%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC240+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 03:08:58 PM UTC 2026
% Result : Theorem 21.55s 4.16s
% Output : CNFRefutation 21.55s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f224ERROR: Could not build tree for root c_53553ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X8] :
( ssItem(X8)
=> ? [X9] :
( memberP(X2,X9)
& X8 != X9
& ssItem(X9) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X8] :
( ssItem(X8)
=> ? [X9] :
( memberP(X2,X9)
& X8 != X9
& ssItem(X9) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X8] :
( ssItem(X8)
& ! [X9] :
( ~ memberP(X2,X9)
| X8 = X9
| ~ ssItem(X9) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X8] :
( ssItem(X8)
& ! [X9] :
( ~ memberP(X2,X9)
| X8 = X9
| ~ ssItem(X9) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f103,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(ennf_transformation,[],[f20]) ).
fof(f104,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(flattening,[],[f103]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f110,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f122,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f137,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ssItem(sK5)
& ! [X9] :
( ~ memberP(sK2,X9)
| sK5 = X9
| ~ ssItem(X9) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ssItem(sK4(X4,X5,X6))
& ~ leq(X4,sK4(X4,X5,X6))
& lt(X4,sK4(X4,X5,X6))
& memberP(X6,sK4(X4,X5,X6))
& memberP(X5,sK4(X4,X5,X6)) )
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK0
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4(X4,X5,X6)),skolemize(X8,sK5)],[f99]) ).
fof(f139,plain,
! [X0] :
( ~ ssList(X0)
| ( cons(sK9(X0),sK8(X0)) = X0
& ssItem(sK9(X0))
& ssList(sK8(X0)) )
| nil = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X1,sK8(X0)),skolemize(X2,sK9(X0))],[f104]) ).
fof(f140,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f141,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(flattening,[],[f140]) ).
fof(f149,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ lt(X0,X1)
| ( leq(X0,X1)
& X0 != X1 ) )
& ( ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f122]) ).
fof(f150,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ lt(X0,X1)
| ( leq(X0,X1)
& X0 != X1 ) )
& ( ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ) ) ) ),
inference(flattening,[],[f149]) ).
fof(f151,plain,
ssList(sK0),
inference(cnf_transformation,[],[f137]) ).
fof(f155,plain,
ssItem(sK5),
inference(cnf_transformation,[],[f137]) ).
fof(f156,plain,
! [X9] :
( ~ memberP(sK2,X9)
| sK5 = X9
| ~ ssItem(X9) ),
inference(cnf_transformation,[],[f137]) ).
fof(f157,plain,
! [X6,X4,X5] :
( ssItem(sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f158,plain,
! [X6,X4,X5] :
( ~ leq(X4,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f159,plain,
! [X6,X4,X5] :
( lt(X4,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f162,plain,
nil != sK0,
inference(cnf_transformation,[],[f137]) ).
fof(f163,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f137]) ).
fof(f168,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f171,plain,
! [X0] :
( ~ ssList(X0)
| cons(sK9(X0),sK8(X0)) = X0
| nil = X0 ),
inference(cnf_transformation,[],[f139]) ).
fof(f172,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK9(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f139]) ).
fof(f173,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK8(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f139]) ).
fof(f177,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f179,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f141]) ).
fof(f185,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f187,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f199,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f210,plain,
nil != sK2,
inference(definition_unfolding,[],[f162,f163]) ).
fof(f213,plain,
! [X6,X4,X5] :
( lt(X4,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f159,f163]) ).
fof(f214,plain,
! [X6,X4,X5] :
( ~ leq(X4,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f158,f163]) ).
fof(f215,plain,
! [X6,X4,X5] :
( ssItem(sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f157,f163]) ).
fof(f217,plain,
ssList(sK2),
inference(definition_unfolding,[],[f151,f163]) ).
tcf(c_49,negated_conjecture,
nil != sK2,
inference(cnf_transformation,[],[f210]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( lt(X1,sK4(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK2 ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ leq(X1,sK4(X1,X0,X2))
| ( app(app(X0,cons(X1,nil)),X2) != sK2 ) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sK4(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK2 ) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] :
( ( X0 = sK5 )
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_56,negated_conjecture,
ssItem(sK5),
inference(cnf_transformation,[],[f155]) ).
tcf(c_60,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f217]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_67,plain,
! [X0: $i] :
( ssList(sK8(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_68,plain,
! [X0: $i] :
( ssItem(sK9(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_69,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(sK9(X0),sK8(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_81,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_83,plain,
ssList(nil),
inference(cnf_transformation,[],[f187]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_109,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_120,plain,
( ( nil = nil )
| ~ ssList(nil)
| ( app(nil,nil) != nil ) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_1653,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2662,plain,
! [X0: $i,X1: $i] :
( ( app(nil,cons(X0,X1)) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_73,c_81]) ).
tcf(c_2797,plain,
( ( nil = sK2 )
| ( cons(sK9(sK2),sK8(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_60,c_69]) ).
tcf(c_2804,plain,
cons(sK9(sK2),sK8(sK2)) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_2797,c_49]) ).
tcf(c_2832,plain,
( memberP(sK2,sK9(sK2))
| ~ ssList(sK8(sK2))
| ~ ssItem(sK9(sK2)) ),
inference(superposition,[status(thm)],[c_2804,c_85]) ).
tcf(c_2862,plain,
( ( sK9(sK2) = sK5 )
| ~ ssList(sK8(sK2))
| ~ ssItem(sK9(sK2)) ),
inference(superposition,[status(thm)],[c_2832,c_55]) ).
tcf(c_2912,plain,
! [X0: $i] :
( ( app(cons(sK5,nil),X0) = cons(sK5,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_56,c_64]) ).
tcf(c_2986,plain,
( ( nil = sK2 )
| ( sK9(sK2) = sK5 )
| ~ ssList(sK2)
| ~ ssList(sK8(sK2)) ),
inference(superposition,[status(thm)],[c_68,c_2862]) ).
tcf(c_2987,plain,
( ( sK9(sK2) = sK5 )
| ~ ssList(sK8(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2986,c_49,c_60]) ).
tcf(c_2996,plain,
( ( nil = sK2 )
| ( sK9(sK2) = sK5 )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_67,c_2987]) ).
tcf(c_2997,plain,
sK9(sK2) = sK5,
inference(forward_subsumption_resolution,[status(thm)],[c_2996,c_49,c_60]) ).
tcf(c_2999,plain,
cons(sK5,sK8(sK2)) = sK2,
inference(demodulation,[status(thm)],[c_2804,c_2997]) ).
tcf(c_3017,plain,
! [X0: $i] :
( ( X0 = nil )
| ( app(cons(sK5,nil),sK8(X0)) = cons(sK5,sK8(X0)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_67,c_2912]) ).
tcf(c_3791,plain,
! [X0: $i] :
( ( nil = sK2 )
| ( sK2 != X0 )
| ( nil != X0 ) ),
inference(instantiation,[status(thm)],[c_1653]) ).
tcf(c_3792,plain,
( ( nil = sK2 )
| ( sK2 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_3791]) ).
tcf(c_4941,plain,
( ssList(sK8(sK2))
| ( sK2 = nil )
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_17350,plain,
! [X0: $i] :
( ( app(nil,cons(sK5,X0)) = cons(sK5,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_56,c_2662]) ).
tcf(c_17393,plain,
app(nil,cons(sK5,nil)) = cons(sK5,nil),
inference(superposition,[status(thm)],[c_83,c_17350]) ).
tcf(c_17874,plain,
! [X0: $i] :
( ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssList(X0)
| ~ leq(sK5,sK4(sK5,nil,X0))
| ( app(cons(sK5,nil),X0) != sK2 ) ),
inference(superposition,[status(thm)],[c_17393,c_53]) ).
tcf(c_17875,plain,
! [X0: $i] :
( lt(sK5,sK4(sK5,nil,X0))
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssList(X0)
| ( app(cons(sK5,nil),X0) != sK2 ) ),
inference(superposition,[status(thm)],[c_17393,c_52]) ).
tcf(c_17878,plain,
! [X0: $i] :
( ssItem(sK4(sK5,nil,X0))
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssList(X0)
| ( app(cons(sK5,nil),X0) != sK2 ) ),
inference(superposition,[status(thm)],[c_17393,c_54]) ).
tcf(c_17893,plain,
! [X0: $i] :
( ssItem(sK4(sK5,nil,X0))
| ~ ssList(X0)
| ( app(cons(sK5,nil),X0) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17878,c_83,c_56]) ).
tcf(c_17905,plain,
! [X0: $i] :
( lt(sK5,sK4(sK5,nil,X0))
| ~ ssList(X0)
| ( app(cons(sK5,nil),X0) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17875,c_83,c_56]) ).
tcf(c_17909,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ leq(sK5,sK4(sK5,nil,X0))
| ( app(cons(sK5,nil),X0) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17874,c_83,c_56]) ).
tcf(c_52652,plain,
( ( nil = sK2 )
| ( app(cons(sK5,nil),sK8(sK2)) = cons(sK5,sK8(sK2)) ) ),
inference(superposition,[status(thm)],[c_60,c_3017]) ).
tcf(c_52734,plain,
( ( nil = sK2 )
| ( app(cons(sK5,nil),sK8(sK2)) = sK2 ) ),
inference(light_normalisation,[status(thm)],[c_52652,c_2999]) ).
tcf(c_52735,plain,
app(cons(sK5,nil),sK8(sK2)) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_52734,c_49]) ).
tcf(c_53246,plain,
( ~ ssList(sK8(sK2))
| ~ leq(sK5,sK4(sK5,nil,sK8(sK2))) ),
inference(superposition,[status(thm)],[c_52735,c_17909]) ).
tcf(c_53247,plain,
( lt(sK5,sK4(sK5,nil,sK8(sK2)))
| ~ ssList(sK8(sK2)) ),
inference(superposition,[status(thm)],[c_52735,c_17905]) ).
tcf(c_53250,plain,
( ssItem(sK4(sK5,nil,sK8(sK2)))
| ~ ssList(sK8(sK2)) ),
inference(superposition,[status(thm)],[c_52735,c_17893]) ).
tcf(c_53498,plain,
ssItem(sK4(sK5,nil,sK8(sK2))),
inference(global_subsumption_just,[status(thm)],[c_53250,c_60,c_83,c_49,c_109,c_120,c_3792,c_4941,c_53250]) ).
tcf(c_53537,plain,
lt(sK5,sK4(sK5,nil,sK8(sK2))),
inference(global_subsumption_just,[status(thm)],[c_53247,c_60,c_83,c_49,c_109,c_120,c_3792,c_4941,c_53247]) ).
tcf(c_53542,plain,
( leq(sK5,sK4(sK5,nil,sK8(sK2)))
| ~ ssItem(sK5)
| ~ ssItem(sK4(sK5,nil,sK8(sK2))) ),
inference(superposition,[status(thm)],[c_53537,c_97]) ).
tcf(c_53543,plain,
leq(sK5,sK4(sK5,nil,sK8(sK2))),
inference(forward_subsumption_resolution,[status(thm)],[c_53542,c_56,c_53498]) ).
tcf(c_53553,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_53543,c_53246,c_4941,c_3792,c_120,c_109,c_49,c_83,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC240+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 17:10:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 21.55/4.16 % SZS status Started for theBenchmark.p
% 21.55/4.16 % SZS status Theorem for theBenchmark.p
% 21.55/4.16
% 21.55/4.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.55/4.16
% 21.55/4.16 % ------ iProver source info
% 21.55/4.16
% 21.55/4.16 % git: date: 2026-07-19 20:42:38 +0200
% 21.55/4.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.55/4.16 % git: non_committed_changes: false
% 21.55/4.16
% 21.55/4.16 % ------ Parsing...
% 21.55/4.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.55/4.16
% 21.55/4.16 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 21.55/4.16
% 21.55/4.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.55/4.16
% 21.55/4.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.55/4.16 % ------ Proving...
% 21.55/4.16 % ------ Problem Properties
% 21.55/4.16
% 21.55/4.16 %
% 21.55/4.16 % clauses 53
% 21.55/4.16 % conjectures 10
% 21.55/4.16 % EPR 19
% 21.55/4.16 % Horn 47
% 21.55/4.16 % unary 9
% 21.55/4.16 % binary 5
% 21.55/4.16 % lits 192
% 21.55/4.16 % lits eq 36
% 21.55/4.16 % fd_pure 0
% 21.55/4.16 % fd_pseudo 0
% 21.55/4.16 % fd_cond 5
% 21.55/4.16 % fd_pseudo_cond 7
% 21.55/4.16 % AC symbols 0
% 21.55/4.16
% 21.55/4.16 % ------ Schedule dynamic 5 is on
% 21.55/4.16
% 21.55/4.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 21.55/4.16
% 21.55/4.16
% 21.55/4.16 % ------
% 21.55/4.16 % Current options:
% 21.55/4.16 % ------
% 21.55/4.16
% 21.55/4.16
% 21.55/4.16 %
% 21.55/4.16
% 21.55/4.16 % ------ Proving...
% 21.55/4.16 %
% 21.55/4.16
% 21.55/4.16 % SZS status Theorem for theBenchmark.p
% 21.55/4.16
% 21.55/4.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.55/4.16
% 21.55/4.16
%------------------------------------------------------------------------------