%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC057+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 : n020.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 08:54:07 AM UTC 2026
% Result : Theorem 94.74s 16.11s
% Output : CNFRefutation 94.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 105 ( 19 unt; 0 def)
% Number of atoms : 332 ( 115 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 391 ( 164 ~; 180 |; 14 &)
% ( 5 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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; 5 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ) ).
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(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(ax49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ) ).
fof(ax50,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X0,X1)
=> rearsegP(app(X2,X0),X1) ) ) ) ) ).
fof(ax51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ) ).
fof(ax55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ) ).
fof(ax58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ) ).
fof(ax79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X2 = X0 ) ) ) ) ).
fof(ax84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ~ frontsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( ( ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ~ frontsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( ( ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| X0 != X2
| X1 != X3
| ~ ssList(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(c15,plain,
( ssList(sK19(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax6]) ).
cnf(c16,plain,
( app(sK19(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ 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(c94,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(c141,plain,
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax49]) ).
cnf(c142,plain,
( ~ rearsegP(X2,X0)
| rearsegP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax50]) ).
cnf(c143,plain,
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax51]) ).
cnf(c148,plain,
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax55]) ).
cnf(c151,plain,
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax58]) ).
cnf(c187,plain,
( ~ ssList(X1)
| X1 = X0
| ~ ssList(X2)
| app(X1,X2) != app(X0,X2)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax79]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
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(c215,plain,
( ~ segmentP(sK254,X0)
| ~ neq(X0,nil)
| ~ segmentP(sK253,X0)
| nil = sK254
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( neq(sK254,nil)
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( neq(sK255,nil)
| nil = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( neq(sK255,nil)
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
( frontsegP(sK256,sK255)
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(equality_resolution,[status(thm)],[c94]) ).
cnf(d1,plain,
( neq(sK255,nil)
| nil = sK254 ),
inference(demodulation,[status(thm)],[c218,c212]) ).
cnf(d2,plain,
( ~ segmentP(sK254,X0)
| ~ segmentP(sK255,X0)
| ~ ssList(X0)
| ~ neq(X0,nil)
| nil = sK254 ),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d3,plain,
( ~ segmentP(sK254,sK255)
| ~ ssList(sK255)
| ~ neq(sK255,nil)
| nil = sK254
| ~ ssList(sK255) ),
inference(resolution,[status(thm)],[c148,d2]) ).
cnf(d4,plain,
( ~ segmentP(sK254,sK255)
| ~ neq(sK255,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c210,d3]) ).
cnf(d5,plain,
( frontsegP(sK254,sK255)
| nil = sK255 ),
inference(demodulation,[status(thm)],[c221,c212]) ).
cnf(d6,plain,
app(nil,sK255) = sK255,
inference(resolution,[status(thm)],[c111,c210]) ).
cnf(d7,plain,
( segmentP(X1,sK255)
| ~ ssList(nil)
| ~ ssList(sK255)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK255,X0) != X1 ),
inference(superposition,[status(thm)],[d6,c21]) ).
cnf(d8,plain,
( segmentP(X1,sK255)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK255,X0) != X1 ),
inference(resolution,[status(thm)],[c210,d7]) ).
cnf(d9,plain,
( segmentP(X1,sK255)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK255,X0) != X1 ),
inference(resolution,[status(thm)],[c97,d8]) ).
cnf(d10,plain,
( nil = sK255
| ~ ssList(sK254)
| ~ ssList(sK255)
| app(sK255,sK15(sK254,sK255)) = sK254 ),
inference(resolution,[status(thm)],[c13,d5]) ).
cnf(d11,plain,
( ~ ssList(sK255)
| nil = sK255
| app(sK255,sK15(sK254,sK255)) = sK254 ),
inference(resolution,[status(thm)],[c209,d10]) ).
cnf(d12,plain,
( nil = sK255
| app(sK255,sK15(sK254,sK255)) = sK254 ),
inference(resolution,[status(thm)],[c210,d11]) ).
cnf(d13,plain,
( nil = sK255
| segmentP(X0,sK255)
| ~ ssList(sK15(sK254,sK255))
| ~ ssList(X0)
| sK254 != X0 ),
inference(superposition,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
( segmentP(sK254,sK255)
| ~ ssList(sK15(sK254,sK255))
| ~ ssList(sK254)
| nil = sK255 ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( segmentP(sK254,sK255)
| ~ ssList(sK15(sK254,sK255))
| nil = sK255 ),
inference(resolution,[status(thm)],[c209,d14]) ).
cnf(d16,plain,
( ~ frontsegP(sK254,sK255)
| ~ ssList(sK254)
| ~ ssList(sK255)
| segmentP(sK254,sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[d15,c12]) ).
cnf(d17,plain,
( segmentP(sK254,sK255)
| ~ frontsegP(sK254,sK255)
| ~ ssList(sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[c209,d16]) ).
cnf(d18,plain,
( segmentP(sK254,sK255)
| ~ frontsegP(sK254,sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d17]) ).
cnf(d19,plain,
( nil = sK255
| segmentP(sK254,sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
( ~ neq(sK255,nil)
| nil = sK254
| nil = sK255 ),
inference(resolution,[status(thm)],[d19,d4]) ).
cnf(d21,plain,
( nil = sK255
| nil = sK255
| nil = sK254 ),
inference(resolution,[status(thm)],[d20,c220]) ).
cnf(d22,plain,
( nil = sK254
| nil = sK254
| neq(nil,nil) ),
inference(superposition,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
( ~ ssList(nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
nil = sK254,
inference(resolution,[status(thm)],[c97,d23]) ).
cnf(d25,plain,
( segmentP(nil,sK255)
| nil = sK255 ),
inference(demodulation,[status(thm)],[d19,d24]) ).
cnf(d26,plain,
( ~ ssList(sK255)
| nil = sK255
| nil = sK255 ),
inference(resolution,[status(thm)],[d25,c151]) ).
cnf(d27,plain,
nil = sK255,
inference(resolution,[status(thm)],[c210,d26]) ).
cnf(d28,plain,
( neq(sK254,nil)
| nil != sK255 ),
inference(demodulation,[status(thm)],[c216,c213]) ).
cnf(d29,plain,
( neq(nil,nil)
| nil != sK255 ),
inference(demodulation,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
( neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
( ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK255)
| nil = X0
| sK255 != app(X0,sK255) ),
inference(superposition,[status(thm)],[d6,c187]) ).
cnf(d32,plain,
( ~ ssList(nil)
| ~ ssList(X0)
| sK255 != app(X0,sK255)
| nil = X0 ),
inference(resolution,[status(thm)],[c210,d31]) ).
cnf(d33,plain,
( ~ ssList(X0)
| sK255 != app(X0,sK255)
| nil = X0 ),
inference(resolution,[status(thm)],[c97,d32]) ).
cnf(d34,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| app(sK19(X0,X0),X0) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c141,c16]) ).
cnf(d35,plain,
app(sK19(sK255,sK255),sK255) = sK255,
inference(resolution,[status(thm)],[d34,c210]) ).
cnf(d36,plain,
( ~ ssList(sK19(sK255,sK255))
| nil = sK19(sK255,sK255)
| sK255 != sK255 ),
inference(superposition,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
( ~ ssList(nil)
| ~ ssList(X0)
| app(sK19(X0,nil),nil) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c143,c16]) ).
cnf(d38,plain,
( ~ ssList(X0)
| app(sK19(X0,nil),nil) = X0 ),
inference(resolution,[status(thm)],[c97,d37]) ).
cnf(d39,plain,
app(sK19(sK255,nil),nil) = sK255,
inference(resolution,[status(thm)],[d38,c210]) ).
cnf(d40,plain,
app(sK255,nil) = sK255,
inference(resolution,[status(thm)],[c194,c210]) ).
cnf(d41,plain,
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK255)
| rearsegP(sK255,X0) ),
inference(superposition,[status(thm)],[d40,c142]) ).
cnf(d42,plain,
( rearsegP(sK255,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c210,d41]) ).
cnf(d43,plain,
( rearsegP(sK255,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c97,d42]) ).
cnf(d44,plain,
( ~ ssList(nil)
| rearsegP(sK255,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d43,c141]) ).
cnf(d45,plain,
rearsegP(sK255,nil),
inference(resolution,[status(thm)],[c97,d44]) ).
cnf(d46,plain,
( ~ ssList(nil)
| ~ ssList(sK255)
| app(sK19(sK255,nil),nil) = sK255 ),
inference(resolution,[status(thm)],[d45,c16]) ).
cnf(d47,plain,
( ~ ssList(sK255)
| ~ ssList(nil)
| sK255 = sK255 ),
inference(demodulation,[status(thm)],[d46,d39]) ).
cnf(d48,plain,
( ~ ssList(nil)
| sK255 = sK255 ),
inference(resolution,[status(thm)],[c210,d47]) ).
cnf(d49,plain,
sK255 = sK255,
inference(resolution,[status(thm)],[c97,d48]) ).
cnf(d50,plain,
( ~ ssList(sK19(sK255,sK255))
| nil = sK19(sK255,sK255) ),
inference(resolution,[status(thm)],[d49,d36]) ).
cnf(d51,plain,
( ~ rearsegP(sK255,sK255)
| ~ ssList(sK255)
| ~ ssList(sK255)
| nil = sK19(sK255,sK255) ),
inference(resolution,[status(thm)],[d50,c15]) ).
cnf(d52,plain,
( ~ rearsegP(sK255,sK255)
| nil = sK19(sK255,sK255) ),
inference(resolution,[status(thm)],[c210,d51]) ).
cnf(d53,plain,
( ~ ssList(sK255)
| nil = sK19(sK255,sK255) ),
inference(resolution,[status(thm)],[d52,c141]) ).
cnf(d54,plain,
nil = sK19(sK255,sK255),
inference(resolution,[status(thm)],[c210,d53]) ).
cnf(d55,plain,
( ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK255)
| X0 = nil
| app(X0,sK255) != sK255 ),
inference(superposition,[status(thm)],[d6,c187]) ).
cnf(d56,plain,
( ~ ssList(nil)
| ~ ssList(X0)
| app(X0,sK255) != sK255
| X0 = nil ),
inference(resolution,[status(thm)],[c210,d55]) ).
cnf(d57,plain,
( ~ ssList(X0)
| app(X0,sK255) != sK255
| X0 = nil ),
inference(resolution,[status(thm)],[c97,d56]) ).
cnf(d58,plain,
( ~ ssList(sK19(sK255,sK255))
| sK19(sK255,sK255) = nil
| sK255 != sK255 ),
inference(superposition,[status(thm)],[d35,d57]) ).
cnf(d59,plain,
( ~ ssList(sK19(sK255,sK255))
| sK255 != sK255
| nil = nil ),
inference(demodulation,[status(thm)],[d58,d54]) ).
cnf(d60,plain,
( ~ ssList(nil)
| sK255 != sK255
| nil = nil ),
inference(demodulation,[status(thm)],[d59,d54]) ).
cnf(d61,plain,
( sK255 != sK255
| nil = nil ),
inference(resolution,[status(thm)],[c97,d60]) ).
cnf(d62,plain,
nil = nil,
inference(resolution,[status(thm)],[d49,d61]) ).
cnf(d63,plain,
neq(nil,nil),
inference(resolution,[status(thm)],[d62,d30]) ).
cnf(d64,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[d63,d0]) ).
cnf(d65,plain,
$false,
inference(resolution,[status(thm)],[c97,d64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC057+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 12:09:49 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 94.74/16.11 % SZS status Theorem for theBenchmark.p
% 94.74/16.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------