%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC309+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 : n012.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 08:54:56 AM UTC 2026
% Result : Theorem 21.11s 5.13s
% Output : CNFRefutation 21.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 179 ( 76 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 238 ( 103 ~; 103 |; 16 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 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 : 56 ( 0 sgn 15 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ) ).
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(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) != X2
& ssList(X7) )
& ssItem(X6) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X0
& app(cons(X4,nil),X5) = X1
& 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)
=> ( ( nil = X3
& nil != X2 )
| ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) != X2
& ssList(X7) )
& ssItem(X6) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X0
& app(cons(X4,nil),X5) = X1
& 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(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
cnf(c101,plain,
( ssList(sK120(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax20]) ).
cnf(c102,plain,
( ssItem(sK121(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax20]) ).
cnf(c103,plain,
( cons(sK121(X0),sK120(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax20]) ).
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(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,
neq(sK254,nil),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( app(X1,cons(X0,nil)) != sK253
| app(cons(X0,nil),X1) != sK254
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( app(cons(X0,nil),X1) != sK256
| app(X1,cons(X0,nil)) = sK255
| ~ ssList(X1)
| ~ ssItem(X0) ),
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(X0)
| ~ ssItem(X1)
| app(cons(X1,nil),X0) != sK254
| app(X0,cons(X1,nil)) != sK255 ),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d2,plain,
( ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(X0)
| app(X1,cons(X0,nil)) != sK255
| cons(X0,app(nil,X1)) != sK254 ),
inference(superposition,[status(thm)],[c110,d1]) ).
cnf(d3,plain,
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,app(nil,X0)) != sK254
| app(X0,cons(X1,nil)) != sK255 ),
inference(resolution,[status(thm)],[c97,d2]) ).
cnf(d4,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssItem(X1)
| app(X0,cons(X1,nil)) != sK255
| cons(X1,X0) != sK254 ),
inference(superposition,[status(thm)],[c111,d3]) ).
cnf(d5,plain,
( ~ ssList(X0)
| ~ ssItem(X1)
| app(cons(X1,nil),X0) != sK254
| app(X0,cons(X1,nil)) = sK255 ),
inference(demodulation,[status(thm)],[c216,c212]) ).
cnf(d6,plain,
( ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(X0)
| app(X1,cons(X0,nil)) = sK255
| cons(X0,app(nil,X1)) != sK254 ),
inference(superposition,[status(thm)],[c110,d5]) ).
cnf(d7,plain,
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,app(nil,X0)) != sK254
| app(X0,cons(X1,nil)) = sK255 ),
inference(resolution,[status(thm)],[c97,d6]) ).
cnf(d8,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssItem(X1)
| app(X0,cons(X1,nil)) = sK255
| cons(X1,X0) != sK254 ),
inference(superposition,[status(thm)],[c111,d7]) ).
cnf(d9,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssList(sK120(X0))
| ~ ssItem(sK121(X0))
| app(sK120(X0),cons(sK121(X0),nil)) = sK255
| X0 != sK254 ),
inference(superposition,[status(thm)],[c103,d8]) ).
cnf(d10,plain,
( ~ ssList(sK120(sK254))
| ~ ssList(sK254)
| ~ ssItem(sK121(sK254))
| nil = sK254
| app(sK120(sK254),cons(sK121(sK254),nil)) = sK255 ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254))
| nil = sK254
| app(sK120(sK254),cons(sK121(sK254),nil)) = sK255 ),
inference(resolution,[status(thm)],[c209,d10]) ).
cnf(d12,plain,
( ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254))
| nil = sK254
| ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254))
| cons(sK121(sK254),sK120(sK254)) != sK254
| sK255 != sK255 ),
inference(superposition,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
( ~ ssList(sK254)
| nil = sK254
| ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254))
| sK255 != sK255
| nil = sK254
| sK254 != sK254 ),
inference(superposition,[status(thm)],[c103,d12]) ).
cnf(d14,plain,
( ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254))
| sK255 != sK255
| sK254 != sK254
| nil = sK254 ),
inference(resolution,[status(thm)],[c209,d13]) ).
cnf(d15,plain,
( ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254))
| sK254 != sK254
| nil = sK254 ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254))
| nil = sK254 ),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( ~ ssList(sK254)
| nil = sK254
| ~ ssItem(sK121(sK254))
| nil = sK254 ),
inference(resolution,[status(thm)],[d16,c101]) ).
cnf(d18,plain,
( ~ ssItem(sK121(sK254))
| nil = sK254 ),
inference(resolution,[status(thm)],[c209,d17]) ).
cnf(d19,plain,
( ~ ssList(sK254)
| nil = sK254
| nil = sK254 ),
inference(resolution,[status(thm)],[d18,c102]) ).
cnf(d20,plain,
nil = sK254,
inference(resolution,[status(thm)],[c209,d19]) ).
cnf(d21,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[c214,d20]) ).
cnf(d22,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[c97,d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC309+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
% 0.05/0.36 % Computer : n012.cluster.edu
% 0.05/0.36 % Model : x86_64 x86_64
% 0.05/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.36 % Memory : 8046.5625MB
% 0.05/0.36 % OS : Linux 6.8.0-71-generic
% 0.05/0.36 % CPULimit : 300
% 0.05/0.36 % WCLimit : 300
% 0.05/0.36 % DateTime : Sat Sep 26 12:45:27 UTC 2026
% 0.05/0.36 % CPUTime :
% 0.05/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.11/5.13 % SZS status Theorem for theBenchmark.p
% 21.11/5.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------