%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC396-1 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:09:37 PM UTC 2026
% Result : Unsatisfiable 70.78s 12.45s
% Output : CNFRefutation 70.78s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f232ERROR: Could not build tree for root c_149680ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
fof(f75,axiom,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
fof(f76,axiom,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
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(f107,axiom,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
fof(f121,axiom,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1) ),
inference(reorient_equations,[],[f121]) ).
fof(f123,axiom,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1) ),
inference(reorient_equations,[],[f123]) ).
fof(f125,axiom,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(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(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(f150,axiom,
! [X2,X0,X1] :
( memberP(cons(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause139) ).
fof(f151,axiom,
! [X2,X0,X1] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
fof(f152,axiom,
! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
fof(f161,axiom,
! [X2,X0,X1] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
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(f170,axiom,
! [X2,X0,X1] :
( memberP(X0,X2)
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ memberP(app(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause158) ).
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(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(f206,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
memberP(sk1,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
~ memberP(sk2,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f214,plain,
memberP(sk3,sk5),
inference(definition_unfolding,[],[f207,f205]) ).
fof(f215,plain,
~ memberP(sk4,sk5),
inference(definition_unfolding,[],[f208,f204]) ).
tcf(c_248,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_249,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_250,negated_conjecture,
ssItem(sk5),
inference(cnf_transformation,[],[f206]) ).
tcf(c_251,negated_conjecture,
memberP(sk3,sk5),
inference(cnf_transformation,[],[f214]) ).
tcf(c_252,negated_conjecture,
~ memberP(sk4,sk5),
inference(cnf_transformation,[],[f215]) ).
tcf(c_253,negated_conjecture,
( ( sk3 = nil )
| ( sk4 != nil ) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_255,negated_conjecture,
( ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ neq(nil,sk3)
| ~ neq(sk4,nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(app(tl(sk3),cons(hd(sk3),nil))) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_257,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_258,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| memberP(X0,X2)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(app(X0,X1),X2) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_259,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_260,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_261,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(cons(X2,X0),X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_263,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_271,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_273,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( app(cons(X2,X1),X0) = cons(X2,app(X1,X0)) )
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(X0,X2),X1) = app(X0,app(X2,X1)) )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_286,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_287,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_290,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( hd(app(X1,X0)) = hd(X1) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_298,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_324,plain,
( ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(instantiation,[status(thm)],[c_273]) ).
tcf(c_336,plain,
( neq(nil,nil)
| ( nil = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_275]) ).
tcf(c_436,plain,
( ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ neq(nil,sk3)
| ~ neq(sk4,nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_255,c_284]) ).
tcf(c_2331,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X0,X2)
| ~ memberP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3578,plain,
( ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssList(nil)
| ~ neq(nil,sk3)
| ~ neq(sk4,nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3)) ),
inference(superposition,[status(thm)],[c_280,c_436]) ).
tcf(c_3585,plain,
( ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ neq(nil,sk3)
| ~ neq(sk4,nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3578,c_271]) ).
tcf(c_3690,plain,
( ( sk4 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ neq(nil,sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3)) ),
inference(superposition,[status(thm)],[c_275,c_3585]) ).
tcf(c_3699,plain,
( ( sk4 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ neq(nil,sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3690,c_271,c_249]) ).
tcf(c_3715,plain,
( ( sk4 = nil )
| ( sk3 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3)) ),
inference(superposition,[status(thm)],[c_275,c_3699]) ).
tcf(c_3724,plain,
( ( sk4 = nil )
| ( sk3 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3715,c_271,c_248]) ).
tcf(c_3730,plain,
( ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ( sk3 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3724,c_253,c_3724]) ).
tcf(c_3731,plain,
( ( sk3 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3)) ),
inference(renaming,[status(thm)],[c_3730]) ).
tcf(c_3740,plain,
( ( sk3 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssList(sk3)
| ~ ssList(tl(sk3)) ),
inference(superposition,[status(thm)],[c_298,c_3731]) ).
tcf(c_3741,plain,
( ( sk3 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssList(tl(sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3740,c_248]) ).
tcf(c_3754,plain,
( ( sk3 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssList(sk3) ),
inference(superposition,[status(thm)],[c_290,c_3741]) ).
tcf(c_3755,plain,
( ( sk3 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3754,c_248]) ).
tcf(c_3840,plain,
! [X0: $i] :
( ( tl(cons(X0,sk3)) = sk3 )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_248,c_288]) ).
tcf(c_3841,plain,
! [X0: $i] :
( ( tl(cons(X0,sk4)) = sk4 )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_249,c_288]) ).
tcf(c_3843,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ( tl(cons(X1,tl(X0))) = tl(X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_290,c_288]) ).
tcf(c_3877,plain,
! [X0: $i] :
( ( hd(cons(X0,nil)) = X0 )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_271,c_296]) ).
tcf(c_3916,plain,
tl(cons(sk5,sk3)) = sk3,
inference(superposition,[status(thm)],[c_250,c_3840]) ).
tcf(c_3926,plain,
tl(cons(sk5,sk4)) = sk4,
inference(superposition,[status(thm)],[c_250,c_3841]) ).
tcf(c_4021,plain,
( ( sk3 = nil )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(superposition,[status(thm)],[c_248,c_287]) ).
tcf(c_4050,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk3) = cons(X0,sk3) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_248,c_265]) ).
tcf(c_4051,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_249,c_265]) ).
tcf(c_4111,plain,
hd(cons(sk5,nil)) = sk5,
inference(superposition,[status(thm)],[c_250,c_3877]) ).
tcf(c_4245,plain,
! [X0: $i] :
( ~ ssItem(sk5)
| ~ ssList(X0)
| ( cons(sk5,X0) != nil ) ),
inference(instantiation,[status(thm)],[c_268]) ).
tcf(c_4246,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ),
inference(instantiation,[status(thm)],[c_4245]) ).
tcf(c_4247,plain,
! [X0: $i] :
( ssList(cons(sk5,X0))
| ~ ssItem(sk5)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_280]) ).
tcf(c_4248,plain,
( ssList(cons(sk5,nil))
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_4247]) ).
tcf(c_4382,plain,
app(cons(sk5,nil),sk3) = cons(sk5,sk3),
inference(superposition,[status(thm)],[c_250,c_4050]) ).
tcf(c_4389,plain,
( ( cons(sk5,nil) = nil )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk3) != nil ) ),
inference(superposition,[status(thm)],[c_4382,c_267]) ).
tcf(c_4390,plain,
( ( sk3 = nil )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk3) != nil ) ),
inference(superposition,[status(thm)],[c_4382,c_266]) ).
tcf(c_4391,plain,
( ssList(cons(sk5,sk3))
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil)) ),
inference(superposition,[status(thm)],[c_4382,c_284]) ).
tcf(c_4392,plain,
( ssList(cons(sk5,sk3))
| ~ ssList(cons(sk5,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4391,c_248]) ).
tcf(c_4395,plain,
( ( sk3 = nil )
| ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk3) != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4390,c_248]) ).
tcf(c_4399,plain,
( ( cons(sk5,nil) = nil )
| ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk3) != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4389,c_248]) ).
tcf(c_4406,plain,
ssList(cons(sk5,sk3)),
inference(global_subsumption_just,[status(thm)],[c_4392,c_250,c_271,c_4248,c_4392]) ).
tcf(c_4437,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk3,sk5)
| ( X1 != sk5 )
| ( X0 != sk3 ) ),
inference(instantiation,[status(thm)],[c_2334]) ).
tcf(c_4448,plain,
app(cons(sk5,nil),sk4) = cons(sk5,sk4),
inference(superposition,[status(thm)],[c_250,c_4051]) ).
tcf(c_4455,plain,
( ( cons(sk5,nil) = nil )
| ~ ssList(sk4)
| ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk4) != nil ) ),
inference(superposition,[status(thm)],[c_4448,c_267]) ).
tcf(c_4456,plain,
( ( sk4 = nil )
| ~ ssList(sk4)
| ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk4) != nil ) ),
inference(superposition,[status(thm)],[c_4448,c_266]) ).
tcf(c_4457,plain,
( ssList(cons(sk5,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(sk5,nil)) ),
inference(superposition,[status(thm)],[c_4448,c_284]) ).
tcf(c_4458,plain,
( ssList(cons(sk5,sk4))
| ~ ssList(cons(sk5,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4457,c_249]) ).
tcf(c_4461,plain,
( ( sk4 = nil )
| ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk4) != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4456,c_249]) ).
tcf(c_4465,plain,
( ( cons(sk5,nil) = nil )
| ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk4) != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4455,c_249]) ).
tcf(c_4473,plain,
ssList(cons(sk5,sk4)),
inference(global_subsumption_just,[status(thm)],[c_4458,c_250,c_271,c_4248,c_4458]) ).
tcf(c_4511,plain,
! [X0: $i] :
( ssItem(hd(cons(sk5,X0)))
| ( cons(sk5,X0) = nil )
| ~ ssList(cons(sk5,X0)) ),
inference(instantiation,[status(thm)],[c_298]) ).
tcf(c_4514,plain,
( ssItem(hd(cons(sk5,nil)))
| ( cons(sk5,nil) = nil )
| ~ ssList(cons(sk5,nil)) ),
inference(instantiation,[status(thm)],[c_4511]) ).
tcf(c_4587,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ( sk3 = nil )
| ~ ssItem(X0)
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ memberP(cons(hd(sk3),nil),X0) ),
inference(superposition,[status(thm)],[c_3755,c_259]) ).
tcf(c_4600,plain,
! [X0: $i] :
( memberP(cons(sk5,sk4),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ~ ssList(cons(sk5,nil)) ),
inference(superposition,[status(thm)],[c_4448,c_259]) ).
tcf(c_4602,plain,
! [X0: $i] :
( memberP(cons(sk5,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ~ ssList(cons(sk5,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4600,c_249]) ).
tcf(c_4631,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ( sk3 = nil )
| ~ ssItem(X0)
| ~ ssList(tl(sk3))
| ~ memberP(tl(sk3),X0)
| ~ ssList(cons(hd(sk3),nil)) ),
inference(superposition,[status(thm)],[c_3755,c_260]) ).
tcf(c_4699,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(app(X0,sk3)) = hd(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_248,c_295]) ).
tcf(c_4700,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(app(X0,sk4)) = hd(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_249,c_295]) ).
tcf(c_4817,plain,
( ( sk3 = nil )
| ( hd(app(sk3,sk3)) = hd(sk3) ) ),
inference(superposition,[status(thm)],[c_248,c_4699]) ).
tcf(c_4979,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(app(X0,sk3)) = app(tl(X0),sk3) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_248,c_286]) ).
tcf(c_4980,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(app(X0,sk4)) = app(tl(X0),sk4) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_249,c_286]) ).
tcf(c_5083,plain,
cons(sk5,sk3) != nil,
inference(global_subsumption_just,[status(thm)],[c_4395,c_250,c_271,c_4246,c_4248,c_4399]) ).
tcf(c_5085,plain,
cons(sk5,sk4) != nil,
inference(global_subsumption_just,[status(thm)],[c_4461,c_250,c_271,c_4246,c_4248,c_4465]) ).
tcf(c_5117,plain,
( ( cons(sk5,sk3) = nil )
| ( tl(app(cons(sk5,sk3),sk3)) = app(tl(cons(sk5,sk3)),sk3) ) ),
inference(superposition,[status(thm)],[c_4406,c_4979]) ).
tcf(c_5125,plain,
( ( cons(sk5,sk3) = nil )
| ( tl(app(cons(sk5,sk3),sk3)) = app(sk3,sk3) ) ),
inference(light_normalisation,[status(thm)],[c_5117,c_3916]) ).
tcf(c_5126,plain,
tl(app(cons(sk5,sk3),sk3)) = app(sk3,sk3),
inference(forward_subsumption_resolution,[status(thm)],[c_5125,c_5083]) ).
tcf(c_5297,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk3 )
| ( sk3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_2331]) ).
tcf(c_5298,plain,
( ( nil = sk3 )
| ( nil != nil )
| ( sk3 != nil ) ),
inference(instantiation,[status(thm)],[c_5297]) ).
tcf(c_5361,plain,
( ( cons(sk5,sk4) = nil )
| ( tl(app(cons(sk5,sk4),sk4)) = app(tl(cons(sk5,sk4)),sk4) ) ),
inference(superposition,[status(thm)],[c_4473,c_4980]) ).
tcf(c_5366,plain,
( ( cons(sk5,sk4) = nil )
| ( tl(app(cons(sk5,sk4),sk4)) = app(sk4,sk4) ) ),
inference(light_normalisation,[status(thm)],[c_5361,c_3926]) ).
tcf(c_5367,plain,
tl(app(cons(sk5,sk4),sk4)) = app(sk4,sk4),
inference(forward_subsumption_resolution,[status(thm)],[c_5366,c_5085]) ).
tcf(c_5492,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,X0),sk3) = cons(X1,app(X0,sk3)) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_248,c_278]) ).
tcf(c_5493,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,X0),sk4) = cons(X1,app(X0,sk4)) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_249,c_278]) ).
tcf(c_5575,plain,
! [X0: $i,X1: $i] :
( ( app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_248,c_283]) ).
tcf(c_5576,plain,
! [X0: $i,X1: $i] :
( ( app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_249,c_283]) ).
tcf(c_6079,plain,
! [X0: $i] :
( ( app(cons(X0,sk3),sk3) = cons(X0,app(sk3,sk3)) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_248,c_5492]) ).
tcf(c_6142,plain,
app(cons(sk5,sk3),sk3) = cons(sk5,app(sk3,sk3)),
inference(superposition,[status(thm)],[c_250,c_6079]) ).
tcf(c_6147,plain,
tl(cons(sk5,app(sk3,sk3))) = app(sk3,sk3),
inference(demodulation,[status(thm)],[c_5126,c_6142]) ).
tcf(c_6158,plain,
( ( cons(sk5,sk3) = nil )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,sk3))
| ( cons(sk5,app(sk3,sk3)) != nil ) ),
inference(superposition,[status(thm)],[c_6142,c_267]) ).
tcf(c_6160,plain,
( ssList(cons(sk5,app(sk3,sk3)))
| ~ ssList(sk3)
| ~ ssList(cons(sk5,sk3)) ),
inference(superposition,[status(thm)],[c_6142,c_284]) ).
tcf(c_6165,plain,
ssList(cons(sk5,app(sk3,sk3))),
inference(forward_subsumption_resolution,[status(thm)],[c_6160,c_248,c_4406]) ).
tcf(c_6174,plain,
cons(sk5,app(sk3,sk3)) != nil,
inference(forward_subsumption_resolution,[status(thm)],[c_6158,c_5083,c_248,c_4406]) ).
tcf(c_6389,plain,
! [X0: $i] :
( ~ ssItem(hd(cons(sk5,X0)))
| ~ memberP(nil,hd(cons(sk5,X0))) ),
inference(instantiation,[status(thm)],[c_263]) ).
tcf(c_6390,plain,
( ~ ssItem(hd(cons(sk5,nil)))
| ~ memberP(nil,hd(cons(sk5,nil))) ),
inference(instantiation,[status(thm)],[c_6389]) ).
tcf(c_6941,plain,
( ssList(app(sk3,sk3))
| ( cons(sk5,app(sk3,sk3)) = nil )
| ~ ssList(cons(sk5,app(sk3,sk3))) ),
inference(superposition,[status(thm)],[c_6147,c_290]) ).
tcf(c_6942,plain,
ssList(app(sk3,sk3)),
inference(forward_subsumption_resolution,[status(thm)],[c_6941,c_6174,c_6165]) ).
tcf(c_6950,plain,
( ( app(sk3,sk3) = nil )
| ( hd(app(app(sk3,sk3),sk4)) = hd(app(sk3,sk3)) ) ),
inference(superposition,[status(thm)],[c_6942,c_4700]) ).
tcf(c_7073,plain,
( ssItem(hd(sk3))
| ( sk3 = nil )
| ~ ssList(sk3) ),
inference(instantiation,[status(thm)],[c_298]) ).
tcf(c_7074,plain,
( ssList(tl(sk3))
| ( sk3 = nil )
| ~ ssList(sk3) ),
inference(instantiation,[status(thm)],[c_290]) ).
tcf(c_7964,plain,
! [X0: $i] :
( ( app(cons(X0,sk4),sk4) = cons(X0,app(sk4,sk4)) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_249,c_5493]) ).
tcf(c_8275,plain,
! [X0: $i,X1: $i] :
( memberP(X1,hd(cons(sk5,X0)))
| ~ memberP(sk3,sk5)
| ( X1 != sk3 )
| ( hd(cons(sk5,X0)) != sk5 ) ),
inference(instantiation,[status(thm)],[c_4437]) ).
tcf(c_8276,plain,
( memberP(nil,hd(cons(sk5,nil)))
| ~ memberP(sk3,sk5)
| ( nil != sk3 )
| ( hd(cons(sk5,nil)) != sk5 ) ),
inference(instantiation,[status(thm)],[c_8275]) ).
tcf(c_8703,plain,
app(cons(sk5,sk4),sk4) = cons(sk5,app(sk4,sk4)),
inference(superposition,[status(thm)],[c_250,c_7964]) ).
tcf(c_8709,plain,
tl(cons(sk5,app(sk4,sk4))) = app(sk4,sk4),
inference(demodulation,[status(thm)],[c_5367,c_8703]) ).
tcf(c_8712,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(cons(sk5,sk4),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ ssList(cons(sk5,sk4))
| ~ memberP(cons(sk5,app(sk4,sk4)),X0) ),
inference(superposition,[status(thm)],[c_8703,c_258]) ).
tcf(c_8713,plain,
( ( cons(sk5,sk4) = nil )
| ~ ssList(sk4)
| ~ ssList(cons(sk5,sk4))
| ( cons(sk5,app(sk4,sk4)) != nil ) ),
inference(superposition,[status(thm)],[c_8703,c_267]) ).
tcf(c_8715,plain,
( ssList(cons(sk5,app(sk4,sk4)))
| ~ ssList(sk4)
| ~ ssList(cons(sk5,sk4)) ),
inference(superposition,[status(thm)],[c_8703,c_284]) ).
tcf(c_8718,plain,
! [X0: $i] :
( memberP(cons(sk5,app(sk4,sk4)),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ ssList(cons(sk5,sk4))
| ~ memberP(cons(sk5,sk4),X0) ),
inference(superposition,[status(thm)],[c_8703,c_260]) ).
tcf(c_8721,plain,
ssList(cons(sk5,app(sk4,sk4))),
inference(forward_subsumption_resolution,[status(thm)],[c_8715,c_249,c_4473]) ).
tcf(c_8730,plain,
cons(sk5,app(sk4,sk4)) != nil,
inference(forward_subsumption_resolution,[status(thm)],[c_8713,c_5085,c_249,c_4473]) ).
tcf(c_8731,plain,
! [X0: $i] :
( memberP(cons(sk5,app(sk4,sk4)),X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk5,sk4),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8718,c_249,c_4473]) ).
tcf(c_8735,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(cons(sk5,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk5,app(sk4,sk4)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8712,c_249,c_4473]) ).
tcf(c_9032,plain,
( ssList(app(sk4,sk4))
| ( cons(sk5,app(sk4,sk4)) = nil )
| ~ ssList(cons(sk5,app(sk4,sk4))) ),
inference(superposition,[status(thm)],[c_8709,c_290]) ).
tcf(c_9034,plain,
ssList(app(sk4,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_9032,c_8730,c_8721]) ).
tcf(c_9224,plain,
! [X0: $i] :
( memberP(app(sk4,sk4),X0)
| ( X0 = sk5 )
| ~ ssItem(sk5)
| ~ ssItem(X0)
| ~ ssList(app(sk4,sk4))
| ~ memberP(cons(sk5,sk4),X0) ),
inference(superposition,[status(thm)],[c_8731,c_257]) ).
tcf(c_9225,plain,
! [X0: $i] :
( memberP(app(sk4,sk4),X0)
| ( X0 = sk5 )
| ~ ssItem(X0)
| ~ memberP(cons(sk5,sk4),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9224,c_250,c_9034]) ).
tcf(c_9264,plain,
! [X0: $i] :
( ( app(app(sk3,X0),sk4) = app(sk3,app(X0,sk4)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_249,c_5575]) ).
tcf(c_10127,plain,
app(app(sk3,sk3),sk4) = app(sk3,app(sk3,sk4)),
inference(superposition,[status(thm)],[c_248,c_9264]) ).
tcf(c_10206,plain,
( ( sk4 = nil )
| ~ ssList(sk4)
| ~ ssList(app(sk3,sk3))
| ( app(sk3,app(sk3,sk4)) != nil ) ),
inference(superposition,[status(thm)],[c_10127,c_266]) ).
tcf(c_10207,plain,
( ssList(app(sk3,app(sk3,sk4)))
| ~ ssList(sk4)
| ~ ssList(app(sk3,sk3)) ),
inference(superposition,[status(thm)],[c_10127,c_284]) ).
tcf(c_10213,plain,
ssList(app(sk3,app(sk3,sk4))),
inference(forward_subsumption_resolution,[status(thm)],[c_10207,c_249,c_6942]) ).
tcf(c_10217,plain,
( ( sk4 = nil )
| ( app(sk3,app(sk3,sk4)) != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10206,c_249,c_6942]) ).
tcf(c_10708,plain,
app(sk3,app(sk3,sk4)) != nil,
inference(global_subsumption_just,[status(thm)],[c_10217,c_250,c_271,c_251,c_324,c_253,c_336,c_4111,c_4246,c_4248,c_4514,c_5298,c_6390,c_8276,c_10217]) ).
tcf(c_11472,plain,
! [X0: $i] :
( ( app(app(sk4,X0),sk4) = app(sk4,app(X0,sk4)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_249,c_5576]) ).
tcf(c_14473,plain,
! [X0: $i] :
( ~ memberP(cons(sk5,app(sk4,sk4)),X0)
| ~ ssItem(X0)
| memberP(cons(sk5,sk4),X0) ),
inference(global_subsumption_just,[status(thm)],[c_8735,c_250,c_271,c_4248,c_4602,c_8735]) ).
tcf(c_14474,plain,
! [X0: $i] :
( memberP(cons(sk5,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk5,app(sk4,sk4)),X0) ),
inference(renaming,[status(thm)],[c_14473]) ).
tcf(c_15575,plain,
( ( app(sk3,sk3) = nil )
| ( hd(app(sk3,app(sk3,sk4))) = hd(app(sk3,sk3)) ) ),
inference(light_normalisation,[status(thm)],[c_6950,c_10127]) ).
tcf(c_15582,plain,
( ssItem(hd(app(sk3,sk3)))
| ( app(sk3,sk3) = nil )
| ( app(sk3,app(sk3,sk4)) = nil )
| ~ ssList(app(sk3,app(sk3,sk4))) ),
inference(superposition,[status(thm)],[c_15575,c_298]) ).
tcf(c_15585,plain,
( ssItem(hd(app(sk3,sk3)))
| ( app(sk3,sk3) = nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15582,c_10708,c_10213]) ).
tcf(c_15638,plain,
( ssItem(hd(sk3))
| ( sk3 = nil )
| ( app(sk3,sk3) = nil ) ),
inference(superposition,[status(thm)],[c_4817,c_15585]) ).
tcf(c_17977,plain,
! [X0: $i] :
( ssList(cons(hd(sk3),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk3)) ),
inference(instantiation,[status(thm)],[c_280]) ).
tcf(c_17978,plain,
( ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sk3)) ),
inference(instantiation,[status(thm)],[c_17977]) ).
tcf(c_19494,plain,
ssItem(hd(sk3)),
inference(global_subsumption_just,[status(thm)],[c_15638,c_250,c_248,c_271,c_251,c_324,c_336,c_4111,c_4246,c_4248,c_4514,c_5298,c_6390,c_7073,c_8276]) ).
tcf(c_19529,plain,
app(cons(hd(sk3),sk4),sk4) = cons(hd(sk3),app(sk4,sk4)),
inference(superposition,[status(thm)],[c_19494,c_7964]) ).
tcf(c_19538,plain,
app(cons(hd(sk3),nil),sk4) = cons(hd(sk3),sk4),
inference(superposition,[status(thm)],[c_19494,c_4051]) ).
tcf(c_21555,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(cons(hd(sk3),nil),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ ssList(cons(hd(sk3),nil))
| ~ memberP(cons(hd(sk3),sk4),X0) ),
inference(superposition,[status(thm)],[c_19538,c_258]) ).
tcf(c_21558,plain,
( ssList(cons(hd(sk3),sk4))
| ~ ssList(sk4)
| ~ ssList(cons(hd(sk3),nil)) ),
inference(superposition,[status(thm)],[c_19538,c_284]) ).
tcf(c_21571,plain,
( ssList(cons(hd(sk3),sk4))
| ~ ssList(cons(hd(sk3),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21558,c_249]) ).
tcf(c_21616,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(cons(hd(sk3),nil),X0)
| ~ ssItem(X0)
| ~ ssList(cons(hd(sk3),nil))
| ~ memberP(cons(hd(sk3),sk4),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21555,c_249]) ).
tcf(c_21637,plain,
ssList(cons(hd(sk3),sk4)),
inference(global_subsumption_just,[status(thm)],[c_21571,c_250,c_248,c_271,c_251,c_324,c_336,c_4111,c_4246,c_4248,c_4514,c_5298,c_6390,c_7073,c_8276,c_17978,c_21571]) ).
tcf(c_21932,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ memberP(cons(hd(sk3),sk4),X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_21616,c_250,c_248,c_271,c_251,c_324,c_336,c_4111,c_4246,c_4248,c_4514,c_4587,c_5298,c_6390,c_7074,c_7073,c_8276,c_17978,c_21616]) ).
tcf(c_21933,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(cons(hd(sk3),sk4),X0) ),
inference(renaming,[status(thm)],[c_21932]) ).
tcf(c_33184,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(cons(hd(sk3),sk4),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ ssList(cons(hd(sk3),sk4))
| ~ memberP(cons(hd(sk3),app(sk4,sk4)),X0) ),
inference(superposition,[status(thm)],[c_19529,c_258]) ).
tcf(c_33243,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(cons(hd(sk3),sk4),X0)
| ~ ssItem(X0)
| ~ memberP(cons(hd(sk3),app(sk4,sk4)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33184,c_249,c_21637]) ).
tcf(c_33289,plain,
app(tl(sk3),cons(hd(sk3),nil)) = sk4,
inference(global_subsumption_just,[status(thm)],[c_436,c_250,c_271,c_251,c_324,c_336,c_3755,c_4111,c_4246,c_4248,c_4514,c_5298,c_6390,c_8276]) ).
tcf(c_33736,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ( tl(cons(X1,tl(X0))) = tl(X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_290,c_288]) ).
tcf(c_33938,plain,
! [X0: $i] :
( ( sk3 = nil )
| ( tl(cons(X0,tl(sk3))) = tl(sk3) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_248,c_33736]) ).
tcf(c_34125,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ memberP(cons(hd(sk3),nil),X0) ),
inference(superposition,[status(thm)],[c_33289,c_259]) ).
tcf(c_39150,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ memberP(cons(hd(sk3),app(sk4,sk4)),X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_33243,c_21933,c_33243]) ).
tcf(c_39151,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(cons(hd(sk3),app(sk4,sk4)),X0) ),
inference(renaming,[status(thm)],[c_39150]) ).
tcf(c_39159,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssItem(hd(sk3))
| ~ ssList(app(sk4,sk4))
| ~ memberP(app(sk4,sk4),X0) ),
inference(superposition,[status(thm)],[c_261,c_39151]) ).
tcf(c_39163,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk4,sk4),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39159,c_19494,c_9034]) ).
tcf(c_53818,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ( tl(cons(X0,tl(sk3))) = tl(sk3) ) ),
inference(global_subsumption_just,[status(thm)],[c_33938,c_250,c_271,c_251,c_324,c_336,c_4111,c_4246,c_4248,c_4514,c_5298,c_6390,c_8276,c_33938]) ).
tcf(c_53819,plain,
! [X0: $i] :
( ( tl(cons(X0,tl(sk3))) = tl(sk3) )
| ~ ssItem(X0) ),
inference(renaming,[status(thm)],[c_53818]) ).
tcf(c_62405,plain,
! [X0: $i] :
( ( sk3 = nil )
| ( tl(cons(X0,tl(sk3))) = tl(sk3) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_248,c_3843]) ).
tcf(c_62702,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ( tl(cons(X0,tl(sk3))) = tl(sk3) ) ),
inference(global_subsumption_just,[status(thm)],[c_62405,c_53819]) ).
tcf(c_62703,plain,
! [X0: $i] :
( ( tl(cons(X0,tl(sk3))) = tl(sk3) )
| ~ ssItem(X0) ),
inference(renaming,[status(thm)],[c_62702]) ).
tcf(c_62708,plain,
tl(cons(sk5,tl(sk3))) = tl(sk3),
inference(superposition,[status(thm)],[c_250,c_62703]) ).
tcf(c_62716,plain,
( ssList(tl(sk3))
| ( cons(sk5,tl(sk3)) = nil )
| ~ ssList(cons(sk5,tl(sk3))) ),
inference(superposition,[status(thm)],[c_62708,c_290]) ).
tcf(c_62977,plain,
ssList(tl(sk3)),
inference(global_subsumption_just,[status(thm)],[c_62716,c_250,c_248,c_271,c_251,c_324,c_336,c_4111,c_4246,c_4248,c_4514,c_5298,c_6390,c_7074,c_8276]) ).
tcf(c_63026,plain,
app(app(sk4,tl(sk3)),sk4) = app(sk4,app(tl(sk3),sk4)),
inference(superposition,[status(thm)],[c_62977,c_11472]) ).
tcf(c_63046,plain,
! [X0: $i] :
( ( app(cons(X0,nil),tl(sk3)) = cons(X0,tl(sk3)) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_62977,c_265]) ).
tcf(c_63514,plain,
app(cons(hd(sk3),nil),tl(sk3)) = cons(hd(sk3),tl(sk3)),
inference(superposition,[status(thm)],[c_19494,c_63046]) ).
tcf(c_74080,plain,
! [X0: $i] :
( memberP(app(sk4,app(tl(sk3),sk4)),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ ssList(app(sk4,tl(sk3)))
| ~ memberP(app(sk4,tl(sk3)),X0) ),
inference(superposition,[status(thm)],[c_63026,c_260]) ).
tcf(c_74118,plain,
! [X0: $i] :
( memberP(app(sk4,app(tl(sk3),sk4)),X0)
| ~ ssItem(X0)
| ~ ssList(app(sk4,tl(sk3)))
| ~ memberP(app(sk4,tl(sk3)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_74080,c_249]) ).
tcf(c_76218,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(app(tl(sk3),sk4),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ ssList(app(sk4,tl(sk3)))
| ~ ssList(app(tl(sk3),sk4))
| ~ memberP(app(sk4,tl(sk3)),X0) ),
inference(superposition,[status(thm)],[c_74118,c_258]) ).
tcf(c_76219,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(app(tl(sk3),sk4),X0)
| ~ ssItem(X0)
| ~ ssList(app(sk4,tl(sk3)))
| ~ ssList(app(tl(sk3),sk4))
| ~ memberP(app(sk4,tl(sk3)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_76218,c_249]) ).
tcf(c_76319,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(app(tl(sk3),sk4),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ ssList(tl(sk3))
| ~ memberP(tl(sk3),X0)
| ~ ssList(app(sk4,tl(sk3)))
| ~ ssList(app(tl(sk3),sk4)) ),
inference(superposition,[status(thm)],[c_259,c_76219]) ).
tcf(c_76320,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(app(tl(sk3),sk4),X0)
| ~ ssItem(X0)
| ~ memberP(tl(sk3),X0)
| ~ ssList(app(sk4,tl(sk3)))
| ~ ssList(app(tl(sk3),sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_76319,c_249,c_62977]) ).
tcf(c_76328,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ memberP(tl(sk3),X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_76320,c_250,c_248,c_271,c_251,c_324,c_336,c_4111,c_4246,c_4248,c_4514,c_4631,c_5298,c_6390,c_7074,c_7073,c_8276,c_17978]) ).
tcf(c_76329,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(tl(sk3),X0) ),
inference(renaming,[status(thm)],[c_76328]) ).
tcf(c_83470,plain,
! [X0: $i] :
( memberP(tl(sk3),X0)
| memberP(cons(hd(sk3),nil),X0)
| ~ ssItem(X0)
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ memberP(cons(hd(sk3),tl(sk3)),X0) ),
inference(superposition,[status(thm)],[c_63514,c_258]) ).
tcf(c_83505,plain,
! [X0: $i] :
( memberP(tl(sk3),X0)
| memberP(cons(hd(sk3),nil),X0)
| ~ ssItem(X0)
| ~ ssList(cons(hd(sk3),nil))
| ~ memberP(cons(hd(sk3),tl(sk3)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_83470,c_62977]) ).
tcf(c_129210,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk3,sk5)
| ( X1 != sk5 )
| ( X0 != sk3 ) ),
inference(instantiation,[status(thm)],[c_2334]) ).
tcf(c_132240,plain,
! [X0: $i] :
( memberP(cons(hd(sk3),tl(sk3)),X0)
| ~ memberP(sk3,sk5)
| ( X0 != sk5 )
| ( cons(hd(sk3),tl(sk3)) != sk3 ) ),
inference(instantiation,[status(thm)],[c_129210]) ).
tcf(c_141242,negated_conjecture,
sk4 != nil,
inference(global_subsumption_just,[status(thm)],[c_253,c_250,c_271,c_251,c_324,c_253,c_336,c_4111,c_4246,c_4248,c_4514,c_5298,c_6390,c_8276]) ).
tcf(c_141403,plain,
! [X0: $i] :
( ( tl(cons(X0,sk4)) = sk4 )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_249,c_288]) ).
tcf(c_141440,plain,
tl(cons(sk5,sk4)) = sk4,
inference(superposition,[status(thm)],[c_250,c_141403]) ).
tcf(c_141662,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_249,c_265]) ).
tcf(c_141812,plain,
app(cons(sk5,nil),sk4) = cons(sk5,sk4),
inference(superposition,[status(thm)],[c_250,c_141662]) ).
tcf(c_141819,plain,
( ( sk4 = nil )
| ~ ssList(sk4)
| ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk4) != nil ) ),
inference(superposition,[status(thm)],[c_141812,c_266]) ).
tcf(c_141820,plain,
( ssList(cons(sk5,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(sk5,nil)) ),
inference(superposition,[status(thm)],[c_141812,c_284]) ).
tcf(c_141821,plain,
( ssList(cons(sk5,sk4))
| ~ ssList(cons(sk5,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_141820,c_249]) ).
tcf(c_141824,plain,
( ~ ssList(cons(sk5,nil))
| ( cons(sk5,sk4) != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_141819,c_141242,c_249]) ).
tcf(c_141947,plain,
ssList(cons(sk5,sk4)),
inference(global_subsumption_just,[status(thm)],[c_141821,c_250,c_271,c_4248,c_4458]) ).
tcf(c_141980,plain,
cons(sk5,sk4) != nil,
inference(global_subsumption_just,[status(thm)],[c_141824,c_250,c_271,c_4246,c_4248,c_4465]) ).
tcf(c_142313,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(app(X0,sk4)) = app(tl(X0),sk4) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_249,c_286]) ).
tcf(c_142458,plain,
( ( cons(sk5,sk4) = nil )
| ( tl(app(cons(sk5,sk4),sk4)) = app(tl(cons(sk5,sk4)),sk4) ) ),
inference(superposition,[status(thm)],[c_141947,c_142313]) ).
tcf(c_142461,plain,
( ( cons(sk5,sk4) = nil )
| ( tl(app(cons(sk5,sk4),sk4)) = app(sk4,sk4) ) ),
inference(light_normalisation,[status(thm)],[c_142458,c_141440]) ).
tcf(c_142462,plain,
tl(app(cons(sk5,sk4),sk4)) = app(sk4,sk4),
inference(forward_subsumption_resolution,[status(thm)],[c_142461,c_141980]) ).
tcf(c_142583,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,X0),sk4) = cons(X1,app(X0,sk4)) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_249,c_278]) ).
tcf(c_144213,plain,
! [X0: $i] :
( ( app(cons(X0,sk4),sk4) = cons(X0,app(sk4,sk4)) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_249,c_142583]) ).
tcf(c_144785,plain,
app(cons(sk5,sk4),sk4) = cons(sk5,app(sk4,sk4)),
inference(superposition,[status(thm)],[c_250,c_144213]) ).
tcf(c_144791,plain,
tl(cons(sk5,app(sk4,sk4))) = app(sk4,sk4),
inference(demodulation,[status(thm)],[c_142462,c_144785]) ).
tcf(c_144795,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(cons(sk5,sk4),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ ssList(cons(sk5,sk4))
| ~ memberP(cons(sk5,app(sk4,sk4)),X0) ),
inference(superposition,[status(thm)],[c_144785,c_258]) ).
tcf(c_144797,plain,
( ( sk4 = nil )
| ~ ssList(sk4)
| ~ ssList(cons(sk5,sk4))
| ( cons(sk5,app(sk4,sk4)) != nil ) ),
inference(superposition,[status(thm)],[c_144785,c_266]) ).
tcf(c_144798,plain,
( ssList(cons(sk5,app(sk4,sk4)))
| ~ ssList(sk4)
| ~ ssList(cons(sk5,sk4)) ),
inference(superposition,[status(thm)],[c_144785,c_284]) ).
tcf(c_144804,plain,
ssList(cons(sk5,app(sk4,sk4))),
inference(forward_subsumption_resolution,[status(thm)],[c_144798,c_249,c_141947]) ).
tcf(c_144806,plain,
cons(sk5,app(sk4,sk4)) != nil,
inference(forward_subsumption_resolution,[status(thm)],[c_144797,c_141242,c_249,c_141947]) ).
tcf(c_144815,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(cons(sk5,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk5,app(sk4,sk4)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_144795,c_249,c_141947]) ).
tcf(c_149399,plain,
( ssList(app(sk4,sk4))
| ( cons(sk5,app(sk4,sk4)) = nil )
| ~ ssList(cons(sk5,app(sk4,sk4))) ),
inference(superposition,[status(thm)],[c_144791,c_290]) ).
tcf(c_149401,plain,
ssList(app(sk4,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_149399,c_144806,c_144804]) ).
tcf(c_149667,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ memberP(cons(sk5,app(sk4,sk4)),X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_144815,c_250,c_248,c_271,c_251,c_324,c_336,c_4021,c_4111,c_4246,c_4248,c_4514,c_5298,c_6390,c_7074,c_7073,c_8276,c_9225,c_14474,c_17978,c_34125,c_39163,c_76329,c_83505,c_132240]) ).
tcf(c_149668,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk5,app(sk4,sk4)),X0) ),
inference(renaming,[status(thm)],[c_149667]) ).
tcf(c_149677,plain,
( memberP(sk4,sk5)
| ~ ssItem(sk5)
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_262,c_149668]) ).
tcf(c_149680,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_149677,c_252,c_250,c_149401]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC396-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 18:02:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 70.78/12.45 % SZS status Started for theBenchmark.p
% 70.78/12.45 % SZS status Unsatisfiable for theBenchmark.p
% 70.78/12.45
% 70.78/12.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 70.78/12.45
% 70.78/12.45 % ------ iProver source info
% 70.78/12.45
% 70.78/12.45 % git: date: 2026-07-19 20:42:38 +0200
% 70.78/12.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 70.78/12.45 % git: non_committed_changes: false
% 70.78/12.45
% 70.78/12.45 % ------ Parsing...% successful
% 70.78/12.45
% 70.78/12.45
% 70.78/12.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 70.78/12.45
% 70.78/12.45 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 70.78/12.45
% 70.78/12.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 70.78/12.45
% 70.78/12.45 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 70.78/12.45 % ------ Proving...
% 70.78/12.45 % ------ Problem Properties
% 70.78/12.45
% 70.78/12.45 %
% 70.78/12.45 % clauses 66
% 70.78/12.45 % conjectures 7
% 70.78/12.45 % EPR 24
% 70.78/12.45 % Horn 49
% 70.78/12.45 % unary 9
% 70.78/12.45 % binary 11
% 70.78/12.45 % lits 247
% 70.78/12.45 % lits eq 49
% 70.78/12.45 % fd_pure 0
% 70.78/12.45 % fd_pseudo 0
% 70.78/12.45 % fd_cond 12
% 70.78/12.45 % fd_pseudo_cond 10
% 70.78/12.45 % AC symbols 0
% 70.78/12.45
% 70.78/12.45 % ------ Schedule dynamic 5 is on
% 70.78/12.45
% 70.78/12.45 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 70.78/12.45
% 70.78/12.45
% 70.78/12.45 % ------
% 70.78/12.45 % Current options:
% 70.78/12.45 % ------
% 70.78/12.45
% 70.78/12.45
% 70.78/12.45 %
% 70.78/12.45
% 70.78/12.45 % ------ Proving...
% 70.78/12.45 % Proof_search_loop: time out after: 6374 full_loop iterations
% 70.78/12.45
% 70.78/12.45 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 70.78/12.45
% 70.78/12.45
% 70.78/12.45 % ------
% 70.78/12.45 % Current options:
% 70.78/12.45 % ------
% 70.78/12.45
% 70.78/12.45
% 70.78/12.45 %
% 70.78/12.45
% 70.78/12.45 % ------ Proving...
% 70.78/12.45 %
% 70.78/12.45
% 70.78/12.45 % SZS status Unsatisfiable for theBenchmark.p
% 70.78/12.45
% 70.78/12.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 70.78/12.46
% 70.78/12.46
%------------------------------------------------------------------------------