%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC306+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 : n001.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 03:09:14 PM UTC 2026
% Result : Theorem 58.52s 9.89s
% Output : CNFRefutation 58.52s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f548ERROR: Could not build tree for root c_38466ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X9] :
( ssItem(X9)
=> ( ~ memberP(X3,X9)
| cons(X9,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( ~ lt(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0 ) ) ) ) ) )
| 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)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X9] :
( ssItem(X9)
=> ( ~ memberP(X3,X9)
| cons(X9,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( ~ lt(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0 ) ) ) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f99,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
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(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X9] :
( ssItem(X9)
& memberP(X3,X9)
& cons(X9,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& lt(X5,X4)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X0 ) ) ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X9] :
( ssItem(X9)
& memberP(X3,X9)
& cons(X9,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& lt(X5,X4)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X0 ) ) ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f235,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f235]) ).
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)
& ( ( nil = sK55
& nil = sK56 )
| ( ssItem(sK62)
& memberP(sK56,sK62)
& sK55 = cons(sK62,nil) ) )
& ssItem(sK57)
& ssItem(sK58)
& ssList(sK59)
& ssList(sK60)
& ssList(sK61)
& lt(sK58,sK57)
& sK53 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61,sK62]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59),skolemize(X7,sK60),skolemize(X8,sK61),skolemize(X9,sK62)],[f222]) ).
fof(f305,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
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(f396,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
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(f500,plain,
( nil = sK55
| ssItem(sK62) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil = sK56
| ssItem(sK62) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil = sK55
| sK55 = cons(sK62,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( nil = sK56
| sK55 = cons(sK62,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
ssList(sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
ssList(sK61),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
lt(sK58,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
sK53 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61),
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f515,plain,
sK55 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61),
inference(definition_unfolding,[],[f512,f513]) ).
fof(f519,plain,
! [X2,X3,X1] :
( ~ ssList(app(X2,cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(app(X2,cons(X1,X3)),X1) ),
inference(equality_resolution,[],[f305]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f519]) ).
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_148,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f396]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
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_168,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f548]) ).
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_242,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
inference(cnf_transformation,[],[f551]) ).
tcf(c_246,negated_conjecture,
app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61) = sK55,
inference(cnf_transformation,[],[f515]) ).
tcf(c_247,negated_conjecture,
lt(sK58,sK57),
inference(cnf_transformation,[],[f511]) ).
tcf(c_248,negated_conjecture,
ssList(sK61),
inference(cnf_transformation,[],[f510]) ).
tcf(c_249,negated_conjecture,
ssList(sK60),
inference(cnf_transformation,[],[f509]) ).
tcf(c_250,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f508]) ).
tcf(c_251,negated_conjecture,
ssItem(sK58),
inference(cnf_transformation,[],[f507]) ).
tcf(c_252,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f506]) ).
tcf(c_253,negated_conjecture,
( ( nil = sK56 )
| ( cons(sK62,nil) = sK55 ) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_254,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK62,nil) = sK55 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_257,negated_conjecture,
( ssItem(sK62)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_258,negated_conjecture,
( ssItem(sK62)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_7653,negated_conjecture,
( ssItem(sK62)
| ( nil = sK55 ) ),
inference(subtyping,[status(esa)],[c_258]) ).
tcf(c_7654,negated_conjecture,
( ssItem(sK62)
| ( nil = sK56 ) ),
inference(subtyping,[status(esa)],[c_257]) ).
tcf(c_7657,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK62,nil) = sK55 ) ),
inference(subtyping,[status(esa)],[c_254]) ).
tcf(c_7658,negated_conjecture,
( ( nil = sK56 )
| ( cons(sK62,nil) = sK55 ) ),
inference(subtyping,[status(esa)],[c_253]) ).
tcf(c_7659,negated_conjecture,
ssItem(sK57),
inference(subtyping,[status(esa)],[c_252]) ).
tcf(c_7660,negated_conjecture,
ssItem(sK58),
inference(subtyping,[status(esa)],[c_251]) ).
tcf(c_7661,negated_conjecture,
ssList(sK59),
inference(subtyping,[status(esa)],[c_250]) ).
tcf(c_7662,negated_conjecture,
ssList(sK60),
inference(subtyping,[status(esa)],[c_249]) ).
tcf(c_7663,negated_conjecture,
ssList(sK61),
inference(subtyping,[status(esa)],[c_248]) ).
tcf(c_7664,negated_conjecture,
lt(sK58,sK57),
inference(subtyping,[status(esa)],[c_247]) ).
tcf(c_7665,negated_conjecture,
app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61) = sK55,
inference(subtyping,[status(esa)],[c_246]) ).
tcf(c_7671,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( ~ ssItem(X0_iProver_ssItem_1)
| ~ lt(X0_iProver_ssItem_1,X0_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_242]) ).
tcf(c_7726,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(nil,X0_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_171]) ).
tcf(c_7727,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(X0_iProver_sP4_1,X1_iProver_ssItem_1)
| ( X0_iProver_ssItem_1 = X1_iProver_ssItem_1 )
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X1_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(cons(X0_iProver_ssItem_1,X0_iProver_sP4_1),X1_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_170]) ).
tcf(c_7729,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(cons(X0_iProver_ssItem_1,X0_iProver_sP4_1),X0_iProver_ssItem_1)
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_168]) ).
tcf(c_7731,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1] :
( memberP(app(X1_iProver_sP4_1,X0_iProver_sP4_1),X0_iProver_ssItem_1)
| ~ ssList(X1_iProver_sP4_1)
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(X0_iProver_sP4_1,X0_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_166]) ).
tcf(c_7732,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1] :
( memberP(app(X0_iProver_sP4_1,X1_iProver_sP4_1),X0_iProver_ssItem_1)
| ~ ssList(X1_iProver_sP4_1)
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(X0_iProver_sP4_1,X0_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_165]) ).
tcf(c_7744,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X1_iProver_sP4_1: iProver_sP4_1] :
( ssList(app(X0_iProver_sP4_1,X1_iProver_sP4_1))
| ~ ssList(X1_iProver_sP4_1)
| ~ ssList(X0_iProver_sP4_1) ),
inference(subtyping,[status(esa)],[c_153]) ).
tcf(c_7749,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1] :
( ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ( cons(X0_iProver_ssItem_1,X0_iProver_sP4_1) != nil ) ),
inference(subtyping,[status(esa)],[c_148]) ).
tcf(c_7756,plain,
ssList(nil),
inference(subtyping,[status(esa)],[c_141]) ).
tcf(c_7757,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1] :
( ssList(cons(X0_iProver_ssItem_1,X0_iProver_sP4_1))
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_140]) ).
tcf(c_7830,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1] :
( memberP(app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,X1_iProver_sP4_1)),X0_iProver_ssItem_1)
| ~ ssList(X1_iProver_sP4_1)
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,X1_iProver_sP4_1))) ),
inference(subtyping,[status(esa)],[c_54]) ).
tcf(c_18685,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(nil,X0_iProver_ssItem_1)
| ( nil = sK55 )
| ( X0_iProver_ssItem_1 = sK62 )
| ~ ssList(nil)
| ~ ssItem(sK62)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(sK55,X0_iProver_ssItem_1) ),
inference(superposition,[status(thm)],[c_7657,c_7727]) ).
tcf(c_18686,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(nil,X0_iProver_ssItem_1)
| ( nil = sK55 )
| ( X0_iProver_ssItem_1 = sK62 )
| ~ ssItem(sK62)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(sK55,X0_iProver_ssItem_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18685,c_7756]) ).
tcf(c_18712,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssList(sK61)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)))
| ~ memberP(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),X0_iProver_ssItem_1) ),
inference(superposition,[status(thm)],[c_7665,c_7732]) ).
tcf(c_18714,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)))
| ~ memberP(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),X0_iProver_ssItem_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18712,c_7663]) ).
tcf(c_18812,plain,
( ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK62)
| ( nil != sK55 ) ),
inference(superposition,[status(thm)],[c_7658,c_7749]) ).
tcf(c_18814,plain,
( ( nil = sK56 )
| ~ ssItem(sK62)
| ( nil != sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18812,c_7756]) ).
tcf(c_19155,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0_iProver_ssItem_1)
| ~ ssList(app(app(sK59,cons(sK57,nil)),sK60))
| ~ ssList(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil))) ),
inference(superposition,[status(thm)],[c_7731,c_18714]) ).
tcf(c_19156,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ ssList(app(app(sK59,cons(sK57,nil)),sK60))
| ~ memberP(app(app(sK59,cons(sK57,nil)),sK60),X0_iProver_ssItem_1)
| ~ ssList(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil))) ),
inference(superposition,[status(thm)],[c_7732,c_18714]) ).
tcf(c_19827,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0_iProver_ssItem_1)
| ~ ssList(app(app(sK59,cons(sK57,nil)),sK60)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19155,c_7744]) ).
tcf(c_19838,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssList(sK60)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0_iProver_ssItem_1)
| ~ ssList(app(sK59,cons(sK57,nil))) ),
inference(superposition,[status(thm)],[c_7744,c_19827]) ).
tcf(c_19839,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ memberP(cons(sK58,nil),X0_iProver_ssItem_1)
| ~ ssList(app(sK59,cons(sK57,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19838,c_7662]) ).
tcf(c_20187,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( ( nil = sK55 )
| ( X0_iProver_ssItem_1 = sK62 )
| ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(sK55,X0_iProver_ssItem_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18686,c_7726,c_7653]) ).
tcf(c_20245,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ ssList(app(app(sK59,cons(sK57,nil)),sK60))
| ~ memberP(app(app(sK59,cons(sK57,nil)),sK60),X0_iProver_ssItem_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19156,c_7744]) ).
tcf(c_20257,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssList(sK60)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ ssList(app(sK59,cons(sK57,nil)))
| ~ memberP(app(sK59,cons(sK57,nil)),X0_iProver_ssItem_1)
| ~ ssList(app(app(sK59,cons(sK57,nil)),sK60)) ),
inference(superposition,[status(thm)],[c_7732,c_20245]) ).
tcf(c_20260,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ ssList(app(sK59,cons(sK57,nil)))
| ~ memberP(app(sK59,cons(sK57,nil)),X0_iProver_ssItem_1)
| ~ ssList(app(app(sK59,cons(sK57,nil)),sK60)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20257,c_7662]) ).
tcf(c_21111,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssList(sK59)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK58,nil),X0_iProver_ssItem_1) ),
inference(superposition,[status(thm)],[c_7744,c_19839]) ).
tcf(c_21112,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK58,nil),X0_iProver_ssItem_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21111,c_7661]) ).
tcf(c_21514,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssList(sK60)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ ssList(app(sK59,cons(sK57,nil)))
| ~ memberP(app(sK59,cons(sK57,nil)),X0_iProver_ssItem_1) ),
inference(superposition,[status(thm)],[c_7744,c_20260]) ).
tcf(c_21515,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(cons(sK58,nil))
| ~ ssList(app(sK59,cons(sK57,nil)))
| ~ memberP(app(sK59,cons(sK57,nil)),X0_iProver_ssItem_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21514,c_7662]) ).
tcf(c_21661,plain,
( ( nil = sK56 )
| ( nil != sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18814,c_7654]) ).
tcf(c_22267,plain,
( memberP(sK55,sK58)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_7729,c_21112]) ).
tcf(c_22268,plain,
( memberP(sK55,sK58)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22267,c_7756,c_7660]) ).
tcf(c_22672,plain,
( memberP(sK55,sK57)
| ~ ssList(sK59)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(cons(sK58,nil))
| ~ ssList(app(sK59,cons(sK57,nil))) ),
inference(superposition,[status(thm)],[c_7830,c_21515]) ).
tcf(c_22674,plain,
( memberP(sK55,sK57)
| ~ ssList(cons(sK58,nil))
| ~ ssList(app(sK59,cons(sK57,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22672,c_7661,c_7756,c_7659]) ).
tcf(c_23442,plain,
( memberP(sK55,sK58)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_7757,c_22268]) ).
tcf(c_23443,plain,
( memberP(sK55,sK58)
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23442,c_7756,c_7660]) ).
tcf(c_24163,plain,
( memberP(sK55,sK57)
| ~ ssList(sK59)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_7744,c_22674]) ).
tcf(c_24164,plain,
( memberP(sK55,sK57)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24163,c_7661]) ).
tcf(c_25899,plain,
( memberP(sK55,sK58)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_7757,c_23443]) ).
tcf(c_25900,plain,
memberP(sK55,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_25899,c_7756,c_7659]) ).
tcf(c_25932,plain,
( ( sK58 = sK62 )
| ( nil = sK55 )
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_25900,c_20187]) ).
tcf(c_25933,plain,
( ( sK58 = sK62 )
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25932,c_7660]) ).
tcf(c_28214,plain,
( memberP(sK55,sK57)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_7757,c_24164]) ).
tcf(c_28215,plain,
( memberP(sK55,sK57)
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28214,c_7756,c_7660]) ).
tcf(c_28241,plain,
( lt(sK62,sK57)
| ( nil = sK55 ) ),
inference(superposition,[status(thm)],[c_25933,c_7664]) ).
tcf(c_29065,plain,
( memberP(sK55,sK57)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_7757,c_28215]) ).
tcf(c_29066,plain,
memberP(sK55,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_29065,c_7756,c_7659]) ).
tcf(c_29102,plain,
( ( sK57 = sK62 )
| ( nil = sK55 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_29066,c_20187]) ).
tcf(c_29103,plain,
( ( sK57 = sK62 )
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29102,c_7659]) ).
tcf(c_29179,plain,
( lt(sK57,sK57)
| ( nil = sK55 ) ),
inference(superposition,[status(thm)],[c_29103,c_28241]) ).
tcf(c_29379,plain,
( ( nil = sK55 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_29179,c_7671]) ).
tcf(c_29381,plain,
nil = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_29379,c_7659]) ).
tcf(c_30068,plain,
nil = sK56,
inference(superposition,[status(thm)],[c_29381,c_21661]) ).
tcf(c_31379,plain,
sK55 = sK56,
inference(superposition,[status(thm)],[c_29381,c_30068]) ).
tcf(c_31457,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(sK56,X0_iProver_ssItem_1) ),
inference(superposition,[status(thm)],[c_30068,c_7726]) ).
tcf(c_31964,plain,
memberP(sK56,sK58),
inference(superposition,[status(thm)],[c_31379,c_25900]) ).
tcf(c_38465,plain,
~ ssItem(sK58),
inference(superposition,[status(thm)],[c_31964,c_31457]) ).
tcf(c_38466,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_38465,c_7660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC306+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 : n001.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 17:37:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 58.52/9.89 % SZS status Started for theBenchmark.p
% 58.52/9.89 % SZS status Theorem for theBenchmark.p
% 58.52/9.89
% 58.52/9.89 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 58.52/9.89
% 58.52/9.89 % ------ iProver source info
% 58.52/9.89
% 58.52/9.89 % git: date: 2026-07-19 20:42:38 +0200
% 58.52/9.89 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 58.52/9.89 % git: non_committed_changes: false
% 58.52/9.89
% 58.52/9.89 % ------ Parsing...
% 58.52/9.89 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 58.52/9.89
% 58.52/9.89 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 58.52/9.89
% 58.52/9.89 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 58.52/9.89
% 58.52/9.89 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 58.52/9.89 % ------ Proving...
% 58.52/9.89 % ------ Problem Properties
% 58.52/9.89
% 58.52/9.89 %
% 58.52/9.89 % clauses 195
% 58.52/9.89 % conjectures 15
% 58.52/9.89 % EPR 61
% 58.52/9.89 % Horn 121
% 58.52/9.89 % unary 25
% 58.52/9.89 % binary 46
% 58.52/9.89 % lits 639
% 58.52/9.89 % lits eq 87
% 58.52/9.89 % fd_pure 0
% 58.52/9.89 % fd_pseudo 0
% 58.52/9.89 % fd_cond 21
% 58.52/9.89 % fd_pseudo_cond 14
% 58.52/9.89 % AC symbols 0
% 58.52/9.89
% 58.52/9.89 % ------ Input Options Time Limit: Unbounded
% 58.52/9.89
% 58.52/9.89
% 58.52/9.89 % ------
% 58.52/9.89 % Current options:
% 58.52/9.89 % ------
% 58.52/9.89
% 58.52/9.89
% 58.52/9.89 %
% 58.52/9.89
% 58.52/9.89 % ------ Proving...
% 58.52/9.89 %
% 58.52/9.89
% 58.52/9.89 % SZS status Theorem for theBenchmark.p
% 58.52/9.89
% 58.52/9.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 58.52/9.89
% 58.52/9.89
%------------------------------------------------------------------------------