%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC376+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 : n020.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 03:09:31 PM UTC 2026
% Result : Theorem 66.55s 17.50s
% Output : CNFRefutation 66.55s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f236ERROR: Could not build tree for root c_227410ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( ( memberP(X0,X4)
& memberP(X1,X4) )
| ( ~ memberP(X0,X4)
& ~ memberP(X1,X4) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( ( memberP(X0,X4)
& memberP(X1,X4) )
| ( ~ memberP(X0,X4)
& ~ memberP(X1,X4) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X2)
| ! [X8] :
( ~ neq(nil,X2)
| hd(X2) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(X2) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| X3 = X5
| ~ ssList(X5) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X4] :
( ssItem(X4)
& ( ~ memberP(X0,X4)
| ~ memberP(X1,X4) )
& ( memberP(X0,X4)
| memberP(X1,X4) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X2)
| ! [X8] :
( ~ neq(nil,X2)
| hd(X2) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(X2) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| X3 = X5
| ~ ssList(X5) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X4] :
( ssItem(X4)
& ( ~ memberP(X0,X4)
| ~ memberP(X1,X4) )
& ( memberP(X0,X4)
| memberP(X1,X4) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f102,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f111,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f122,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f122]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f132,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f133,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f137,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f138,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f137]) ).
fof(f140,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f141,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(flattening,[],[f140]) ).
fof(f142,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK2)
| ! [X8] :
( ~ neq(nil,sK2)
| hd(sK2) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(sK2) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| sK3 = X5
| ~ ssList(X5) )
& neq(sK2,nil) )
| ~ neq(sK3,nil) )
& ( nil != sK3
| nil = sK2 )
& ssItem(sK4)
& ( ~ memberP(sK0,sK4)
| ~ memberP(sK1,sK4) )
& ( memberP(sK0,sK4)
| memberP(sK1,sK4) )
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f147,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f149,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK9(X0)
& ssItem(sK9(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f127]) ).
fof(f150,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f132]) ).
fof(f151,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f150]) ).
fof(f152,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f133]) ).
fof(f153,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f152]) ).
fof(f157,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK12(X0)
& ssList(sK12(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X1,sK12(X0))],[f138]) ).
fof(f158,plain,
ssList(sK0),
inference(cnf_transformation,[],[f142]) ).
fof(f159,plain,
ssList(sK1),
inference(cnf_transformation,[],[f142]) ).
fof(f163,plain,
( neq(sK2,nil)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f142]) ).
fof(f164,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f142]) ).
fof(f165,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f142]) ).
fof(f166,plain,
( ~ memberP(sK0,sK4)
| ~ memberP(sK1,sK4) ),
inference(cnf_transformation,[],[f142]) ).
fof(f167,plain,
( memberP(sK0,sK4)
| memberP(sK1,sK4) ),
inference(cnf_transformation,[],[f142]) ).
fof(f168,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f142]) ).
fof(f169,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f142]) ).
fof(f173,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f175,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f182,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2)) ),
inference(cnf_transformation,[],[f111]) ).
fof(f191,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f193,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
fof(f196,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f198,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f123]) ).
fof(f200,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK9(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK9(X0)) ),
inference(cnf_transformation,[],[f149]) ).
fof(f202,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f203,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f204,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f151]) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(cons(X1,X2),X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f208,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f216,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK12(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f217,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK12(X0)) ),
inference(cnf_transformation,[],[f157]) ).
fof(f219,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f141]) ).
fof(f220,plain,
( memberP(sK2,sK4)
| memberP(sK3,sK4) ),
inference(definition_unfolding,[],[f167,f169,f168]) ).
fof(f221,plain,
( ~ memberP(sK2,sK4)
| ~ memberP(sK3,sK4) ),
inference(definition_unfolding,[],[f166,f169,f168]) ).
fof(f222,plain,
ssList(sK3),
inference(definition_unfolding,[],[f159,f169]) ).
fof(f223,plain,
ssList(sK2),
inference(definition_unfolding,[],[f158,f168]) ).
tcf(c_49,negated_conjecture,
( memberP(sK2,sK4)
| memberP(sK3,sK4) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_50,negated_conjecture,
( ~ memberP(sK2,sK4)
| ~ memberP(sK3,sK4) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_51,negated_conjecture,
ssItem(sK4),
inference(cnf_transformation,[],[f165]) ).
tcf(c_52,negated_conjecture,
( ( sK2 = nil )
| ( sK3 != nil ) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_53,negated_conjecture,
( neq(sK2,nil)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_54,negated_conjecture,
( ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(tl(sK2))
| ~ neq(nil,sK2)
| ~ neq(sK3,nil)
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ ssList(app(tl(sK2),cons(hd(sK2),nil))) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_57,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f222]) ).
tcf(c_58,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f223]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(X1,X0),X2) = app(X1,app(X0,X2)) )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_82,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_85,plain,
ssList(nil),
inference(cnf_transformation,[],[f196]) ).
tcf(c_87,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_89,plain,
! [X0: $i] :
( ssItem(sK9(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_90,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK9(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_92,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_93,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(cons(X2,X0),X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| memberP(X0,X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ memberP(app(X0,X1),X2) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_105,plain,
! [X0: $i] :
( ssList(sK12(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_106,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK12(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_108,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_111,plain,
( ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_127,plain,
( neq(nil,nil)
| ( nil = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_336,plain,
( ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(tl(sK2))
| ~ neq(nil,sK2)
| ~ neq(sK3,nil)
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_54,c_80]) ).
tcf(c_1891,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X0,X2)
| ~ memberP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( neq(X0,X2)
| ~ neq(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3136,plain,
( ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(nil)
| ~ ssList(tl(sK2))
| ~ neq(nil,sK2)
| ~ neq(sK3,nil)
| ~ ssItem(hd(sK2)) ),
inference(superposition,[status(thm)],[c_71,c_336]) ).
tcf(c_3145,plain,
( ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(tl(sK2))
| ~ neq(nil,sK2)
| ~ neq(sK3,nil)
| ~ ssItem(hd(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3136,c_85]) ).
tcf(c_3298,plain,
( ( sK3 = nil )
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ ssList(tl(sK2))
| ~ neq(nil,sK2)
| ~ ssItem(hd(sK2)) ),
inference(superposition,[status(thm)],[c_81,c_3145]) ).
tcf(c_3305,plain,
( ( sK3 = nil )
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(tl(sK2))
| ~ neq(nil,sK2)
| ~ ssItem(hd(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3298,c_85,c_57]) ).
tcf(c_3325,plain,
( ( sK2 = nil )
| ( sK3 = nil )
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(tl(sK2))
| ~ ssItem(hd(sK2)) ),
inference(superposition,[status(thm)],[c_81,c_3305]) ).
tcf(c_3326,plain,
( ( sK2 = nil )
| ( sK3 = nil )
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(tl(sK2))
| ~ ssItem(hd(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3325,c_85,c_58]) ).
tcf(c_3332,plain,
( ( sK2 = nil )
| ~ ssItem(hd(sK2))
| ~ ssList(tl(sK2))
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_3326,c_52,c_3326]) ).
tcf(c_3333,plain,
( ( sK2 = nil )
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(tl(sK2))
| ~ ssItem(hd(sK2)) ),
inference(renaming,[status(thm)],[c_3332]) ).
tcf(c_3342,plain,
( ( sK2 = nil )
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(sK2)
| ~ ssList(tl(sK2)) ),
inference(superposition,[status(thm)],[c_92,c_3333]) ).
tcf(c_3343,plain,
( ( sK2 = nil )
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(tl(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3342,c_58]) ).
tcf(c_3356,plain,
( ( sK2 = nil )
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_108,c_3343]) ).
tcf(c_3357,plain,
( ( sK2 = nil )
| ( app(tl(sK2),cons(hd(sK2),nil)) = sK3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3356,c_58]) ).
tcf(c_3401,plain,
( ( sK2 = nil )
| ( hd(sK2) = sK9(sK2) ) ),
inference(superposition,[status(thm)],[c_58,c_90]) ).
tcf(c_3403,plain,
! [X0: $i,X1: $i] :
( ( cons(X0,X1) = nil )
| ( hd(cons(X0,X1)) = sK9(cons(X0,X1)) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_71,c_90]) ).
tcf(c_3473,plain,
( ( sK2 = nil )
| ( tl(sK2) = sK12(sK2) ) ),
inference(superposition,[status(thm)],[c_58,c_106]) ).
tcf(c_3526,plain,
( ssItem(hd(sK2))
| ( sK2 = nil )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_3401,c_89]) ).
tcf(c_3527,plain,
( ssItem(hd(sK2))
| ( sK2 = nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3526,c_58]) ).
tcf(c_3613,plain,
( ssList(tl(sK2))
| ( sK2 = nil )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_3473,c_105]) ).
tcf(c_3614,plain,
( ssList(tl(sK2))
| ( sK2 = nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3613,c_58]) ).
tcf(c_3642,plain,
! [X0: $i] :
( ssList(cons(sK4,X0))
| ~ ssItem(sK4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_3643,plain,
( ssList(cons(sK4,nil))
| ~ ssList(nil)
| ~ ssItem(sK4) ),
inference(instantiation,[status(thm)],[c_3642]) ).
tcf(c_3648,plain,
! [X0: $i] :
( ~ ssItem(sK4)
| ~ ssList(X0)
| ( cons(sK4,X0) != nil ) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3649,plain,
( ~ ssList(nil)
| ~ ssItem(sK4)
| ( cons(sK4,nil) != nil ) ),
inference(instantiation,[status(thm)],[c_3648]) ).
tcf(c_3992,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sK3,sK4)
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_1892]) ).
tcf(c_4067,plain,
( ( sK2 = nil )
| ( cons(hd(sK2),tl(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_58,c_87]) ).
tcf(c_4134,plain,
! [X0: $i] :
( ( app(cons(sK4,nil),X0) = cons(sK4,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_51,c_62]) ).
tcf(c_4289,plain,
! [X0: $i] :
( ssItem(sK9(cons(sK4,X0)))
| ( cons(sK4,X0) = nil )
| ~ ssList(cons(sK4,X0)) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_4294,plain,
( ssItem(sK9(cons(sK4,nil)))
| ( cons(sK4,nil) = nil )
| ~ ssList(cons(sK4,nil)) ),
inference(instantiation,[status(thm)],[c_4289]) ).
tcf(c_4364,plain,
app(cons(sK4,nil),sK3) = cons(sK4,sK3),
inference(superposition,[status(thm)],[c_57,c_4134]) ).
tcf(c_4406,plain,
( ssList(cons(sK4,sK3))
| ~ ssList(sK3)
| ~ ssList(cons(sK4,nil)) ),
inference(superposition,[status(thm)],[c_4364,c_80]) ).
tcf(c_4407,plain,
( ssList(cons(sK4,sK3))
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4406,c_57]) ).
tcf(c_4464,plain,
ssList(cons(sK4,sK3)),
inference(global_subsumption_just,[status(thm)],[c_4407,c_51,c_85,c_3643,c_4407]) ).
tcf(c_4466,plain,
app(cons(sK4,nil),cons(sK4,sK3)) = cons(sK4,cons(sK4,sK3)),
inference(superposition,[status(thm)],[c_4464,c_4134]) ).
tcf(c_4760,plain,
! [X0: $i] :
( memberP(sK2,X0)
| ( sK2 = nil )
| ~ ssItem(X0)
| ~ ssList(tl(sK2))
| ~ ssItem(hd(sK2))
| ~ memberP(tl(sK2),X0) ),
inference(superposition,[status(thm)],[c_4067,c_95]) ).
tcf(c_4823,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ( sK2 = nil )
| ~ ssItem(X0)
| ~ ssList(tl(sK2))
| ~ memberP(tl(sK2),X0)
| ~ ssList(cons(hd(sK2),nil)) ),
inference(superposition,[status(thm)],[c_3357,c_97]) ).
tcf(c_4894,plain,
! [X0: $i] :
( memberP(cons(sK4,sK3),X0)
| ~ ssList(sK3)
| ~ ssItem(X0)
| ~ memberP(sK3,X0)
| ~ ssList(cons(sK4,nil)) ),
inference(superposition,[status(thm)],[c_4364,c_98]) ).
tcf(c_4901,plain,
! [X0: $i] :
( memberP(cons(sK4,sK3),X0)
| ~ ssItem(X0)
| ~ memberP(sK3,X0)
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4894,c_57]) ).
tcf(c_5039,plain,
! [X0: $i] :
( neq(sK3,X0)
| ( X0 = sK3 )
| ~ ssList(sK3)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_5040,plain,
( neq(sK3,nil)
| ( nil = sK3 )
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(instantiation,[status(thm)],[c_5039]) ).
tcf(c_5366,plain,
! [X0: $i,X1: $i] :
( ( cons(sK4,app(X0,X1)) = app(cons(sK4,X0),X1) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_51,c_63]) ).
tcf(c_5593,plain,
! [X0: $i] :
( memberP(tl(sK2),X0)
| memberP(cons(hd(sK2),nil),X0)
| ( sK2 = nil )
| ~ ssItem(X0)
| ~ ssList(tl(sK2))
| ~ memberP(sK3,X0)
| ~ ssList(cons(hd(sK2),nil)) ),
inference(superposition,[status(thm)],[c_3357,c_99]) ).
tcf(c_5720,plain,
! [X0: $i] :
( memberP(cons(sK4,sK3),X0)
| ~ ssItem(X0)
| ~ memberP(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_4901,c_51,c_85,c_3643,c_4901]) ).
tcf(c_7042,plain,
! [X0: $i] :
( ( cons(sK4,app(X0,sK3)) = app(cons(sK4,X0),sK3) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_57,c_5366]) ).
tcf(c_7043,plain,
! [X0: $i] :
( ( cons(sK4,app(X0,sK2)) = app(cons(sK4,X0),sK2) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_58,c_5366]) ).
tcf(c_7182,plain,
cons(sK4,app(sK3,sK3)) = app(cons(sK4,sK3),sK3),
inference(superposition,[status(thm)],[c_57,c_7042]) ).
tcf(c_7192,plain,
cons(sK4,app(cons(sK4,sK3),sK3)) = app(cons(sK4,cons(sK4,sK3)),sK3),
inference(superposition,[status(thm)],[c_4464,c_7042]) ).
tcf(c_7231,plain,
( ssList(app(cons(sK4,sK3),sK3))
| ~ ssItem(sK4)
| ~ ssList(app(sK3,sK3)) ),
inference(superposition,[status(thm)],[c_7182,c_71]) ).
tcf(c_7236,plain,
( ssList(app(cons(sK4,sK3),sK3))
| ~ ssList(app(sK3,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7231,c_51]) ).
tcf(c_7925,plain,
cons(sK4,app(cons(sK4,sK3),sK2)) = app(cons(sK4,cons(sK4,sK3)),sK2),
inference(superposition,[status(thm)],[c_4464,c_7043]) ).
tcf(c_9421,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sK2,sK4)
| ( X1 != sK4 )
| ( X0 != sK2 ) ),
inference(instantiation,[status(thm)],[c_1892]) ).
tcf(c_9461,plain,
! [X0: $i] :
( ~ ssItem(sK9(cons(sK4,X0)))
| ~ memberP(nil,sK9(cons(sK4,X0))) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_9462,plain,
( ~ ssItem(sK9(cons(sK4,nil)))
| ~ memberP(nil,sK9(cons(sK4,nil))) ),
inference(instantiation,[status(thm)],[c_9461]) ).
tcf(c_17153,plain,
( ssList(cons(sK4,cons(sK4,sK3)))
| ~ ssList(cons(sK4,nil))
| ~ ssList(cons(sK4,sK3)) ),
inference(superposition,[status(thm)],[c_4466,c_80]) ).
tcf(c_17156,plain,
! [X0: $i] :
( memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK4,nil))
| ~ ssList(cons(sK4,sK3))
| ~ memberP(cons(sK4,sK3),X0) ),
inference(superposition,[status(thm)],[c_4466,c_98]) ).
tcf(c_17159,plain,
( ssList(cons(sK4,cons(sK4,sK3)))
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17153,c_4464]) ).
tcf(c_17166,plain,
! [X0: $i] :
( memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK4,nil))
| ~ memberP(cons(sK4,sK3),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17156,c_4464]) ).
tcf(c_17363,plain,
ssList(cons(sK4,cons(sK4,sK3))),
inference(global_subsumption_just,[status(thm)],[c_17159,c_51,c_85,c_3643,c_17159]) ).
tcf(c_22748,plain,
! [X0: $i] :
( neq(sK2,X0)
| ( X0 = sK2 )
| ~ ssList(sK2)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_22749,plain,
( neq(sK2,nil)
| ( nil = sK2 )
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_22748]) ).
tcf(c_22754,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK2 )
| ( sK2 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1891]) ).
tcf(c_22755,plain,
( ( nil = sK2 )
| ( nil != nil )
| ( sK2 != nil ) ),
inference(instantiation,[status(thm)],[c_22754]) ).
tcf(c_27988,plain,
! [X0: $i,X1: $i] :
( ( cons(X0,X1) = nil )
| ( hd(cons(X0,X1)) = sK9(cons(X0,X1)) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_71,c_90]) ).
tcf(c_28023,plain,
! [X0: $i] :
( ( hd(cons(sK4,X0)) = sK4 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_51,c_91]) ).
tcf(c_28248,plain,
hd(cons(sK4,nil)) = sK4,
inference(superposition,[status(thm)],[c_85,c_28023]) ).
tcf(c_32988,plain,
! [X0: $i,X1: $i] :
( memberP(X1,sK9(cons(sK4,X0)))
| ~ memberP(sK3,sK4)
| ( X1 != sK3 )
| ( sK9(cons(sK4,X0)) != sK4 ) ),
inference(instantiation,[status(thm)],[c_3992]) ).
tcf(c_32989,plain,
( memberP(nil,sK9(cons(sK4,nil)))
| ~ memberP(sK3,sK4)
| ( nil != sK3 )
| ( sK9(cons(sK4,nil)) != sK4 ) ),
inference(instantiation,[status(thm)],[c_32988]) ).
tcf(c_39413,plain,
! [X0: $i] :
( memberP(app(cons(sK4,cons(sK4,sK3)),sK3),X0)
| ~ ssItem(sK4)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK3))
| ~ memberP(app(cons(sK4,sK3),sK3),X0) ),
inference(superposition,[status(thm)],[c_7192,c_95]) ).
tcf(c_39429,plain,
! [X0: $i] :
( memberP(app(cons(sK4,cons(sK4,sK3)),sK3),X0)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK3))
| ~ memberP(app(cons(sK4,sK3),sK3),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39413,c_51]) ).
tcf(c_39909,plain,
! [X0: $i,X1: $i] :
( memberP(X1,sK9(cons(sK4,X0)))
| ~ memberP(sK2,sK4)
| ( X1 != sK2 )
| ( sK9(cons(sK4,X0)) != sK4 ) ),
inference(instantiation,[status(thm)],[c_9421]) ).
tcf(c_39910,plain,
( memberP(nil,sK9(cons(sK4,nil)))
| ~ memberP(sK2,sK4)
| ( nil != sK2 )
| ( sK9(cons(sK4,nil)) != sK4 ) ),
inference(instantiation,[status(thm)],[c_39909]) ).
tcf(c_40486,plain,
! [X0: $i] :
( memberP(sK3,X0)
| memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssList(sK3)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK3))
| ~ ssList(cons(sK4,cons(sK4,sK3)))
| ~ memberP(app(cons(sK4,sK3),sK3),X0) ),
inference(superposition,[status(thm)],[c_39429,c_99]) ).
tcf(c_40487,plain,
! [X0: $i] :
( memberP(sK3,X0)
| memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK3))
| ~ memberP(app(cons(sK4,sK3),sK3),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40486,c_57,c_17363]) ).
tcf(c_40500,plain,
! [X0: $i] :
( ~ memberP(app(cons(sK4,sK3),sK3),X0)
| ~ ssList(app(cons(sK4,sK3),sK3))
| ~ ssItem(X0)
| memberP(cons(sK4,cons(sK4,sK3)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_40487,c_51,c_85,c_3643,c_4901,c_17166,c_40487]) ).
tcf(c_40501,plain,
! [X0: $i] :
( memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK3))
| ~ memberP(app(cons(sK4,sK3),sK3),X0) ),
inference(renaming,[status(thm)],[c_40500]) ).
tcf(c_40512,plain,
! [X0: $i] :
( memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssList(sK3)
| ~ ssItem(X0)
| ~ memberP(sK3,X0)
| ~ ssList(cons(sK4,sK3))
| ~ ssList(app(cons(sK4,sK3),sK3)) ),
inference(superposition,[status(thm)],[c_98,c_40501]) ).
tcf(c_40520,plain,
! [X0: $i] :
( memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ memberP(sK3,X0)
| ~ ssList(app(cons(sK4,sK3),sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40512,c_57,c_4464]) ).
tcf(c_43318,plain,
! [X0: $i,X1: $i,X2: $i] :
( neq(X0,X1)
| ~ neq(sK2,X2)
| ( X1 != X2 )
| ( X0 != sK2 ) ),
inference(instantiation,[status(thm)],[c_1894]) ).
tcf(c_43319,plain,
( neq(nil,nil)
| ~ neq(sK2,nil)
| ( nil != nil )
| ( nil != sK2 ) ),
inference(instantiation,[status(thm)],[c_43318]) ).
tcf(c_44249,plain,
! [X0: $i] :
( memberP(app(cons(sK4,cons(sK4,sK3)),sK2),X0)
| ~ ssItem(sK4)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ memberP(app(cons(sK4,sK3),sK2),X0) ),
inference(superposition,[status(thm)],[c_7925,c_95]) ).
tcf(c_44265,plain,
! [X0: $i] :
( memberP(app(cons(sK4,cons(sK4,sK3)),sK2),X0)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ memberP(app(cons(sK4,sK3),sK2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44249,c_51]) ).
tcf(c_45490,plain,
! [X0: $i] :
( memberP(sK2,X0)
| memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssList(sK2)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ ssList(cons(sK4,cons(sK4,sK3)))
| ~ memberP(app(cons(sK4,sK3),sK2),X0) ),
inference(superposition,[status(thm)],[c_44265,c_99]) ).
tcf(c_45491,plain,
! [X0: $i] :
( memberP(sK2,X0)
| memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ memberP(app(cons(sK4,sK3),sK2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45490,c_58,c_17363]) ).
tcf(c_64378,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( hd(cons(X0,X1)) = sK9(cons(X0,X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_27988,c_64,c_3403]) ).
tcf(c_64379,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X0,X1)) = sK9(cons(X0,X1)) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(renaming,[status(thm)],[c_64378]) ).
tcf(c_64387,plain,
! [X0: $i] :
( ( hd(cons(sK4,X0)) = sK9(cons(sK4,X0)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_51,c_64379]) ).
tcf(c_67035,plain,
hd(cons(sK4,nil)) = sK9(cons(sK4,nil)),
inference(superposition,[status(thm)],[c_85,c_64387]) ).
tcf(c_67048,plain,
sK9(cons(sK4,nil)) = sK4,
inference(light_normalisation,[status(thm)],[c_67035,c_28248]) ).
tcf(c_135444,negated_conjecture,
neq(sK2,nil),
inference(global_subsumption_just,[status(thm)],[c_53,c_58,c_57,c_51,c_85,c_49,c_53,c_3643,c_3649,c_4294,c_5040,c_9462,c_22749,c_32989,c_39910,c_67048]) ).
tcf(c_135453,plain,
app(tl(sK2),cons(hd(sK2),nil)) = sK3,
inference(global_subsumption_just,[status(thm)],[c_336,c_58,c_57,c_51,c_85,c_49,c_53,c_111,c_127,c_3357,c_3643,c_3649,c_4294,c_5040,c_9462,c_22749,c_22755,c_32989,c_39910,c_43319,c_67048]) ).
tcf(c_135661,plain,
( ( sK2 = nil )
| ( hd(sK2) = sK9(sK2) ) ),
inference(superposition,[status(thm)],[c_58,c_90]) ).
tcf(c_135693,plain,
hd(sK2) = sK9(sK2),
inference(global_subsumption_just,[status(thm)],[c_135661,c_58,c_57,c_51,c_85,c_49,c_53,c_111,c_127,c_3401,c_3643,c_3649,c_4294,c_5040,c_9462,c_22749,c_22755,c_32989,c_39910,c_43319,c_67048]) ).
tcf(c_135695,plain,
( ssItem(hd(sK2))
| ( sK2 = nil )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_135693,c_89]) ).
tcf(c_135696,plain,
( ssItem(hd(sK2))
| ( sK2 = nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_135695,c_58]) ).
tcf(c_135699,plain,
ssItem(hd(sK2)),
inference(global_subsumption_just,[status(thm)],[c_135696,c_58,c_57,c_51,c_85,c_49,c_53,c_111,c_127,c_3527,c_3643,c_3649,c_4294,c_5040,c_9462,c_22749,c_22755,c_32989,c_39910,c_43319,c_67048]) ).
tcf(c_135746,plain,
( ( sK2 = nil )
| ( tl(sK2) = sK12(sK2) ) ),
inference(superposition,[status(thm)],[c_58,c_106]) ).
tcf(c_135905,plain,
tl(sK2) = sK12(sK2),
inference(global_subsumption_just,[status(thm)],[c_135746,c_85,c_111,c_127,c_3473,c_22755,c_43319,c_135444]) ).
tcf(c_135907,plain,
( ssList(tl(sK2))
| ( sK2 = nil )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_135905,c_105]) ).
tcf(c_135908,plain,
( ssList(tl(sK2))
| ( sK2 = nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_135907,c_58]) ).
tcf(c_135911,plain,
ssList(tl(sK2)),
inference(global_subsumption_just,[status(thm)],[c_135908,c_85,c_111,c_127,c_3614,c_22755,c_43319,c_135444]) ).
tcf(c_136105,plain,
( ( sK2 = nil )
| ( cons(hd(sK2),tl(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_58,c_87]) ).
tcf(c_136165,plain,
! [X0: $i] :
( ( app(cons(sK4,nil),X0) = cons(sK4,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_51,c_62]) ).
tcf(c_136166,plain,
! [X0: $i] :
( ( app(cons(hd(sK2),nil),X0) = cons(hd(sK2),X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_135699,c_62]) ).
tcf(c_136239,plain,
cons(hd(sK2),tl(sK2)) = sK2,
inference(global_subsumption_just,[status(thm)],[c_136105,c_58,c_57,c_51,c_85,c_49,c_53,c_111,c_127,c_3643,c_3649,c_4067,c_4294,c_5040,c_9462,c_22749,c_22755,c_32989,c_39910,c_43319,c_67048]) ).
tcf(c_136256,plain,
app(cons(sK4,nil),sK3) = cons(sK4,sK3),
inference(superposition,[status(thm)],[c_57,c_136165]) ).
tcf(c_136297,plain,
( ssList(cons(sK4,sK3))
| ~ ssList(sK3)
| ~ ssList(cons(sK4,nil)) ),
inference(superposition,[status(thm)],[c_136256,c_80]) ).
tcf(c_136298,plain,
( ssList(cons(sK4,sK3))
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_136297,c_57]) ).
tcf(c_136303,plain,
ssList(cons(sK4,sK3)),
inference(global_subsumption_just,[status(thm)],[c_136298,c_51,c_85,c_3643,c_4407]) ).
tcf(c_136305,plain,
app(cons(sK4,nil),cons(sK4,sK3)) = cons(sK4,cons(sK4,sK3)),
inference(superposition,[status(thm)],[c_136303,c_136165]) ).
tcf(c_136791,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ ssList(tl(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ memberP(cons(hd(sK2),nil),X0) ),
inference(superposition,[status(thm)],[c_135453,c_98]) ).
tcf(c_136814,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ ssList(cons(hd(sK2),nil))
| ~ memberP(cons(hd(sK2),nil),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_136791,c_135911]) ).
tcf(c_136945,plain,
! [X0: $i,X1: $i] :
( ( cons(sK4,app(X0,X1)) = app(cons(sK4,X0),X1) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_51,c_63]) ).
tcf(c_137142,plain,
! [X0: $i] :
( ( cons(sK4,app(X0,sK2)) = app(cons(sK4,X0),sK2) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_58,c_136945]) ).
tcf(c_137281,plain,
! [X0: $i,X1: $i] :
( ( app(app(sK3,X0),X1) = app(sK3,app(X0,X1)) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_57,c_76]) ).
tcf(c_139258,plain,
cons(sK4,app(cons(sK4,sK3),sK2)) = app(cons(sK4,cons(sK4,sK3)),sK2),
inference(superposition,[status(thm)],[c_136303,c_137142]) ).
tcf(c_140454,plain,
! [X0: $i] :
( ( app(app(sK3,X0),sK2) = app(sK3,app(X0,sK2)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_58,c_137281]) ).
tcf(c_141418,plain,
app(app(sK3,tl(sK2)),sK2) = app(sK3,app(tl(sK2),sK2)),
inference(superposition,[status(thm)],[c_135911,c_140454]) ).
tcf(c_144936,plain,
( ssList(cons(sK4,cons(sK4,sK3)))
| ~ ssList(cons(sK4,nil))
| ~ ssList(cons(sK4,sK3)) ),
inference(superposition,[status(thm)],[c_136305,c_80]) ).
tcf(c_144942,plain,
( ssList(cons(sK4,cons(sK4,sK3)))
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_144936,c_136303]) ).
tcf(c_145004,plain,
ssList(cons(sK4,cons(sK4,sK3))),
inference(global_subsumption_just,[status(thm)],[c_144942,c_51,c_85,c_3643,c_17159]) ).
tcf(c_161837,plain,
app(cons(hd(sK2),nil),tl(sK2)) = cons(hd(sK2),tl(sK2)),
inference(superposition,[status(thm)],[c_135911,c_136166]) ).
tcf(c_161873,plain,
app(cons(hd(sK2),nil),tl(sK2)) = sK2,
inference(light_normalisation,[status(thm)],[c_161837,c_136239]) ).
tcf(c_162626,plain,
! [X0: $i] :
( memberP(tl(sK2),X0)
| memberP(cons(hd(sK2),nil),X0)
| ~ ssItem(X0)
| ~ ssList(tl(sK2))
| ~ memberP(sK2,X0)
| ~ ssList(cons(hd(sK2),nil)) ),
inference(superposition,[status(thm)],[c_161873,c_99]) ).
tcf(c_162631,plain,
! [X0: $i] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ ssList(tl(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ memberP(cons(hd(sK2),nil),X0) ),
inference(superposition,[status(thm)],[c_161873,c_97]) ).
tcf(c_162635,plain,
! [X0: $i] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ ssList(cons(hd(sK2),nil))
| ~ memberP(cons(hd(sK2),nil),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162631,c_135911]) ).
tcf(c_162640,plain,
! [X0: $i] :
( memberP(tl(sK2),X0)
| memberP(cons(hd(sK2),nil),X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(cons(hd(sK2),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162626,c_135911]) ).
tcf(c_170616,plain,
( ssList(app(sK3,sK3))
| ~ ssList(sK3) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_189050,plain,
! [X0: $i] :
( ssList(cons(hd(sK2),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sK2)) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_189051,plain,
( ssList(cons(hd(sK2),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sK2)) ),
inference(instantiation,[status(thm)],[c_189050]) ).
tcf(c_190919,plain,
! [X0: $i] :
( memberP(app(cons(sK4,cons(sK4,sK3)),sK2),X0)
| ~ ssItem(sK4)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ memberP(app(cons(sK4,sK3),sK2),X0) ),
inference(superposition,[status(thm)],[c_139258,c_95]) ).
tcf(c_190935,plain,
! [X0: $i] :
( memberP(app(cons(sK4,cons(sK4,sK3)),sK2),X0)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ memberP(app(cons(sK4,sK3),sK2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_190919,c_51]) ).
tcf(c_192730,plain,
! [X0: $i] :
( memberP(sK2,X0)
| memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssList(sK2)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ ssList(cons(sK4,cons(sK4,sK3)))
| ~ memberP(app(cons(sK4,sK3),sK2),X0) ),
inference(superposition,[status(thm)],[c_190935,c_99]) ).
tcf(c_192731,plain,
! [X0: $i] :
( memberP(sK2,X0)
| memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ memberP(app(cons(sK4,sK3),sK2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192730,c_58,c_145004]) ).
tcf(c_192742,plain,
! [X0: $i] :
( ~ memberP(app(cons(sK4,sK3),sK2),X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ ssItem(X0)
| memberP(cons(sK4,cons(sK4,sK3)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_192731,c_58,c_57,c_51,c_85,c_49,c_53,c_111,c_127,c_3527,c_3614,c_3643,c_3649,c_4294,c_4823,c_5040,c_7236,c_9462,c_22749,c_22755,c_32989,c_39910,c_40520,c_43319,c_45491,c_67048,c_136814,c_162640,c_170616,c_189051]) ).
tcf(c_192743,plain,
! [X0: $i] :
( memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ ssList(app(cons(sK4,sK3),sK2))
| ~ memberP(app(cons(sK4,sK3),sK2),X0) ),
inference(renaming,[status(thm)],[c_192742]) ).
tcf(c_192754,plain,
! [X0: $i] :
( memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssList(sK2)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(cons(sK4,sK3))
| ~ ssList(app(cons(sK4,sK3),sK2)) ),
inference(superposition,[status(thm)],[c_98,c_192743]) ).
tcf(c_192766,plain,
! [X0: $i] :
( memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(app(cons(sK4,sK3),sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192754,c_58,c_136303]) ).
tcf(c_194920,plain,
! [X0: $i] :
( memberP(cons(sK4,cons(sK4,sK3)),X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_192766,c_58,c_57,c_51,c_85,c_49,c_53,c_111,c_127,c_3527,c_3614,c_3643,c_3649,c_4294,c_4823,c_5040,c_7236,c_9462,c_22749,c_22755,c_32989,c_39910,c_40520,c_43319,c_67048,c_136814,c_162640,c_170616,c_189051]) ).
tcf(c_194930,plain,
! [X0: $i] :
( memberP(cons(sK4,sK3),X0)
| ( X0 = sK4 )
| ~ ssItem(sK4)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(cons(sK4,sK3)) ),
inference(superposition,[status(thm)],[c_194920,c_96]) ).
tcf(c_194936,plain,
! [X0: $i] :
( memberP(cons(sK4,sK3),X0)
| ( X0 = sK4 )
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_194930,c_51,c_136303]) ).
tcf(c_194948,plain,
! [X0: $i] :
( memberP(cons(sK4,sK3),X0)
| ~ memberP(sK2,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_194936,c_58,c_57,c_51,c_85,c_49,c_53,c_111,c_127,c_3527,c_3614,c_3643,c_3649,c_4294,c_4823,c_5040,c_5720,c_9462,c_22749,c_22755,c_32989,c_39910,c_43319,c_67048,c_136814,c_162640,c_189051]) ).
tcf(c_194949,plain,
! [X0: $i] :
( memberP(cons(sK4,sK3),X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(renaming,[status(thm)],[c_194948]) ).
tcf(c_194964,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ( X0 = sK4 )
| ~ ssList(sK3)
| ~ ssItem(sK4)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_194949,c_96]) ).
tcf(c_194972,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ( X0 = sK4 )
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_194964,c_57,c_51]) ).
tcf(c_195024,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ memberP(sK2,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_194972,c_58,c_57,c_51,c_85,c_49,c_53,c_111,c_127,c_3527,c_3614,c_3643,c_3649,c_4294,c_4823,c_5040,c_9462,c_22749,c_22755,c_32989,c_39910,c_43319,c_67048,c_136814,c_162640,c_189051]) ).
tcf(c_195025,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(renaming,[status(thm)],[c_195024]) ).
tcf(c_225653,plain,
! [X0: $i] :
( memberP(sK2,X0)
| memberP(app(sK3,tl(sK2)),X0)
| ~ ssList(sK2)
| ~ ssItem(X0)
| ~ ssList(app(sK3,tl(sK2)))
| ~ memberP(app(sK3,app(tl(sK2),sK2)),X0) ),
inference(superposition,[status(thm)],[c_141418,c_99]) ).
tcf(c_225710,plain,
! [X0: $i] :
( memberP(sK2,X0)
| memberP(app(sK3,tl(sK2)),X0)
| ~ ssItem(X0)
| ~ ssList(app(sK3,tl(sK2)))
| ~ memberP(app(sK3,app(tl(sK2),sK2)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_225653,c_58]) ).
tcf(c_227203,plain,
! [X0: $i] :
( memberP(sK2,X0)
| memberP(app(sK3,tl(sK2)),X0)
| ~ ssList(sK3)
| ~ ssItem(X0)
| ~ memberP(sK3,X0)
| ~ ssList(app(sK3,tl(sK2)))
| ~ ssList(app(tl(sK2),sK2)) ),
inference(superposition,[status(thm)],[c_97,c_225710]) ).
tcf(c_227207,plain,
! [X0: $i] :
( memberP(sK2,X0)
| memberP(app(sK3,tl(sK2)),X0)
| ~ ssItem(X0)
| ~ memberP(sK3,X0)
| ~ ssList(app(sK3,tl(sK2)))
| ~ ssList(app(tl(sK2),sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_227203,c_57]) ).
tcf(c_227249,plain,
! [X0: $i] :
( memberP(sK2,X0)
| ~ memberP(sK3,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_227207,c_85,c_111,c_127,c_3527,c_3614,c_4760,c_5593,c_22755,c_43319,c_135444,c_162635,c_189051]) ).
tcf(c_227250,plain,
! [X0: $i] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(sK3,X0) ),
inference(renaming,[status(thm)],[c_227249]) ).
tcf(c_227262,plain,
( memberP(sK2,sK4)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_49,c_227250]) ).
tcf(c_227267,plain,
memberP(sK2,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_227262,c_51]) ).
tcf(c_227408,plain,
( memberP(sK3,sK4)
| ~ ssItem(sK4) ),
inference(superposition,[status(thm)],[c_227267,c_195025]) ).
tcf(c_227409,plain,
memberP(sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_227408,c_51]) ).
tcf(c_227410,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_227409,c_227267,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC376+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 17:56:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 66.55/17.50 % SZS status Started for theBenchmark.p
% 66.55/17.50 % SZS status Theorem for theBenchmark.p
% 66.55/17.50
% 66.55/17.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 66.55/17.50
% 66.55/17.50 % ------ iProver source info
% 66.55/17.50
% 66.55/17.50 % git: date: 2026-07-19 20:42:38 +0200
% 66.55/17.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 66.55/17.50 % git: non_committed_changes: false
% 66.55/17.50
% 66.55/17.50 % ------ Parsing...
% 66.55/17.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 66.55/17.50
% 66.55/17.50 % ------ 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 %
% 66.55/17.50
% 66.55/17.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 66.55/17.50
% 66.55/17.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 66.55/17.50 % ------ Proving...
% 66.55/17.50 % ------ Problem Properties
% 66.55/17.50
% 66.55/17.50 %
% 66.55/17.50 % clauses 58
% 66.55/17.50 % conjectures 7
% 66.55/17.50 % EPR 16
% 66.55/17.50 % Horn 40
% 66.55/17.50 % unary 8
% 66.55/17.50 % binary 9
% 66.55/17.50 % lits 191
% 66.55/17.50 % lits eq 53
% 66.55/17.50 % fd_pure 0
% 66.55/17.50 % fd_pseudo 0
% 66.55/17.50 % fd_cond 12
% 66.55/17.50 % fd_pseudo_cond 8
% 66.55/17.50 % AC symbols 0
% 66.55/17.50
% 66.55/17.50 % ------ Schedule dynamic 5 is on
% 66.55/17.50
% 66.55/17.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 66.55/17.50
% 66.55/17.50
% 66.55/17.50 % ------
% 66.55/17.50 % Current options:
% 66.55/17.50 % ------
% 66.55/17.50
% 66.55/17.50
% 66.55/17.50 %
% 66.55/17.50
% 66.55/17.50 % ------ Proving...
% 66.55/17.50 % Proof_search_loop: time out after: 4398 full_loop iterations
% 66.55/17.50
% 66.55/17.50 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 66.55/17.50
% 66.55/17.50
% 66.55/17.50 % ------
% 66.55/17.50 % Current options:
% 66.55/17.50 % ------
% 66.55/17.50
% 66.55/17.50
% 66.55/17.50 %
% 66.55/17.50
% 66.55/17.50 % ------ Proving...
% 66.55/17.50 %
% 66.55/17.50
% 66.55/17.50 % SZS status Theorem for theBenchmark.p
% 66.55/17.50
% 66.55/17.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 66.55/17.50
% 66.55/17.50
%------------------------------------------------------------------------------