%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC123+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 03:07:59 PM UTC 2026
% Result : Theorem 51.35s 7.91s
% Output : CNFRefutation 51.35s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f540ERROR: Could not build tree for root c_117200ERROR: 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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax73) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
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)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ? [X4] :
( equalelemsP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| ~ 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)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ? [X4] :
( equalelemsP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| ~ 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(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
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(f175,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(ennf_transformation,[],[f57]) ).
fof(f185,plain,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f186,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f187,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f186]) ).
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)
& ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& 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)
& ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& 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(f290,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(X1,sK51(X0))],[f187]) ).
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)
& ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,sK55)
| ~ frontsegP(sK56,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4) )
& equalelemsP(sK55)
& frontsegP(sK56,sK55)
& 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(f311,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(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(f396,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
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(f442,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(cnf_transformation,[],[f175]) ).
fof(f467,plain,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f185]) ).
fof(f469,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK51(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f470,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f290]) ).
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,
( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,sK55)
| ~ frontsegP(sK56,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
frontsegP(sK56,sK55),
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,
( ~ segmentP(sK56,sK55)
| ~ neq(sK55,nil) ),
inference(definition_unfolding,[],[f500,f505,f506,f505]) ).
fof(f509,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f506]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f505]) ).
fof(f514,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f311]) ).
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_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f514]) ).
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,[],[f540]) ).
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_148,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f396]) ).
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,[],[f542]) ).
tcf(c_194,plain,
! [X0: $i] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f442]) ).
tcf(c_217,plain,
! [X0: $i] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f467]) ).
tcf(c_219,plain,
! [X0: $i] :
( ssItem(sK51(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f470]) ).
tcf(c_220,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK51(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f469]) ).
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,[],[f507]) ).
tcf(c_247,negated_conjecture,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f503]) ).
tcf(c_249,negated_conjecture,
! [X0: $i] :
( ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0)
| ~ neq(sK55,X0) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_250,negated_conjecture,
( ~ segmentP(sK56,sK55)
| ~ neq(sK55,nil) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f509]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f510]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
tcf(c_3229,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equalelemsP(X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X2,sK55)
| ~ frontsegP(sK56,X2)
| ( X1 != X2 )
| ( X0 != sK55 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_249]) ).
tcf(c_3230,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ ssList(sK55)
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3229]) ).
tcf(c_3232,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ equalelemsP(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3230,c_254,c_3230]) ).
tcf(c_3233,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3232]) ).
tcf(c_3255,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK56,sK55)
| ( X1 != nil )
| ( X0 != sK55 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_250]) ).
tcf(c_3256,plain,
( ( sK55 = nil )
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ segmentP(sK56,sK55) ),
inference(unflattening,[status(thm)],[c_3255]) ).
tcf(c_3257,plain,
( ( sK55 = nil )
| ~ segmentP(sK56,sK55) ),
inference(global_subsumption_just,[status(thm)],[c_3256,c_254,c_141,c_3256]) ).
tcf(c_3269,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_246]) ).
tcf(c_3270,plain,
( ~ ssList(nil)
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3269]) ).
tcf(c_3271,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3270,c_141,c_3270]) ).
tcf(c_9354,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_3271]) ).
tcf(c_9355,plain,
( ( sK55 = nil )
| ~ segmentP(sK56,sK55) ),
inference(demodulation,[status(thm)],[c_3257]) ).
tcf(c_9356,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3233]) ).
tcf(c_9357,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_9358,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_9360,negated_conjecture,
frontsegP(sK56,sK55),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_12541,plain,
app(nil,sK55) = sK55,
inference(superposition,[status(thm)],[c_9357,c_155]) ).
tcf(c_13834,plain,
( ( nil = sK56 )
| ( hd(sK56) = sK51(sK56) ) ),
inference(superposition,[status(thm)],[c_9358,c_220]) ).
tcf(c_13838,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_13834,c_9354]) ).
tcf(c_14009,plain,
( ( nil = sK56 )
| ( tl(sK56) = sK52(sK56) ) ),
inference(superposition,[status(thm)],[c_9358,c_222]) ).
tcf(c_14013,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14009,c_9354]) ).
tcf(c_14159,plain,
( ssItem(hd(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_13838,c_219]) ).
tcf(c_14160,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14159,c_9354,c_9358]) ).
tcf(c_14169,plain,
( ssList(tl(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_14013,c_221]) ).
tcf(c_14170,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14169,c_9354,c_9358]) ).
tcf(c_14181,plain,
app(nil,tl(sK56)) = tl(sK56),
inference(superposition,[status(thm)],[c_14170,c_155]) ).
tcf(c_14527,plain,
( frontsegP(tl(sK56),nil)
| ~ ssList(nil)
| ~ ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_14181,c_377]) ).
tcf(c_14528,plain,
frontsegP(tl(sK56),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_14527,c_141,c_14170]) ).
tcf(c_15957,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_16156,plain,
( ( app(sK55,sK11(sK56,sK55)) = sK56 )
| ~ ssList(sK55)
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_9360,c_63]) ).
tcf(c_16171,plain,
app(sK55,sK11(sK56,sK55)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_16156,c_9357,c_9358]) ).
tcf(c_22270,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(hd(sK56))
| ( cons(hd(sK56),X0) != nil ) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_22271,plain,
! [X0: $i] :
( ssList(cons(hd(sK56),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_22276,plain,
( equalelemsP(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_217]) ).
tcf(c_22281,plain,
( ssList(cons(hd(sK56),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_22271]) ).
tcf(c_22282,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK56))
| ( cons(hd(sK56),nil) != nil ) ),
inference(instantiation,[status(thm)],[c_22270]) ).
tcf(c_24800,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_15957]) ).
tcf(c_24815,plain,
! [X0: $i] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12541,c_24800]) ).
tcf(c_24859,plain,
! [X0: $i] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24815,c_9357,c_141]) ).
tcf(c_25890,plain,
( segmentP(sK56,sK55)
| ~ ssList(sK11(sK56,sK55)) ),
inference(superposition,[status(thm)],[c_16171,c_24859]) ).
tcf(c_26549,plain,
( segmentP(sK56,sK55)
| ~ ssList(sK55)
| ~ ssList(sK56)
| ~ frontsegP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_62,c_25890]) ).
tcf(c_26550,plain,
segmentP(sK56,sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_26549,c_9357,c_9358,c_9360]) ).
tcf(c_99899,plain,
sK55 = nil,
inference(global_subsumption_just,[status(thm)],[c_9355,c_3257,c_26550]) ).
tcf(c_99911,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,nil)
| ~ frontsegP(sK56,X0) ),
inference(light_normalisation,[status(thm)],[c_9356,c_99899]) ).
tcf(c_100059,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ frontsegP(sK56,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_99911,c_194]) ).
tcf(c_103908,plain,
( ( nil = sK56 )
| ( hd(sK56) = sK51(sK56) ) ),
inference(superposition,[status(thm)],[c_9358,c_220]) ).
tcf(c_103909,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_103908,c_9354]) ).
tcf(c_104033,plain,
( ( nil = sK56 )
| ( tl(sK56) = sK52(sK56) ) ),
inference(superposition,[status(thm)],[c_9358,c_222]) ).
tcf(c_104034,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_104033,c_9354]) ).
tcf(c_104318,plain,
( ssItem(hd(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_103909,c_219]) ).
tcf(c_104319,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_104318,c_9354,c_9358]) ).
tcf(c_104326,plain,
( ssList(tl(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_104034,c_221]) ).
tcf(c_104327,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_104326,c_9354,c_9358]) ).
tcf(c_105761,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_9358,c_224]) ).
tcf(c_105763,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_105761,c_9354]) ).
tcf(c_110246,plain,
! [X0: $i] :
( frontsegP(sK56,cons(hd(sK56),X0))
| ~ ssList(X0)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ frontsegP(tl(sK56),X0) ),
inference(superposition,[status(thm)],[c_105763,c_177]) ).
tcf(c_110273,plain,
! [X0: $i] :
( frontsegP(sK56,cons(hd(sK56),X0))
| ~ ssList(X0)
| ~ frontsegP(tl(sK56),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_110246,c_104327,c_104319]) ).
tcf(c_117167,plain,
! [X0: $i] :
( ( cons(hd(sK56),X0) = nil )
| ~ ssList(X0)
| ~ frontsegP(tl(sK56),X0)
| ~ equalelemsP(cons(hd(sK56),X0))
| ~ ssList(cons(hd(sK56),X0)) ),
inference(superposition,[status(thm)],[c_110273,c_100059]) ).
tcf(c_117199,plain,
( ( cons(hd(sK56),nil) = nil )
| ~ ssList(nil)
| ~ frontsegP(tl(sK56),nil)
| ~ equalelemsP(cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(instantiation,[status(thm)],[c_117167]) ).
tcf(c_117200,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_117199,c_22282,c_22281,c_22276,c_14528,c_14160,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC123+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 16:28:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 51.35/7.91 % SZS status Started for theBenchmark.p
% 51.35/7.91 % SZS status Theorem for theBenchmark.p
% 51.35/7.91
% 51.35/7.91 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 51.35/7.91
% 51.35/7.91 % ------ iProver source info
% 51.35/7.91
% 51.35/7.91 % git: date: 2026-07-19 20:42:38 +0200
% 51.35/7.91 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 51.35/7.91 % git: non_committed_changes: false
% 51.35/7.91
% 51.35/7.91 % ------ Parsing...
% 51.35/7.91 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 51.35/7.91
% 51.35/7.91 % ------ 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 %
% 51.35/7.91
% 51.35/7.91 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 51.35/7.91
% 51.35/7.91 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 51.35/7.91 % ------ Proving...
% 51.35/7.91 % ------ Problem Properties
% 51.35/7.91
% 51.35/7.91 %
% 51.35/7.91 % clauses 189
% 51.35/7.91 % conjectures 4
% 51.35/7.91 % EPR 58
% 51.35/7.91 % Horn 121
% 51.35/7.91 % unary 21
% 51.35/7.91 % binary 42
% 51.35/7.91 % lits 635
% 51.35/7.91 % lits eq 83
% 51.35/7.91 % fd_pure 0
% 51.35/7.91 % fd_pseudo 0
% 51.35/7.91 % fd_cond 22
% 51.35/7.91 % fd_pseudo_cond 14
% 51.35/7.91 % AC symbols 0
% 51.35/7.91
% 51.35/7.91 % ------ Schedule dynamic 5 is on
% 51.35/7.91
% 51.35/7.91 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 51.35/7.91
% 51.35/7.91
% 51.35/7.91 % ------
% 51.35/7.91 % Current options:
% 51.35/7.91 % ------
% 51.35/7.91
% 51.35/7.91
% 51.35/7.91 %
% 51.35/7.91
% 51.35/7.91 % ------ Proving...
% 51.35/7.91 %
% 51.35/7.91
% 51.35/7.91 % SZS status Theorem for theBenchmark.p
% 51.35/7.91
% 51.35/7.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 51.35/7.91
% 51.35/7.91
%------------------------------------------------------------------------------