%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV376+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 09:02:12 AM UTC 2026
% Result : Theorem 6.06s 3.63s
% Output : CNFRefutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 48 ( 25 ~; 13 |; 0 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l12_induction,axiom,
( ! [X0,X1,X2,X3,X4,X5] :
( 'succ$ucpq'(triple(X0,X1,X2),triple(X3,X4,X5))
=> ( ~ ok(triple(X3,X4,X5))
=> ~ ok('im$usucc$ucpq'(triple(X3,X4,X5))) ) )
=> ! [X6,X7,X8] :
( ~ ok(triple(X6,X7,X8))
=> ! [X9,X10,X11] :
( 'succ$ucpq'(triple(X6,X7,X8),triple(X9,X10,X11))
=> ~ ok(triple(X9,X10,X11)) ) ) ) ).
fof(l12_l13,lemma,
! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> ~ ok('im$usucc$ucpq'(triple(X0,X1,X2))) ) ).
fof(l12_co,conjecture,
! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> ! [X3,X4,X5] :
( 'succ$ucpq'(triple(X0,X1,X2),triple(X3,X4,X5))
=> ~ ok(triple(X3,X4,X5)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> ! [X3,X4,X5] :
( 'succ$ucpq'(triple(X0,X1,X2),triple(X3,X4,X5))
=> ~ ok(triple(X3,X4,X5)) ) ),
inference(negate_conjecture,[status(cth)],[l12_co]) ).
cnf(c1,plain,
( ~ ok(triple(X3,X4,X5))
| ~ 'succ$ucpq'(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| ~ ok(triple(sK3,sK4,sK5)) ),
inference(clausification,[status(esa)],[l12_induction]) ).
cnf(c2,plain,
( ~ ok(triple(X3,X4,X5))
| ~ 'succ$ucpq'(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| ok('im$usucc$ucpq'(triple(sK3,sK4,sK5))) ),
inference(clausification,[status(esa)],[l12_induction]) ).
cnf(c3,plain,
( ~ ok('im$usucc$ucpq'(triple(X0,X1,X2)))
| ok(triple(X0,X1,X2)) ),
inference(clausification,[status(esa)],[l12_l13]) ).
cnf(c54,plain,
~ ok(triple(sK132,sK133,sK134)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c55,plain,
'succ$ucpq'(triple(sK132,sK133,sK134),triple(sK135,sK136,sK137)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c56,plain,
ok(triple(sK135,sK136,sK137)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ok('im$usucc$ucpq'(triple(sK3,sK4,sK5)))
| ok(triple(sK132,sK133,sK134))
| ~ ok(triple(sK135,sK136,sK137)) ),
inference(resolution,[status(thm)],[c2,c55]) ).
cnf(d1,plain,
( ok('im$usucc$ucpq'(triple(sK3,sK4,sK5)))
| ~ ok(triple(sK135,sK136,sK137)) ),
inference(resolution,[status(thm)],[c54,d0]) ).
cnf(d2,plain,
ok('im$usucc$ucpq'(triple(sK3,sK4,sK5))),
inference(resolution,[status(thm)],[c56,d1]) ).
cnf(d3,plain,
ok(triple(sK3,sK4,sK5)),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( ~ ok(triple(sK3,sK4,sK5))
| ok(triple(sK132,sK133,sK134))
| ~ ok(triple(sK135,sK136,sK137)) ),
inference(resolution,[status(thm)],[c55,c1]) ).
cnf(d5,plain,
( ~ ok(triple(sK135,sK136,sK137))
| ~ ok(triple(sK3,sK4,sK5)) ),
inference(resolution,[status(thm)],[c54,d4]) ).
cnf(d6,plain,
~ ok(triple(sK3,sK4,sK5)),
inference(resolution,[status(thm)],[c56,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV376+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n005.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 13:39:16 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.06/3.63 % SZS status Theorem for theBenchmark.p
% 6.06/3.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------