%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC083+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 : n005.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 03:07:49 PM UTC 2026
% Result : Theorem 14.54s 2.80s
% Output : CNFRefutation 14.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 139 ( 50 unt; 3 def)
% Number of atoms : 528 ( 80 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 563 ( 247 ~; 233 |; 52 &)
% ( 6 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 159 ( 0 sgn 138 !; 21 ?; 40 :)
% 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(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(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
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] :
( ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( app(X5,X7) != X3
| app(app(X5,X6),X7) != X2
| ~ ssList(X7) ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| 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] :
( ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( app(X5,X7) != X3
| app(app(X5,X6),X7) != X2
| ~ ssList(X7) ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3
| ~ ssList(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(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(f154,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f155,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ) ) ),
inference(flattening,[],[f154]) ).
fof(f172,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
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] :
( ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( app(X5,X7) = X3
& app(app(X5,X6),X7) = X2
& ssList(X7) ) ) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f239,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(f240,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,[],[f239]) ).
fof(f241,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))],[f240]) ).
fof(f245,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(f246,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,[],[f245]) ).
fof(f247,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))],[f246]) ).
fof(f272,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f295,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK57)
& ssList(sK58)
& sK56 = app(sK57,sK59)
& sK55 = app(app(sK57,sK58),sK59)
& ssList(sK59)
& ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X5,sK57),skolemize(X6,sK58),skolemize(X7,sK59)],[f221]) ).
fof(f308,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f241]) ).
fof(f309,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ssList(sK11(X0,X1)) ),
inference(cnf_transformation,[],[f241]) ).
fof(f310,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f241]) ).
fof(f317,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,[],[f247]) ).
fof(f386,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f400,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f402,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f423,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f439,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f481,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f496,plain,
ssList(sK54),
inference(cnf_transformation,[],[f295]) ).
fof(f498,plain,
ssList(sK57),
inference(cnf_transformation,[],[f295]) ).
fof(f499,plain,
ssList(sK58),
inference(cnf_transformation,[],[f295]) ).
fof(f500,plain,
sK56 = app(sK57,sK59),
inference(cnf_transformation,[],[f295]) ).
fof(f501,plain,
sK55 = app(app(sK57,sK58),sK59),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
ssList(sK59),
inference(cnf_transformation,[],[f295]) ).
fof(f503,plain,
! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f295]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f504,f506]) ).
fof(f509,plain,
! [X4] :
( ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f503,f506,f505]) ).
fof(f510,plain,
ssList(sK56),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f511,plain,
ssList(sK55),
inference(definition_unfolding,[],[f495,f505]) ).
fof(f515,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f310]) ).
fof(f517,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,[],[f317]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ssList(sK11(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( app(X1,sK11(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f308]) ).
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,[],[f517]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f386]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f388]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f400]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f402]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f423]) ).
tcf(c_192,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f439]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f481]) ).
tcf(c_247,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f508]) ).
tcf(c_248,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f509]) ).
tcf(c_249,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f502]) ).
tcf(c_250,negated_conjecture,
app(app(sK57,sK58),sK59) = sK55,
inference(cnf_transformation,[],[f501]) ).
tcf(c_251,negated_conjecture,
app(sK57,sK59) = sK56,
inference(cnf_transformation,[],[f500]) ).
tcf(c_252,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f499]) ).
tcf(c_253,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f498]) ).
tcf(c_255,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f510]) ).
tcf(c_256,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f511]) ).
tcf(c_378,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_3224,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_248]) ).
tcf(c_3225,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3224]) ).
tcf(c_3227,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3225,c_141,c_3225]) ).
tcf(c_3228,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3227]) ).
tcf(c_3255,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ( nil != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_247,c_248]) ).
tcf(c_3256,plain,
( ~ ssList(sK56)
| ~ segmentP(sK55,sK56)
| ~ segmentP(sK56,sK56) ),
inference(unflattening,[status(thm)],[c_3255]) ).
tcf(c_3257,plain,
( ~ segmentP(sK56,sK56)
| ~ segmentP(sK55,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_3256,c_255,c_3256]) ).
tcf(c_3258,plain,
( ~ segmentP(sK55,sK56)
| ~ segmentP(sK56,sK56) ),
inference(renaming,[status(thm)],[c_3257]) ).
tcf(c_8883,definition,
iPr_def_10 = app(sK57,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8884,definition,
iPr_def_11 = app(sK57,sK58),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8885,definition,
iPr_def_12 = app(iPr_def_11,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8886,plain,
( ~ segmentP(sK55,sK56)
| ~ segmentP(sK56,sK56) ),
inference(demodulation,[status(thm)],[c_3258]) ).
tcf(c_8888,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3228]) ).
tcf(c_8889,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_256]) ).
tcf(c_8890,negated_conjecture,
ssList(sK57),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_8891,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_252]) ).
tcf(c_8892,negated_conjecture,
iPr_def_10 = sK56,
inference(demodulation,[status(thm)],[c_251,c_8883]) ).
tcf(c_8893,negated_conjecture,
iPr_def_12 = sK55,
inference(demodulation,[status(thm)],[c_250,c_8884,c_8885]) ).
tcf(c_8894,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_8895,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_255]) ).
tcf(c_11735,plain,
ssList(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_8889,c_8893]) ).
tcf(c_11736,plain,
ssList(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_8895,c_8892]) ).
tcf(c_11738,plain,
( ~ segmentP(iPr_def_12,iPr_def_10)
| ~ segmentP(iPr_def_10,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_8886,c_8892,c_8893]) ).
tcf(c_11741,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(iPr_def_12,X0)
| ~ segmentP(iPr_def_10,X0) ),
inference(light_normalisation,[status(thm)],[c_8888,c_8892,c_8893]) ).
tcf(c_11838,plain,
( ~ ssList(iPr_def_10)
| ~ segmentP(iPr_def_12,iPr_def_10) ),
inference(superposition,[status(thm)],[c_192,c_11738]) ).
tcf(c_11840,plain,
~ segmentP(iPr_def_12,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_11838,c_11736]) ).
tcf(c_12075,plain,
app(nil,sK59) = sK59,
inference(superposition,[status(thm)],[c_8894,c_155]) ).
tcf(c_12077,plain,
app(nil,sK57) = sK57,
inference(superposition,[status(thm)],[c_8890,c_155]) ).
tcf(c_12159,plain,
app(iPr_def_12,nil) = iPr_def_12,
inference(superposition,[status(thm)],[c_11735,c_232]) ).
tcf(c_12274,plain,
( ssList(iPr_def_11)
| ~ ssList(sK58)
| ~ ssList(sK57) ),
inference(superposition,[status(thm)],[c_8884,c_153]) ).
tcf(c_12289,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_12274,c_8891,c_8890]) ).
tcf(c_13173,plain,
( frontsegP(iPr_def_11,sK57)
| ~ ssList(sK58)
| ~ ssList(sK57) ),
inference(superposition,[status(thm)],[c_8884,c_378]) ).
tcf(c_13214,plain,
frontsegP(iPr_def_11,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_13173,c_8891,c_8890]) ).
tcf(c_18467,plain,
! [X0: $i] :
( frontsegP(iPr_def_12,X0)
| ~ ssList(iPr_def_11)
| ~ ssList(sK59)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_8885,c_176]) ).
tcf(c_18544,plain,
! [X0: $i] :
( frontsegP(iPr_def_12,X0)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_11,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18467,c_12289,c_8894]) ).
tcf(c_21668,plain,
( frontsegP(iPr_def_12,sK57)
| ~ ssList(sK57) ),
inference(superposition,[status(thm)],[c_13214,c_18544]) ).
tcf(c_21671,plain,
frontsegP(iPr_def_12,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_21668,c_8890]) ).
tcf(c_21674,plain,
( ( app(sK57,sK11(iPr_def_12,sK57)) = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK57) ),
inference(superposition,[status(thm)],[c_21671,c_63]) ).
tcf(c_21675,plain,
app(sK57,sK11(iPr_def_12,sK57)) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_21674,c_11735,c_8890]) ).
tcf(c_27688,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),sK59)
| ~ ssList(iPr_def_11)
| ~ ssList(sK59)
| ~ ssList(X0)
| ~ ssList(app(app(iPr_def_11,sK59),X0)) ),
inference(superposition,[status(thm)],[c_8885,c_67]) ).
tcf(c_27691,plain,
! [X0: $i] :
( segmentP(app(sK57,X0),sK57)
| ~ ssList(sK57)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK57),X0)) ),
inference(superposition,[status(thm)],[c_12077,c_67]) ).
tcf(c_27817,plain,
! [X0: $i] :
( segmentP(app(sK57,X0),sK57)
| ~ ssList(sK57)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(sK57,X0)) ),
inference(light_normalisation,[status(thm)],[c_27691,c_12077]) ).
tcf(c_27818,plain,
! [X0: $i] :
( segmentP(app(sK57,X0),sK57)
| ~ ssList(X0)
| ~ ssList(app(sK57,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27817,c_8890,c_141]) ).
tcf(c_27832,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),sK59)
| ~ ssList(iPr_def_11)
| ~ ssList(sK59)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_12,X0)) ),
inference(light_normalisation,[status(thm)],[c_27688,c_8885]) ).
tcf(c_27833,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),sK59)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_12,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27832,c_12289,c_8894]) ).
tcf(c_29737,plain,
( segmentP(iPr_def_10,sK57)
| ~ ssList(sK59)
| ~ ssList(app(sK57,sK59)) ),
inference(superposition,[status(thm)],[c_8883,c_27818]) ).
tcf(c_29742,plain,
( segmentP(iPr_def_12,sK57)
| ~ ssList(sK11(iPr_def_12,sK57))
| ~ ssList(app(sK57,sK11(iPr_def_12,sK57))) ),
inference(superposition,[status(thm)],[c_21675,c_27818]) ).
tcf(c_29748,plain,
( segmentP(iPr_def_10,sK57)
| ~ ssList(iPr_def_10)
| ~ ssList(sK59) ),
inference(light_normalisation,[status(thm)],[c_29737,c_8883]) ).
tcf(c_29749,plain,
segmentP(iPr_def_10,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_29748,c_11736,c_8894]) ).
tcf(c_29752,plain,
( segmentP(iPr_def_12,sK57)
| ~ ssList(iPr_def_12)
| ~ ssList(sK11(iPr_def_12,sK57)) ),
inference(light_normalisation,[status(thm)],[c_29742,c_21675]) ).
tcf(c_29753,plain,
( segmentP(iPr_def_12,sK57)
| ~ ssList(sK11(iPr_def_12,sK57)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29752,c_11735]) ).
tcf(c_30547,plain,
( segmentP(iPr_def_12,sK57)
| ~ ssList(iPr_def_12)
| ~ ssList(sK57)
| ~ frontsegP(iPr_def_12,sK57) ),
inference(superposition,[status(thm)],[c_62,c_29753]) ).
tcf(c_30548,plain,
segmentP(iPr_def_12,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_30547,c_11735,c_8890,c_21671]) ).
tcf(c_30552,plain,
( ( nil = sK57 )
| ~ ssList(sK57)
| ~ segmentP(iPr_def_10,sK57) ),
inference(superposition,[status(thm)],[c_30548,c_11741]) ).
tcf(c_30553,plain,
nil = sK57,
inference(forward_subsumption_resolution,[status(thm)],[c_30552,c_8890,c_29749]) ).
tcf(c_30608,plain,
app(nil,sK59) = iPr_def_10,
inference(demodulation,[status(thm)],[c_8883,c_30553]) ).
tcf(c_30610,plain,
sK59 = iPr_def_10,
inference(demodulation,[status(thm)],[c_12075,c_30608]) ).
tcf(c_31287,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_10)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_12,X0)) ),
inference(light_normalisation,[status(thm)],[c_27833,c_30610]) ).
tcf(c_31297,plain,
( segmentP(iPr_def_12,iPr_def_10)
| ~ ssList(nil)
| ~ ssList(app(iPr_def_12,nil)) ),
inference(superposition,[status(thm)],[c_12159,c_31287]) ).
tcf(c_31302,plain,
( segmentP(iPr_def_12,iPr_def_10)
| ~ ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(light_normalisation,[status(thm)],[c_31297,c_12159]) ).
tcf(c_31303,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_31302,c_11840,c_11735,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 16:17:32 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 14.54/2.80 % SZS status Started for theBenchmark.p
% 14.54/2.80 % SZS status Theorem for theBenchmark.p
% 14.54/2.80
% 14.54/2.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.54/2.80
% 14.54/2.80 % ------ iProver source info
% 14.54/2.80
% 14.54/2.80 % git: date: 2026-07-19 20:42:38 +0200
% 14.54/2.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.54/2.80 % git: non_committed_changes: false
% 14.54/2.80
% 14.54/2.80 % ------ Parsing...
% 14.54/2.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.54/2.80
% 14.54/2.80 % ------ 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 %
% 14.54/2.80
% 14.54/2.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.54/2.80
% 14.54/2.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.54/2.80 % ------ Proving...
% 14.54/2.80 % ------ Problem Properties
% 14.54/2.80
% 14.54/2.80 %
% 14.54/2.80 % clauses 193
% 14.54/2.80 % conjectures 7
% 14.54/2.80 % EPR 59
% 14.54/2.80 % Horn 125
% 14.54/2.80 % unary 27
% 14.54/2.80 % binary 41
% 14.54/2.80 % lits 635
% 14.54/2.80 % lits eq 85
% 14.54/2.80 % fd_pure 0
% 14.54/2.80 % fd_pseudo 0
% 14.54/2.80 % fd_cond 22
% 14.54/2.80 % fd_pseudo_cond 14
% 14.54/2.80 % AC symbols 0
% 14.54/2.80
% 14.54/2.80 % ------ Schedule dynamic 5 is on
% 14.54/2.80
% 14.54/2.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 14.54/2.80
% 14.54/2.80
% 14.54/2.80 % ------
% 14.54/2.80 % Current options:
% 14.54/2.80 % ------
% 14.54/2.80
% 14.54/2.80
% 14.54/2.80 %
% 14.54/2.80
% 14.54/2.80 % ------ Proving...
% 14.54/2.80 %
% 14.54/2.80
% 14.54/2.80 % SZS status Theorem for theBenchmark.p
% 14.54/2.80
% 14.54/2.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.54/2.80
% 14.54/2.80
%------------------------------------------------------------------------------