%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC377+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 : n003.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 03:09:32 PM UTC 2026
% Result : Theorem 7.17s 3.46s
% Output : CNFRefutation 7.17s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f544ERROR: Could not build tree for root c_21038ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X2 ) ) ) )
| ( 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/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X2 ) ) ) )
| ( 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(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f146,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(f147,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(f148,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f196,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != app(X1,X0)
| X2 = X0 ) ) ),
inference(ennf_transformation,[],[f80]) ).
fof(f197,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != app(X1,X0)
| X2 = X0 ) ) ),
inference(flattening,[],[f196]) ).
fof(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f199,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(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2 ) ) )
& ( 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(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2 ) ) )
& ( 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,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f277,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,[],[f146]) ).
fof(f278,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,[],[f277]) ).
fof(f279,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,[],[f147]) ).
fof(f280,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,[],[f279]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ~ neq(sK56,nil)
| ( ssItem(sK58)
& ssList(sK59)
& sK56 = app(sK59,cons(sK58,nil))
& sK55 = app(cons(sK58,nil),sK59) ) )
& ( nil != sK56
| nil = sK55 )
& ssItem(sK57)
& ( ~ memberP(sK53,sK57)
| ~ memberP(sK54,sK57) )
& ( memberP(sK53,sK57)
| memberP(sK54,sK57) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59)],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f413,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f416,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f280]) ).
fof(f419,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f476,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f197]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f478,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| ssItem(sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( ~ neq(sK56,nil)
| ssList(sK59) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( ~ neq(sK56,nil)
| sK56 = app(sK59,cons(sK58,nil)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( ~ neq(sK56,nil)
| sK55 = app(cons(sK58,nil),sK59) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( ~ memberP(sK53,sK57)
| ~ memberP(sK54,sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( memberP(sK53,sK57)
| memberP(sK54,sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
( memberP(sK55,sK57)
| memberP(sK56,sK57) ),
inference(definition_unfolding,[],[f507,f509,f508]) ).
fof(f511,plain,
( ~ memberP(sK55,sK57)
| ~ memberP(sK56,sK57) ),
inference(definition_unfolding,[],[f506,f509,f508]) ).
fof(f512,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f509]) ).
fof(f513,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f508]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f415]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f414]) ).
tcf(c_167,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,[],[f413]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f544]) ).
tcf(c_170,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,[],[f416]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X0,X2) ) ),
inference(cnf_transformation,[],[f476]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f477]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(X0,X1),X2) = app(X0,app(X1,X2)) )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f478]) ).
tcf(c_246,negated_conjecture,
( memberP(sK55,sK57)
| memberP(sK56,sK57) ),
inference(cnf_transformation,[],[f510]) ).
tcf(c_247,negated_conjecture,
( ~ memberP(sK55,sK57)
| ~ memberP(sK56,sK57) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_248,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f505]) ).
tcf(c_249,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_250,negated_conjecture,
( ( app(cons(sK58,nil),sK59) = sK55 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_251,negated_conjecture,
( ( app(sK59,cons(sK58,nil)) = sK56 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_252,negated_conjecture,
( ssList(sK59)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_253,negated_conjecture,
( ssItem(sK58)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_256,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f512]) ).
tcf(c_257,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f513]) ).
tcf(c_419,plain,
( ( nil = sK56 )
| ( app(cons(sK58,nil),sK59) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_250]) ).
tcf(c_420,plain,
( ( nil = sK56 )
| ( app(sK59,cons(sK58,nil)) = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_251]) ).
tcf(c_421,plain,
( ssList(sK59)
| ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_252]) ).
tcf(c_422,plain,
( ssItem(sK58)
| ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_253]) ).
tcf(c_443,plain,
! [X0: $i] :
( ( app(cons(sK57,nil),X0) = cons(sK57,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_248,c_227]) ).
tcf(c_753,plain,
( ssItem(sK58)
| ( nil = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_422,c_256,c_141,c_422]) ).
tcf(c_774,plain,
( ssList(sK59)
| ( nil = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_421,c_256,c_141,c_421]) ).
tcf(c_832,plain,
( ( nil = sK56 )
| ( app(cons(sK58,nil),sK59) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_250]) ).
tcf(c_833,plain,
( ( nil = sK56 )
| ( app(sK59,cons(sK58,nil)) = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_251]) ).
tcf(c_835,plain,
( ssItem(sK58)
| ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_253]) ).
tcf(c_836,plain,
( ( nil = sK56 )
| ( app(sK59,cons(sK58,nil)) = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_420,c_256,c_141,c_420]) ).
tcf(c_845,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_836,c_167]) ).
tcf(c_851,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK59,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_836,c_165]) ).
tcf(c_852,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(superposition,[status(thm)],[c_836,c_166]) ).
tcf(c_872,plain,
( ( nil = sK56 )
| ( app(cons(sK58,nil),sK59) = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_419,c_256,c_141,c_419]) ).
tcf(c_880,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_872,c_167]) ).
tcf(c_886,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(superposition,[status(thm)],[c_872,c_165]) ).
tcf(c_887,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK59,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_872,c_166]) ).
tcf(c_915,plain,
( ( nil = sK56 )
| ( app(cons(sK57,nil),sK59) = cons(sK57,sK59) ) ),
inference(superposition,[status(thm)],[c_774,c_443]) ).
tcf(c_916,plain,
app(cons(sK57,nil),sK56) = cons(sK57,sK56),
inference(superposition,[status(thm)],[c_256,c_443]) ).
tcf(c_917,plain,
app(cons(sK57,nil),sK55) = cons(sK57,sK55),
inference(superposition,[status(thm)],[c_257,c_443]) ).
tcf(c_975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(app(X2,X3),cons(X0,X1)) = app(X2,app(X3,cons(X0,X1))) )
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_140,c_228]) ).
tcf(c_1422,plain,
( ssItem(sK58)
| ( nil = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_835,c_753]) ).
tcf(c_1498,plain,
( ( nil = sK56 )
| ( app(sK59,cons(sK58,nil)) = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_833,c_256,c_141,c_420]) ).
tcf(c_1507,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1498,c_167]) ).
tcf(c_1513,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK59,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1498,c_165]) ).
tcf(c_1514,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(superposition,[status(thm)],[c_1498,c_166]) ).
tcf(c_1558,plain,
( ( nil = sK56 )
| ( app(cons(sK58,nil),sK59) = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_832,c_256,c_141,c_419]) ).
tcf(c_1566,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1558,c_167]) ).
tcf(c_1572,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(superposition,[status(thm)],[c_1558,c_165]) ).
tcf(c_1573,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK59,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1558,c_166]) ).
tcf(c_1797,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK59,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_851,c_256,c_141,c_421,c_851]) ).
tcf(c_1798,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK59,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_1797]) ).
tcf(c_1810,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(superposition,[status(thm)],[c_140,c_1798]) ).
tcf(c_1833,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( nil = sK56 )
| ( app(app(X1,X2),cons(sK58,X0)) = app(X1,app(X2,cons(sK58,X0))) )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_1422,c_975]) ).
tcf(c_1834,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ memberP(cons(sK58,nil),X0)
| ~ ssList(cons(sK58,nil))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_852,c_256,c_141,c_421,c_852]) ).
tcf(c_1835,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(renaming,[status(thm)],[c_1834]) ).
tcf(c_1849,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK56,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_845,c_256,c_141,c_421,c_845]) ).
tcf(c_1850,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_1849]) ).
tcf(c_1864,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(nil,X0)
| ( nil = sK56 )
| ( X0 = sK58 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1850,c_170]) ).
tcf(c_1922,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK59,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_887,c_256,c_141,c_421,c_887]) ).
tcf(c_1923,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK59,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_1922]) ).
tcf(c_1935,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(superposition,[status(thm)],[c_140,c_1923]) ).
tcf(c_1947,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ memberP(cons(sK58,nil),X0)
| ~ ssList(cons(sK58,nil))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_886,c_256,c_141,c_421,c_886]) ).
tcf(c_1948,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(renaming,[status(thm)],[c_1947]) ).
tcf(c_1962,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1850,c_1948]) ).
tcf(c_1964,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK55,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_880,c_256,c_141,c_421,c_880]) ).
tcf(c_1965,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_1964]) ).
tcf(c_1979,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(nil,X0)
| ( nil = sK56 )
| ( X0 = sK58 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1965,c_170]) ).
tcf(c_1981,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_1965,c_1835]) ).
tcf(c_2032,plain,
! [X0: $i] :
( ( X0 = sK55 )
| ~ ssList(sK55)
| ~ ssList(X0)
| ~ ssList(cons(sK57,nil))
| ( app(cons(sK57,nil),X0) != cons(sK57,sK55) ) ),
inference(superposition,[status(thm)],[c_917,c_226]) ).
tcf(c_2077,plain,
! [X0: $i] :
( memberP(sK56,X0)
| memberP(cons(sK57,nil),X0)
| ~ ssList(sK56)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK57,sK56),X0) ),
inference(superposition,[status(thm)],[c_916,c_167]) ).
tcf(c_3170,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ memberP(sK59,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1513,c_256,c_141,c_422,c_1810]) ).
tcf(c_3171,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(renaming,[status(thm)],[c_3170]) ).
tcf(c_3204,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ memberP(cons(sK58,nil),X0)
| ~ ssList(cons(sK58,nil))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1514,c_1835]) ).
tcf(c_3205,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(renaming,[status(thm)],[c_3204]) ).
tcf(c_3218,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK56,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1507,c_1850]) ).
tcf(c_3219,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_3218]) ).
tcf(c_3307,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ memberP(sK59,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1573,c_256,c_141,c_422,c_1935]) ).
tcf(c_3308,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(renaming,[status(thm)],[c_3307]) ).
tcf(c_3345,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ memberP(cons(sK58,nil),X0)
| ~ ssList(cons(sK58,nil))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1572,c_1948]) ).
tcf(c_3346,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0) ),
inference(renaming,[status(thm)],[c_3345]) ).
tcf(c_3359,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_3219,c_3346]) ).
tcf(c_3377,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK55,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1566,c_1965]) ).
tcf(c_3378,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(cons(sK58,nil),X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_3377]) ).
tcf(c_3393,plain,
! [X0: $i] :
( memberP(sK59,X0)
| memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(superposition,[status(thm)],[c_3378,c_3205]) ).
tcf(c_5026,plain,
! [X0: $i,X1: $i] :
( ( nil = sK56 )
| ( app(app(X1,sK56),cons(sK58,X0)) = app(X1,app(sK56,cons(sK58,X0))) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_256,c_1833]) ).
tcf(c_5111,plain,
! [X0: $i] :
( memberP(sK59,X0)
| ~ ssList(cons(sK58,nil))
| ~ memberP(sK56,X0)
| ~ ssItem(X0)
| ( X0 = sK58 )
| ( nil = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_1864,c_256,c_141,c_171,c_422,c_1864]) ).
tcf(c_5112,plain,
! [X0: $i] :
( memberP(sK59,X0)
| ( nil = sK56 )
| ( X0 = sK58 )
| ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_5111]) ).
tcf(c_5126,plain,
! [X0: $i] :
( memberP(sK59,X0)
| ( nil = sK56 )
| ( X0 = sK58 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK56,X0) ),
inference(superposition,[status(thm)],[c_140,c_5112]) ).
tcf(c_5149,plain,
! [X0: $i] :
( ~ ssList(cons(sK58,nil))
| ~ memberP(sK56,X0)
| ~ ssItem(X0)
| ( nil = sK56 )
| memberP(sK55,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1962,c_1962,c_3308]) ).
tcf(c_5150,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_5149]) ).
tcf(c_5162,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK56,X0) ),
inference(superposition,[status(thm)],[c_140,c_5150]) ).
tcf(c_5164,plain,
! [X0: $i] :
( ~ ssList(cons(sK58,nil))
| ~ memberP(sK55,X0)
| ~ ssItem(X0)
| ( nil = sK56 )
| memberP(sK56,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1981,c_1981,c_3171]) ).
tcf(c_5165,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(cons(sK58,nil)) ),
inference(renaming,[status(thm)],[c_5164]) ).
tcf(c_5177,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_140,c_5165]) ).
tcf(c_5179,plain,
! [X0: $i] :
( memberP(sK59,X0)
| ~ memberP(sK55,X0)
| ~ ssItem(X0)
| ( X0 = sK58 )
| ( nil = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_1979,c_256,c_141,c_422,c_5126,c_5177]) ).
tcf(c_5180,plain,
! [X0: $i] :
( memberP(sK59,X0)
| ( nil = sK56 )
| ( X0 = sK58 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(renaming,[status(thm)],[c_5179]) ).
tcf(c_5192,plain,
( memberP(sK59,sK57)
| memberP(sK56,sK57)
| ( sK57 = sK58 )
| ( nil = sK56 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_246,c_5180]) ).
tcf(c_5279,plain,
! [X0: $i] :
( ( X0 = sK55 )
| ( app(cons(sK57,nil),X0) != cons(sK57,sK55) )
| ~ ssList(cons(sK57,nil))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2032,c_257,c_2032]) ).
tcf(c_5280,plain,
! [X0: $i] :
( ( X0 = sK55 )
| ~ ssList(X0)
| ~ ssList(cons(sK57,nil))
| ( app(cons(sK57,nil),X0) != cons(sK57,sK55) ) ),
inference(renaming,[status(thm)],[c_5279]) ).
tcf(c_5291,plain,
( ( sK55 = sK59 )
| ( nil = sK56 )
| ~ ssList(sK59)
| ~ ssList(cons(sK57,nil))
| ( cons(sK57,sK55) != cons(sK57,sK59) ) ),
inference(superposition,[status(thm)],[c_915,c_5280]) ).
tcf(c_5376,plain,
! [X0: $i] :
( memberP(sK56,X0)
| memberP(cons(sK57,nil),X0)
| ~ memberP(cons(sK57,sK56),X0)
| ~ ssList(cons(sK57,nil))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2077,c_256,c_2077]) ).
tcf(c_5377,plain,
! [X0: $i] :
( memberP(sK56,X0)
| memberP(cons(sK57,nil),X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK57,sK56),X0) ),
inference(renaming,[status(thm)],[c_5376]) ).
tcf(c_5389,plain,
( memberP(sK56,sK57)
| memberP(cons(sK57,nil),sK57)
| ~ ssList(sK56)
| ~ ssItem(sK57)
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_168,c_5377]) ).
tcf(c_9548,plain,
! [X0: $i] :
( ~ memberP(sK56,X0)
| ~ ssItem(X0)
| ( nil = sK56 )
| memberP(sK55,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3359,c_256,c_141,c_422,c_5162]) ).
tcf(c_9549,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK56,X0) ),
inference(renaming,[status(thm)],[c_9548]) ).
tcf(c_9582,plain,
! [X0: $i] :
( ~ memberP(sK55,X0)
| ~ ssItem(X0)
| ( nil = sK56 )
| memberP(sK56,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3393,c_256,c_141,c_422,c_5177]) ).
tcf(c_9583,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(renaming,[status(thm)],[c_9582]) ).
tcf(c_9593,plain,
( memberP(sK56,sK57)
| ( nil = sK56 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_246,c_9583]) ).
tcf(c_18342,plain,
! [X0: $i] :
( memberP(sK55,X0)
| ( nil = sK56 )
| ~ ssItem(X0)
| ~ memberP(sK56,X0) ),
inference(global_subsumption_just,[status(thm)],[c_5162,c_9549]) ).
tcf(c_18365,plain,
( ( nil = sK56 )
| memberP(sK56,sK57) ),
inference(global_subsumption_just,[status(thm)],[c_5192,c_248,c_9593]) ).
tcf(c_18366,plain,
( memberP(sK56,sK57)
| ( nil = sK56 ) ),
inference(renaming,[status(thm)],[c_18365]) ).
tcf(c_18371,plain,
( ( nil = sK56 )
| ~ memberP(sK55,sK57) ),
inference(superposition,[status(thm)],[c_18366,c_247]) ).
tcf(c_18372,plain,
( memberP(sK55,sK57)
| ( nil = sK56 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_18366,c_18342]) ).
tcf(c_18838,plain,
nil = sK56,
inference(global_subsumption_just,[status(thm)],[c_5026,c_248,c_18371,c_18372]) ).
tcf(c_18888,plain,
nil = sK55,
inference(superposition,[status(thm)],[c_18838,c_249]) ).
tcf(c_18889,plain,
( ~ memberP(sK55,sK57)
| ~ memberP(nil,sK57) ),
inference(superposition,[status(thm)],[c_18838,c_247]) ).
tcf(c_19017,plain,
( memberP(sK56,sK57)
| memberP(nil,sK57) ),
inference(demodulation,[status(thm)],[c_246,c_18888]) ).
tcf(c_20913,plain,
nil = sK56,
inference(global_subsumption_just,[status(thm)],[c_5291,c_248,c_18371,c_18372]) ).
tcf(c_21034,plain,
memberP(sK56,sK57),
inference(global_subsumption_just,[status(thm)],[c_5389,c_246,c_19017,c_18889]) ).
tcf(c_21036,plain,
memberP(nil,sK57),
inference(light_normalisation,[status(thm)],[c_21034,c_20913]) ).
tcf(c_21037,plain,
~ ssItem(sK57),
inference(superposition,[status(thm)],[c_21036,c_171]) ).
tcf(c_21038,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_248,c_21037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC377+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 17:57:06 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.44
% 0.14/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.44
% 0.14/0.44 % Detected problem language: tptp
% 0.14/0.46 % Proving...
% 7.17/3.46 % SZS status Started for theBenchmark.p
% 7.17/3.46 % SZS status Theorem for theBenchmark.p
% 7.17/3.46
% 7.17/3.46 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.17/3.46
% 7.17/3.46 % ------ iProver source info
% 7.17/3.46
% 7.17/3.46 % git: date: 2026-07-19 20:42:38 +0200
% 7.17/3.46 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.17/3.46 % git: non_committed_changes: false
% 7.17/3.46
% 7.17/3.46 % ------ Parsing...
% 7.17/3.46 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.17/3.46 % ------ Proving...
% 7.17/3.46 % ------ Problem Properties
% 7.17/3.46
% 7.17/3.46 %
% 7.17/3.46 % clauses 209
% 7.17/3.46 % conjectures 12
% 7.17/3.46 % EPR 74
% 7.17/3.46 % Horn 137
% 7.17/3.46 % unary 17
% 7.17/3.46 % binary 60
% 7.17/3.46 % lits 689
% 7.17/3.46 % lits eq 85
% 7.17/3.46 % fd_pure 0
% 7.17/3.46 % fd_pseudo 0
% 7.17/3.46 % fd_cond 21
% 7.17/3.46 % fd_pseudo_cond 17
% 7.17/3.46 % AC symbols 0
% 7.17/3.46
% 7.17/3.46 % ------ Input Options Time Limit: Unbounded
% 7.17/3.46
% 7.17/3.46
% 7.17/3.46 % ------
% 7.17/3.46 % Current options:
% 7.17/3.46 % ------
% 7.17/3.46
% 7.17/3.46
% 7.17/3.46 %
% 7.17/3.46
% 7.17/3.46 % ------ Proving...
% 7.17/3.46 %
% 7.17/3.46
% 7.17/3.46 % SZS status Theorem for theBenchmark.p
% 7.17/3.46
% 7.17/3.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.17/3.47
% 7.17/3.47
%------------------------------------------------------------------------------