_12,sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_9631,c_237938]) ).
tcf(c_237947,plain,
memberP(iPr_def_12,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_237944,c_261]) ).
tcf(c_237966,plain,
( frontsegP(iPr_def_13,sk7)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_9632,c_842]) ).
tcf(c_237967,plain,
( frontsegP(iPr_def_14,iPr_def_13)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_9633,c_842]) ).
tcf(c_238001,plain,
! [X0: $i] :
( frontsegP(skaf82(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf82(X0)) ),
inference(superposition,[status(thm)],[c_237719,c_842]) ).
tcf(c_238024,plain,
( frontsegP(iPr_def_14,nil)
| ~ ssList(iPr_def_14)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_237825,c_842]) ).
tcf(c_238031,plain,
frontsegP(iPr_def_14,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_238024,c_237823,c_261]) ).
tcf(c_238043,plain,
frontsegP(iPr_def_14,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_237967,c_237819,c_237812]) ).
tcf(c_238044,plain,
frontsegP(iPr_def_13,sk7),
inference(forward_subsumption_resolution,[status(thm)],[c_237966,c_237812,c_9647]) ).
tcf(c_238065,plain,
! [X0: $i] : frontsegP(skaf82(X0),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_238001,c_261,c_266]) ).
tcf(c_238158,plain,
( rearsegP(iPr_def_13,nil)
| ~ ssList(iPr_def_13)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_237822,c_843]) ).
tcf(c_238159,plain,
rearsegP(iPr_def_13,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_238158,c_237819,c_261]) ).
tcf(c_238236,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_349,c_443,c_261,c_9630,c_13671,c_16819,c_20752,c_24631,c_29655,c_31125]) ).
tcf(c_238246,plain,
! [X0: $i,X1: $i] : tl(cons(X0,skaf82(X1))) = skaf82(X1),
inference(superposition,[status(thm)],[c_266,c_238236]) ).
tcf(c_238328,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_350,c_443,c_261,c_9630,c_13805,c_16819,c_20752,c_24631,c_29655,c_31125]) ).
tcf(c_238338,plain,
! [X0: $i,X1: $i] : hd(cons(X0,skaf82(X1))) = X0,
inference(superposition,[status(thm)],[c_266,c_238328]) ).
tcf(c_238571,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_303,c_357]) ).
tcf(c_238721,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_303,c_362]) ).
tcf(c_238843,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_373,c_443,c_261,c_9630,c_15025,c_16819,c_20752,c_24631,c_29655,c_31125]) ).
tcf(c_238850,plain,
! [X0: $i] : app(cons(X0,nil),sk7) = cons(X0,sk7),
inference(superposition,[status(thm)],[c_9647,c_238843]) ).
tcf(c_238937,plain,
( ( sk7 = nil )
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_9632,c_371]) ).
tcf(c_239006,plain,
( ( sk7 = nil )
| ( nil != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_238937,c_237812,c_9647]) ).
tcf(c_239009,plain,
nil != iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_239006,c_15384]) ).
tcf(c_239069,plain,
cons(sk5,sk7) = app(iPr_def_12,sk7),
inference(superposition,[status(thm)],[c_9631,c_238850]) ).
tcf(c_240149,plain,
( ( app(skaf46(iPr_def_13,nil),nil) = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_238159,c_384]) ).
tcf(c_240167,plain,
app(skaf46(iPr_def_13,nil),nil) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_240149,c_237819,c_261]) ).
tcf(c_240246,plain,
( ( app(nil,skaf45(iPr_def_14,nil)) = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_238031,c_385]) ).
tcf(c_240274,plain,
app(nil,skaf45(iPr_def_14,nil)) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_240246,c_237823,c_261]) ).
tcf(c_240841,plain,
! [X0: $i] :
( frontsegP(iPr_def_15,X0)
| ~ ssList(iPr_def_14)
| ~ ssList(sk8)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_14,X0) ),
inference(superposition,[status(thm)],[c_9634,c_390]) ).
tcf(c_240943,plain,
! [X0: $i] :
( frontsegP(iPr_def_15,X0)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_14,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_240841,c_237823,c_9646]) ).
tcf(c_241175,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_393,c_31562]) ).
tcf(c_241176,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(renaming,[status(thm)],[c_241175]) ).
tcf(c_241187,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_9633,c_241176]) ).
tcf(c_241188,plain,
! [X0: $i] :
( memberP(iPr_def_15,X0)
| ~ ssList(iPr_def_14)
| ~ ssList(sk8)
| ~ memberP(iPr_def_14,X0) ),
inference(superposition,[status(thm)],[c_9634,c_241176]) ).
tcf(c_241260,plain,
! [X0: $i] :
( memberP(iPr_def_15,X0)
| ~ memberP(iPr_def_14,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_241188,c_237823,c_9646]) ).
tcf(c_241263,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_241187,c_237819,c_237812]) ).
tcf(c_241424,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_394,c_31561]) ).
tcf(c_241425,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(renaming,[status(thm)],[c_241424]) ).
tcf(c_241435,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_9632,c_241425]) ).
tcf(c_241518,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_241435,c_237812,c_9647]) ).
tcf(c_241829,plain,
! [X0: $i] :
( ( skaf82(X0) = nil )
| ~ ssList(nil)
| ~ ssList(skaf82(X0))
| ~ frontsegP(nil,skaf82(X0)) ),
inference(superposition,[status(thm)],[c_238065,c_382]) ).
tcf(c_241830,plain,
! [X0: $i] :
( ( skaf82(X0) = nil )
| ~ frontsegP(nil,skaf82(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_241829,c_261,c_266]) ).
tcf(c_241860,plain,
memberP(iPr_def_13,sk5),
inference(superposition,[status(thm)],[c_237947,c_241518]) ).
tcf(c_242638,plain,
! [X0: $i] :
( frontsegP(X0,sk7)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ frontsegP(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_238044,c_407]) ).
tcf(c_242695,plain,
! [X0: $i] :
( frontsegP(X0,sk7)
| ~ ssList(X0)
| ~ frontsegP(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_242638,c_237819,c_9647]) ).
tcf(c_244602,plain,
! [X0: $i] :
( ( X0 = sk7 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ~ ssList(X0)
| ( app(X0,iPr_def_12) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_9632,c_404]) ).
tcf(c_244753,plain,
! [X0: $i] :
( ( X0 = sk7 )
| ~ ssList(X0)
| ( app(X0,iPr_def_12) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_244602,c_237812,c_9647]) ).
tcf(c_245467,plain,
( frontsegP(iPr_def_15,iPr_def_13)
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_238043,c_240943]) ).
tcf(c_245470,plain,
frontsegP(iPr_def_15,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_245467,c_237819]) ).
tcf(c_245516,plain,
( frontsegP(iPr_def_14,sk7)
| ~ ssList(iPr_def_14) ),
inference(superposition,[status(thm)],[c_238043,c_242695]) ).
tcf(c_245518,plain,
frontsegP(iPr_def_14,sk7),
inference(forward_subsumption_resolution,[status(thm)],[c_245516,c_237823]) ).
tcf(c_245659,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_414,c_31551]) ).
tcf(c_245672,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sk9 )
| ~ ssList(nil)
| ~ memberP(iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_237644,c_245659]) ).
tcf(c_245679,plain,
! [X0: $i] :
( ( X0 = sk9 )
| ~ memberP(iPr_def_15,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_245672,c_109414,c_261]) ).
tcf(c_246181,plain,
( ( app(iPr_def_13,skaf45(iPr_def_15,iPr_def_13)) = iPr_def_15 )
| ~ ssList(iPr_def_15)
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_245470,c_385]) ).
tcf(c_246188,plain,
app(iPr_def_13,skaf45(iPr_def_15,iPr_def_13)) = iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_246181,c_237592,c_237819]) ).
tcf(c_246201,plain,
( ( app(sk7,skaf45(iPr_def_14,sk7)) = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_245518,c_385]) ).
tcf(c_246207,plain,
app(sk7,skaf45(iPr_def_14,sk7)) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_246201,c_237823,c_9647]) ).
tcf(c_248712,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(app(app(sk7,iPr_def_12),X0)) ),
inference(superposition,[status(thm)],[c_9632,c_426]) ).
tcf(c_248791,plain,
! [X0: $i] :
( segmentP(app(iPr_def_14,X0),skaf45(iPr_def_14,sk7))
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(skaf45(iPr_def_14,sk7))
| ~ ssList(app(app(sk7,skaf45(iPr_def_14,sk7)),X0)) ),
inference(superposition,[status(thm)],[c_246207,c_426]) ).
tcf(c_248883,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_13,X0)) ),
inference(light_normalisation,[status(thm)],[c_248712,c_9632]) ).
tcf(c_248884,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_248883,c_237812,c_9647]) ).
tcf(c_249122,plain,
! [X0: $i] :
( segmentP(app(iPr_def_14,X0),skaf45(iPr_def_14,sk7))
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(skaf45(iPr_def_14,sk7))
| ~ ssList(app(iPr_def_14,X0)) ),
inference(light_normalisation,[status(thm)],[c_248791,c_246207]) ).
tcf(c_249123,plain,
! [X0: $i] :
( segmentP(app(iPr_def_14,X0),skaf45(iPr_def_14,sk7))
| ~ ssList(X0)
| ~ ssList(app(iPr_def_14,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_249122,c_9647,c_304]) ).
tcf(c_249413,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_427,c_31546]) ).
tcf(c_254017,plain,
( segmentP(iPr_def_14,iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(app(iPr_def_13,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_9633,c_248884]) ).
tcf(c_254024,plain,
( segmentP(iPr_def_14,iPr_def_12)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_254017,c_9633]) ).
tcf(c_254025,plain,
segmentP(iPr_def_14,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_254024,c_237823,c_237812]) ).
tcf(c_254138,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_254025,c_380]) ).
tcf(c_254139,plain,
( ( iPr_def_12 = iPr_def_14 )
| ~ segmentP(iPr_def_12,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_254138,c_237823,c_237812]) ).
tcf(c_255275,plain,
( ( sk7 = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ( iPr_def_13 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9633,c_244753]) ).
tcf(c_255276,plain,
( ( sk7 = nil )
| ~ ssList(nil)
| ( iPr_def_12 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_237817,c_244753]) ).
tcf(c_255277,plain,
( ( sk7 = nil )
| ( iPr_def_12 != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_255276,c_261]) ).
tcf(c_255280,plain,
( ( sk7 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_255275,c_237819]) ).
tcf(c_258212,plain,
memberP(iPr_def_14,sk5),
inference(superposition,[status(thm)],[c_241860,c_241263]) ).
tcf(c_258218,plain,
memberP(iPr_def_15,sk5),
inference(superposition,[status(thm)],[c_258212,c_241260]) ).
tcf(c_262673,plain,
! [X0: $i] :
( frontsegP(cons(sk5,sk7),X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_239069,c_390]) ).
tcf(c_262685,plain,
! [X0: $i] :
( frontsegP(cons(sk5,sk7),X0)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_262673,c_237812,c_9647]) ).
tcf(c_264172,plain,
! [X0: $i,X1: $i] :
( frontsegP(sk7,X1)
| ~ ssList(sk7)
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(superposition,[status(thm)],[c_262685,c_249413]) ).
tcf(c_264191,plain,
! [X0: $i,X1: $i] :
( frontsegP(sk7,X1)
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_264172,c_9647]) ).
tcf(c_266282,plain,
skaf46(iPr_def_13,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_240167,c_237680]) ).
tcf(c_268420,plain,
skaf45(iPr_def_14,nil) = iPr_def_14,
inference(demodulation,[status(thm)],[c_240274,c_237743]) ).
tcf(c_269902,plain,
sk5 = sk9,
inference(superposition,[status(thm)],[c_258218,c_245679]) ).
tcf(c_269955,plain,
cons(sk9,nil) = iPr_def_12,
inference(demodulation,[status(thm)],[c_9631,c_269902]) ).
tcf(c_269957,plain,
iPr_def_12 = iPr_def_15,
inference(demodulation,[status(thm)],[c_237644,c_269955]) ).
tcf(c_269958,plain,
! [X0: $i] :
( ( X0 = sk9 )
| ~ memberP(iPr_def_12,X0) ),
inference(demodulation,[status(thm)],[c_245679,c_269957]) ).
tcf(c_270023,plain,
frontsegP(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_245470,c_269957]) ).
tcf(c_270050,plain,
app(iPr_def_14,sk8) = iPr_def_12,
inference(demodulation,[status(thm)],[c_9634,c_269957]) ).
tcf(c_270559,plain,
app(iPr_def_13,skaf45(iPr_def_12,iPr_def_13)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_246188,c_269957]) ).
tcf(c_270573,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ ssList(iPr_def_13)
| ~ memberP(iPr_def_13,X0)
| ~ ssList(skaf45(iPr_def_12,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_270559,c_241176]) ).
tcf(c_270580,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_270573,c_237819,c_304]) ).
tcf(c_278759,plain,
! [X0: $i] :
( segmentP(app(iPr_def_14,X0),skaf45(iPr_def_14,sk7))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_249123,c_35217]) ).
tcf(c_278765,plain,
( segmentP(iPr_def_12,skaf45(iPr_def_14,sk7))
| ~ ssList(sk8) ),
inference(superposition,[status(thm)],[c_270050,c_278759]) ).
tcf(c_278772,plain,
segmentP(iPr_def_12,skaf45(iPr_def_14,sk7)),
inference(forward_subsumption_resolution,[status(thm)],[c_278765,c_9646]) ).
tcf(c_279185,plain,
iPr_def_13 != iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_255280,c_31853,c_32144]) ).
tcf(c_286851,plain,
( ( skaf46(iPr_def_13,nil) = nil )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_266282,c_238571]) ).
tcf(c_286890,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_286851,c_266282]) ).
tcf(c_286891,plain,
cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_286890,c_239009]) ).
tcf(c_312923,plain,
( ( skaf46(iPr_def_13,nil) = nil )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_266282,c_238721]) ).
tcf(c_312972,plain,
( ( nil = iPr_def_13 )
| ( cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_312923,c_266282]) ).
tcf(c_312973,plain,
cons(skaf83(iPr_def_13),skaf82(iPr_def_13)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_312972,c_239009]) ).
tcf(c_331528,plain,
( memberP(iPr_def_13,skaf83(iPr_def_13))
| ~ ssList(skaf82(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_312973,c_237938]) ).
tcf(c_331559,plain,
skaf83(iPr_def_13) = hd(iPr_def_13),
inference(superposition,[status(thm)],[c_312973,c_238338]) ).
tcf(c_331560,plain,
skaf82(iPr_def_13) = tl(iPr_def_13),
inference(superposition,[status(thm)],[c_312973,c_238246]) ).
tcf(c_331561,plain,
memberP(iPr_def_13,skaf83(iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_331528,c_266]) ).
tcf(c_332935,plain,
memberP(iPr_def_13,hd(iPr_def_13)),
inference(light_normalisation,[status(thm)],[c_331561,c_331559]) ).
tcf(c_332937,plain,
memberP(iPr_def_12,hd(iPr_def_13)),
inference(superposition,[status(thm)],[c_332935,c_270580]) ).
tcf(c_332994,plain,
hd(iPr_def_13) = sk9,
inference(superposition,[status(thm)],[c_332937,c_269958]) ).
tcf(c_333002,plain,
cons(sk9,tl(iPr_def_13)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_286891,c_332994]) ).
tcf(c_345029,plain,
( ( skaf82(iPr_def_13) = nil )
| ~ frontsegP(nil,tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_331560,c_241830]) ).
tcf(c_345039,plain,
ssList(tl(iPr_def_13)),
inference(superposition,[status(thm)],[c_331560,c_266]) ).
tcf(c_345040,plain,
( ( tl(iPr_def_13) = nil )
| ~ frontsegP(nil,tl(iPr_def_13)) ),
inference(light_normalisation,[status(thm)],[c_345029,c_331560]) ).
tcf(c_365754,plain,
! [X0: $i,X1: $i] :
( frontsegP(sk7,X1)
| ~ ssList(X1)
| ~ frontsegP(iPr_def_12,cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_264191,c_237802]) ).
tcf(c_365825,plain,
( frontsegP(sk7,tl(iPr_def_13))
| ~ frontsegP(iPr_def_12,iPr_def_13)
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_333002,c_365754]) ).
tcf(c_365826,plain,
frontsegP(sk7,tl(iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_365825,c_270023,c_345039]) ).
tcf(c_367398,plain,
! [X0: $i] :
( frontsegP(X0,tl(iPr_def_13))
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(tl(iPr_def_13))
| ~ frontsegP(X0,sk7) ),
inference(superposition,[status(thm)],[c_365826,c_407]) ).
tcf(c_367409,plain,
! [X0: $i] :
( frontsegP(X0,tl(iPr_def_13))
| ~ ssList(X0)
| ~ frontsegP(X0,sk7) ),
inference(forward_subsumption_resolution,[status(thm)],[c_367398,c_9647,c_345039]) ).
tcf(c_368332,plain,
( ( tl(iPr_def_13) = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,sk7)
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_367409,c_337]) ).
tcf(c_368347,plain,
( ( tl(iPr_def_13) = nil )
| ~ frontsegP(nil,sk7) ),
inference(forward_subsumption_resolution,[status(thm)],[c_368332,c_261,c_345039]) ).
tcf(c_375621,plain,
tl(iPr_def_13) = nil,
inference(global_subsumption_just,[status(thm)],[c_368347,c_150365,c_270023,c_345039,c_345040]) ).
tcf(c_375675,plain,
cons(sk9,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_333002,c_375621]) ).
tcf(c_375689,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_375675,c_269955]) ).
tcf(c_375718,plain,
sk7 = nil,
inference(backward_subsumption_resolution,[status(thm)],[c_255277,c_375689]) ).
tcf(c_375852,plain,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_279185,c_375689]) ).
tcf(c_376269,plain,
segmentP(iPr_def_12,skaf45(iPr_def_14,nil)),
inference(demodulation,[status(thm)],[c_278772,c_375718]) ).
tcf(c_376532,plain,
segmentP(iPr_def_12,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_376269,c_268420]) ).
tcf(c_376533,plain,
iPr_def_12 = iPr_def_14,
inference(backward_subsumption_resolution,[status(thm)],[c_254139,c_376532]) ).
tcf(c_377288,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_375852,c_376533]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC172-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 16:47:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 71.33/17.92 % SZS status Started for theBenchmark.p
% 71.33/17.92 % SZS status Unsatisfiable for theBenchmark.p
% 71.33/17.92
% 71.33/17.92 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 71.33/17.92
% 71.33/17.92 % ------ iProver source info
% 71.33/17.92
% 71.33/17.92 % git: date: 2026-07-19 20:42:38 +0200
% 71.33/17.92 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 71.33/17.92 % git: non_committed_changes: false
% 71.33/17.92
% 71.33/17.92 % ------ Parsing...% successful
% 71.33/17.92
% 71.33/17.92
% 71.33/17.92 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 71.33/17.92
% 71.33/17.92 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 3 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 71.33/17.92
% 71.33/17.92 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 71.33/17.92
% 71.33/17.92 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 71.33/17.92 % ------ Proving...
% 71.33/17.92 % ------ Problem Properties
% 71.33/17.92
% 71.33/17.92 %
% 71.33/17.92 % clauses 197
% 71.33/17.92 % conjectures 13
% 71.33/17.92 % EPR 67
% 71.33/17.92 % Horn 161
% 71.33/17.92 % unary 70
% 71.33/17.92 % binary 27
% 71.33/17.92 % lits 575
% 71.33/17.92 % lits eq 88
% 71.33/17.92 % fd_pure 0
% 71.33/17.92 % fd_pseudo 0
% 71.33/17.92 % fd_cond 17
% 71.33/17.92 % fd_pseudo_cond 14
% 71.33/17.92 % AC symbols 0
% 71.33/17.92
% 71.33/17.92 % ------ Schedule dynamic 5 is on
% 71.33/17.92
% 71.33/17.92 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 71.33/17.92
% 71.33/17.92
% 71.33/17.92 % ------
% 71.33/17.92 % Current options:
% 71.33/17.92 % ------
% 71.33/17.92
% 71.33/17.92
% 71.33/17.92 %
% 71.33/17.92
% 71.33/17.92 % ------ Proving...
% 71.33/17.92 % Proof_search_loop: time out after: 9384 full_loop iterations
% 71.33/17.92
% 71.33/17.92 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 71.33/17.92
% 71.33/17.92
% 71.33/17.92 % ------
% 71.33/17.92 % Current options:
% 71.33/17.92 % ------
% 71.33/17.92
% 71.33/17.92
% 71.33/17.92 %
% 71.33/17.92
% 71.33/17.92 % ------ Proving...
% 71.33/17.92 %
% 71.33/17.92
% 71.33/17.92 % SZS status Unsatisfiable for theBenchmark.p
% 71.33/17.92
% 71.33/17.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 71.33/17.93
% 71.33/17.93
%------------------------------------------------------------------------------