%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC354+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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:09:26 PM UTC 2026
% Result : Theorem 8.42s 6.96s
% Output : CNFRefutation 8.42s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f548ERROR: Could not build tree for root c_29643ERROR: 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/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
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(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( segmentP(X1,X0)
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& hd(X3) = X5
& cons(X5,nil) = X4
& ssItem(X5) )
& X2 != X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| 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)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( segmentP(X1,X0)
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& hd(X3) = X5
& cons(X5,nil) = X4
& ssItem(X5) )
& X2 != X4
& 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(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(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(f188,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f188]) ).
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(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ~ segmentP(X1,X0)
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ 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)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ~ segmentP(X1,X0)
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ 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(f291,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X1,sK52(X0))],[f189]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( ~ segmentP(sK54,sK53)
& ! [X4] :
( ! [X5] :
( ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| sK55 = X4
| ~ 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(f397,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
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(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK52(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f472,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f291]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| ~ segmentP(sK54,sK53) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK55 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
! [X4,X5] :
( neq(sK54,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK55 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
! [X4,X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK55 = X4
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f503,f507]) ).
fof(f512,plain,
( ~ neq(sK56,nil)
| ~ segmentP(sK56,sK55) ),
inference(definition_unfolding,[],[f500,f507,f506]) ).
fof(f513,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
fof(f514,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f520,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]) ).
fof(f542,plain,
! [X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| ~ ssItem(X5)
| cons(X5,nil) = sK55
| ~ ssList(cons(X5,nil)) ),
inference(equality_resolution,[],[f510]) ).
fof(f543,plain,
( neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| sK55 = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(equality_resolution,[],[f542]) ).
fof(f544,plain,
! [X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| ~ ssItem(X5)
| cons(X5,nil) = sK55
| ~ ssList(cons(X5,nil)) ),
inference(equality_resolution,[],[f502]) ).
fof(f545,plain,
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| sK55 = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(equality_resolution,[],[f544]) ).
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,[],[f520]) ).
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,[],[f548]) ).
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_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f397]) ).
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,[],[f550]) ).
tcf(c_180,plain,
! [X0: $i] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f428]) ).
tcf(c_221,plain,
! [X0: $i] :
( ssList(sK52(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f472]) ).
tcf(c_222,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK52(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f471]) ).
tcf(c_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f553]) ).
tcf(c_247,negated_conjecture,
( neq(sK56,nil)
| ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(cnf_transformation,[],[f543]) ).
tcf(c_248,negated_conjecture,
( ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(cnf_transformation,[],[f545]) ).
tcf(c_250,negated_conjecture,
( ~ segmentP(sK56,sK55)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f513]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f514]) ).
tcf(c_369,negated_conjecture,
~ segmentP(sK56,sK55),
inference(global_subsumption_just,[status(thm)],[c_250,c_246,c_250]) ).
tcf(c_383,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_247,c_246]) ).
tcf(c_385,plain,
( ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_248,c_246,c_248]) ).
tcf(c_386,negated_conjecture,
( ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(renaming,[status(thm)],[c_385]) ).
tcf(c_3222,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( cons(hd(sK56),nil) = sK55 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ( X1 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_386]) ).
tcf(c_3223,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),nil) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil)
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(unflattening,[status(thm)],[c_3222]) ).
tcf(c_3224,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_3223,c_253,c_141,c_3223]) ).
tcf(c_3242,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_383]) ).
tcf(c_3243,plain,
( ~ ssList(nil)
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3242]) ).
tcf(c_3244,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3243,c_141,c_3243]) ).
tcf(c_3249,plain,
( ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3224,c_3244]) ).
tcf(c_8848,definition,
iPr_def_10 = hd(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8849,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8850,plain,
( ( iPr_def_11 = sK55 )
| ~ ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_3249,c_8848,c_8849]) ).
tcf(c_8851,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_3244]) ).
tcf(c_8852,negated_conjecture,
~ segmentP(sK56,sK55),
inference(demodulation,[status(thm)],[c_369]) ).
tcf(c_8853,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8854,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_12006,plain,
app(nil,sK55) = sK55,
inference(superposition,[status(thm)],[c_8853,c_155]) ).
tcf(c_12151,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8849,c_140]) ).
tcf(c_12154,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12151,c_141]) ).
tcf(c_12168,plain,
( ( sK55 = iPr_def_11 )
| ~ ssItem(iPr_def_10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_8850,c_12154]) ).
tcf(c_12289,plain,
( ssItem(iPr_def_10)
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8848,c_149]) ).
tcf(c_12291,plain,
ssItem(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12289,c_8851,c_8854]) ).
tcf(c_12296,plain,
sK55 = iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_12168,c_12291]) ).
tcf(c_12303,plain,
app(nil,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_12006,c_12296]) ).
tcf(c_12304,plain,
~ segmentP(sK56,iPr_def_11),
inference(demodulation,[status(thm)],[c_8852,c_12296]) ).
tcf(c_12305,plain,
ssList(iPr_def_11),
inference(demodulation,[status(thm)],[c_8853,c_12296]) ).
tcf(c_14469,plain,
( ( nil = sK56 )
| ( tl(sK56) = sK52(sK56) ) ),
inference(superposition,[status(thm)],[c_8854,c_222]) ).
tcf(c_14473,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14469,c_8851]) ).
tcf(c_14841,plain,
( ssList(tl(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_14473,c_221]) ).
tcf(c_14842,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14841,c_8851,c_8854]) ).
tcf(c_15798,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_8854,c_224]) ).
tcf(c_15803,plain,
( ( nil = sK56 )
| ( cons(iPr_def_10,tl(sK56)) = sK56 ) ),
inference(light_normalisation,[status(thm)],[c_15798,c_8848]) ).
tcf(c_15804,plain,
cons(iPr_def_10,tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_15803,c_8851]) ).
tcf(c_19443,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_8849,c_177]) ).
tcf(c_19453,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19443,c_141,c_12291]) ).
tcf(c_19867,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_19453,c_180,c_19453]) ).
tcf(c_19875,plain,
( frontsegP(sK56,iPr_def_11)
| ~ ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_15804,c_19867]) ).
tcf(c_19879,plain,
frontsegP(sK56,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_19875,c_14842]) ).
tcf(c_19900,plain,
( ( app(iPr_def_11,sK11(sK56,iPr_def_11)) = sK56 )
| ~ ssList(iPr_def_11)
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_19879,c_63]) ).
tcf(c_19901,plain,
app(iPr_def_11,sK11(sK56,iPr_def_11)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_19900,c_12305,c_8854]) ).
tcf(c_25106,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_25782,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_25106]) ).
tcf(c_25797,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_12303,c_25782]) ).
tcf(c_25861,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25797,c_12305,c_141]) ).
tcf(c_29616,plain,
( segmentP(sK56,iPr_def_11)
| ~ ssList(sK11(sK56,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_19901,c_25861]) ).
tcf(c_29621,plain,
~ ssList(sK11(sK56,iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_29616,c_12304]) ).
tcf(c_29642,plain,
( ~ ssList(iPr_def_11)
| ~ ssList(sK56)
| ~ frontsegP(sK56,iPr_def_11) ),
inference(superposition,[status(thm)],[c_62,c_29621]) ).
tcf(c_29643,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_29642,c_12305,c_8854,c_19879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC354+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.56 % Computer : n001.cluster.edu
% 0.09/5.56 % Model : x86_64 x86_64
% 0.09/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.56 % Memory : 8046.5625MB
% 0.09/5.56 % OS : Linux 6.8.0-71-generic
% 0.09/5.56 % CPULimit : 300
% 0.09/5.56 % WCLimit : 300
% 0.09/5.56 % DateTime : Thu Sep 24 17:53:29 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.09/5.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.60 Running first-order theorem proving
% 0.13/5.61 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
% 0.13/5.62
% 0.13/5.62 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.62
% 0.13/5.62 % Detected problem language: tptp
% 0.13/5.63 % Proving...
% 8.42/6.96 % SZS status Started for theBenchmark.p
% 8.42/6.96 % SZS status Theorem for theBenchmark.p
% 8.42/6.96
% 8.42/6.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.42/6.96
% 8.42/6.96 % ------ iProver source info
% 8.42/6.96
% 8.42/6.96 % git: date: 2026-07-19 20:42:38 +0200
% 8.42/6.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.42/6.96 % git: non_committed_changes: false
% 8.42/6.96
% 8.42/6.96 % ------ Parsing...
% 8.42/6.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.42/6.96
% 8.42/6.96 % ------ 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 %
% 8.42/6.96
% 8.42/6.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.42/6.96
% 8.42/6.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.42/6.96 % ------ Proving...
% 8.42/6.96 % ------ Problem Properties
% 8.42/6.96
% 8.42/6.96 %
% 8.42/6.96 % clauses 187
% 8.42/6.96 % conjectures 3
% 8.42/6.96 % EPR 54
% 8.42/6.96 % Horn 119
% 8.42/6.96 % unary 22
% 8.42/6.96 % binary 40
% 8.42/6.96 % lits 627
% 8.42/6.96 % lits eq 82
% 8.42/6.96 % fd_pure 0
% 8.42/6.96 % fd_pseudo 0
% 8.42/6.96 % fd_cond 21
% 8.42/6.96 % fd_pseudo_cond 14
% 8.42/6.96 % AC symbols 0
% 8.42/6.96
% 8.42/6.96 % ------ Schedule dynamic 5 is on
% 8.42/6.96
% 8.42/6.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.42/6.96
% 8.42/6.96
% 8.42/6.96 % ------
% 8.42/6.96 % Current options:
% 8.42/6.96 % ------
% 8.42/6.96
% 8.42/6.96
% 8.42/6.96 %
% 8.42/6.96
% 8.42/6.96 % ------ Proving...
% 8.42/6.96 %
% 8.42/6.96
% 8.42/6.96 % SZS status Theorem for theBenchmark.p
% 8.42/6.96
% 8.42/6.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.42/6.96
% 8.42/6.96
%------------------------------------------------------------------------------