%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC065+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 : n020.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 08:54:08 AM UTC 2026
% Result : Theorem 24.55s 8.80s
% Output : CNFRefutation 24.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 79 ( 22 unt; 0 def)
% Number of atoms : 250 ( 96 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 290 ( 119 ~; 121 |; 23 &)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 22 !; 11 ?)
% 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(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ) ).
fof(ax55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ) ).
fof(ax83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X8] :
( segmentP(X0,X8)
& segmentP(X1,X8)
& neq(X8,nil)
& ssList(X8) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X8] :
( segmentP(X0,X8)
& segmentP(X1,X8)
& neq(X8,nil)
& ssList(X8) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c17,plain,
( app(X0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(X1,X2)
| ~ 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(c94,plain,
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax15]) ).
cnf(c95,plain,
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax15]) ).
cnf(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c140,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[ax48]) ).
cnf(c148,plain,
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax55]) ).
cnf(c191,plain,
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax83]) ).
cnf(c192,plain,
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax83]) ).
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(c214,plain,
ssList(sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
app(sK255,sK257) = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( nil != sK255
| nil = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( ~ neq(X0,nil)
| ~ ssList(X0)
| nil = sK254
| ~ segmentP(sK254,X0)
| ~ segmentP(sK253,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
( neq(sK254,nil)
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(equality_resolution,[status(thm)],[c94]) ).
cnf(d1,plain,
app(sK253,sK257) = sK256,
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d2,plain,
app(sK253,sK257) = sK254,
inference(demodulation,[status(thm)],[d1,c212]) ).
cnf(d3,plain,
( ~ ssList(sK253)
| ~ ssList(sK257)
| nil = sK253
| nil != sK254 ),
inference(superposition,[status(thm)],[d2,c192]) ).
cnf(d4,plain,
( ~ ssList(sK257)
| nil != sK254
| nil = sK253 ),
inference(resolution,[status(thm)],[c208,d3]) ).
cnf(d5,plain,
( nil != sK254
| nil = sK253 ),
inference(resolution,[status(thm)],[c214,d4]) ).
cnf(d6,plain,
( nil = sK256
| nil != sK253 ),
inference(demodulation,[status(thm)],[c218,c213]) ).
cnf(d7,plain,
( nil = sK254
| nil != sK253 ),
inference(demodulation,[status(thm)],[d6,c212]) ).
cnf(d8,plain,
app(nil,sK253) = sK253,
inference(resolution,[status(thm)],[c111,c208]) ).
cnf(d9,plain,
( segmentP(X1,sK253)
| ~ ssList(nil)
| ~ ssList(sK253)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(superposition,[status(thm)],[d8,c21]) ).
cnf(d10,plain,
( segmentP(X1,sK253)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(resolution,[status(thm)],[c208,d9]) ).
cnf(d11,plain,
( segmentP(X1,sK253)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(resolution,[status(thm)],[c97,d10]) ).
cnf(d12,plain,
( segmentP(X0,sK253)
| ~ ssList(sK257)
| ~ ssList(X0)
| sK254 != X0 ),
inference(superposition,[status(thm)],[d2,d11]) ).
cnf(d13,plain,
( segmentP(X0,sK253)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c214,d12]) ).
cnf(d14,plain,
( segmentP(sK254,sK253)
| ~ ssList(sK254) ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
segmentP(sK254,sK253),
inference(resolution,[status(thm)],[c209,d14]) ).
cnf(d16,plain,
( ~ segmentP(sK253,sK253)
| ~ ssList(sK253)
| ~ neq(sK253,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d15,c220]) ).
cnf(d17,plain,
( ~ segmentP(sK253,sK253)
| ~ neq(sK253,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c208,d16]) ).
cnf(d18,plain,
( ~ ssList(sK253)
| ~ neq(sK253,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d17,c148]) ).
cnf(d19,plain,
( ~ neq(sK253,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c208,d18]) ).
cnf(d20,plain,
( ~ ssList(sK253)
| ~ ssList(nil)
| sK253 = nil
| nil = sK254 ),
inference(resolution,[status(thm)],[d19,c95]) ).
cnf(d21,plain,
( ~ ssList(nil)
| sK253 = nil
| nil = sK254 ),
inference(resolution,[status(thm)],[c208,d20]) ).
cnf(d22,plain,
( sK253 = nil
| nil = sK254 ),
inference(resolution,[status(thm)],[c97,d21]) ).
cnf(d23,plain,
( nil = sK254
| nil = sK254
| nil != nil ),
inference(superposition,[status(thm)],[d22,d7]) ).
cnf(d24,plain,
nil = sK254,
inference(equality_resolution,[status(thm)],[d23]) ).
cnf(d25,plain,
nil = sK253,
inference(resolution,[status(thm)],[d24,d5]) ).
cnf(d26,plain,
( neq(nil,nil)
| nil != sK253 ),
inference(demodulation,[status(thm)],[c221,d24]) ).
cnf(d27,plain,
( neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
( ~ ssList(sK253)
| ~ ssList(sK257)
| nil = sK257
| nil != sK254 ),
inference(superposition,[status(thm)],[d2,c191]) ).
cnf(d29,plain,
( ~ ssList(sK257)
| nil = sK257
| nil != sK254 ),
inference(resolution,[status(thm)],[c208,d28]) ).
cnf(d30,plain,
( nil = sK257
| nil != sK254 ),
inference(resolution,[status(thm)],[c214,d29]) ).
cnf(d31,plain,
nil = sK257,
inference(resolution,[status(thm)],[d24,d30]) ).
cnf(d32,plain,
( rearsegP(X0,sK257)
| ~ ssList(sK257)
| ~ ssList(X0)
| ~ ssList(sK253)
| sK254 != X0 ),
inference(superposition,[status(thm)],[d2,c17]) ).
cnf(d33,plain,
( rearsegP(X0,sK257)
| ~ ssList(sK257)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c208,d32]) ).
cnf(d34,plain,
( rearsegP(X0,sK257)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c214,d33]) ).
cnf(d35,plain,
( rearsegP(sK254,sK257)
| ~ ssList(sK254) ),
inference(equality_resolution,[status(thm)],[d34]) ).
cnf(d36,plain,
rearsegP(sK254,sK257),
inference(resolution,[status(thm)],[c209,d35]) ).
cnf(d37,plain,
( ~ rearsegP(sK257,sK254)
| ~ ssList(sK254)
| ~ ssList(sK257)
| sK257 = sK254 ),
inference(resolution,[status(thm)],[c140,d36]) ).
cnf(d38,plain,
( ~ rearsegP(sK257,sK254)
| ~ ssList(sK257)
| sK257 = sK254 ),
inference(resolution,[status(thm)],[c209,d37]) ).
cnf(d39,plain,
( ~ rearsegP(sK257,sK254)
| sK257 = sK254 ),
inference(resolution,[status(thm)],[c214,d38]) ).
cnf(d40,plain,
( ~ rearsegP(sK257,sK254)
| sK257 = nil ),
inference(demodulation,[status(thm)],[d39,d24]) ).
cnf(d41,plain,
( ~ rearsegP(sK257,nil)
| sK257 = nil ),
inference(demodulation,[status(thm)],[d40,d24]) ).
cnf(d42,plain,
( ~ rearsegP(sK257,nil)
| nil = nil ),
inference(demodulation,[status(thm)],[d41,d31]) ).
cnf(d43,plain,
( ~ rearsegP(nil,nil)
| nil = nil ),
inference(demodulation,[status(thm)],[d42,d31]) ).
cnf(d44,plain,
rearsegP(nil,sK257),
inference(demodulation,[status(thm)],[d36,d24]) ).
cnf(d45,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm)],[d44,d31]) ).
cnf(d46,plain,
nil = nil,
inference(resolution,[status(thm)],[d45,d43]) ).
cnf(d47,plain,
neq(nil,nil),
inference(resolution,[status(thm)],[d46,d27]) ).
cnf(d48,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[d47,d0]) ).
cnf(d49,plain,
$false,
inference(resolution,[status(thm)],[c97,d48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC065+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n020.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 12:11:10 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.55/8.80 % SZS status Theorem for theBenchmark.p
% 24.55/8.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------