%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC075+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 08:54:10 AM UTC 2026
% Result : Theorem 9.31s 3.42s
% Output : CNFRefutation 9.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 8
% Syntax : Number of formulae : 95 ( 37 unt; 0 def)
% Number of atoms : 256 ( 68 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 302 ( 141 ~; 127 |; 12 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 22 !; 5 ?)
% 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(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(ax48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ) ).
fof(ax84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( nil = X0
& nil = X1 )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( app(X6,X5) != X2
| app(X5,X6) != X3
| ~ ssList(X6) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( nil = X0
& nil = X1 )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( app(X6,X5) != X2
| app(X5,X6) != X3
| ~ ssList(X6) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
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(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(c140,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[ax48]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
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,
( ~ segmentP(sK253,X0)
| ~ segmentP(sK254,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
ssList(sK258),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
ssList(sK259),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
app(sK258,sK259) = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
app(sK259,sK258) = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( nil != sK253
| nil != sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
app(nil,sK258) = sK258,
inference(resolution,[status(thm)],[c111,c215]) ).
cnf(d1,plain,
( segmentP(X1,sK258)
| ~ ssList(nil)
| ~ ssList(sK258)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK258,X0) != X1 ),
inference(superposition,[status(thm)],[d0,c21]) ).
cnf(d2,plain,
( segmentP(X1,sK258)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK258,X0) != X1 ),
inference(resolution,[status(thm)],[c215,d1]) ).
cnf(d3,plain,
( segmentP(X1,sK258)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK258,X0) != X1 ),
inference(resolution,[status(thm)],[c97,d2]) ).
cnf(d4,plain,
app(sK258,sK259) = sK254,
inference(demodulation,[status(thm)],[c217,c212]) ).
cnf(d5,plain,
( segmentP(X0,sK258)
| ~ ssList(sK259)
| ~ ssList(X0)
| sK254 != X0 ),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( segmentP(X0,sK258)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c216,d5]) ).
cnf(d7,plain,
( segmentP(sK254,sK258)
| ~ ssList(sK254) ),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
segmentP(sK254,sK258),
inference(resolution,[status(thm)],[c209,d7]) ).
cnf(d9,plain,
( ~ segmentP(sK253,sK258)
| ~ ssList(sK258)
| ~ neq(sK258,nil) ),
inference(resolution,[status(thm)],[d8,c214]) ).
cnf(d10,plain,
( ~ segmentP(sK253,sK258)
| ~ neq(sK258,nil) ),
inference(resolution,[status(thm)],[c215,d9]) ).
cnf(d11,plain,
app(sK253,nil) = sK253,
inference(resolution,[status(thm)],[c194,c208]) ).
cnf(d12,plain,
app(sK259,sK258) = sK253,
inference(demodulation,[status(thm)],[c218,c213]) ).
cnf(d13,plain,
( segmentP(X1,sK258)
| ~ ssList(sK259)
| ~ ssList(sK258)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(superposition,[status(thm)],[d12,c21]) ).
cnf(d14,plain,
( segmentP(X1,sK258)
| ~ ssList(sK258)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(resolution,[status(thm)],[c216,d13]) ).
cnf(d15,plain,
( segmentP(X1,sK258)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(resolution,[status(thm)],[c215,d14]) ).
cnf(d16,plain,
( segmentP(app(sK253,X0),sK258)
| ~ ssList(X0)
| ~ ssList(app(sK253,X0)) ),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( ~ ssList(app(sK253,nil))
| ~ ssList(nil)
| segmentP(sK253,sK258) ),
inference(superposition,[status(thm)],[d11,d16]) ).
cnf(d18,plain,
( segmentP(sK253,sK258)
| ~ ssList(nil)
| ~ ssList(sK253) ),
inference(demodulation,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
( segmentP(sK253,sK258)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c208,d18]) ).
cnf(d20,plain,
segmentP(sK253,sK258),
inference(resolution,[status(thm)],[c97,d19]) ).
cnf(d21,plain,
~ neq(sK258,nil),
inference(resolution,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
( ~ ssList(sK258)
| ~ ssList(nil)
| sK258 = nil ),
inference(resolution,[status(thm)],[d21,c95]) ).
cnf(d23,plain,
( ~ ssList(nil)
| sK258 = nil ),
inference(resolution,[status(thm)],[c215,d22]) ).
cnf(d24,plain,
sK258 = nil,
inference(resolution,[status(thm)],[c97,d23]) ).
cnf(d25,plain,
app(nil,sK259) = sK254,
inference(demodulation,[status(thm)],[d4,d24]) ).
cnf(d26,plain,
app(nil,sK259) = sK259,
inference(resolution,[status(thm)],[c111,c216]) ).
cnf(d27,plain,
sK254 = sK259,
inference(demodulation,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
app(sK259,nil) = sK253,
inference(demodulation,[status(thm)],[d12,d24]) ).
cnf(d29,plain,
app(sK254,nil) = sK253,
inference(demodulation,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
app(sK254,nil) = sK254,
inference(resolution,[status(thm)],[c194,c209]) ).
cnf(d31,plain,
sK253 = sK254,
inference(demodulation,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
( segmentP(X1,sK259)
| ~ ssList(sK258)
| ~ ssList(sK259)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK254,X0) != X1 ),
inference(superposition,[status(thm)],[d4,c21]) ).
cnf(d33,plain,
( segmentP(X1,sK259)
| ~ ssList(sK258)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK254,X0) != X1 ),
inference(resolution,[status(thm)],[c216,d32]) ).
cnf(d34,plain,
( segmentP(X1,sK259)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK254,X0) != X1 ),
inference(resolution,[status(thm)],[c215,d33]) ).
cnf(d35,plain,
( segmentP(app(sK254,X0),sK259)
| ~ ssList(X0)
| ~ ssList(app(sK254,X0)) ),
inference(equality_resolution,[status(thm)],[d34]) ).
cnf(d36,plain,
( ~ ssList(app(sK254,nil))
| ~ ssList(nil)
| segmentP(sK254,sK259) ),
inference(superposition,[status(thm)],[d30,d35]) ).
cnf(d37,plain,
( segmentP(sK254,sK259)
| ~ ssList(nil)
| ~ ssList(sK254) ),
inference(demodulation,[status(thm)],[d36,d30]) ).
cnf(d38,plain,
( segmentP(sK254,sK259)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c209,d37]) ).
cnf(d39,plain,
segmentP(sK254,sK259),
inference(resolution,[status(thm)],[c97,d38]) ).
cnf(d40,plain,
( ~ segmentP(sK253,sK259)
| ~ ssList(sK259)
| ~ neq(sK259,nil) ),
inference(resolution,[status(thm)],[d39,c214]) ).
cnf(d41,plain,
( ~ segmentP(sK253,sK259)
| ~ neq(sK259,nil) ),
inference(resolution,[status(thm)],[c216,d40]) ).
cnf(d42,plain,
( ~ segmentP(sK253,sK259)
| ~ neq(sK254,nil) ),
inference(demodulation,[status(thm)],[d41,d27]) ).
cnf(d43,plain,
( ~ segmentP(sK253,sK254)
| ~ neq(sK254,nil) ),
inference(demodulation,[status(thm)],[d42,d27]) ).
cnf(d44,plain,
( ~ segmentP(sK253,sK254)
| ~ neq(sK253,nil) ),
inference(demodulation,[status(thm)],[d43,d31]) ).
cnf(d45,plain,
( ~ segmentP(sK253,sK253)
| ~ neq(sK253,nil) ),
inference(demodulation,[status(thm)],[d44,d31]) ).
cnf(d46,plain,
segmentP(sK254,sK254),
inference(demodulation,[status(thm)],[d39,d27]) ).
cnf(d47,plain,
segmentP(sK253,sK254),
inference(demodulation,[status(thm)],[d46,d31]) ).
cnf(d48,plain,
segmentP(sK253,sK253),
inference(demodulation,[status(thm)],[d47,d31]) ).
cnf(d49,plain,
~ neq(sK253,nil),
inference(resolution,[status(thm)],[d48,d45]) ).
cnf(d50,plain,
( ~ ssList(sK253)
| ~ ssList(nil)
| sK253 = nil ),
inference(resolution,[status(thm)],[d49,c95]) ).
cnf(d51,plain,
( ~ ssList(nil)
| sK253 = nil ),
inference(resolution,[status(thm)],[c208,d50]) ).
cnf(d52,plain,
sK253 = nil,
inference(resolution,[status(thm)],[c97,d51]) ).
cnf(d53,plain,
( rearsegP(X0,sK258)
| ~ ssList(sK258)
| ~ ssList(X0)
| ~ ssList(sK259)
| sK253 != X0 ),
inference(superposition,[status(thm)],[d12,c17]) ).
cnf(d54,plain,
( rearsegP(X0,sK258)
| ~ ssList(sK258)
| ~ ssList(X0)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c216,d53]) ).
cnf(d55,plain,
( rearsegP(X0,sK258)
| ~ ssList(X0)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c215,d54]) ).
cnf(d56,plain,
( rearsegP(sK253,sK258)
| ~ ssList(sK253) ),
inference(equality_resolution,[status(thm)],[d55]) ).
cnf(d57,plain,
rearsegP(sK253,sK258),
inference(resolution,[status(thm)],[c208,d56]) ).
cnf(d58,plain,
( ~ rearsegP(sK258,sK253)
| ~ ssList(sK253)
| ~ ssList(sK258)
| sK258 = sK253 ),
inference(resolution,[status(thm)],[c140,d57]) ).
cnf(d59,plain,
( ~ rearsegP(sK258,sK253)
| ~ ssList(sK258)
| sK258 = sK253 ),
inference(resolution,[status(thm)],[c208,d58]) ).
cnf(d60,plain,
( ~ rearsegP(sK258,sK253)
| sK258 = sK253 ),
inference(resolution,[status(thm)],[c215,d59]) ).
cnf(d61,plain,
( ~ rearsegP(sK258,sK253)
| nil = sK253 ),
inference(demodulation,[status(thm)],[d60,d24]) ).
cnf(d62,plain,
( ~ rearsegP(nil,sK253)
| nil = sK253 ),
inference(demodulation,[status(thm)],[d61,d24]) ).
cnf(d63,plain,
( nil != sK253
| nil != sK253 ),
inference(demodulation,[status(thm)],[c219,d31]) ).
cnf(d64,plain,
~ rearsegP(nil,sK253),
inference(resolution,[status(thm)],[d63,d62]) ).
cnf(d65,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm)],[d64,d52]) ).
cnf(d66,plain,
rearsegP(sK253,nil),
inference(demodulation,[status(thm)],[d57,d24]) ).
cnf(d67,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm)],[d66,d52]) ).
cnf(d68,plain,
$false,
inference(resolution,[status(thm)],[d67,d65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC075+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.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 12:12:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.31/3.42 % SZS status Theorem for theBenchmark.p
% 9.31/3.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------