%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC087-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 03:07:50 PM UTC 2026
% Result : Unsatisfiable 50.93s 13.01s
% Output : CNFRefutation 50.93s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f258ERROR: Could not build tree for root c_138628ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause47) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).
fof(f57,axiom,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
fof(f72,axiom,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
fof(f77,axiom,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause77) ).
fof(f78,axiom,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause78) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f96,axiom,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
fof(f97,axiom,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
fof(f99,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| nil != cons(X0,X1) ),
inference(reorient_equations,[],[f98]) ).
fof(f101,axiom,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,axiom,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
fof(f107,axiom,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
fof(f119,axiom,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
fof(f125,axiom,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f129,axiom,
! [X0,X1] :
( hd(app(X1,X0)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause123) ).
fof(f142,axiom,
! [X0,X1] :
( app(skaf46(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause131) ).
fof(f144,axiom,
! [X0,X1] :
( tl(app(X1,X0)) = app(tl(X1),X0)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause133) ).
fof(f151,axiom,
! [X2,X0,X1] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
fof(f154,axiom,
! [X2,X0,X1] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause143) ).
fof(f163,axiom,
! [X2,X0,X1] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause151) ).
fof(f169,axiom,
! [X2,X0,X1] :
( cons(X0,app(X1,X2)) = app(cons(X0,X1),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause161) ).
fof(f174,plain,
! [X2,X0,X1] :
( X0 = X2
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(reorient_equations,[],[f173]) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
fof(f191,axiom,
! [X0,X1] :
( nil = X0
| X0 = X1
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| hd(X0) != hd(X1)
| tl(X0) != tl(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause177) ).
fof(f193,axiom,
! [X2,X3,X0,X1,X4] :
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f210,negated_conjecture,
! [X0] :
( ~ neq(sk4,nil)
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f218,plain,
! [X0] :
( ~ neq(sk4,nil)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f210,f204,f205]) ).
fof(f226,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f229,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f233,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(f236,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_253,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_292,plain,
! [X0: $i] : ssItem(skaf44(X0)),
inference(cnf_transformation,[],[f47]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_302,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_316,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_318,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_319,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_322,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_323,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_346,plain,
! [X0: $i] :
( ( cons(skaf44(X0),nil) = X0 )
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_349,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_360,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_361,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( hd(app(X1,X0)) = hd(X1) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] :
( ( app(skaf46(X0,X1),X1) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( tl(app(X1,X0)) = app(tl(X1),X0) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_385,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_388,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_396,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_402,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( app(cons(X2,X0),X1) = cons(X2,app(X0,X1)) )
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_406,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_418,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,[],[f233]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( X0 = nil )
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( hd(X0) != hd(X1) )
| ( tl(X0) != tl(X1) ) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_424,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,[],[f236]) ).
tcf(c_433,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_434,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_435,negated_conjecture,
neq(sk4,nil),
inference(cnf_transformation,[],[f257]) ).
tcf(c_437,negated_conjecture,
( neq(sk4,nil)
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_438,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(sk4,nil)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_439,negated_conjecture,
( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ neq(sk4,nil)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_561,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0) ),
inference(global_subsumption_just,[status(thm)],[c_438,c_435,c_438]) ).
tcf(c_562,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ neq(X0,nil) ),
inference(renaming,[status(thm)],[c_561]) ).
tcf(c_563,negated_conjecture,
neq(sk4,nil),
inference(global_subsumption_just,[status(thm)],[c_437,c_435]) ).
tcf(c_565,plain,
( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ ssList(app(tl(sk4),cons(hd(sk4),nil)))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4)) ),
inference(global_subsumption_just,[status(thm)],[c_439,c_435,c_439]) ).
tcf(c_566,negated_conjecture,
( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
inference(renaming,[status(thm)],[c_565]) ).
tcf(c_798,plain,
( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_566,c_330]) ).
tcf(c_799,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_388,c_330]) ).
tcf(c_3566,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ( nil != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_563,c_562]) ).
tcf(c_3567,plain,
( ~ ssList(sk4)
| ~ segmentP(sk4,sk4)
| ~ segmentP(sk3,sk4) ),
inference(unflattening,[status(thm)],[c_3566]) ).
tcf(c_3568,plain,
( ~ segmentP(sk3,sk4)
| ~ segmentP(sk4,sk4) ),
inference(global_subsumption_just,[status(thm)],[c_3567,c_434,c_3567]) ).
tcf(c_3569,plain,
( ~ segmentP(sk4,sk4)
| ~ segmentP(sk3,sk4) ),
inference(renaming,[status(thm)],[c_3568]) ).
tcf(c_3600,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_563,c_360]) ).
tcf(c_3601,plain,
( ~ ssList(sk4)
| ( sk4 != nil ) ),
inference(unflattening,[status(thm)],[c_3600]) ).
tcf(c_3602,plain,
sk4 != nil,
inference(global_subsumption_just,[status(thm)],[c_3601,c_434,c_3601]) ).
tcf(c_3628,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_562,c_345]) ).
tcf(c_3629,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(unflattening,[status(thm)],[c_3628]) ).
tcf(c_3631,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3629,c_253,c_3629]) ).
tcf(c_3632,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(renaming,[status(thm)],[c_3631]) ).
tcf(c_3667,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_798,c_345]) ).
tcf(c_3668,plain,
( ( sk4 = nil )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(unflattening,[status(thm)],[c_3667]) ).
tcf(c_3669,plain,
( ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ~ ssItem(hd(sk4))
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) ),
inference(global_subsumption_just,[status(thm)],[c_3668,c_434,c_253,c_3601,c_3668]) ).
tcf(c_3670,plain,
( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(renaming,[status(thm)],[c_3669]) ).
tcf(c_6630,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_317]) ).
tcf(c_6631,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_317]) ).
tcf(c_6632,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_317]) ).
tcf(c_6633,definition,
iPr_def_12 = hd(sk4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6634,definition,
iPr_def_13 = cons(iPr_def_12,nil),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6635,definition,
iPr_def_14 = tl(sk4),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_6636,definition,
iPr_def_15 = app(iPr_def_14,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_6637,plain,
( ( iPr_def_15 = sk3 )
| ~ ssItem(iPr_def_12)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13) ),
inference(demodulation,[status(thm)],[c_3670,c_6636,c_6635,c_6633,c_6634]) ).
tcf(c_6638,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(demodulation,[status(thm)],[c_3632]) ).
tcf(c_6639,plain,
sk4 != nil,
inference(demodulation,[status(thm)],[c_3602]) ).
tcf(c_6640,plain,
( ~ segmentP(sk4,sk4)
| ~ segmentP(sk3,sk4) ),
inference(demodulation,[status(thm)],[c_3569]) ).
tcf(c_6641,negated_conjecture,
ssList(sk4),
inference(demodulation,[status(thm)],[c_434]) ).
tcf(c_6642,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_433]) ).
tcf(c_9201,plain,
( ( sk3 = iPr_def_15 )
| ~ iPr_def_10
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_6630,c_6637]) ).
tcf(c_9338,plain,
app(sk3,nil) = sk3,
inference(superposition,[status(thm)],[c_6642,c_318]) ).
tcf(c_9339,plain,
app(sk4,nil) = sk4,
inference(superposition,[status(thm)],[c_6641,c_318]) ).
tcf(c_9588,plain,
app(nil,sk4) = sk4,
inference(superposition,[status(thm)],[c_6641,c_319]) ).
tcf(c_9650,plain,
( ssList(iPr_def_14)
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_6635,c_322]) ).
tcf(c_9654,plain,
ssList(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_9650,c_6639,c_6641]) ).
tcf(c_9665,plain,
( ( sk3 = iPr_def_15 )
| ~ iPr_def_10
| ~ ssList(iPr_def_13) ),
inference(backward_subsumption_resolution,[status(thm)],[c_9201,c_9654]) ).
tcf(c_9666,plain,
( ( sk3 = iPr_def_15 )
| ~ ssItem(iPr_def_12)
| ~ ssList(iPr_def_13) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6637,c_9654]) ).
tcf(c_9679,plain,
( ssItem(iPr_def_12)
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_6633,c_323]) ).
tcf(c_9680,plain,
ssItem(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9679,c_6639,c_6641]) ).
tcf(c_9718,plain,
app(nil,iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_9654,c_319]) ).
tcf(c_9736,plain,
( ssList(iPr_def_13)
| ~ ssItem(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6634,c_331]) ).
tcf(c_9740,plain,
ssList(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_9736,c_9680,c_253]) ).
tcf(c_9790,plain,
sk3 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_9665,c_9666,c_9680,c_9740]) ).
tcf(c_9794,plain,
app(iPr_def_15,nil) = iPr_def_15,
inference(demodulation,[status(thm)],[c_9338,c_9790]) ).
tcf(c_9796,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(iPr_def_15,X0)
| ~ segmentP(sk4,X0) ),
inference(demodulation,[status(thm)],[c_6638,c_9790]) ).
tcf(c_9797,plain,
( ~ segmentP(iPr_def_15,sk4)
| ~ segmentP(sk4,sk4) ),
inference(demodulation,[status(thm)],[c_6640,c_9790]) ).
tcf(c_9798,plain,
ssList(iPr_def_15),
inference(demodulation,[status(thm)],[c_6642,c_9790]) ).
tcf(c_9877,plain,
( ~ ssList(sk4)
| ~ segmentP(iPr_def_15,sk4) ),
inference(superposition,[status(thm)],[c_302,c_9797]) ).
tcf(c_9878,plain,
~ segmentP(iPr_def_15,sk4),
inference(forward_subsumption_resolution,[status(thm)],[c_9877,c_6641]) ).
tcf(c_10078,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_331,c_361]) ).
tcf(c_10082,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10078,c_253]) ).
tcf(c_10094,plain,
! [X0: $i] :
( ( tl(cons(X0,sk4)) = sk4 )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6641,c_341]) ).
tcf(c_10278,plain,
! [X0: $i] :
( ( hd(cons(X0,sk4)) = X0 )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6641,c_342]) ).
tcf(c_10466,plain,
( ~ ssItem(iPr_def_12)
| ~ ssList(nil)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6634,c_343]) ).
tcf(c_10467,plain,
nil != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_10466,c_9680,c_253]) ).
tcf(c_10491,plain,
tl(cons(iPr_def_12,sk4)) = sk4,
inference(superposition,[status(thm)],[c_9680,c_10094]) ).
tcf(c_10570,plain,
hd(cons(iPr_def_12,sk4)) = iPr_def_12,
inference(superposition,[status(thm)],[c_9680,c_10278]) ).
tcf(c_10752,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6641,c_349]) ).
tcf(c_10792,plain,
( ( sk4 = nil )
| ( cons(iPr_def_12,iPr_def_14) = sk4 ) ),
inference(light_normalisation,[status(thm)],[c_10752,c_6633,c_6635]) ).
tcf(c_10793,plain,
cons(iPr_def_12,iPr_def_14) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_10792,c_6639]) ).
tcf(c_11094,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6641,c_365]) ).
tcf(c_11127,plain,
! [X0: $i] :
( ( app(cons(X0,nil),iPr_def_14) = cons(X0,iPr_def_14) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_9654,c_365]) ).
tcf(c_11330,plain,
app(cons(iPr_def_12,nil),sk4) = cons(iPr_def_12,sk4),
inference(superposition,[status(thm)],[c_9680,c_11094]) ).
tcf(c_11331,plain,
app(iPr_def_13,sk4) = cons(iPr_def_12,sk4),
inference(light_normalisation,[status(thm)],[c_11330,c_6634]) ).
tcf(c_11551,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(app(X0,sk4)) = hd(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6641,c_368]) ).
tcf(c_11777,plain,
( ( nil = iPr_def_13 )
| ( hd(app(iPr_def_13,sk4)) = hd(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_9740,c_11551]) ).
tcf(c_11783,plain,
( ( nil = iPr_def_13 )
| ( hd(iPr_def_13) = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_11777,c_10570,c_11331]) ).
tcf(c_11784,plain,
hd(iPr_def_13) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_11783,c_10467]) ).
tcf(c_13271,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(app(X0,sk4)) = app(tl(X0),sk4) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6641,c_378]) ).
tcf(c_13599,plain,
( ( nil = iPr_def_13 )
| ( tl(app(iPr_def_13,sk4)) = app(tl(iPr_def_13),sk4) ) ),
inference(superposition,[status(thm)],[c_9740,c_13271]) ).
tcf(c_13605,plain,
( ( nil = iPr_def_13 )
| ( app(tl(iPr_def_13),sk4) = sk4 ) ),
inference(light_normalisation,[status(thm)],[c_13599,c_10491,c_11331]) ).
tcf(c_13606,plain,
app(tl(iPr_def_13),sk4) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_13605,c_10467]) ).
tcf(c_15286,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,sk4),X0) = cons(X1,app(sk4,X0)) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6641,c_402]) ).
tcf(c_16056,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ( app(X0,sk4) != sk4 ) ),
inference(superposition,[status(thm)],[c_9588,c_396]) ).
tcf(c_16103,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ( app(X0,sk4) != sk4 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16056,c_253,c_6641]) ).
tcf(c_17132,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = iPr_def_12 )
| ~ ssItem(iPr_def_12)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_6634,c_406]) ).
tcf(c_17134,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = iPr_def_12 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17132,c_9680,c_253]) ).
tcf(c_17391,plain,
! [X0: $i] :
( ( app(cons(X0,sk4),sk4) = cons(X0,app(sk4,sk4)) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6641,c_15286]) ).
tcf(c_17601,plain,
app(cons(iPr_def_12,sk4),sk4) = cons(iPr_def_12,app(sk4,sk4)),
inference(superposition,[status(thm)],[c_9680,c_17391]) ).
tcf(c_19999,plain,
! [X0: $i] :
( segmentP(app(iPr_def_15,X0),iPr_def_13)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ ssList(X0)
| ~ ssList(app(app(iPr_def_14,iPr_def_13),X0)) ),
inference(superposition,[status(thm)],[c_6636,c_418]) ).
tcf(c_20024,plain,
! [X0: $i] :
( segmentP(app(iPr_def_14,X0),iPr_def_14)
| ~ ssList(iPr_def_14)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(app(nil,iPr_def_14),X0)) ),
inference(superposition,[status(thm)],[c_9718,c_418]) ).
tcf(c_20076,plain,
! [X0: $i] :
( segmentP(app(iPr_def_14,X0),iPr_def_14)
| ~ ssList(iPr_def_14)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_14,X0)) ),
inference(light_normalisation,[status(thm)],[c_20024,c_9718]) ).
tcf(c_20077,plain,
! [X0: $i] :
( segmentP(app(iPr_def_14,X0),iPr_def_14)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_14,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20076,c_9654,c_253]) ).
tcf(c_20091,plain,
! [X0: $i] :
( segmentP(app(iPr_def_15,X0),iPr_def_13)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_15,X0)) ),
inference(light_normalisation,[status(thm)],[c_19999,c_6636]) ).
tcf(c_20092,plain,
! [X0: $i] :
( segmentP(app(iPr_def_15,X0),iPr_def_13)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_15,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20091,c_9654,c_9740]) ).
tcf(c_20581,plain,
( singletonP(iPr_def_13)
| ~ ssItem(iPr_def_12) ),
inference(superposition,[status(thm)],[c_6634,c_10082]) ).
tcf(c_20583,plain,
singletonP(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_20581,c_9680]) ).
tcf(c_21139,plain,
! [X0: $i] :
( ( sk4 = nil )
| ( X0 = nil )
| ( X0 = sk4 )
| ~ ssList(sk4)
| ~ ssList(X0)
| ( hd(X0) != hd(sk4) )
| ( tl(X0) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6635,c_422]) ).
tcf(c_21159,plain,
! [X0: $i] :
( ( sk4 = nil )
| ( X0 = nil )
| ( X0 = sk4 )
| ~ ssList(sk4)
| ~ ssList(X0)
| ( hd(X0) != iPr_def_12 )
| ( tl(X0) != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_21139,c_6633]) ).
tcf(c_21160,plain,
! [X0: $i] :
( ( X0 = nil )
| ( X0 = sk4 )
| ~ ssList(X0)
| ( hd(X0) != iPr_def_12 )
| ( tl(X0) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21159,c_6639,c_6641]) ).
tcf(c_21564,plain,
( ( cons(skaf44(iPr_def_13),nil) = iPr_def_13 )
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_20583,c_346]) ).
tcf(c_21565,plain,
cons(skaf44(iPr_def_13),nil) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_21564,c_9740]) ).
tcf(c_22228,plain,
( ( tl(iPr_def_13) = nil )
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_13606,c_16103]) ).
tcf(c_22730,plain,
( memberP(iPr_def_13,skaf44(iPr_def_13))
| ~ ssList(nil)
| ~ ssItem(skaf44(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_21565,c_383]) ).
tcf(c_22764,plain,
memberP(iPr_def_13,skaf44(iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_22730,c_253,c_292]) ).
tcf(c_24430,plain,
( ( nil = iPr_def_13 )
| ( tl(iPr_def_13) = nil )
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_322,c_22228]) ).
tcf(c_24431,plain,
tl(iPr_def_13) = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_24430,c_10467,c_9740]) ).
tcf(c_25082,plain,
( ( nil = iPr_def_13 )
| ( sk4 = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ( nil != iPr_def_14 )
| ( hd(iPr_def_13) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_24431,c_21160]) ).
tcf(c_25086,plain,
( ( nil = iPr_def_13 )
| ( sk4 = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ( nil != iPr_def_14 ) ),
inference(ground_joinability,[status(thm)],[c_25082,c_11784]) ).
tcf(c_25087,plain,
( ( sk4 = iPr_def_13 )
| ( nil != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25086,c_10467,c_9740]) ).
tcf(c_29185,plain,
( ssList(cons(iPr_def_12,sk4))
| ~ ssList(iPr_def_13)
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_11331,c_330]) ).
tcf(c_29189,plain,
! [X0: $i] :
( memberP(cons(iPr_def_12,sk4),X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_11331,c_385]) ).
tcf(c_29196,plain,
ssList(cons(iPr_def_12,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_29185,c_9740,c_6641]) ).
tcf(c_29205,plain,
! [X0: $i] :
( memberP(cons(iPr_def_12,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29189,c_9740,c_6641]) ).
tcf(c_29296,plain,
! [X0: $i] :
( ssList(app(sk4,X0))
| ~ ssList(sk4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_29385,plain,
app(nil,cons(iPr_def_12,sk4)) = cons(iPr_def_12,sk4),
inference(superposition,[status(thm)],[c_29196,c_319]) ).
tcf(c_29509,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ( X0 = iPr_def_12 )
| ~ ssItem(iPr_def_12)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_29205,c_406]) ).
tcf(c_29510,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ( X0 = iPr_def_12 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29509,c_9680,c_6641]) ).
tcf(c_29968,plain,
! [X0: $i] :
( ~ memberP(iPr_def_13,X0)
| ~ ssItem(X0)
| ( X0 = iPr_def_12 ) ),
inference(global_subsumption_just,[status(thm)],[c_29510,c_316,c_17134]) ).
tcf(c_29969,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(renaming,[status(thm)],[c_29968]) ).
tcf(c_29978,plain,
( ( skaf44(iPr_def_13) = iPr_def_12 )
| ~ ssItem(skaf44(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_22764,c_29969]) ).
tcf(c_29981,plain,
skaf44(iPr_def_13) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_29978,c_292]) ).
tcf(c_29987,plain,
cons(iPr_def_12,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_21565,c_29981]) ).
tcf(c_30686,plain,
! [X0: $i] :
( ~ ssItem(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ ssList(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0)))
| ~ duplicatefreeP(app(app(nil,cons(iPr_def_12,sk4)),cons(iPr_def_12,X0))) ),
inference(superposition,[status(thm)],[c_29385,c_424]) ).
tcf(c_30714,plain,
! [X0: $i] :
( ~ ssItem(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ duplicatefreeP(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0)))
| ~ ssList(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0))) ),
inference(light_normalisation,[status(thm)],[c_30686,c_29385]) ).
tcf(c_30715,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ duplicatefreeP(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0)))
| ~ ssList(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30714,c_9680,c_253,c_6641]) ).
tcf(c_30908,plain,
( ~ ssList(iPr_def_14)
| ~ ssList(app(cons(iPr_def_12,sk4),sk4))
| ~ duplicatefreeP(app(cons(iPr_def_12,sk4),cons(iPr_def_12,iPr_def_14))) ),
inference(superposition,[status(thm)],[c_10793,c_30715]) ).
tcf(c_30910,plain,
( ~ ssList(iPr_def_14)
| ~ duplicatefreeP(cons(iPr_def_12,app(sk4,sk4)))
| ~ ssList(cons(iPr_def_12,app(sk4,sk4))) ),
inference(light_normalisation,[status(thm)],[c_30908,c_10793,c_17601]) ).
tcf(c_30911,plain,
( ~ duplicatefreeP(cons(iPr_def_12,app(sk4,sk4)))
| ~ ssList(cons(iPr_def_12,app(sk4,sk4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30910,c_9654]) ).
tcf(c_104106,plain,
( ssList(cons(iPr_def_12,app(sk4,sk4)))
| ~ ssList(sk4)
| ~ ssList(cons(iPr_def_12,sk4)) ),
inference(superposition,[status(thm)],[c_17601,c_330]) ).
tcf(c_104143,plain,
ssList(cons(iPr_def_12,app(sk4,sk4))),
inference(forward_subsumption_resolution,[status(thm)],[c_104106,c_6641,c_29196]) ).
tcf(c_104817,plain,
( duplicatefreeP(cons(iPr_def_12,app(sk4,sk4)))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_104143,c_6631]) ).
tcf(c_131321,plain,
! [X0: $i] : app(cons(X0,nil),iPr_def_14) = cons(X0,iPr_def_14),
inference(global_subsumption_just,[status(thm)],[c_11127,c_6630,c_6632,c_11127,c_30911,c_104143,c_104817]) ).
tcf(c_131330,plain,
! [X0: $i] :
( rearsegP(cons(X0,iPr_def_14),iPr_def_14)
| ~ ssList(iPr_def_14)
| ~ ssList(cons(X0,nil)) ),
inference(superposition,[status(thm)],[c_131321,c_799]) ).
tcf(c_131343,plain,
! [X0: $i] :
( rearsegP(cons(X0,iPr_def_14),iPr_def_14)
| ~ ssList(cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_131330,c_9654]) ).
tcf(c_131418,plain,
( rearsegP(sk4,iPr_def_14)
| ~ ssList(cons(iPr_def_12,nil)) ),
inference(superposition,[status(thm)],[c_10793,c_131343]) ).
tcf(c_131422,plain,
( rearsegP(sk4,iPr_def_14)
| ~ ssList(iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_131418,c_29987]) ).
tcf(c_131423,plain,
rearsegP(sk4,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_131422,c_9740]) ).
tcf(c_131884,plain,
( ( app(skaf46(sk4,iPr_def_14),iPr_def_14) = sk4 )
| ~ ssList(iPr_def_14)
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_131423,c_376]) ).
tcf(c_131887,plain,
app(skaf46(sk4,iPr_def_14),iPr_def_14) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_131884,c_9654,c_6641]) ).
tcf(c_132424,plain,
! [X0: $i] :
( segmentP(app(sk4,X0),iPr_def_14)
| ~ ssList(iPr_def_14)
| ~ ssList(X0)
| ~ ssList(skaf46(sk4,iPr_def_14))
| ~ ssList(app(app(skaf46(sk4,iPr_def_14),iPr_def_14),X0)) ),
inference(superposition,[status(thm)],[c_131887,c_418]) ).
tcf(c_132456,plain,
! [X0: $i] :
( segmentP(app(sk4,X0),iPr_def_14)
| ~ ssList(iPr_def_14)
| ~ ssList(X0)
| ~ ssList(skaf46(sk4,iPr_def_14))
| ~ ssList(app(sk4,X0)) ),
inference(light_normalisation,[status(thm)],[c_132424,c_131887]) ).
tcf(c_132457,plain,
! [X0: $i] :
( segmentP(app(sk4,X0),iPr_def_14)
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_132456,c_9654,c_295]) ).
tcf(c_133469,plain,
( segmentP(iPr_def_15,iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ ssList(app(iPr_def_14,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_6636,c_20077]) ).
tcf(c_133477,plain,
( segmentP(iPr_def_15,iPr_def_14)
| ~ ssList(iPr_def_15)
| ~ ssList(iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_133469,c_6636]) ).
tcf(c_133478,plain,
segmentP(iPr_def_15,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_133477,c_9798,c_9740]) ).
tcf(c_134737,plain,
( segmentP(iPr_def_15,iPr_def_13)
| ~ ssList(nil)
| ~ ssList(app(iPr_def_15,nil)) ),
inference(superposition,[status(thm)],[c_9794,c_20092]) ).
tcf(c_134742,plain,
( segmentP(iPr_def_15,iPr_def_13)
| ~ ssList(iPr_def_15)
| ~ ssList(nil) ),
inference(light_normalisation,[status(thm)],[c_134737,c_9794]) ).
tcf(c_134743,plain,
segmentP(iPr_def_15,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_134742,c_9798,c_253]) ).
tcf(c_136414,plain,
! [X0: $i] :
( segmentP(app(sk4,X0),iPr_def_14)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_132457,c_434,c_29296,c_132457]) ).
tcf(c_136421,plain,
( segmentP(sk4,iPr_def_14)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_9339,c_136414]) ).
tcf(c_136426,plain,
segmentP(sk4,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_136421,c_253]) ).
tcf(c_137691,plain,
( ( nil = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ segmentP(iPr_def_15,iPr_def_14) ),
inference(superposition,[status(thm)],[c_136426,c_9796]) ).
tcf(c_137692,plain,
nil = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_137691,c_9654,c_133478]) ).
tcf(c_137699,plain,
sk4 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_25087,c_137692]) ).
tcf(c_138624,plain,
~ segmentP(iPr_def_15,iPr_def_13),
inference(demodulation,[status(thm)],[c_9878,c_137699]) ).
tcf(c_138628,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_138624,c_134743]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC087-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.38 % Computer : n014.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 16:18:39 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 50.93/13.01 % SZS status Started for theBenchmark.p
% 50.93/13.01 % SZS status Unsatisfiable for theBenchmark.p
% 50.93/13.01
% 50.93/13.01 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 50.93/13.01
% 50.93/13.01 % ------ iProver source info
% 50.93/13.01
% 50.93/13.01 % git: date: 2026-07-19 20:42:38 +0200
% 50.93/13.01 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 50.93/13.01 % git: non_committed_changes: false
% 50.93/13.01
% 50.93/13.01 % ------ Parsing...% successful
% 50.93/13.01
% 50.93/13.01
% 50.93/13.01 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 50.93/13.01
% 50.93/13.01 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 50.93/13.01
% 50.93/13.01 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 50.93/13.01
% 50.93/13.01 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 50.93/13.01 % ------ Proving...
% 50.93/13.01 % ------ Problem Properties
% 50.93/13.01
% 50.93/13.01 %
% 50.93/13.01 % clauses 187
% 50.93/13.01 % conjectures 2
% 50.93/13.01 % EPR 58
% 50.93/13.01 % Horn 159
% 50.93/13.01 % unary 65
% 50.93/13.01 % binary 22
% 50.93/13.01 % lits 558
% 50.93/13.01 % lits eq 76
% 50.93/13.01 % fd_pure 0
% 50.93/13.01 % fd_pseudo 0
% 50.93/13.01 % fd_cond 16
% 50.93/13.01 % fd_pseudo_cond 14
% 50.93/13.01 % AC symbols 0
% 50.93/13.01
% 50.93/13.01 % ------ Schedule dynamic 5 is on
% 50.93/13.01
% 50.93/13.01 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 50.93/13.01
% 50.93/13.01
% 50.93/13.01 % ------
% 50.93/13.01 % Current options:
% 50.93/13.01 % ------
% 50.93/13.01
% 50.93/13.01
% 50.93/13.01 %
% 50.93/13.01
% 50.93/13.01 % ------ Proving...
% 50.93/13.01 %
% 50.93/13.01
% 50.93/13.01 % SZS status Unsatisfiable for theBenchmark.p
% 50.93/13.01
% 50.93/13.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.93/13.02
% 50.93/13.02
%------------------------------------------------------------------------------