%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC008+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 : n007.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 08:53:55 AM UTC 2026
% Result : Theorem 43.48s 6.08s
% Output : CNFRefutation 43.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 20 unt; 0 def)
% Number of atoms : 208 ( 51 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 253 ( 112 ~; 100 |; 18 &)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 20 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax40,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X0,X1) )
=> frontsegP(X0,X2) ) ) ) ) ).
fof(ax42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ) ).
fof(ax43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ) ).
fof(ax45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ) ).
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)
=> ( ? [X7] :
( equalelemsP(X7)
& segmentP(X7,X2)
& frontsegP(X3,X7)
& neq(X2,X7)
& ssList(X7) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X7] :
( equalelemsP(X7)
& segmentP(X7,X2)
& frontsegP(X3,X7)
& neq(X2,X7)
& ssList(X7) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| 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(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c129,plain,
( ~ frontsegP(X2,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X2)
| frontsegP(X0,X1) ),
inference(clausification,[status(esa)],[ax40]) ).
cnf(c131,plain,
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax42]) ).
cnf(c132,plain,
( ~ ssList(X2)
| frontsegP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(clausification,[status(esa)],[ax43]) ).
cnf(c136,plain,
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax45]) ).
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(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,
frontsegP(sK256,sK255),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( ~ ssList(X2)
| app(app(X1,X0),X2) != sK254
| app(X1,X2) != sK253
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
app(sK255,nil) = sK255,
inference(resolution,[status(thm)],[c194,c210]) ).
cnf(d1,plain,
( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X2),X1) != sK254
| app(X0,X1) != sK255 ),
inference(demodulation,[status(thm)],[c216,c213]) ).
cnf(d2,plain,
( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X2),X1) != sK256
| app(X0,X1) != sK255 ),
inference(demodulation,[status(thm)],[d1,c212]) ).
cnf(d3,plain,
( ~ ssList(sK256)
| ~ ssList(sK255)
| app(sK255,sK15(sK256,sK255)) = sK256 ),
inference(resolution,[status(thm)],[c13,c214]) ).
cnf(d4,plain,
( ~ ssList(sK256)
| app(sK255,sK15(sK256,sK255)) = sK256 ),
inference(resolution,[status(thm)],[c210,d3]) ).
cnf(d5,plain,
app(sK255,sK15(sK256,sK255)) = sK256,
inference(resolution,[status(thm)],[c211,d4]) ).
cnf(d6,plain,
( ~ ssList(X0)
| ~ ssList(sK255)
| ~ ssList(sK15(sK256,sK255))
| app(sK255,X0) != sK255
| app(sK256,X0) != sK256 ),
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( ~ ssList(sK15(sK256,sK255))
| ~ ssList(X0)
| app(sK256,X0) != sK256
| app(sK255,X0) != sK255 ),
inference(resolution,[status(thm)],[c210,d6]) ).
cnf(d8,plain,
app(sK256,nil) = sK256,
inference(resolution,[status(thm)],[c194,c211]) ).
cnf(d9,plain,
( ~ ssList(sK15(sK256,sK255))
| ~ ssList(nil)
| app(sK255,nil) != sK255
| sK256 != sK256 ),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ ssList(sK15(sK256,sK255))
| ~ ssList(nil)
| sK256 != sK256
| sK255 != sK255 ),
inference(demodulation,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( ~ ssList(sK15(sK256,sK255))
| sK256 != sK256
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c97,d10]) ).
cnf(d12,plain,
( ~ ssList(X0)
| ~ ssList(nil)
| app(nil,sK15(X0,nil)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c136,c13]) ).
cnf(d13,plain,
( ~ ssList(X0)
| app(nil,sK15(X0,nil)) = X0 ),
inference(resolution,[status(thm)],[c97,d12]) ).
cnf(d14,plain,
app(nil,sK15(sK256,nil)) = sK256,
inference(resolution,[status(thm)],[d13,c211]) ).
cnf(d15,plain,
( frontsegP(sK256,X0)
| ~ frontsegP(sK255,X0)
| ~ ssList(sK256)
| ~ ssList(sK255)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c129,c214]) ).
cnf(d16,plain,
( frontsegP(sK256,X0)
| ~ frontsegP(sK255,X0)
| ~ ssList(sK256)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c210,d15]) ).
cnf(d17,plain,
( frontsegP(sK256,X0)
| ~ frontsegP(sK255,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c211,d16]) ).
cnf(d18,plain,
( ~ ssList(sK255)
| frontsegP(sK256,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d17,c136]) ).
cnf(d19,plain,
( frontsegP(sK256,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c210,d18]) ).
cnf(d20,plain,
frontsegP(sK256,nil),
inference(resolution,[status(thm)],[c97,d19]) ).
cnf(d21,plain,
( ~ ssList(sK256)
| ~ ssList(nil)
| app(nil,sK15(sK256,nil)) = sK256 ),
inference(resolution,[status(thm)],[d20,c13]) ).
cnf(d22,plain,
( ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = sK256 ),
inference(demodulation,[status(thm)],[d21,d14]) ).
cnf(d23,plain,
( ~ ssList(nil)
| sK256 = sK256 ),
inference(resolution,[status(thm)],[c211,d22]) ).
cnf(d24,plain,
sK256 = sK256,
inference(resolution,[status(thm)],[c97,d23]) ).
cnf(d25,plain,
( ~ ssList(sK15(sK256,sK255))
| sK255 != sK255 ),
inference(resolution,[status(thm)],[d24,d11]) ).
cnf(d26,plain,
app(nil,sK15(sK255,nil)) = sK255,
inference(resolution,[status(thm)],[d13,c210]) ).
cnf(d27,plain,
app(nil,sK255) = sK255,
inference(resolution,[status(thm)],[c111,c210]) ).
cnf(d28,plain,
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK255)
| frontsegP(sK255,X0) ),
inference(superposition,[status(thm)],[d27,c132]) ).
cnf(d29,plain,
( frontsegP(sK255,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c210,d28]) ).
cnf(d30,plain,
( frontsegP(sK255,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c97,d29]) ).
cnf(d31,plain,
( ~ ssList(nil)
| frontsegP(sK255,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d30,c131]) ).
cnf(d32,plain,
frontsegP(sK255,nil),
inference(resolution,[status(thm)],[c97,d31]) ).
cnf(d33,plain,
( ~ ssList(sK255)
| ~ ssList(nil)
| app(nil,sK15(sK255,nil)) = sK255 ),
inference(resolution,[status(thm)],[d32,c13]) ).
cnf(d34,plain,
( ~ ssList(sK255)
| ~ ssList(nil)
| sK255 = sK255 ),
inference(demodulation,[status(thm)],[d33,d26]) ).
cnf(d35,plain,
( ~ ssList(nil)
| sK255 = sK255 ),
inference(resolution,[status(thm)],[c210,d34]) ).
cnf(d36,plain,
sK255 = sK255,
inference(resolution,[status(thm)],[c97,d35]) ).
cnf(d37,plain,
~ ssList(sK15(sK256,sK255)),
inference(resolution,[status(thm)],[d36,d25]) ).
cnf(d38,plain,
( ~ frontsegP(sK256,sK255)
| ~ ssList(sK256)
| ~ ssList(sK255) ),
inference(resolution,[status(thm)],[d37,c12]) ).
cnf(d39,plain,
( ~ frontsegP(sK256,sK255)
| ~ ssList(sK256) ),
inference(resolution,[status(thm)],[c210,d38]) ).
cnf(d40,plain,
~ frontsegP(sK256,sK255),
inference(resolution,[status(thm)],[c211,d39]) ).
cnf(d41,plain,
$false,
inference(resolution,[status(thm)],[c214,d40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC008+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
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 12:01:24 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.48/6.08 % SZS status Theorem for theBenchmark.p
% 43.48/6.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------