%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC032+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 : n019.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 08:54:01 AM UTC 2026
% Result : Theorem 24.38s 8.92s
% Output : CNFRefutation 24.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 103 ( 51 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 111 ( 39 ~; 40 |; 17 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 13 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ) ).
fof(ax46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ strictorderedP(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)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ strictorderedP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c14,plain,
( ~ ssList(X2)
| app(X2,X0) != X1
| ~ ssList(X1)
| frontsegP(X1,X2)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax5]) ).
cnf(c137,plain,
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax46]) ).
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(c219,plain,
( nil = sK253
| nil = sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c222,plain,
( nil != sK254
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( nil = sK256
| nil != sK253 ),
inference(demodulation,[status(thm)],[c218,c213]) ).
cnf(d1,plain,
( nil = sK254
| nil != sK253 ),
inference(demodulation,[status(thm)],[d0,c212]) ).
cnf(d2,plain,
app(sK253,sK257) = sK256,
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d3,plain,
app(sK253,sK257) = sK254,
inference(demodulation,[status(thm)],[d2,c212]) ).
cnf(d4,plain,
( frontsegP(X0,sK253)
| ~ ssList(X0)
| ~ ssList(sK257)
| ~ ssList(sK253)
| sK254 != X0 ),
inference(superposition,[status(thm)],[d3,c14]) ).
cnf(d5,plain,
( frontsegP(X0,sK253)
| ~ ssList(sK257)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c208,d4]) ).
cnf(d6,plain,
( frontsegP(X0,sK253)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c214,d5]) ).
cnf(d7,plain,
( frontsegP(sK254,sK253)
| ~ ssList(sK254) ),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
frontsegP(sK254,sK253),
inference(resolution,[status(thm)],[c209,d7]) ).
cnf(d9,plain,
( nil = sK253
| frontsegP(nil,sK253) ),
inference(superposition,[status(thm)],[c219,d8]) ).
cnf(d10,plain,
( nil = sK253
| ~ ssList(sK253)
| nil = sK253 ),
inference(resolution,[status(thm)],[c137,d9]) ).
cnf(d11,plain,
nil = sK253,
inference(resolution,[status(thm)],[c208,d10]) ).
cnf(d12,plain,
nil = sK254,
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
nil != sK254,
inference(resolution,[status(thm)],[d11,c222]) ).
cnf(d14,plain,
nil != nil,
inference(demodulation,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
$false,
inference(equality_resolution,[status(thm)],[d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC032+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
% 0.10/5.38 % Computer : n019.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 12:06:12 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.38/8.92 % SZS status Theorem for theBenchmark.p
% 24.38/8.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------