%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC294+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 08:54:53 AM UTC 2026
% Result : Theorem 18.11s 4.52s
% Output : CNFRefutation 18.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 92 ( 16 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 94 ( 37 ~; 40 |; 3 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ) ).
fof(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ) ).
fof(ax68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ) ).
fof(ax69,axiom,
strictorderedP(nil) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( neq(X3,nil)
& ~ singletonP(X2) )
| strictorderedP(X0)
| ~ segmentP(X3,X2)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( neq(X3,nil)
& ~ singletonP(X2) )
| strictorderedP(X0)
| ~ segmentP(X3,X2)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c9,plain,
( ssItem(sK11(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c10,plain,
( cons(sK11(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax4]) ).
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(c151,plain,
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax58]) ).
cnf(c168,plain,
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax68]) ).
cnf(c169,plain,
strictorderedP(nil),
inference(clausification,[status(esa)],[ax69]) ).
cnf(c210,plain,
ssList(sK255),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c211,plain,
ssList(sK256),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c213,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
segmentP(sK256,sK255),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
~ strictorderedP(sK253),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( ~ neq(sK256,nil)
| singletonP(sK255) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| ~ ssItem(sK11(X0))
| strictorderedP(X0) ),
inference(superposition,[status(thm)],[c10,c168]) ).
cnf(d1,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| strictorderedP(X0)
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[d0,c9]) ).
cnf(d2,plain,
~ strictorderedP(sK255),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d3,plain,
( singletonP(sK255)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c216]) ).
cnf(d4,plain,
( singletonP(sK255)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d3]) ).
cnf(d5,plain,
( singletonP(sK255)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d4]) ).
cnf(d6,plain,
( singletonP(sK255)
| segmentP(nil,sK255) ),
inference(superposition,[status(thm)],[d5,c214]) ).
cnf(d7,plain,
( ~ ssList(sK255)
| nil = sK255
| singletonP(sK255) ),
inference(resolution,[status(thm)],[d6,c151]) ).
cnf(d8,plain,
( singletonP(sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[c210,d7]) ).
cnf(d9,plain,
( singletonP(sK255)
| ~ strictorderedP(nil) ),
inference(superposition,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
singletonP(sK255),
inference(resolution,[status(thm)],[c169,d9]) ).
cnf(d11,plain,
( strictorderedP(sK255)
| ~ ssList(sK255) ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
strictorderedP(sK255),
inference(resolution,[status(thm)],[c210,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d2,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC294+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 12:43:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.11/4.52 % SZS status Theorem for theBenchmark.p
% 18.11/4.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------