%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC045+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 : n008.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 08:54:04 AM UTC 2026
% Result : Theorem 46.63s 6.68s
% Output : CNFRefutation 46.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 12
% Syntax : Number of formulae : 78 ( 12 unt; 0 def)
% Number of atoms : 335 ( 56 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 472 ( 215 ~; 210 |; 15 &)
% ( 5 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 27 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ) ).
fof(ax5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = 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(ax16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ) ).
fof(ax20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ) ).
fof(ax21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ) ).
fof(ax26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ) ).
fof(ax58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ) ).
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)
=> ( ? [X4] :
( ( ( memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
| ( ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) )
& ~ memberP(X2,X4) ) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3
| nil != X1 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ( ( memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
| ( ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) )
& ~ memberP(X2,X4) ) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3
| nil != X1 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c8,plain,
( ~ ssList(X3)
| app(X1,cons(X0,X3)) != X2
| ~ ssList(X2)
| memberP(X2,X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax3]) ).
cnf(c14,plain,
( ~ ssList(X2)
| app(X2,X0) != X1
| ~ ssList(X1)
| frontsegP(X1,X2)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax5]) ).
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(c96,plain,
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax16]) ).
cnf(c101,plain,
( ssList(sK120(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax20]) ).
cnf(c102,plain,
( ssItem(sK121(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax20]) ).
cnf(c103,plain,
( cons(sK121(X0),sK120(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax20]) ).
cnf(c104,plain,
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax21]) ).
cnf(c109,plain,
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax26]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c137,plain,
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax46]) ).
cnf(c151,plain,
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax58]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
cnf(c209,plain,
ssList(sK254),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c210,plain,
ssList(sK255),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c212,plain,
nil = sK254,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c213,plain,
sK254 = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
nil != sK253,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( ~ memberP(sK255,X0)
| ssList(sK259(X0))
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( ~ memberP(sK255,X0)
| segmentP(sK256,app(app(cons(X0,nil),sK259(X0)),cons(X0,nil)))
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ ssList(cons(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X2)
| memberP(X2,X0)
| ~ ssItem(X0)
| cons(X0,X1) != X2 ),
inference(superposition,[status(thm)],[c111,c8]) ).
cnf(d1,plain,
ssList(nil),
inference(demodulation,[status(thm)],[c209,c212]) ).
cnf(d2,plain,
( ~ ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| memberP(X2,X0)
| ~ ssItem(X0)
| cons(X0,X1) != X2 ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| memberP(cons(X0,X1),X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssList(cons(sK121(X0),sK120(X0)))
| ~ ssList(sK120(X0))
| ~ ssItem(sK121(X0))
| memberP(X0,sK121(X0)) ),
inference(superposition,[status(thm)],[c103,d3]) ).
cnf(d5,plain,
( ~ ssList(sK120(X0))
| ~ ssItem(sK121(X0))
| ~ ssList(sK120(X0))
| ~ ssList(X0)
| memberP(X0,sK121(X0))
| ~ ssItem(sK121(X0))
| nil = X0 ),
inference(resolution,[status(thm)],[d4,c96]) ).
cnf(d6,plain,
nil = sK256,
inference(demodulation,[status(thm)],[c213,c212]) ).
cnf(d7,plain,
( segmentP(nil,app(app(cons(X0,nil),sK259(X0)),cons(X0,nil)))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(demodulation,[status(thm)],[c218,d6]) ).
cnf(d8,plain,
( ~ memberP(sK255,X0)
| ~ ssItem(X0)
| ~ ssList(app(app(cons(X0,nil),sK259(X0)),cons(X0,nil)))
| nil = app(app(cons(X0,nil),sK259(X0)),cons(X0,nil)) ),
inference(resolution,[status(thm)],[c151,d7]) ).
cnf(d9,plain,
( ~ ssList(app(app(cons(X0,nil),sK259(X0)),cons(X0,nil)))
| ~ memberP(sK255,X0)
| ~ ssItem(X0)
| segmentP(X1,sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ ssList(X1)
| nil != X1 ),
inference(superposition,[status(thm)],[d8,c21]) ).
cnf(d10,plain,
( segmentP(nil,sK259(X0))
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ ssList(app(app(cons(X0,nil),sK259(X0)),cons(X0,nil)))
| ~ ssList(nil)
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( segmentP(nil,sK259(X0))
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ ssList(app(app(cons(X0,nil),sK259(X0)),cons(X0,nil)))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d1,d10]) ).
cnf(d12,plain,
( ~ ssList(app(cons(X0,nil),sK259(X0)))
| ~ ssList(cons(X0,nil))
| segmentP(nil,sK259(X0))
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d11,c109]) ).
cnf(d13,plain,
( ~ ssList(cons(X0,nil))
| ~ ssList(sK259(X0))
| segmentP(nil,sK259(X0))
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d12,c109]) ).
cnf(d14,plain,
( ~ ssList(nil)
| ~ ssItem(X0)
| segmentP(nil,sK259(X0))
| ~ ssList(sK259(X0))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d13,c96]) ).
cnf(d15,plain,
( segmentP(nil,sK259(X0))
| ~ ssList(sK259(X0))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d1,d14]) ).
cnf(d16,plain,
( ~ ssList(sK259(X0))
| nil = sK259(X0)
| ~ ssList(sK259(X0))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d15,c151]) ).
cnf(d17,plain,
( ~ ssList(sK259(X0))
| ~ memberP(sK255,X0)
| ~ ssItem(X0)
| ~ memberP(sK255,X0)
| ~ ssItem(X0)
| segmentP(nil,app(app(cons(X0,nil),nil),cons(X0,nil))) ),
inference(superposition,[status(thm)],[d16,d7]) ).
cnf(d18,plain,
( ~ ssList(cons(X0,nil))
| ~ ssList(sK259(X0))
| ~ memberP(sK255,X0)
| ~ ssItem(X0)
| segmentP(nil,app(cons(X0,nil),cons(X0,nil))) ),
inference(superposition,[status(thm)],[c194,d17]) ).
cnf(d19,plain,
( ~ ssList(app(cons(X0,nil),cons(X0,nil)))
| nil = app(cons(X0,nil),cons(X0,nil))
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d18,c151]) ).
cnf(d20,plain,
( ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ ssList(app(cons(X0,nil),cons(X0,nil)))
| ~ memberP(sK255,X0)
| ~ ssItem(X0)
| frontsegP(X1,cons(X0,nil))
| ~ ssList(X1)
| ~ ssList(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| nil != X1 ),
inference(superposition,[status(thm)],[d19,c14]) ).
cnf(d21,plain,
( frontsegP(nil,cons(X0,nil))
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ ssList(app(cons(X0,nil),cons(X0,nil)))
| ~ ssList(nil)
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[d20]) ).
cnf(d22,plain,
( frontsegP(nil,cons(X0,nil))
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ ssList(app(cons(X0,nil),cons(X0,nil)))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d1,d21]) ).
cnf(d23,plain,
( ~ ssList(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| frontsegP(nil,cons(X0,nil))
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d22,c109]) ).
cnf(d24,plain,
( ~ ssList(cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d23,c137]) ).
cnf(d25,plain,
( ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK255,X0)
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssItem(X0)
| nil != nil ),
inference(superposition,[status(thm)],[d24,c104]) ).
cnf(d26,plain,
( ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK255,X0)
| ~ ssItem(X0)
| nil != nil ),
inference(resolution,[status(thm)],[d1,d25]) ).
cnf(d27,plain,
( ~ ssList(sK259(X0))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
( ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(sK259(X0))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d27,c96]) ).
cnf(d29,plain,
( ~ ssList(sK259(X0))
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d1,d28]) ).
cnf(d30,plain,
( ssList(sK259(sK121(sK255)))
| ~ ssItem(sK121(sK255))
| ~ ssList(sK120(sK255))
| ~ ssList(sK255)
| ~ ssItem(sK121(sK255))
| nil = sK255 ),
inference(resolution,[status(thm)],[d5,c217]) ).
cnf(d31,plain,
( ssList(sK259(sK121(sK255)))
| ~ ssList(sK120(sK255))
| ~ ssItem(sK121(sK255))
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d30]) ).
cnf(d32,plain,
nil != sK255,
inference(demodulation,[status(thm)],[c215,c214]) ).
cnf(d33,plain,
( ssList(sK259(sK121(sK255)))
| ~ ssList(sK120(sK255))
| ~ ssItem(sK121(sK255)) ),
inference(resolution,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
( ~ memberP(sK255,sK121(sK255))
| ~ ssItem(sK121(sK255))
| ~ ssList(sK120(sK255))
| ~ ssItem(sK121(sK255)) ),
inference(resolution,[status(thm)],[d33,d29]) ).
cnf(d35,plain,
( ~ ssList(sK120(sK255))
| ~ ssList(sK255)
| ~ ssItem(sK121(sK255))
| nil = sK255
| ~ ssList(sK120(sK255))
| ~ ssItem(sK121(sK255)) ),
inference(resolution,[status(thm)],[d34,d5]) ).
cnf(d36,plain,
( ~ ssList(sK120(sK255))
| ~ ssItem(sK121(sK255))
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d35]) ).
cnf(d37,plain,
( ~ ssList(sK120(sK255))
| ~ ssItem(sK121(sK255)) ),
inference(resolution,[status(thm)],[d32,d36]) ).
cnf(d38,plain,
( ~ ssList(sK255)
| nil = sK255
| ~ ssItem(sK121(sK255)) ),
inference(resolution,[status(thm)],[d37,c101]) ).
cnf(d39,plain,
( ~ ssItem(sK121(sK255))
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d38]) ).
cnf(d40,plain,
~ ssItem(sK121(sK255)),
inference(resolution,[status(thm)],[d32,d39]) ).
cnf(d41,plain,
( ~ ssList(sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[d40,c102]) ).
cnf(d42,plain,
nil = sK255,
inference(resolution,[status(thm)],[c210,d41]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d32,d42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC045+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
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 12:08:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.63/6.68 % SZS status Theorem for theBenchmark.p
% 46.63/6.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------