%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC058+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 : n007.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 03:07:42 PM UTC 2026
% Result : Theorem 5.94s 2.27s
% Output : CNFRefutation 5.94s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f230ERROR: Could not build tree for root c_15950ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f47,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X0,X1) )
=> rearsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax47) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax48) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax49) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ~ rearsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( ( ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ~ rearsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( ( ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( rearsegP(X3,X2)
& neq(X2,nil) )
| ( nil = X2
& nil = X3 ) )
& ( ( ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f109,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f110,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| rearsegP(X0,X2) ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f112,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| rearsegP(X0,X2) ) ) ),
inference(flattening,[],[f111]) ).
fof(f113,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f114,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f137,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f138,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f139,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ( ( rearsegP(sK3,sK2)
& neq(sK2,nil) )
| ( nil = sK2
& nil = sK3 ) )
& ( ( ! [X4] :
( ~ segmentP(sK0,X4)
| ~ segmentP(sK1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& sK0 = sK2
& sK1 = sK3
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f98]) ).
fof(f145,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f113]) ).
fof(f146,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ? [X3] :
( app(X3,X1) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f145]) ).
fof(f147,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ( app(sK8(X0,X1),X1) = X0
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1))],[f146]) ).
fof(f148,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f149,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f123]) ).
fof(f150,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(rectify,[],[f149]) ).
fof(f151,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0
& ssList(sK10(X0,X1))
& ssList(sK9(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f150]) ).
fof(f154,plain,
ssList(sK0),
inference(cnf_transformation,[],[f139]) ).
fof(f155,plain,
ssList(sK1),
inference(cnf_transformation,[],[f139]) ).
fof(f157,plain,
( rearsegP(sK3,sK2)
| nil = sK2 ),
inference(cnf_transformation,[],[f139]) ).
fof(f158,plain,
( neq(sK2,nil)
| nil = sK2 ),
inference(cnf_transformation,[],[f139]) ).
fof(f159,plain,
( rearsegP(sK3,sK2)
| nil = sK3 ),
inference(cnf_transformation,[],[f139]) ).
fof(f160,plain,
( neq(sK2,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f139]) ).
fof(f161,plain,
! [X4] :
( ~ segmentP(sK0,X4)
| ~ segmentP(sK1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil != sK0 ),
inference(cnf_transformation,[],[f139]) ).
fof(f162,plain,
( neq(sK1,nil)
| nil != sK0 ),
inference(cnf_transformation,[],[f139]) ).
fof(f163,plain,
! [X4] :
( ~ segmentP(sK0,X4)
| ~ segmentP(sK1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f165,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f139]) ).
fof(f166,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f139]) ).
fof(f179,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f184,plain,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f185,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f110]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| rearsegP(X0,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f187,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| app(sK8(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f188,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ssList(sK8(X0,X1)) ),
inference(cnf_transformation,[],[f147]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
fof(f190,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f194,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f207,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f130]) ).
fof(f214,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f137]) ).
fof(f215,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f217,plain,
! [X4] :
( ~ segmentP(sK2,X4)
| ~ segmentP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK3 ),
inference(definition_unfolding,[],[f163,f166,f166,f165]) ).
fof(f218,plain,
( neq(sK3,nil)
| nil != sK2 ),
inference(definition_unfolding,[],[f162,f165,f166]) ).
fof(f219,plain,
! [X4] :
( ~ segmentP(sK2,X4)
| ~ segmentP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil != sK2 ),
inference(definition_unfolding,[],[f161,f165,f166,f165]) ).
fof(f220,plain,
ssList(sK3),
inference(definition_unfolding,[],[f155,f166]) ).
fof(f221,plain,
ssList(sK2),
inference(definition_unfolding,[],[f154,f165]) ).
fof(f225,plain,
! [X2,X1] :
( ~ ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X2,X1),X1) ),
inference(equality_resolution,[],[f189]) ).
fof(f227,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f200]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( ( sK3 = nil )
| ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_52,negated_conjecture,
( neq(sK3,nil)
| ( nil != sK2 ) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ~ neq(X0,nil)
| ( nil != sK2 ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_54,negated_conjecture,
( neq(sK2,nil)
| ( sK3 = nil ) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_55,negated_conjecture,
( rearsegP(sK3,sK2)
| ( sK3 = nil ) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_56,negated_conjecture,
( neq(sK2,nil)
| ( nil = sK2 ) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_57,negated_conjecture,
( rearsegP(sK3,sK2)
| ( nil = sK2 ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_59,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f220]) ).
tcf(c_60,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f221]) ).
tcf(c_65,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_72,plain,
ssList(nil),
inference(cnf_transformation,[],[f179]) ).
tcf(c_77,plain,
! [X0: $i] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( rearsegP(X0,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( ssList(sK8(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( ( app(sK8(X0,X1),X1) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_84,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_87,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_100,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_107,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_109,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_110,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_118,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_80,c_108,c_80]) ).
tcf(c_915,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( nil != sK2 )
| ( X0 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_65]) ).
tcf(c_916,plain,
( ~ ssList(sK3)
| ( nil != sK2 )
| ( sK3 != nil ) ),
inference(unflattening,[status(thm)],[c_915]) ).
tcf(c_931,plain,
! [X0: $i] :
( ( sK3 = nil )
| ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ( nil != sK2 )
| ( nil != nil )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_54]) ).
tcf(c_932,plain,
( ( sK3 = nil )
| ~ ssList(sK2)
| ~ segmentP(sK2,sK2)
| ~ segmentP(sK3,sK2)
| ( nil != sK2 ) ),
inference(unflattening,[status(thm)],[c_931]) ).
tcf(c_933,plain,
( ~ segmentP(sK2,sK2)
| ~ segmentP(sK3,sK2)
| ( nil != sK2 ) ),
inference(global_subsumption_just,[status(thm)],[c_932,c_60,c_59,c_916,c_932]) ).
tcf(c_944,plain,
! [X0: $i] :
( ( nil = sK2 )
| ( sK3 = nil )
| ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ( nil != nil )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_56]) ).
tcf(c_945,plain,
( ( nil = sK2 )
| ( sK3 = nil )
| ~ ssList(sK2)
| ~ segmentP(sK2,sK2)
| ~ segmentP(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_944]) ).
tcf(c_946,plain,
( ~ segmentP(sK2,sK2)
| ~ segmentP(sK3,sK2)
| ( sK3 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_945,c_60,c_933,c_945]) ).
tcf(c_947,plain,
( ( sK3 = nil )
| ~ segmentP(sK2,sK2)
| ~ segmentP(sK3,sK2) ),
inference(renaming,[status(thm)],[c_946]) ).
tcf(c_1063,plain,
! [X0: $i] :
( ( sK3 = nil )
| ~ ssList(X0)
| ( X0 != sK2 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_65]) ).
tcf(c_1064,plain,
( ( sK3 = nil )
| ~ ssList(nil)
| ( nil != sK2 ) ),
inference(unflattening,[status(thm)],[c_1063]) ).
tcf(c_1065,plain,
nil != sK2,
inference(global_subsumption_just,[status(thm)],[c_1064,c_59,c_72,c_916,c_1064]) ).
tcf(c_1091,negated_conjecture,
rearsegP(sK3,sK2),
inference(global_subsumption_just,[status(thm)],[c_55,c_57,c_1065]) ).
tcf(c_2372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3180,plain,
app(sK3,nil) = sK3,
inference(superposition,[status(thm)],[c_59,c_100]) ).
tcf(c_3181,plain,
app(sK2,nil) = sK2,
inference(superposition,[status(thm)],[c_60,c_100]) ).
tcf(c_3188,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_60,c_107]) ).
tcf(c_3198,plain,
( rearsegP(sK2,nil)
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_3181,c_145]) ).
tcf(c_3203,plain,
rearsegP(sK2,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_3198,c_60,c_72]) ).
tcf(c_3693,plain,
( ( nil = sK2 )
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ rearsegP(nil,sK2) ),
inference(superposition,[status(thm)],[c_3203,c_78]) ).
tcf(c_3698,plain,
~ rearsegP(nil,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_3693,c_1065,c_60,c_72]) ).
tcf(c_3739,plain,
( ( app(sK8(sK3,sK2),sK2) = sK3 )
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_1091,c_82]) ).
tcf(c_3761,plain,
app(sK8(sK3,sK2),sK2) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_3739,c_60,c_59]) ).
tcf(c_3826,plain,
! [X0: $i] :
( rearsegP(X0,sK2)
| ~ ssList(sK2)
| ~ ssList(sK3)
| ~ ssList(X0)
| ~ rearsegP(X0,sK3) ),
inference(superposition,[status(thm)],[c_1091,c_79]) ).
tcf(c_3845,plain,
! [X0: $i] :
( rearsegP(X0,sK2)
| ~ ssList(X0)
| ~ rearsegP(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3826,c_60,c_59]) ).
tcf(c_3873,plain,
( rearsegP(nil,sK2)
| ~ ssList(nil)
| ~ rearsegP(nil,sK3) ),
inference(instantiation,[status(thm)],[c_3845]) ).
tcf(c_5041,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK2),X0)) ),
inference(superposition,[status(thm)],[c_3188,c_90]) ).
tcf(c_5047,plain,
! [X0: $i] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(sK8(sK3,sK2))
| ~ ssList(app(app(sK8(sK3,sK2),sK2),X0)) ),
inference(superposition,[status(thm)],[c_3761,c_90]) ).
tcf(c_5061,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_5041,c_3188]) ).
tcf(c_5062,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5061,c_60,c_72]) ).
tcf(c_5105,plain,
! [X0: $i] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(sK8(sK3,sK2))
| ~ ssList(app(sK3,X0)) ),
inference(light_normalisation,[status(thm)],[c_5047,c_3761]) ).
tcf(c_5106,plain,
! [X0: $i] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(X0)
| ~ ssList(sK8(sK3,sK2))
| ~ ssList(app(sK3,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5105,c_60]) ).
tcf(c_6476,plain,
( segmentP(sK2,sK2)
| ~ ssList(nil)
| ~ ssList(app(sK2,nil)) ),
inference(superposition,[status(thm)],[c_3181,c_5062]) ).
tcf(c_6480,plain,
( segmentP(sK2,sK2)
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(light_normalisation,[status(thm)],[c_6476,c_3181]) ).
tcf(c_6481,plain,
segmentP(sK2,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_6480,c_60,c_72]) ).
tcf(c_12563,plain,
! [X0: $i,X1: $i] :
( rearsegP(nil,sK3)
| ~ rearsegP(X1,X0)
| ( nil != X1 )
| ( sK3 != X0 ) ),
inference(instantiation,[status(thm)],[c_2372]) ).
tcf(c_12564,plain,
( rearsegP(nil,sK3)
| ~ rearsegP(nil,nil)
| ( nil != nil )
| ( sK3 != nil ) ),
inference(instantiation,[status(thm)],[c_12563]) ).
tcf(c_15918,plain,
( segmentP(sK3,sK2)
| ~ ssList(nil)
| ~ ssList(sK8(sK3,sK2))
| ~ ssList(app(sK3,nil)) ),
inference(superposition,[status(thm)],[c_3180,c_5106]) ).
tcf(c_15922,plain,
( segmentP(sK3,sK2)
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ ssList(sK8(sK3,sK2)) ),
inference(light_normalisation,[status(thm)],[c_15918,c_3180]) ).
tcf(c_15923,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK8(sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15922,c_72,c_59]) ).
tcf(c_15947,plain,
~ ssList(sK8(sK3,sK2)),
inference(global_subsumption_just,[status(thm)],[c_15923,c_72,c_109,c_110,c_118,c_947,c_3698,c_3873,c_6481,c_12564,c_15923]) ).
tcf(c_15949,plain,
( ~ ssList(sK2)
| ~ ssList(sK3)
| ~ rearsegP(sK3,sK2) ),
inference(superposition,[status(thm)],[c_81,c_15947]) ).
tcf(c_15950,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15949,c_60,c_59,c_1091]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC058+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.36 % Computer : n007.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Thu Sep 24 16:07:07 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 5.94/2.27 % SZS status Started for theBenchmark.p
% 5.94/2.27 % SZS status Theorem for theBenchmark.p
% 5.94/2.27
% 5.94/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.94/2.27
% 5.94/2.27 % ------ iProver source info
% 5.94/2.27
% 5.94/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 5.94/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.94/2.27 % git: non_committed_changes: false
% 5.94/2.27
% 5.94/2.27 % ------ Parsing...
% 5.94/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.94/2.27
% 5.94/2.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 5.94/2.27
% 5.94/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.94/2.27
% 5.94/2.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.94/2.27 % ------ Proving...
% 5.94/2.27 % ------ Problem Properties
% 5.94/2.27
% 5.94/2.27 %
% 5.94/2.27 % clauses 51
% 5.94/2.27 % conjectures 3
% 5.94/2.27 % EPR 23
% 5.94/2.27 % Horn 47
% 5.94/2.27 % unary 11
% 5.94/2.27 % binary 6
% 5.94/2.27 % lits 163
% 5.94/2.27 % lits eq 36
% 5.94/2.27 % fd_pure 0
% 5.94/2.27 % fd_pseudo 0
% 5.94/2.27 % fd_cond 7
% 5.94/2.27 % fd_pseudo_cond 6
% 5.94/2.27 % AC symbols 0
% 5.94/2.27
% 5.94/2.27 % ------ Schedule dynamic 5 is on
% 5.94/2.27
% 5.94/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.94/2.27
% 5.94/2.27
% 5.94/2.27 % ------
% 5.94/2.27 % Current options:
% 5.94/2.27 % ------
% 5.94/2.27
% 5.94/2.27
% 5.94/2.27 %
% 5.94/2.27
% 5.94/2.27 % ------ Proving...
% 5.94/2.27 %
% 5.94/2.27
% 5.94/2.27 % SZS status Theorem for theBenchmark.p
% 5.94/2.27
% 5.94/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.94/2.28
% 5.94/2.28
%------------------------------------------------------------------------------