%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC070+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 : n014.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 08:54:10 AM UTC 2026
% Result : Theorem 16.59s 19.39s
% Output : CNFRefutation 16.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 11 unt; 0 def)
% Number of atoms : 182 ( 57 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 219 ( 93 ~; 96 |; 13 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 15 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = 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(ax17,axiom,
ssList(nil) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ) ).
fof(ax57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ~ frontsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( nil = X0
& nil = X1 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ~ frontsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( nil = X0
& nil = X1 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c12,plain,
( ssList(sK15(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax5]) ).
cnf(c13,plain,
( app(X1,sK15(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax5]) ).
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(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(c150,plain,
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax57]) ).
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,
( ~ segmentP(sK253,X0)
| ~ segmentP(sK254,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( nil != sK253
| nil != sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( neq(sK255,nil)
| nil = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( neq(sK255,nil)
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( frontsegP(sK256,sK255)
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ segmentP(sK254,X0)
| ~ segmentP(sK255,X0)
| ~ ssList(X0)
| ~ neq(X0,nil) ),
inference(demodulation,[status(thm)],[c214,c213]) ).
cnf(d1,plain,
( ~ segmentP(sK256,X0)
| ~ segmentP(sK255,X0)
| ~ ssList(X0)
| ~ neq(X0,nil) ),
inference(demodulation,[status(thm)],[d0,c212]) ).
cnf(d2,plain,
app(nil,sK255) = sK255,
inference(resolution,[status(thm)],[c111,c210]) ).
cnf(d3,plain,
( segmentP(X1,sK255)
| ~ ssList(nil)
| ~ ssList(sK255)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK255,X0) != X1 ),
inference(superposition,[status(thm)],[d2,c21]) ).
cnf(d4,plain,
( segmentP(X1,sK255)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK255,X0) != X1 ),
inference(resolution,[status(thm)],[c210,d3]) ).
cnf(d5,plain,
( segmentP(X1,sK255)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK255,X0) != X1 ),
inference(resolution,[status(thm)],[c97,d4]) ).
cnf(d6,plain,
( nil = sK255
| ~ ssList(sK256)
| ~ ssList(sK255)
| app(sK255,sK15(sK256,sK255)) = sK256 ),
inference(resolution,[status(thm)],[c13,c219]) ).
cnf(d7,plain,
( ~ ssList(sK256)
| nil = sK255
| app(sK255,sK15(sK256,sK255)) = sK256 ),
inference(resolution,[status(thm)],[c210,d6]) ).
cnf(d8,plain,
( nil = sK255
| app(sK255,sK15(sK256,sK255)) = sK256 ),
inference(resolution,[status(thm)],[c211,d7]) ).
cnf(d9,plain,
( nil = sK255
| segmentP(X0,sK255)
| ~ ssList(sK15(sK256,sK255))
| ~ ssList(X0)
| sK256 != X0 ),
inference(superposition,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( segmentP(sK256,sK255)
| ~ ssList(sK15(sK256,sK255))
| ~ ssList(sK256)
| nil = sK255 ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( segmentP(sK256,sK255)
| ~ ssList(sK15(sK256,sK255))
| nil = sK255 ),
inference(resolution,[status(thm)],[c211,d10]) ).
cnf(d12,plain,
( ~ frontsegP(sK256,sK255)
| ~ ssList(sK256)
| ~ ssList(sK255)
| segmentP(sK256,sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[d11,c12]) ).
cnf(d13,plain,
( segmentP(sK256,sK255)
| ~ frontsegP(sK256,sK255)
| ~ ssList(sK256)
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d12]) ).
cnf(d14,plain,
( segmentP(sK256,sK255)
| ~ frontsegP(sK256,sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[c211,d13]) ).
cnf(d15,plain,
( nil = sK255
| segmentP(sK256,sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[d14,c219]) ).
cnf(d16,plain,
( ~ segmentP(sK255,sK255)
| ~ ssList(sK255)
| ~ neq(sK255,nil)
| nil = sK255 ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( ~ segmentP(sK255,sK255)
| ~ neq(sK255,nil)
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d16]) ).
cnf(d18,plain,
( ~ ssList(sK255)
| ~ neq(sK255,nil)
| nil = sK255 ),
inference(resolution,[status(thm)],[d17,c148]) ).
cnf(d19,plain,
( ~ neq(sK255,nil)
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d18]) ).
cnf(d20,plain,
( nil = sK255
| nil = sK255 ),
inference(resolution,[status(thm)],[d19,c218]) ).
cnf(d21,plain,
( neq(nil,nil)
| nil = sK256 ),
inference(demodulation,[status(thm)],[c216,d20]) ).
cnf(d22,plain,
( ~ segmentP(sK255,nil)
| ~ ssList(nil)
| ~ neq(nil,nil)
| ~ ssList(sK256) ),
inference(resolution,[status(thm)],[c150,d1]) ).
cnf(d23,plain,
( ~ segmentP(sK255,nil)
| ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(resolution,[status(thm)],[c211,d22]) ).
cnf(d24,plain,
( ~ segmentP(sK255,nil)
| ~ neq(nil,nil) ),
inference(resolution,[status(thm)],[c97,d23]) ).
cnf(d25,plain,
( ~ ssList(sK255)
| ~ neq(nil,nil) ),
inference(resolution,[status(thm)],[d24,c150]) ).
cnf(d26,plain,
~ neq(nil,nil),
inference(resolution,[status(thm)],[c210,d25]) ).
cnf(d27,plain,
nil = sK256,
inference(resolution,[status(thm)],[d26,d21]) ).
cnf(d28,plain,
( nil != sK254
| nil != sK255 ),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d29,plain,
( nil != sK256
| nil != sK255 ),
inference(demodulation,[status(thm)],[d28,c212]) ).
cnf(d30,plain,
nil != sK256,
inference(resolution,[status(thm)],[d20,d29]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[d30,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC070+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 : n014.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 12:11:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.59/19.39 % SZS status Theorem for theBenchmark.p
% 16.59/19.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------