%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC418+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 : n002.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 08:55:19 AM UTC 2026
% Result : Theorem 52.30s 7.27s
% Output : CNFRefutation 52.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 11 unt; 0 def)
% Number of atoms : 308 ( 103 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 445 ( 199 ~; 188 |; 32 &)
% ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 22 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ) ).
fof(ax24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ) ).
fof(ax26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ) ).
fof(ax27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = 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)
=> ( ( neq(X3,nil)
& ? [X7] :
( ? [X8] :
( ? [X9] :
( neq(nil,X3)
& ? [X10] :
( neq(nil,X3)
& hd(X3) = X10
& cons(X10,nil) = X9
& ssItem(X10) )
& app(X8,X9) = X7
& tl(X3) = X8
& ssList(X9) )
& ssList(X8) )
& X2 != X7
& ssList(X7) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X6,cons(X4,nil)),X5) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ? [X7] :
( ? [X8] :
( ? [X9] :
( neq(nil,X3)
& ? [X10] :
( neq(nil,X3)
& hd(X3) = X10
& cons(X10,nil) = X9
& ssItem(X10) )
& app(X8,X9) = X7
& tl(X3) = X8
& ssList(X9) )
& ssList(X8) )
& X2 != X7
& ssList(X7) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X6,cons(X4,nil)),X5) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c94,plain,
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax15]) ).
cnf(c95,plain,
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax15]) ).
cnf(c96,plain,
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax16]) ).
cnf(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
cnf(c105,plain,
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax22]) ).
cnf(c107,plain,
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax24]) ).
cnf(c109,plain,
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax26]) ).
cnf(c110,plain,
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax27]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c186,plain,
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax78]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
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,
neq(sK254,nil),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( app(app(X2,cons(X1,nil)),X0) != sK253
| ~ ssList(X2)
| ~ ssItem(X1)
| app(app(X0,cons(X1,nil)),X2) != sK254
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( sK255 = X2
| ~ ssList(X0)
| tl(sK256) != X0
| hd(sK256) != X3
| ~ neq(sK256,nil)
| ~ ssList(X1)
| ~ ssItem(X3)
| cons(X3,nil) != X1
| ~ ssList(X2)
| ~ neq(nil,sK256)
| app(X0,X1) != X2 ),
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,
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| app(app(X2,cons(X1,nil)),X0) != sK253
| app(app(X0,cons(X1,nil)),X2) != sK256 ),
inference(demodulation,[status(thm)],[c215,c212]) ).
cnf(d2,plain,
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| app(app(X2,cons(X1,nil)),X0) != sK255
| app(app(X0,cons(X1,nil)),X2) != sK256 ),
inference(demodulation,[status(thm)],[d1,c213]) ).
cnf(d3,plain,
( ~ ssList(cons(X0,nil))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| app(app(X1,cons(X0,nil)),nil) != sK255
| app(cons(X0,nil),X1) != sK256 ),
inference(superposition,[status(thm)],[c111,d2]) ).
cnf(d4,plain,
( ~ ssList(cons(X1,nil))
| ~ ssList(X0)
| ~ ssItem(X1)
| app(cons(X1,nil),X0) != sK256
| app(app(X0,cons(X1,nil)),nil) != sK255 ),
inference(resolution,[status(thm)],[c97,d3]) ).
cnf(d5,plain,
( ~ ssList(app(X0,cons(X1,nil)))
| ~ ssList(cons(X1,nil))
| ~ ssList(X0)
| ~ ssItem(X1)
| app(cons(X1,nil),X0) != sK256
| app(X0,cons(X1,nil)) != sK255 ),
inference(superposition,[status(thm)],[c194,d4]) ).
cnf(d6,plain,
( ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssList(app(X1,cons(X0,nil)))
| ~ ssList(X1)
| ~ ssItem(X0)
| app(X1,cons(X0,nil)) != sK255
| cons(X0,app(nil,X1)) != sK256 ),
inference(superposition,[status(thm)],[c110,d5]) ).
cnf(d7,plain,
( ~ ssList(cons(X1,nil))
| ~ ssList(app(X0,cons(X1,nil)))
| ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,app(nil,X0)) != sK256
| app(X0,cons(X1,nil)) != sK255 ),
inference(resolution,[status(thm)],[c97,d6]) ).
cnf(d8,plain,
( ~ ssList(X0)
| ~ ssList(cons(X1,nil))
| ~ ssList(app(X0,cons(X1,nil)))
| ~ ssList(X0)
| ~ ssItem(X1)
| app(X0,cons(X1,nil)) != sK255
| cons(X1,X0) != sK256 ),
inference(superposition,[status(thm)],[c111,d7]) ).
cnf(d9,plain,
neq(sK256,nil),
inference(demodulation,[status(thm)],[c214,c212]) ).
cnf(d10,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ neq(nil,sK256)
| ~ ssItem(X3)
| sK255 = X2
| tl(sK256) != X0
| hd(sK256) != X3
| cons(X3,nil) != X1
| app(X0,X1) != X2 ),
inference(resolution,[status(thm)],[d9,c217]) ).
cnf(d11,plain,
( ~ ssList(X0)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ neq(nil,sK256)
| ~ ssItem(X1)
| sK255 = X2
| tl(sK256) != X0
| hd(sK256) != X1
| app(X0,cons(X1,nil)) != X2 ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( ~ ssList(cons(X0,nil))
| ~ ssList(X1)
| ~ ssList(app(X1,cons(X0,nil)))
| ~ neq(nil,sK256)
| ~ ssItem(X0)
| sK255 = app(X1,cons(X0,nil))
| tl(sK256) != X1
| hd(sK256) != X0 ),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( ~ ssList(cons(X0,nil))
| ~ ssList(app(tl(sK256),cons(X0,nil)))
| ~ ssList(tl(sK256))
| ~ neq(nil,sK256)
| ~ ssItem(X0)
| sK255 = app(tl(sK256),cons(X0,nil))
| hd(sK256) != X0 ),
inference(equality_resolution,[status(thm)],[d12]) ).
cnf(d14,plain,
( ~ ssList(tl(sK256))
| ~ ssList(cons(hd(sK256),nil))
| ~ ssList(app(tl(sK256),cons(hd(sK256),nil)))
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| sK255 = app(tl(sK256),cons(hd(sK256),nil)) ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( ~ ssList(tl(sK256))
| ~ ssList(cons(hd(sK256),nil))
| ~ ssList(app(tl(sK256),cons(hd(sK256),nil)))
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| ~ ssList(cons(hd(sK256),nil))
| ~ ssList(app(tl(sK256),cons(hd(sK256),nil)))
| ~ ssList(tl(sK256))
| ~ ssItem(hd(sK256))
| cons(hd(sK256),tl(sK256)) != sK256
| sK255 != sK255 ),
inference(superposition,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
( ~ ssList(sK256)
| nil = sK256
| ~ ssList(tl(sK256))
| ~ ssList(cons(hd(sK256),nil))
| ~ ssList(app(tl(sK256),cons(hd(sK256),nil)))
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| sK255 != sK255
| sK256 != sK256 ),
inference(superposition,[status(thm)],[c186,d15]) ).
cnf(d17,plain,
( ~ ssList(tl(sK256))
| ~ ssList(cons(hd(sK256),nil))
| ~ ssList(app(tl(sK256),cons(hd(sK256),nil)))
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| sK256 != sK256
| sK255 != sK255
| nil = sK256 ),
inference(resolution,[status(thm)],[c211,d16]) ).
cnf(d18,plain,
( ~ ssList(tl(sK256))
| ~ ssList(cons(hd(sK256),nil))
| ~ ssList(app(tl(sK256),cons(hd(sK256),nil)))
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| sK255 != sK255
| nil = sK256 ),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( ~ ssList(tl(sK256))
| ~ ssList(cons(hd(sK256),nil))
| ~ ssList(app(tl(sK256),cons(hd(sK256),nil)))
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| nil = sK256 ),
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
( ~ ssList(tl(sK256))
| ~ ssList(cons(hd(sK256),nil))
| ~ ssList(tl(sK256))
| ~ ssList(cons(hd(sK256),nil))
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[d19,c109]) ).
cnf(d21,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK256))
| ~ ssList(tl(sK256))
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[d20,c96]) ).
cnf(d22,plain,
( ~ ssList(tl(sK256))
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[c97,d21]) ).
cnf(d23,plain,
( ~ ssList(sK256)
| nil = sK256
| ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[d22,c107]) ).
cnf(d24,plain,
( ~ neq(nil,sK256)
| ~ ssItem(hd(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[c211,d23]) ).
cnf(d25,plain,
( ~ ssList(nil)
| ~ ssList(sK256)
| nil = sK256
| ~ ssItem(hd(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[d24,c95]) ).
cnf(d26,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[c211,d25]) ).
cnf(d27,plain,
( ~ ssItem(hd(sK256))
| nil = sK256 ),
inference(resolution,[status(thm)],[c97,d26]) ).
cnf(d28,plain,
( ~ ssList(sK256)
| nil = sK256
| nil = sK256 ),
inference(resolution,[status(thm)],[d27,c105]) ).
cnf(d29,plain,
nil = sK256,
inference(resolution,[status(thm)],[c211,d28]) ).
cnf(d30,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[d9,d29]) ).
cnf(d31,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[c97,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC418+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
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:03:55 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.30/7.27 % SZS status Theorem for theBenchmark.p
% 52.30/7.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------