%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC409+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 : n017.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 08:55:17 AM UTC 2026
% Result : Theorem 94.99s 28.96s
% Output : CNFRefutation 94.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 15 unt; 0 def)
% Number of atoms : 258 ( 70 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 330 ( 131 ~; 158 |; 12 &)
% ( 3 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 26 !; 8 ?)
% 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(ax16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ) ).
fof(ax27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
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(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| ! [X6] :
( ssItem(X6)
=> ( memberP(X0,X6)
| ~ memberP(X1,X6) ) )
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| ! [X6] :
( ssItem(X6)
=> ( memberP(X0,X6)
| ~ memberP(X1,X6) ) )
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(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(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(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(c110,plain,
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax27]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
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(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,
( app(cons(X0,nil),X1) != sK256
| app(X1,cons(X0,nil)) = sK255
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
ssItem(sK259),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
memberP(sK254,sK259),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
~ memberP(sK253,sK259),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
memberP(sK256,sK259),
inference(demodulation,[status(thm)],[c216,c212]) ).
cnf(d1,plain,
( ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(X0)
| app(X1,cons(X0,nil)) = sK255
| cons(X0,app(nil,X1)) != sK256 ),
inference(superposition,[status(thm)],[c110,c214]) ).
cnf(d2,plain,
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,app(nil,X0)) != sK256
| app(X0,cons(X1,nil)) = sK255 ),
inference(resolution,[status(thm)],[c97,d1]) ).
cnf(d3,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssItem(X1)
| app(X0,cons(X1,nil)) = sK255
| cons(X1,X0) != sK256 ),
inference(superposition,[status(thm)],[c111,d2]) ).
cnf(d4,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssList(sK120(X0))
| ~ ssItem(sK121(X0))
| app(sK120(X0),cons(sK121(X0),nil)) = sK255
| X0 != sK256 ),
inference(superposition,[status(thm)],[c103,d3]) ).
cnf(d5,plain,
( ~ ssList(sK120(sK256))
| ~ ssList(sK256)
| ~ ssItem(sK121(sK256))
| nil = sK256
| app(sK120(sK256),cons(sK121(sK256),nil)) = sK255 ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ ssList(sK120(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256
| app(sK120(sK256),cons(sK121(sK256),nil)) = sK255 ),
inference(resolution,[status(thm)],[c211,d5]) ).
cnf(d7,plain,
( ~ ssList(sK120(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256
| ~ ssList(sK120(sK256))
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(X0,sK121(sK256))
| ~ ssItem(sK121(sK256))
| sK255 != X0 ),
inference(superposition,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
( ~ ssList(sK120(sK256))
| ~ ssList(X0)
| memberP(X0,sK121(sK256))
| ~ ssItem(sK121(sK256))
| sK255 != X0
| nil = sK256 ),
inference(resolution,[status(thm)],[c97,d7]) ).
cnf(d9,plain,
( ~ ssList(sK120(sK256))
| ~ ssList(sK255)
| memberP(sK255,sK121(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256 ),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
( ~ ssList(sK120(sK256))
| memberP(sK255,sK121(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[c210,d9]) ).
cnf(d11,plain,
( ~ ssList(sK120(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256
| ~ ssList(cons(sK121(sK256),nil))
| ~ ssList(sK120(sK256))
| ~ memberP(sK120(sK256),X0)
| ~ ssItem(X0)
| memberP(sK255,X0) ),
inference(superposition,[status(thm)],[d6,c122]) ).
cnf(d12,plain,
( ~ ssList(nil)
| ~ ssItem(sK121(sK256))
| ~ ssList(sK120(sK256))
| memberP(sK255,X0)
| ~ memberP(sK120(sK256),X0)
| ~ ssItem(sK121(sK256))
| ~ ssItem(X0)
| nil = sK256 ),
inference(resolution,[status(thm)],[d11,c96]) ).
cnf(d13,plain,
( ~ ssList(sK120(sK256))
| memberP(sK255,X0)
| ~ memberP(sK120(sK256),X0)
| ~ ssItem(sK121(sK256))
| ~ ssItem(X0)
| nil = sK256 ),
inference(resolution,[status(thm)],[c97,d12]) ).
cnf(d14,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssList(sK120(X0))
| memberP(sK120(X0),X1)
| ~ ssItem(X1)
| ~ ssItem(sK121(X0))
| X1 = sK121(X0)
| ~ memberP(X0,X1) ),
inference(superposition,[status(thm)],[c103,c124]) ).
cnf(d15,plain,
( ~ ssList(sK120(sK256))
| memberP(sK255,X0)
| ~ ssItem(sK121(sK256))
| ~ ssItem(X0)
| nil = sK256
| ~ ssList(sK120(sK256))
| ~ ssList(sK256)
| ~ memberP(sK256,X0)
| ~ ssItem(sK121(sK256))
| ~ ssItem(X0)
| nil = sK256
| X0 = sK121(sK256) ),
inference(resolution,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
( ~ ssList(sK120(sK256))
| ~ memberP(sK256,X0)
| memberP(sK255,X0)
| ~ ssItem(sK121(sK256))
| ~ ssItem(X0)
| nil = sK256
| X0 = sK121(sK256) ),
inference(resolution,[status(thm)],[c211,d15]) ).
cnf(d17,plain,
( ~ ssList(sK120(sK256))
| ~ memberP(sK256,X0)
| memberP(sK255,X0)
| ~ ssItem(sK121(sK256))
| ~ ssItem(X0)
| nil = sK256
| ~ ssList(sK120(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256
| memberP(sK255,X0) ),
inference(superposition,[status(thm)],[d16,d10]) ).
cnf(d18,plain,
( ~ ssList(sK256)
| nil = sK256
| ~ memberP(sK256,X0)
| memberP(sK255,X0)
| ~ ssItem(sK121(sK256))
| ~ ssItem(X0)
| nil = sK256 ),
inference(resolution,[status(thm)],[d17,c101]) ).
cnf(d19,plain,
( ~ memberP(sK256,X0)
| memberP(sK255,X0)
| ~ ssItem(sK121(sK256))
| ~ ssItem(X0)
| nil = sK256 ),
inference(resolution,[status(thm)],[c211,d18]) ).
cnf(d20,plain,
( memberP(sK255,sK259)
| ~ ssItem(sK121(sK256))
| ~ ssItem(sK259)
| nil = sK256 ),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
( memberP(sK255,sK259)
| ~ ssItem(sK121(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[c215,d20]) ).
cnf(d22,plain,
~ memberP(sK255,sK259),
inference(demodulation,[status(thm)],[c217,c213]) ).
cnf(d23,plain,
( ~ ssItem(sK121(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( ~ ssList(sK256)
| nil = sK256
| nil = sK256 ),
inference(resolution,[status(thm)],[d23,c102]) ).
cnf(d25,plain,
nil = sK256,
inference(resolution,[status(thm)],[c211,d24]) ).
cnf(d26,plain,
memberP(nil,sK259),
inference(demodulation,[status(thm)],[d0,d25]) ).
cnf(d27,plain,
~ ssItem(sK259),
inference(resolution,[status(thm)],[d26,c127]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[c215,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC409+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.54 % Computer : n017.cluster.edu
% 0.08/5.54 % Model : x86_64 x86_64
% 0.08/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.54 % Memory : 8046.5625MB
% 0.08/5.54 % OS : Linux 6.8.0-71-generic
% 0.08/5.54 % CPULimit : 300
% 0.08/5.54 % WCLimit : 300
% 0.08/5.54 % DateTime : Sat Sep 26 12:55:10 UTC 2026
% 0.08/5.54 % CPUTime :
% 0.08/5.54 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 94.99/28.96 % SZS status Theorem for theBenchmark.p
% 94.99/28.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------