%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC188+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 : n005.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 03:08:35 PM UTC 2026
% Result : Theorem 64.73s 11.13s
% Output : CNFRefutation 64.73s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f549ERROR: Could not build tree for root c_36588ERROR: 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(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 )
& ! [X8] :
( ssItem(X8)
=> ( ? [X9] :
( leq(X9,X8)
& memberP(X3,X9)
& X8 != X9
& ssItem(X9) )
| ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( X4 = X5
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != 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 )
& ! [X8] :
( ssItem(X8)
=> ( ? [X9] :
( leq(X9,X8)
& memberP(X3,X9)
& X8 != X9
& ssItem(X9) )
| ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( X4 = X5
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != 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(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 )
| ? [X8] :
( ssItem(X8)
& ! [X9] :
( ~ leq(X9,X8)
| ~ memberP(X3,X9)
| X8 = X9
| ~ ssItem(X9) )
& memberP(X3,X8)
& cons(X8,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = 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 )
| ? [X8] :
( ssItem(X8)
& ! [X9] :
( ~ leq(X9,X8)
| ~ memberP(X3,X9)
| X8 = X9
| ~ ssItem(X9) )
& memberP(X3,X8)
& cons(X8,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = 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(sK61)
& ! [X9] :
( ~ leq(X9,sK61)
| ~ memberP(sK56,X9)
| sK61 = X9
| ~ ssItem(X9) )
& memberP(sK56,sK61)
& sK55 = cons(sK61,nil) ) )
& ssItem(sK57)
& ssItem(sK58)
& ssList(sK59)
& ssList(sK60)
& sK57 != sK58
& sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61]),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)],[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(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(sK61) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( nil = sK55
| sK55 = cons(sK61,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
ssList(sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
sK57 != sK58,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f514,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f516,plain,
sK55 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(definition_unfolding,[],[f513,f514]) ).
fof(f520,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,[],[f520]) ).
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_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,[],[f549]) ).
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_246,negated_conjecture,
app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60) = sK55,
inference(cnf_transformation,[],[f516]) ).
tcf(c_247,negated_conjecture,
sK57 != sK58,
inference(cnf_transformation,[],[f512]) ).
tcf(c_248,negated_conjecture,
ssList(sK60),
inference(cnf_transformation,[],[f511]) ).
tcf(c_249,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f510]) ).
tcf(c_250,negated_conjecture,
ssItem(sK58),
inference(cnf_transformation,[],[f509]) ).
tcf(c_251,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f508]) ).
tcf(c_253,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK61,nil) = sK55 ) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_259,negated_conjecture,
( ssItem(sK61)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_7712,negated_conjecture,
( ssItem(sK61)
| ( nil = sK55 ) ),
inference(subtyping,[status(esa)],[c_259]) ).
tcf(c_7718,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK61,nil) = sK55 ) ),
inference(subtyping,[status(esa)],[c_253]) ).
tcf(c_7720,negated_conjecture,
ssItem(sK57),
inference(subtyping,[status(esa)],[c_251]) ).
tcf(c_7721,negated_conjecture,
ssItem(sK58),
inference(subtyping,[status(esa)],[c_250]) ).
tcf(c_7722,negated_conjecture,
ssList(sK59),
inference(subtyping,[status(esa)],[c_249]) ).
tcf(c_7723,negated_conjecture,
ssList(sK60),
inference(subtyping,[status(esa)],[c_248]) ).
tcf(c_7724,negated_conjecture,
sK57 != sK58,
inference(subtyping,[status(esa)],[c_247]) ).
tcf(c_7725,negated_conjecture,
app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60) = sK55,
inference(subtyping,[status(esa)],[c_246]) ).
tcf(c_7786,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_7787,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_7789,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_7791,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_7792,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_7804,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_7816,plain,
ssList(nil),
inference(subtyping,[status(esa)],[c_141]) ).
tcf(c_7817,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_7890,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_19092,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(nil,X0_iProver_ssItem_1)
| ( nil = sK55 )
| ( X0_iProver_ssItem_1 = sK61 )
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(sK55,X0_iProver_ssItem_1) ),
inference(superposition,[status(thm)],[c_7718,c_7787]) ).
tcf(c_19093,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(nil,X0_iProver_ssItem_1)
| ( nil = sK55 )
| ( X0_iProver_ssItem_1 = sK61 )
| ~ ssItem(sK61)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(sK55,X0_iProver_ssItem_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19092,c_7816]) ).
tcf(c_19110,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssList(sK60)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)))
| ~ memberP(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),X0_iProver_ssItem_1) ),
inference(superposition,[status(thm)],[c_7725,c_7792]) ).
tcf(c_19112,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( memberP(sK55,X0_iProver_ssItem_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ~ ssList(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)))
| ~ memberP(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),X0_iProver_ssItem_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19110,c_7723]) ).
tcf(c_19526,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)))
| ~ ssList(app(app(sK59,cons(sK57,nil)),cons(sK58,nil))) ),
inference(superposition,[status(thm)],[c_7791,c_19112]) ).
tcf(c_19527,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)),cons(sK58,nil))) ),
inference(superposition,[status(thm)],[c_7792,c_19112]) ).
tcf(c_20278,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_19526,c_7804]) ).
tcf(c_20289,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_7804,c_20278]) ).
tcf(c_20290,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_20289,c_7722]) ).
tcf(c_20297,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_19527,c_7804]) ).
tcf(c_20310,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_7890,c_20297]) ).
tcf(c_20312,plain,
( memberP(sK55,sK57)
| ~ ssList(cons(sK58,nil))
| ~ ssList(app(sK59,cons(sK57,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20310,c_7722,c_7816,c_7720]) ).
tcf(c_20467,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( ( nil = sK55 )
| ( X0_iProver_ssItem_1 = sK61 )
| ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(sK55,X0_iProver_ssItem_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19093,c_7786,c_7712]) ).
tcf(c_21052,plain,
( memberP(sK55,sK58)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_7789,c_20290]) ).
tcf(c_21053,plain,
( memberP(sK55,sK58)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21052,c_7816,c_7721]) ).
tcf(c_21429,plain,
( memberP(sK55,sK57)
| ~ ssList(sK59)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_7804,c_20312]) ).
tcf(c_21430,plain,
( memberP(sK55,sK57)
| ~ ssList(cons(sK58,nil))
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21429,c_7722]) ).
tcf(c_22571,plain,
( memberP(sK55,sK58)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_7817,c_21053]) ).
tcf(c_22572,plain,
( memberP(sK55,sK58)
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22571,c_7816,c_7721]) ).
tcf(c_22576,plain,
( memberP(sK55,sK57)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_7817,c_21430]) ).
tcf(c_22577,plain,
( memberP(sK55,sK57)
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22576,c_7816,c_7721]) ).
tcf(c_23332,plain,
( memberP(sK55,sK58)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_7817,c_22572]) ).
tcf(c_23333,plain,
memberP(sK55,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_23332,c_7816,c_7720]) ).
tcf(c_23357,plain,
( ( sK58 = sK61 )
| ( nil = sK55 )
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_23333,c_20467]) ).
tcf(c_23358,plain,
( ( sK58 = sK61 )
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23357,c_7721]) ).
tcf(c_23743,plain,
( memberP(sK55,sK57)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_7817,c_22577]) ).
tcf(c_23744,plain,
memberP(sK55,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_23743,c_7816,c_7720]) ).
tcf(c_23778,plain,
( ( sK57 = sK61 )
| ( nil = sK55 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_23744,c_20467]) ).
tcf(c_23779,plain,
( ( sK57 = sK61 )
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23778,c_7720]) ).
tcf(c_26173,plain,
( ( nil = sK55 )
| ( sK57 != sK61 ) ),
inference(superposition,[status(thm)],[c_23358,c_7724]) ).
tcf(c_36500,plain,
nil = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_26173,c_23779]) ).
tcf(c_36515,plain,
memberP(nil,sK57),
inference(superposition,[status(thm)],[c_36500,c_23744]) ).
tcf(c_36543,plain,
~ ssItem(sK57),
inference(superposition,[status(thm)],[c_36515,c_7786]) ).
tcf(c_36588,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_36543,c_7720]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC188+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.45 % Computer : n005.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 16:52:19 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.53
% 0.24/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.53
% 0.24/0.53 % Detected problem language: tptp
% 0.24/0.55 % Proving...
% 64.73/11.13 % SZS status Started for theBenchmark.p
% 64.73/11.13 % SZS status Theorem for theBenchmark.p
% 64.73/11.13
% 64.73/11.13 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 64.73/11.13
% 64.73/11.13 % ------ iProver source info
% 64.73/11.13
% 64.73/11.13 % git: date: 2026-07-19 20:42:38 +0200
% 64.73/11.13 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 64.73/11.13 % git: non_committed_changes: false
% 64.73/11.13
% 64.73/11.13 % ------ Parsing...
% 64.73/11.13 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 64.73/11.13
% 64.73/11.13 % ------ 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 %
% 64.73/11.13
% 64.73/11.13 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 64.73/11.13
% 64.73/11.13 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 64.73/11.13 % ------ Proving...
% 64.73/11.13 % ------ Problem Properties
% 64.73/11.13
% 64.73/11.13 %
% 64.73/11.13 % clauses 196
% 64.73/11.13 % conjectures 16
% 64.73/11.13 % EPR 62
% 64.73/11.13 % Horn 120
% 64.73/11.13 % unary 24
% 64.73/11.13 % binary 46
% 64.73/11.13 % lits 648
% 64.73/11.13 % lits eq 92
% 64.73/11.13 % fd_pure 0
% 64.73/11.13 % fd_pseudo 0
% 64.73/11.13 % fd_cond 23
% 64.73/11.13 % fd_pseudo_cond 14
% 64.73/11.13 % AC symbols 0
% 64.73/11.13
% 64.73/11.13 % ------ Input Options Time Limit: Unbounded
% 64.73/11.13
% 64.73/11.13
% 64.73/11.13 % ------
% 64.73/11.13 % Current options:
% 64.73/11.13 % ------
% 64.73/11.13
% 64.73/11.13
% 64.73/11.13 %
% 64.73/11.13
% 64.73/11.13 % ------ Proving...
% 64.73/11.13 %
% 64.73/11.13
% 64.73/11.13 % SZS status Theorem for theBenchmark.p
% 64.73/11.13
% 64.73/11.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 64.73/11.13
% 64.73/11.13
%------------------------------------------------------------------------------