%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC396+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 08:55:14 AM UTC 2026
% Result : Theorem 92.99s 36.45s
% Output : CNFRefutation 92.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 15 unt; 0 def)
% Number of atoms : 391 ( 88 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 556 ( 237 ~; 258 |; 26 &)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 28 !; 10 ?)
% 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(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ) ).
fof(ax24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ) ).
fof(ax26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ) ).
fof(ax36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ) ).
fof(ax37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ) ).
fof(ax38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ) ).
fof(ax78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
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(c95,plain,
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax15]) ).
cnf(c96,plain,
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax16]) ).
cnf(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
cnf(c105,plain,
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax22]) ).
cnf(c107,plain,
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax24]) ).
cnf(c109,plain,
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax26]) ).
cnf(c122,plain,
( ~ memberP(X2,X0)
| memberP(app(X2,X1),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax36]) ).
cnf(c124,plain,
( memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| X2 = X0
| ~ memberP(cons(X0,X1),X2) ),
inference(clausification,[status(esa)],[ax37]) ).
cnf(c127,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax38]) ).
cnf(c186,plain,
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax78]) ).
cnf(c210,plain,
ssList(sK255),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c211,plain,
ssList(sK256),
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,
ssItem(sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
memberP(sK253,sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
~ memberP(sK254,sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( nil != sK256
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( ~ neq(sK256,nil)
| ~ ssList(X3)
| ~ ssItem(X1)
| app(X3,X2) != X0
| sK256 = X0
| tl(sK255) != X3
| ~ ssList(X2)
| hd(sK255) != X1
| ~ neq(nil,sK255)
| cons(X1,nil) != X2
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
memberP(sK255,sK257),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d1,plain,
( ~ ssList(X0)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(X1)
| sK256 = X2
| tl(sK255) != X0
| hd(sK255) != X1
| app(X0,cons(X1,nil)) != X2 ),
inference(equality_resolution,[status(thm)],[c219]) ).
cnf(d2,plain,
( ~ ssList(cons(X0,nil))
| ~ ssList(X1)
| ~ ssList(app(X1,cons(X0,nil)))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(X0)
| sK256 = app(X1,cons(X0,nil))
| tl(sK255) != X1
| hd(sK255) != X0 ),
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
( ~ ssList(cons(X0,nil))
| ~ ssList(app(tl(sK255),cons(X0,nil)))
| ~ ssList(tl(sK255))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(X0)
| sK256 = app(tl(sK255),cons(X0,nil))
| hd(sK255) != X0 ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
( ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil))
| ~ ssList(app(tl(sK255),cons(hd(sK255),nil)))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| sK256 = app(tl(sK255),cons(hd(sK255),nil)) ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil))
| ~ ssList(app(tl(sK255),cons(hd(sK255),nil)))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssList(tl(sK255))
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(X0,hd(sK255))
| ~ ssItem(hd(sK255))
| sK256 != X0 ),
inference(superposition,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
( ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil))
| ~ ssList(app(tl(sK255),cons(hd(sK255),nil)))
| ~ ssList(X0)
| memberP(X0,hd(sK255))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| sK256 != X0 ),
inference(resolution,[status(thm)],[c97,d5]) ).
cnf(d7,plain,
( ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil))
| ~ ssList(app(tl(sK255),cons(hd(sK255),nil)))
| ~ ssList(sK256)
| memberP(sK256,hd(sK255))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255)) ),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
( ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil))
| ~ ssList(app(tl(sK255),cons(hd(sK255),nil)))
| memberP(sK256,hd(sK255))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255)) ),
inference(resolution,[status(thm)],[c211,d7]) ).
cnf(d9,plain,
( ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil))
| memberP(sK256,hd(sK255))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil)) ),
inference(resolution,[status(thm)],[c109,d8]) ).
cnf(d10,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK255))
| ~ ssList(tl(sK255))
| memberP(sK256,hd(sK255))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255)) ),
inference(resolution,[status(thm)],[d9,c96]) ).
cnf(d11,plain,
( ~ ssList(tl(sK255))
| memberP(sK256,hd(sK255))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255)) ),
inference(resolution,[status(thm)],[c97,d10]) ).
cnf(d12,plain,
( ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil))
| ~ ssList(app(tl(sK255),cons(hd(sK255),nil)))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssList(cons(hd(sK255),nil))
| ~ ssList(tl(sK255))
| ~ memberP(tl(sK255),X0)
| ~ ssItem(X0)
| memberP(sK256,X0) ),
inference(superposition,[status(thm)],[d4,c122]) ).
cnf(d13,plain,
( ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil))
| ~ ssList(tl(sK255))
| ~ ssList(cons(hd(sK255),nil))
| memberP(sK256,X0)
| ~ memberP(tl(sK255),X0)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d12,c109]) ).
cnf(d14,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK255))
| ~ ssList(tl(sK255))
| memberP(sK256,X0)
| ~ memberP(tl(sK255),X0)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d13,c96]) ).
cnf(d15,plain,
( ~ ssList(tl(sK255))
| memberP(sK256,X0)
| ~ memberP(tl(sK255),X0)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c97,d14]) ).
cnf(d16,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssList(tl(X0))
| memberP(tl(X0),X1)
| ~ ssItem(X1)
| ~ ssItem(hd(X0))
| X1 = hd(X0)
| ~ memberP(X0,X1) ),
inference(superposition,[status(thm)],[c186,c124]) ).
cnf(d17,plain,
( ~ ssList(tl(sK255))
| memberP(sK256,X0)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssItem(X0)
| ~ ssList(tl(sK255))
| ~ ssList(sK255)
| ~ memberP(sK255,X0)
| ~ ssItem(hd(sK255))
| ~ ssItem(X0)
| nil = sK255
| X0 = hd(sK255) ),
inference(resolution,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
( ~ ssList(tl(sK255))
| memberP(sK256,X0)
| ~ memberP(sK255,X0)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssItem(X0)
| nil = sK255
| X0 = hd(sK255) ),
inference(resolution,[status(thm)],[c210,d17]) ).
cnf(d19,plain,
( ~ ssList(tl(sK255))
| memberP(sK256,X0)
| ~ memberP(sK255,X0)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssItem(X0)
| nil = sK255
| ~ ssList(tl(sK255))
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| memberP(sK256,X0) ),
inference(superposition,[status(thm)],[d18,d11]) ).
cnf(d20,plain,
( ~ ssList(sK255)
| nil = sK255
| memberP(sK256,X0)
| ~ memberP(sK255,X0)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssItem(X0)
| nil = sK255 ),
inference(resolution,[status(thm)],[d19,c107]) ).
cnf(d21,plain,
( memberP(sK256,X0)
| ~ memberP(sK255,X0)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssItem(X0)
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d20]) ).
cnf(d22,plain,
( memberP(sK256,sK257)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| ~ ssItem(sK257)
| nil = sK255 ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
( memberP(sK256,sK257)
| ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| nil = sK255 ),
inference(resolution,[status(thm)],[c214,d22]) ).
cnf(d24,plain,
~ memberP(sK256,sK257),
inference(demodulation,[status(thm)],[c216,c212]) ).
cnf(d25,plain,
( ~ neq(sK256,nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| nil = sK255 ),
inference(resolution,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
( ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| nil = sK255 ),
inference(resolution,[status(thm)],[d25,c95]) ).
cnf(d27,plain,
( ~ ssList(nil)
| ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| sK256 = nil
| nil = sK255 ),
inference(resolution,[status(thm)],[c211,d26]) ).
cnf(d28,plain,
( ~ neq(nil,sK255)
| ~ ssItem(hd(sK255))
| sK256 = nil
| nil = sK255 ),
inference(resolution,[status(thm)],[c97,d27]) ).
cnf(d29,plain,
( ~ ssList(nil)
| ~ ssList(sK255)
| nil = sK255
| ~ ssItem(hd(sK255))
| sK256 = nil
| nil = sK255 ),
inference(resolution,[status(thm)],[d28,c95]) ).
cnf(d30,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK255))
| sK256 = nil
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d29]) ).
cnf(d31,plain,
( ~ ssItem(hd(sK255))
| sK256 = nil
| nil = sK255 ),
inference(resolution,[status(thm)],[c97,d30]) ).
cnf(d32,plain,
( ~ ssList(sK255)
| nil = sK255
| sK256 = nil
| nil = sK255 ),
inference(resolution,[status(thm)],[d31,c105]) ).
cnf(d33,plain,
( sK256 = nil
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d32]) ).
cnf(d34,plain,
( nil = sK255
| nil = sK255
| nil != nil ),
inference(superposition,[status(thm)],[d33,c217]) ).
cnf(d35,plain,
nil = sK255,
inference(equality_resolution,[status(thm)],[d34]) ).
cnf(d36,plain,
memberP(nil,sK257),
inference(demodulation,[status(thm)],[d0,d35]) ).
cnf(d37,plain,
~ ssItem(sK257),
inference(resolution,[status(thm)],[d36,c127]) ).
cnf(d38,plain,
$false,
inference(resolution,[status(thm)],[c214,d37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC396+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/15.46 % Computer : n015.cluster.edu
% 0.10/15.46 % Model : x86_64 x86_64
% 0.10/15.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.46 % Memory : 8046.5625MB
% 0.10/15.46 % OS : Linux 6.8.0-71-generic
% 0.10/15.46 % CPULimit : 300
% 0.10/15.46 % WCLimit : 300
% 0.10/15.46 % DateTime : Sat Sep 26 13:01:29 UTC 2026
% 0.10/15.47 % CPUTime :
% 0.10/15.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 92.99/36.45 % SZS status Theorem for theBenchmark.p
% 92.99/36.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------