%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 11.09s 1.98s
% Output : CNFRefutation 11.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 51 ( 17 ~; 15 |; 5 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 34 ( 1 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [X0] :
( ordinal(X0)
=> ( 'epsilon$uconnected'(X0)
& 'epsilon$utransitive'(X0) ) ) ).
fof(d2_ordinal1,axiom,
! [X0] :
( 'epsilon$utransitive'(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ) ).
fof(t2_subset,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ) ).
fof(t4_subset,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ) ).
fof(t7_boole,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ) ).
fof(t19_ordinal1,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( 'epsilon$utransitive'(X2)
=> ( ( in(X0,X1)
& in(X2,X0) )
=> in(X2,X1) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( 'epsilon$utransitive'(X2)
=> ( ( in(X0,X1)
& in(X2,X0) )
=> in(X2,X1) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t19_ordinal1]) ).
cnf(c2,plain,
( 'epsilon$utransitive'(X0)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[cc1_ordinal1]) ).
cnf(c9,plain,
( subset(X1,X0)
| ~ in(X1,X0)
| ~ 'epsilon$utransitive'(X0) ),
inference(clausification,[status(esa)],[d2_ordinal1]) ).
cnf(c46,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c48,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c49,plain,
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t4_subset]) ).
cnf(c52,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t7_boole]) ).
cnf(c55,plain,
ordinal(sK43),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c57,plain,
in(sK44,sK42),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c58,plain,
in(sK42,sK43),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
~ in(sK44,sK43),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(sK42,sK43)
| ~ 'epsilon$utransitive'(sK43) ),
inference(resolution,[status(thm)],[c58,c9]) ).
cnf(d1,plain,
'epsilon$utransitive'(sK43),
inference(resolution,[status(thm)],[c2,c55]) ).
cnf(d2,plain,
subset(sK42,sK43),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ subset(X1,X2)
| element(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c49,c48]) ).
cnf(d4,plain,
( element(X0,sK43)
| ~ in(X0,sK42) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
element(sK44,sK43),
inference(resolution,[status(thm)],[d4,c57]) ).
cnf(d6,plain,
( empty(sK43)
| in(sK44,sK43) ),
inference(resolution,[status(thm)],[d5,c46]) ).
cnf(d7,plain,
empty(sK43),
inference(resolution,[status(thm)],[c59,d6]) ).
cnf(d8,plain,
~ empty(sK43),
inference(resolution,[status(thm)],[c52,c58]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 02:35:53 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.09/1.98 % SZS status Theorem for theBenchmark.p
% 11.09/1.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------