%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM394+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:12:38 AM UTC 2026
% Result : Theorem 12.06s 6.98s
% Output : CNFRefutation 12.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 77 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 73 ( 26 ~; 30 |; 5 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 23 ( 2 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [X0] :
( ordinal(X0)
=> ( 'epsilon$uconnected'(X0)
& 'epsilon$utransitive'(X0) ) ) ).
fof(d2_ordinal1,axiom,
! [X0] :
( 'epsilon$utransitive'(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ) ).
fof(redefinition_r1_ordinal1,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( 'ordinal$usubset'(X0,X1)
<=> subset(X0,X1) ) ) ).
fof(reflexivity_r1_ordinal1,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> 'ordinal$usubset'(X0,X0) ) ).
fof(t24_ordinal1,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ) ).
fof(t26_ordinal1,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
| 'ordinal$usubset'(X0,X1) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
| 'ordinal$usubset'(X0,X1) ) ) ),
inference(negate_conjecture,[status(cth)],[t26_ordinal1]) ).
cnf(c2,plain,
( 'epsilon$utransitive'(X0)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[cc1_ordinal1]) ).
cnf(c10,plain,
( subset(X1,X0)
| ~ in(X1,X0)
| ~ 'epsilon$utransitive'(X0) ),
inference(clausification,[status(esa)],[d2_ordinal1]) ).
cnf(c46,plain,
( ~ subset(X0,X1)
| 'ordinal$usubset'(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[redefinition_r1_ordinal1]) ).
cnf(c47,plain,
( 'ordinal$usubset'(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[reflexivity_r1_ordinal1]) ).
cnf(c50,plain,
( ~ ordinal(X0)
| in(X1,X0)
| X0 = X1
| ~ ordinal(X1)
| in(X0,X1) ),
inference(clausification,[status(esa)],[t24_ordinal1]) ).
cnf(c59,plain,
ordinal(sK50),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c60,plain,
ordinal(sK51),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c61,plain,
~ 'ordinal$usubset'(sK50,sK51),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c62,plain,
~ in(sK51,sK50),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ ordinal(sK50)
| ~ ordinal(sK51)
| in(sK50,sK51)
| sK51 = sK50 ),
inference(resolution,[status(thm)],[c50,c62]) ).
cnf(d1,plain,
( ~ ordinal(sK51)
| in(sK50,sK51)
| sK51 = sK50 ),
inference(resolution,[status(thm)],[c59,d0]) ).
cnf(d2,plain,
( in(sK50,sK51)
| sK51 = sK50 ),
inference(resolution,[status(thm)],[c60,d1]) ).
cnf(d3,plain,
( subset(sK50,sK51)
| ~ 'epsilon$utransitive'(sK51)
| sK51 = sK50 ),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d4,plain,
'epsilon$utransitive'(sK51),
inference(resolution,[status(thm)],[c2,c60]) ).
cnf(d5,plain,
( subset(sK50,sK51)
| sK51 = sK50 ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( 'ordinal$usubset'(sK50,sK51)
| ~ ordinal(sK50)
| ~ ordinal(sK51)
| sK51 = sK50 ),
inference(resolution,[status(thm)],[d5,c46]) ).
cnf(d7,plain,
( 'ordinal$usubset'(sK50,sK51)
| ~ ordinal(sK51)
| sK51 = sK50 ),
inference(resolution,[status(thm)],[c59,d6]) ).
cnf(d8,plain,
( 'ordinal$usubset'(sK50,sK51)
| sK51 = sK50 ),
inference(resolution,[status(thm)],[c60,d7]) ).
cnf(d9,plain,
sK51 = sK50,
inference(resolution,[status(thm)],[c61,d8]) ).
cnf(d10,plain,
~ 'ordinal$usubset'(sK50,sK50),
inference(demodulation,[status(thm)],[c61,d9]) ).
cnf(d11,plain,
( 'ordinal$usubset'(sK50,sK50)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c47,c59]) ).
cnf(d12,plain,
'ordinal$usubset'(sK50,sK50),
inference(resolution,[status(thm)],[d11,c59]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM394+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n014.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 02:38:07 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.06/6.98 % SZS status Theorem for theBenchmark.p
% 12.06/6.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------