%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC108+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 : Sun Sep 27 08:54:18 AM UTC 2026
% Result : Theorem 59.27s 18.59s
% Output : CNFRefutation 59.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 14 unt; 0 def)
% Number of atoms : 227 ( 68 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 258 ( 101 ~; 125 |; 9 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ) ).
fof(ax7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ) ).
fof(ax55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ) ).
fof(ax56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ) ).
fof(ax84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ~ rearsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ~ rearsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c15,plain,
( ssList(sK19(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax6]) ).
cnf(c16,plain,
( app(sK19(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax6]) ).
cnf(c21,plain,
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| segmentP(X0,X1) ),
inference(clausification,[status(esa)],[ax7]) ).
cnf(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
cnf(c144,plain,
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax52]) ).
cnf(c148,plain,
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax55]) ).
cnf(c149,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| segmentP(app(app(X0,X1),X2),X3) ),
inference(clausification,[status(esa)],[ax56]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
cnf(c208,plain,
ssList(sK253),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c209,plain,
ssList(sK254),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c212,plain,
sK254 = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c213,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( ~ segmentP(sK254,sK253)
| ~ neq(sK253,nil)
| nil = sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( neq(sK254,nil)
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( ~ segmentP(sK254,sK253)
| ~ neq(sK253,nil)
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( neq(sK255,nil)
| nil = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( neq(sK255,nil)
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
( rearsegP(sK256,sK255)
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( rearsegP(sK256,sK255)
| nil = sK253 ),
inference(demodulation,[status(thm)],[c221,c213]) ).
cnf(d1,plain,
( rearsegP(sK254,sK255)
| nil = sK253 ),
inference(demodulation,[status(thm)],[d0,c212]) ).
cnf(d2,plain,
( rearsegP(sK254,sK253)
| nil = sK253 ),
inference(demodulation,[status(thm)],[d1,c213]) ).
cnf(d3,plain,
( neq(sK255,nil)
| nil = sK253 ),
inference(demodulation,[status(thm)],[c220,c213]) ).
cnf(d4,plain,
( neq(sK253,nil)
| nil = sK253 ),
inference(demodulation,[status(thm)],[d3,c213]) ).
cnf(d5,plain,
app(sK254,nil) = sK254,
inference(resolution,[status(thm)],[c194,c209]) ).
cnf(d6,plain,
( nil = sK253
| ~ ssList(sK253)
| ~ ssList(sK254)
| app(sK19(sK254,sK253),sK253) = sK254 ),
inference(resolution,[status(thm)],[c16,d2]) ).
cnf(d7,plain,
( ~ ssList(sK254)
| nil = sK253
| app(sK19(sK254,sK253),sK253) = sK254 ),
inference(resolution,[status(thm)],[c208,d6]) ).
cnf(d8,plain,
( nil = sK253
| app(sK19(sK254,sK253),sK253) = sK254 ),
inference(resolution,[status(thm)],[c209,d7]) ).
cnf(d9,plain,
( nil = sK253
| segmentP(X1,sK253)
| ~ ssList(sK19(sK254,sK253))
| ~ ssList(sK253)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK254,X0) != X1 ),
inference(superposition,[status(thm)],[d8,c21]) ).
cnf(d10,plain,
( segmentP(X1,sK253)
| ~ ssList(sK19(sK254,sK253))
| ~ ssList(X0)
| ~ ssList(X1)
| nil = sK253
| app(sK254,X0) != X1 ),
inference(resolution,[status(thm)],[c208,d9]) ).
cnf(d11,plain,
( segmentP(app(sK254,X0),sK253)
| ~ ssList(sK19(sK254,sK253))
| ~ ssList(X0)
| ~ ssList(app(sK254,X0))
| nil = sK253 ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( ~ ssList(sK19(sK254,sK253))
| ~ ssList(app(sK254,nil))
| ~ ssList(nil)
| nil = sK253
| segmentP(sK254,sK253) ),
inference(superposition,[status(thm)],[d5,d11]) ).
cnf(d13,plain,
( segmentP(sK254,sK253)
| ~ ssList(sK19(sK254,sK253))
| ~ ssList(nil)
| ~ ssList(sK254)
| nil = sK253 ),
inference(demodulation,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( segmentP(sK254,sK253)
| ~ ssList(sK19(sK254,sK253))
| ~ ssList(nil)
| nil = sK253 ),
inference(resolution,[status(thm)],[c209,d13]) ).
cnf(d15,plain,
( segmentP(sK254,sK253)
| ~ ssList(sK19(sK254,sK253))
| nil = sK253 ),
inference(resolution,[status(thm)],[c97,d14]) ).
cnf(d16,plain,
( ~ rearsegP(sK254,sK253)
| ~ ssList(sK253)
| ~ ssList(sK254)
| segmentP(sK254,sK253)
| nil = sK253 ),
inference(resolution,[status(thm)],[d15,c15]) ).
cnf(d17,plain,
( segmentP(sK254,sK253)
| ~ rearsegP(sK254,sK253)
| ~ ssList(sK254)
| nil = sK253 ),
inference(resolution,[status(thm)],[c208,d16]) ).
cnf(d18,plain,
( segmentP(sK254,sK253)
| ~ rearsegP(sK254,sK253)
| nil = sK253 ),
inference(resolution,[status(thm)],[c209,d17]) ).
cnf(d19,plain,
( nil = sK253
| segmentP(sK254,sK253)
| nil = sK253 ),
inference(resolution,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
( ~ neq(sK253,nil)
| nil = sK254
| nil = sK253 ),
inference(resolution,[status(thm)],[d19,c215]) ).
cnf(d21,plain,
( nil = sK253
| nil = sK254
| nil = sK253 ),
inference(resolution,[status(thm)],[d20,d4]) ).
cnf(d22,plain,
( nil = sK253
| nil = sK253
| rearsegP(nil,sK253) ),
inference(superposition,[status(thm)],[d21,d2]) ).
cnf(d23,plain,
( ~ ssList(sK253)
| nil = sK253
| nil = sK253 ),
inference(resolution,[status(thm)],[d22,c144]) ).
cnf(d24,plain,
nil = sK253,
inference(resolution,[status(thm)],[c208,d23]) ).
cnf(d25,plain,
( neq(sK255,nil)
| nil = sK254 ),
inference(demodulation,[status(thm)],[c218,c212]) ).
cnf(d26,plain,
( neq(sK253,nil)
| nil = sK254 ),
inference(demodulation,[status(thm)],[d25,c213]) ).
cnf(d27,plain,
( neq(nil,nil)
| nil = sK254 ),
inference(demodulation,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
( ~ segmentP(sK254,sK253)
| ~ neq(sK253,nil) ),
inference(resolution,[status(thm)],[d24,c217]) ).
cnf(d29,plain,
( ~ segmentP(sK254,sK253)
| ~ neq(nil,nil) ),
inference(demodulation,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
( ~ segmentP(sK254,nil)
| ~ neq(nil,nil) ),
inference(demodulation,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
( ~ segmentP(nil,X1)
| ~ ssList(nil)
| ~ ssList(sK254)
| ~ ssList(X0)
| ~ ssList(X1)
| segmentP(app(sK254,X0),X1) ),
inference(superposition,[status(thm)],[d5,c149]) ).
cnf(d32,plain,
( ~ segmentP(nil,X0)
| segmentP(app(sK254,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c209,d31]) ).
cnf(d33,plain,
( ~ segmentP(nil,X1)
| segmentP(app(sK254,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c97,d32]) ).
cnf(d34,plain,
( ~ segmentP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| segmentP(sK254,X0) ),
inference(superposition,[status(thm)],[d5,d33]) ).
cnf(d35,plain,
( segmentP(sK254,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c97,d34]) ).
cnf(d36,plain,
( ~ ssList(nil)
| segmentP(sK254,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d35,c148]) ).
cnf(d37,plain,
segmentP(sK254,nil),
inference(resolution,[status(thm)],[c97,d36]) ).
cnf(d38,plain,
~ neq(nil,nil),
inference(resolution,[status(thm)],[d37,d30]) ).
cnf(d39,plain,
nil = sK254,
inference(resolution,[status(thm)],[d38,d27]) ).
cnf(d40,plain,
neq(sK254,nil),
inference(resolution,[status(thm)],[d24,c216]) ).
cnf(d41,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
$false,
inference(resolution,[status(thm)],[d38,d41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC108+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.45 % Computer : n015.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Sat Sep 26 12:19:04 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 59.27/18.59 % SZS status Theorem for theBenchmark.p
% 59.27/18.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------