%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC089+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 : n006.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 03:07:50 PM UTC 2026
% Result : Theorem 94.21s 13.51s
% Output : CNFRefutation 94.21s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f544ERROR: Could not build tree for root c_140961ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| 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)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f103,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(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) != X0 ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(flattening,[],[f129]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f157,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(ennf_transformation,[],[f45]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f192]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X2)
| ! [X8] :
( ~ neq(nil,X2)
| hd(X2) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(X2) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| X3 = X5
| ~ ssList(X5) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X2)
| ! [X8] :
( ~ neq(nil,X2)
| hd(X2) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(X2) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| X3 = X5
| ~ ssList(X5) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f240,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f241,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X3] :
( app(X1,X3) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f240]) ).
fof(f242,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f241]) ).
fof(f246,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,[],[f103]) ).
fof(f247,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,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1))
& ssList(sK13(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK55)
| ! [X8] :
( ~ neq(nil,sK55)
| hd(sK55) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(sK55) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| sK56 = X5
| ~ ssList(X5) )
& neq(sK55,nil) )
| ~ neq(sK56,nil) )
& ( nil != sK56
| nil = sK55 )
& ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f309,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f242]) ).
fof(f310,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ssList(sK11(X0,X1)) ),
inference(cnf_transformation,[],[f242]) ).
fof(f318,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,[],[f248]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f390,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f397,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f399,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f428,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(cnf_transformation,[],[f157]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f504,f506]) ).
fof(f508,plain,
! [X4] :
( ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f503,f506,f505]) ).
fof(f509,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f506]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f505]) ).
fof(f516,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,[],[f318]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ssList(sK11(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( app(X1,sK11(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_67,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,[],[f516]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_139,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f544]) ).
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_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f390]) ).
tcf(c_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_151,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f399]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f403]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f546]) ).
tcf(c_180,plain,
! [X0: $i] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f428]) ).
tcf(c_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f507]) ).
tcf(c_247,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_249,negated_conjecture,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_250,negated_conjecture,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(sK56,nil)
| ~ neq(nil,sK55)
| ~ ssList(cons(hd(sK55),nil))
| ~ ssList(app(tl(sK55),cons(hd(sK55),nil))) ),
inference(cnf_transformation,[],[f549]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f509]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f510]) ).
tcf(c_367,negated_conjecture,
neq(sK55,nil),
inference(global_subsumption_just,[status(thm)],[c_249,c_246,c_249]) ).
tcf(c_381,plain,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(app(tl(sK55),cons(hd(sK55),nil)))
| ~ ssList(cons(hd(sK55),nil))
| ~ neq(nil,sK55) ),
inference(global_subsumption_just,[status(thm)],[c_250,c_246,c_250]) ).
tcf(c_382,negated_conjecture,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(nil,sK55)
| ~ ssList(cons(hd(sK55),nil))
| ~ ssList(app(tl(sK55),cons(hd(sK55),nil))) ),
inference(renaming,[status(thm)],[c_381]) ).
tcf(c_811,plain,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(nil,sK55)
| ~ ssList(cons(hd(sK55),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_382,c_153]) ).
tcf(c_3247,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK55,X1)
| ~ segmentP(sK56,X1)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).
tcf(c_3248,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3247]) ).
tcf(c_3250,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3248,c_141,c_3248]) ).
tcf(c_3251,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3250]) ).
tcf(c_3269,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(cons(hd(sK55),nil))
| ( X1 != sK55 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_811]) ).
tcf(c_3270,plain,
( ( nil = sK55 )
| ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(cons(hd(sK55),nil)) ),
inference(unflattening,[status(thm)],[c_3269]) ).
tcf(c_3271,plain,
( ( nil = sK55 )
| ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(cons(hd(sK55),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_3270,c_254,c_141,c_3270]) ).
tcf(c_3301,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK55 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_367]) ).
tcf(c_3302,plain,
( ~ ssList(nil)
| ( nil != sK55 ) ),
inference(unflattening,[status(thm)],[c_3301]) ).
tcf(c_3303,plain,
nil != sK55,
inference(global_subsumption_just,[status(thm)],[c_3302,c_141,c_3302]) ).
tcf(c_3308,plain,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(cons(hd(sK55),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3271,c_3303]) ).
tcf(c_8974,definition,
iPr_def_10 = hd(sK55),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8975,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8976,definition,
iPr_def_12 = tl(sK55),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8977,definition,
iPr_def_13 = app(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8980,plain,
( ( iPr_def_13 = sK56 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_3308,c_8977,c_8976,c_8974,c_8975]) ).
tcf(c_8981,plain,
nil != sK55,
inference(demodulation,[status(thm)],[c_3303]) ).
tcf(c_8983,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3251]) ).
tcf(c_8984,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8985,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_12367,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8975,c_140]) ).
tcf(c_12370,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12367,c_141]) ).
tcf(c_12404,plain,
( ( sK56 = iPr_def_13 )
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_8980,c_12370]) ).
tcf(c_12414,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8974,c_149]) ).
tcf(c_12415,plain,
ssItem(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12414,c_8981,c_8984]) ).
tcf(c_12416,plain,
ssList(iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_12370,c_12415]) ).
tcf(c_12526,plain,
( ssList(iPr_def_12)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8976,c_151]) ).
tcf(c_12529,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_12526,c_8981,c_8984]) ).
tcf(c_19904,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(superposition,[status(thm)],[c_8975,c_177]) ).
tcf(c_19918,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19904,c_141,c_12415]) ).
tcf(c_33702,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(app(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_33748,plain,
sK56 = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_12404,c_12404,c_12415,c_12529]) ).
tcf(c_57336,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_19918,c_180,c_19918]) ).
tcf(c_84979,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_153,c_67,c_33702]) ).
tcf(c_115818,plain,
ssList(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_8985,c_33748]) ).
tcf(c_115826,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(iPr_def_13,X0)
| ~ segmentP(sK55,X0) ),
inference(light_normalisation,[status(thm)],[c_8983,c_33748]) ).
tcf(c_116264,plain,
app(iPr_def_13,nil) = iPr_def_13,
inference(superposition,[status(thm)],[c_115818,c_232]) ).
tcf(c_116330,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8975,c_140]) ).
tcf(c_116333,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116330,c_141]) ).
tcf(c_116362,plain,
ssList(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_116333,c_12416]) ).
tcf(c_116365,plain,
app(nil,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_116362,c_155]) ).
tcf(c_116372,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8974,c_149]) ).
tcf(c_116373,plain,
ssItem(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_116372,c_8981,c_8984]) ).
tcf(c_116380,plain,
( ssList(iPr_def_12)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8976,c_151]) ).
tcf(c_116383,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_116380,c_8981,c_8984]) ).
tcf(c_117478,plain,
( ~ ssList(nil)
| ~ ssItem(iPr_def_10)
| ( nil != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_8975,c_142]) ).
tcf(c_117479,plain,
nil != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_117478,c_141,c_116373]) ).
tcf(c_119357,plain,
( ( nil = sK55 )
| ( cons(hd(sK55),tl(sK55)) = sK55 ) ),
inference(superposition,[status(thm)],[c_8984,c_224]) ).
tcf(c_119367,plain,
( ( nil = sK55 )
| ( cons(iPr_def_10,iPr_def_12) = sK55 ) ),
inference(light_normalisation,[status(thm)],[c_119357,c_8974,c_8976]) ).
tcf(c_119368,plain,
cons(iPr_def_10,iPr_def_12) = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_119367,c_8981]) ).
tcf(c_123547,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(superposition,[status(thm)],[c_8975,c_177]) ).
tcf(c_123563,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[c_123547,c_141,c_116373]) ).
tcf(c_123983,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_123563,c_57336]) ).
tcf(c_123990,plain,
( frontsegP(sK55,iPr_def_11)
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_119368,c_123983]) ).
tcf(c_123994,plain,
frontsegP(sK55,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_123990,c_116383]) ).
tcf(c_124145,plain,
( ( app(iPr_def_11,sK11(sK55,iPr_def_11)) = sK55 )
| ~ ssList(iPr_def_11)
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_123994,c_63]) ).
tcf(c_124146,plain,
app(iPr_def_11,sK11(sK55,iPr_def_11)) = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_124145,c_116362,c_8984]) ).
tcf(c_130092,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_84979]) ).
tcf(c_130106,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8977,c_130092]) ).
tcf(c_130107,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_11)
| ~ ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_116365,c_130092]) ).
tcf(c_130187,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_130107,c_116362,c_141]) ).
tcf(c_130190,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_130106,c_116383,c_116362]) ).
tcf(c_137489,plain,
( segmentP(sK55,iPr_def_11)
| ~ ssList(sK11(sK55,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_124146,c_130187]) ).
tcf(c_137529,plain,
( segmentP(iPr_def_13,iPr_def_11)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_116264,c_130190]) ).
tcf(c_137534,plain,
segmentP(iPr_def_13,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_137529,c_141]) ).
tcf(c_140955,plain,
( segmentP(sK55,iPr_def_11)
| ~ ssList(iPr_def_11)
| ~ ssList(sK55)
| ~ frontsegP(sK55,iPr_def_11) ),
inference(superposition,[status(thm)],[c_62,c_137489]) ).
tcf(c_140956,plain,
segmentP(sK55,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_140955,c_116362,c_8984,c_123994]) ).
tcf(c_140960,plain,
( ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ~ segmentP(iPr_def_13,iPr_def_11) ),
inference(superposition,[status(thm)],[c_140956,c_115826]) ).
tcf(c_140961,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_140960,c_117479,c_116362,c_137534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC089+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n006.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 16:20:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 94.21/13.51 % SZS status Started for theBenchmark.p
% 94.21/13.51 % SZS status Theorem for theBenchmark.p
% 94.21/13.51
% 94.21/13.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 94.21/13.51
% 94.21/13.51 % ------ iProver source info
% 94.21/13.51
% 94.21/13.51 % git: date: 2026-07-19 20:42:38 +0200
% 94.21/13.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 94.21/13.51 % git: non_committed_changes: false
% 94.21/13.51
% 94.21/13.51 % ------ Parsing...
% 94.21/13.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 94.21/13.51
% 94.21/13.51 % ------ 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: 5 0s sf_e pe_s pe_e %
% 94.21/13.51
% 94.21/13.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 94.21/13.51
% 94.21/13.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 94.21/13.51 % ------ Proving...
% 94.21/13.51 % ------ Problem Properties
% 94.21/13.51
% 94.21/13.51 %
% 94.21/13.51 % clauses 192
% 94.21/13.51 % conjectures 2
% 94.21/13.51 % EPR 57
% 94.21/13.51 % Horn 124
% 94.21/13.51 % unary 24
% 94.21/13.51 % binary 42
% 94.21/13.51 % lits 638
% 94.21/13.51 % lits eq 86
% 94.21/13.51 % fd_pure 0
% 94.21/13.51 % fd_pseudo 0
% 94.21/13.51 % fd_cond 22
% 94.21/13.51 % fd_pseudo_cond 14
% 94.21/13.51 % AC symbols 0
% 94.21/13.51
% 94.21/13.51 % ------ Schedule dynamic 5 is on
% 94.21/13.51
% 94.21/13.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 94.21/13.51
% 94.21/13.51
% 94.21/13.51 % ------
% 94.21/13.51 % Current options:
% 94.21/13.51 % ------
% 94.21/13.51
% 94.21/13.51
% 94.21/13.51 %
% 94.21/13.51
% 94.21/13.51 % ------ Proving...
% 94.21/13.51 % Proof_search_loop: time out after: 4308 full_loop iterations
% 94.21/13.51
% 94.21/13.51 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 94.21/13.51
% 94.21/13.51
% 94.21/13.51 % ------
% 94.21/13.51 % Current options:
% 94.21/13.51 % ------
% 94.21/13.51
% 94.21/13.51
% 94.21/13.51 %
% 94.21/13.51
% 94.21/13.51 % ------ Proving...
% 94.21/13.51 %
% 94.21/13.51
% 94.21/13.51 % SZS status Theorem for theBenchmark.p
% 94.21/13.51
% 94.21/13.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 94.21/13.51
% 94.21/13.51
%------------------------------------------------------------------------------