%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC211+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 08:54:37 AM UTC 2026
% Result : Theorem 41.79s 9.68s
% Output : CNFRefutation 41.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 174 ( 61 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 211 ( 86 ~; 93 |; 12 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 18 !; 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(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
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(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 )
| neq(X0,nil)
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| 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 )
| neq(X0,nil)
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| 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(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(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,
neq(sK254,nil),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( app(cons(X0,nil),X1) != sK256
| app(X1,cons(X0,nil)) = sK255
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
~ neq(sK253,nil),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ neq(sK255,nil),
inference(demodulation,[status(thm)],[c216,c213]) ).
cnf(d1,plain,
( ~ ssList(sK255)
| ~ ssList(nil)
| sK255 = nil ),
inference(resolution,[status(thm)],[c95,d0]) ).
cnf(d2,plain,
( ~ ssList(nil)
| sK255 = nil ),
inference(resolution,[status(thm)],[c210,d1]) ).
cnf(d3,plain,
sK255 = nil,
inference(resolution,[status(thm)],[c97,d2]) ).
cnf(d4,plain,
( ~ ssList(X0)
| ~ ssItem(X1)
| app(cons(X1,nil),X0) != sK256
| app(X0,cons(X1,nil)) = nil ),
inference(demodulation,[status(thm)],[c215,d3]) ).
cnf(d5,plain,
( ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(X0)
| app(X1,cons(X0,nil)) = nil
| cons(X0,app(nil,X1)) != sK256 ),
inference(superposition,[status(thm)],[c110,d4]) ).
cnf(d6,plain,
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,app(nil,X0)) != sK256
| app(X0,cons(X1,nil)) = nil ),
inference(resolution,[status(thm)],[c97,d5]) ).
cnf(d7,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssItem(X1)
| app(X0,cons(X1,nil)) = nil
| cons(X1,X0) != sK256 ),
inference(superposition,[status(thm)],[c111,d6]) ).
cnf(d8,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssList(sK120(X0))
| ~ ssItem(sK121(X0))
| app(sK120(X0),cons(sK121(X0),nil)) = nil
| X0 != sK256 ),
inference(superposition,[status(thm)],[c103,d7]) ).
cnf(d9,plain,
( ~ ssList(sK120(sK256))
| ~ ssList(sK256)
| ~ ssItem(sK121(sK256))
| nil = sK256
| app(sK120(sK256),cons(sK121(sK256),nil)) = nil ),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
( ~ ssList(sK120(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256
| app(sK120(sK256),cons(sK121(sK256),nil)) = nil ),
inference(resolution,[status(thm)],[c211,d9]) ).
cnf(d11,plain,
( ~ ssList(sK120(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256
| ~ ssList(sK120(sK256))
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(X0,sK121(sK256))
| ~ ssItem(sK121(sK256))
| nil != X0 ),
inference(superposition,[status(thm)],[d10,c8]) ).
cnf(d12,plain,
( ~ ssList(sK120(sK256))
| ~ ssList(X0)
| memberP(X0,sK121(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256
| nil != X0 ),
inference(resolution,[status(thm)],[c97,d11]) ).
cnf(d13,plain,
( ~ ssList(sK120(sK256))
| ~ ssList(nil)
| memberP(nil,sK121(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256 ),
inference(equality_resolution,[status(thm)],[d12]) ).
cnf(d14,plain,
( ~ ssList(sK120(sK256))
| memberP(nil,sK121(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[c97,d13]) ).
cnf(d15,plain,
( ~ ssItem(sK121(sK256))
| ~ ssList(sK120(sK256))
| ~ ssItem(sK121(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[d14,c127]) ).
cnf(d16,plain,
( ~ ssList(sK256)
| nil = sK256
| ~ ssItem(sK121(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[d15,c101]) ).
cnf(d17,plain,
( ~ ssItem(sK121(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[c211,d16]) ).
cnf(d18,plain,
( ~ ssList(sK256)
| nil = sK256
| nil = sK256 ),
inference(resolution,[status(thm)],[d17,c102]) ).
cnf(d19,plain,
nil = sK256,
inference(resolution,[status(thm)],[c211,d18]) ).
cnf(d20,plain,
neq(sK256,nil),
inference(demodulation,[status(thm)],[c214,c212]) ).
cnf(d21,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
~ neq(nil,nil),
inference(demodulation,[status(thm)],[d0,d3]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[d22,d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC211+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
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 12:32:24 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.79/9.68 % SZS status Theorem for theBenchmark.p
% 41.79/9.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------