%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC182+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 : n018.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 08:54:32 AM UTC 2026
% Result : Theorem 23.01s 5.43s
% Output : CNFRefutation 23.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 20 unt; 0 def)
% Number of atoms : 160 ( 39 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 174 ( 72 ~; 67 |; 5 &)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 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 : 49 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ) ).
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(ax16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ) ).
fof(ax26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ) ).
fof(ax38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ) ).
fof(ax52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ) ).
fof(ax58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ) ).
fof(ax84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ( ~ memberP(X6,X4)
& ~ memberP(X5,X4) )
| app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) )
| X0 != X2
| X1 != X3
| nil != X2 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ( ~ memberP(X6,X4)
& ~ memberP(X5,X4) )
| app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) )
| X0 != X2
| X1 != X3
| nil != X2 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c17,plain,
( app(X0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(X1,X2)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax6]) ).
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(c96,plain,
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax16]) ).
cnf(c109,plain,
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax26]) ).
cnf(c127,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax38]) ).
cnf(c144,plain,
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax52]) ).
cnf(c151,plain,
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax58]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
cnf(c210,plain,
ssList(sK255),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c212,plain,
nil = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
ssItem(sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
ssList(sK258),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
ssList(sK259),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
app(app(sK258,cons(sK257,nil)),sK259) = sK253,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( memberP(sK259,sK257)
| memberP(sK258,sK257) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
app(sK258,nil) = sK258,
inference(resolution,[status(thm)],[c194,c216]) ).
cnf(d1,plain,
sK253 = nil,
inference(demodulation,[status(thm)],[c214,c212]) ).
cnf(d2,plain,
app(app(sK258,cons(sK257,nil)),sK259) = nil,
inference(demodulation,[status(thm)],[c218,d1]) ).
cnf(d3,plain,
( segmentP(X0,cons(sK257,nil))
| ~ ssList(sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(sK259)
| ~ ssList(X0)
| nil != X0 ),
inference(superposition,[status(thm)],[d2,c21]) ).
cnf(d4,plain,
( segmentP(X0,cons(sK257,nil))
| ~ ssList(sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| nil != X0 ),
inference(resolution,[status(thm)],[c217,d3]) ).
cnf(d5,plain,
( segmentP(X0,cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| nil != X0 ),
inference(resolution,[status(thm)],[c216,d4]) ).
cnf(d6,plain,
( segmentP(nil,cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| ~ ssList(nil) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
ssList(nil),
inference(demodulation,[status(thm)],[c210,c212]) ).
cnf(d8,plain,
( segmentP(nil,cons(sK257,nil))
| ~ ssList(cons(sK257,nil)) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ ssList(cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| nil = cons(sK257,nil) ),
inference(resolution,[status(thm)],[c151,d8]) ).
cnf(d10,plain,
( ~ ssList(nil)
| ~ ssItem(sK257)
| nil = cons(sK257,nil) ),
inference(resolution,[status(thm)],[d9,c96]) ).
cnf(d11,plain,
( ~ ssItem(sK257)
| nil = cons(sK257,nil) ),
inference(resolution,[status(thm)],[d7,d10]) ).
cnf(d12,plain,
nil = cons(sK257,nil),
inference(resolution,[status(thm)],[c215,d11]) ).
cnf(d13,plain,
( rearsegP(X0,sK259)
| ~ ssList(sK259)
| ~ ssList(X0)
| ~ ssList(app(sK258,cons(sK257,nil)))
| nil != X0 ),
inference(superposition,[status(thm)],[d2,c17]) ).
cnf(d14,plain,
( rearsegP(X0,sK259)
| ~ ssList(app(sK258,cons(sK257,nil)))
| ~ ssList(X0)
| nil != X0 ),
inference(resolution,[status(thm)],[c217,d13]) ).
cnf(d15,plain,
( rearsegP(nil,sK259)
| ~ ssList(app(sK258,cons(sK257,nil)))
| ~ ssList(nil) ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( rearsegP(nil,sK259)
| ~ ssList(app(sK258,cons(sK257,nil))) ),
inference(resolution,[status(thm)],[d7,d15]) ).
cnf(d17,plain,
( rearsegP(nil,sK259)
| ~ ssList(sK258)
| ~ ssList(cons(sK257,nil)) ),
inference(resolution,[status(thm)],[c109,d16]) ).
cnf(d18,plain,
( rearsegP(nil,sK259)
| ~ ssList(cons(sK257,nil)) ),
inference(resolution,[status(thm)],[c216,d17]) ).
cnf(d19,plain,
( ~ ssList(nil)
| ~ ssItem(sK257)
| rearsegP(nil,sK259) ),
inference(resolution,[status(thm)],[d18,c96]) ).
cnf(d20,plain,
( rearsegP(nil,sK259)
| ~ ssItem(sK257) ),
inference(resolution,[status(thm)],[d7,d19]) ).
cnf(d21,plain,
rearsegP(nil,sK259),
inference(resolution,[status(thm)],[c215,d20]) ).
cnf(d22,plain,
( ~ ssList(sK259)
| nil = sK259 ),
inference(resolution,[status(thm)],[d21,c144]) ).
cnf(d23,plain,
nil = sK259,
inference(resolution,[status(thm)],[c217,d22]) ).
cnf(d24,plain,
app(app(sK258,cons(sK257,nil)),nil) = nil,
inference(demodulation,[status(thm)],[d2,d23]) ).
cnf(d25,plain,
app(app(sK258,nil),nil) = nil,
inference(demodulation,[status(thm)],[d24,d12]) ).
cnf(d26,plain,
app(sK258,nil) = nil,
inference(demodulation,[status(thm)],[d25,d0]) ).
cnf(d27,plain,
nil = sK258,
inference(demodulation,[status(thm)],[d0,d26]) ).
cnf(d28,plain,
( memberP(nil,sK257)
| memberP(sK258,sK257) ),
inference(demodulation,[status(thm)],[c219,d23]) ).
cnf(d29,plain,
( memberP(nil,sK257)
| memberP(nil,sK257) ),
inference(demodulation,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
~ ssItem(sK257),
inference(resolution,[status(thm)],[d29,c127]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[c215,d30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC182+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 12:29:22 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.01/5.43 % SZS status Theorem for theBenchmark.p
% 23.01/5.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------