%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC092+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 : n016.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 08:54:14 AM UTC 2026
% Result : Theorem 18.30s 13.47s
% Output : CNFRefutation 18.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 18 unt; 0 def)
% Number of atoms : 141 ( 40 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 161 ( 63 ~; 58 |; 22 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 16 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X8,X6)
& app(X9,cons(X8,nil)) = X2
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(X2,X5) != X3 ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(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 = X2
& nil != X3 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X8,X6)
& app(X9,cons(X8,nil)) = X2
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(X2,X5) != X3 ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
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(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(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c148,plain,
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax55]) ).
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,
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,
( ~ segmentP(sK253,X0)
| ~ segmentP(sK254,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
ssList(sK258),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
app(sK255,sK258) = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( nil != sK255
| nil = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ segmentP(sK254,X0)
| ~ segmentP(sK255,X0)
| ~ ssList(X0)
| ~ neq(X0,nil) ),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d1,plain,
( ~ segmentP(sK254,sK255)
| ~ ssList(sK255)
| ~ neq(sK255,nil)
| ~ ssList(sK255) ),
inference(resolution,[status(thm)],[c148,d0]) ).
cnf(d2,plain,
( ~ segmentP(sK254,sK255)
| ~ neq(sK255,nil) ),
inference(resolution,[status(thm)],[c210,d1]) ).
cnf(d3,plain,
app(nil,sK255) = sK255,
inference(resolution,[status(thm)],[c111,c210]) ).
cnf(d4,plain,
( segmentP(X1,sK255)
| ~ ssList(nil)
| ~ ssList(sK255)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK255,X0) != X1 ),
inference(superposition,[status(thm)],[d3,c21]) ).
cnf(d5,plain,
( segmentP(X1,sK255)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK255,X0) != X1 ),
inference(resolution,[status(thm)],[c210,d4]) ).
cnf(d6,plain,
( segmentP(X1,sK255)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK255,X0) != X1 ),
inference(resolution,[status(thm)],[c97,d5]) ).
cnf(d7,plain,
app(sK255,sK258) = sK254,
inference(demodulation,[status(thm)],[c217,c212]) ).
cnf(d8,plain,
( segmentP(X0,sK255)
| ~ ssList(sK258)
| ~ ssList(X0)
| sK254 != X0 ),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( segmentP(X0,sK255)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c216,d8]) ).
cnf(d10,plain,
( segmentP(sK254,sK255)
| ~ ssList(sK254) ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
segmentP(sK254,sK255),
inference(resolution,[status(thm)],[c209,d10]) ).
cnf(d12,plain,
~ neq(sK255,nil),
inference(resolution,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
( ~ ssList(sK255)
| ~ ssList(nil)
| sK255 = nil ),
inference(resolution,[status(thm)],[d12,c95]) ).
cnf(d14,plain,
( ~ ssList(nil)
| sK255 = nil ),
inference(resolution,[status(thm)],[c210,d13]) ).
cnf(d15,plain,
sK255 = nil,
inference(resolution,[status(thm)],[c97,d14]) ).
cnf(d16,plain,
( nil = sK254
| nil != sK255 ),
inference(demodulation,[status(thm)],[c220,c212]) ).
cnf(d17,plain,
( nil = sK254
| nil != nil ),
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
nil = sK254,
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[c214,d18]) ).
cnf(d20,plain,
~ neq(nil,nil),
inference(demodulation,[status(thm)],[d12,d15]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC092+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
% 0.09/10.37 % Computer : n016.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sat Sep 26 12:19:11 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.30/13.47 % SZS status Theorem for theBenchmark.p
% 18.30/13.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------