%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU236+3 : 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 : n018.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 08:41:24 AM UTC 2026
% Result : Theorem 11.67s 10.50s
% Output : CNFRefutation 11.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 16 unt; 0 def)
% Number of atoms : 145 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 149 ( 62 ~; 64 |; 6 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [X0] :
( ordinal(X0)
=> ( 'epsilon$uconnected'(X0)
& 'epsilon$utransitive'(X0) ) ) ).
fof(d1_ordinal1,axiom,
! [X0] : succ(X0) = 'set$uunion2'(X0,singleton(X0)) ).
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
fof(d2_ordinal1,axiom,
! [X0] :
( 'epsilon$utransitive'(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(fc3_ordinal1,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(succ(X0))
& 'epsilon$uconnected'(succ(X0))
& 'epsilon$utransitive'(succ(X0))
& ~ empty(succ(X0)) ) ) ).
fof(redefinition_r1_ordinal1,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( 'ordinal$usubset'(X0,X1)
<=> subset(X0,X1) ) ) ).
fof(t10_ordinal1,axiom,
! [X0] : in(X0,succ(X0)) ).
fof(t8_xboole_1,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset('set$uunion2'(X0,X2),X1) ) ).
fof(t33_ordinal1,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> 'ordinal$usubset'(succ(X0),X1) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> 'ordinal$usubset'(succ(X0),X1) ) ) ),
inference(negate_conjecture,[status(cth)],[t33_ordinal1]) ).
cnf(c2,plain,
( 'epsilon$utransitive'(X0)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[cc1_ordinal1]) ).
cnf(c14,plain,
succ(X0) = 'set$uunion2'(X0,singleton(X0)),
inference(clausification,[status(esa)],[d1_ordinal1]) ).
cnf(c15,plain,
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c21,plain,
( subset(X1,X0)
| ~ in(X1,X0)
| ~ 'epsilon$utransitive'(X0) ),
inference(clausification,[status(esa)],[d2_ordinal1]) ).
cnf(c24,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c25,plain,
( in(sK23(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c26,plain,
( ~ in(sK23(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c46,plain,
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[fc3_ordinal1]) ).
cnf(c87,plain,
( subset(X0,X1)
| ~ 'ordinal$usubset'(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[redefinition_r1_ordinal1]) ).
cnf(c88,plain,
( ~ subset(X0,X1)
| 'ordinal$usubset'(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[redefinition_r1_ordinal1]) ).
cnf(c91,plain,
in(X0,succ(X0)),
inference(clausification,[status(esa)],[t10_ordinal1]) ).
cnf(c102,plain,
( subset('set$uunion2'(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t8_xboole_1]) ).
cnf(c103,plain,
ordinal(sK77),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c104,plain,
ordinal(sK78),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c106,plain,
( 'ordinal$usubset'(succ(sK77),sK78)
| in(sK77,sK78) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c107,plain,
( ~ in(sK77,sK78)
| ~ 'ordinal$usubset'(succ(sK77),sK78) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subset(singleton(X0),X1)
| ~ subset(X0,X1)
| subset(succ(X0),X1) ),
inference(superposition,[status(thm)],[c14,c102]) ).
cnf(d1,plain,
( in(sK77,sK78)
| subset(succ(sK77),sK78)
| ~ ordinal(succ(sK77))
| ~ ordinal(sK78) ),
inference(resolution,[status(thm)],[c87,c106]) ).
cnf(d2,plain,
( subset(succ(sK77),sK78)
| ~ ordinal(succ(sK77))
| in(sK77,sK78) ),
inference(resolution,[status(thm)],[c104,d1]) ).
cnf(d3,plain,
( ~ in(X0,succ(sK77))
| in(X0,sK78)
| ~ ordinal(succ(sK77))
| in(sK77,sK78) ),
inference(resolution,[status(thm)],[d2,c24]) ).
cnf(d4,plain,
( ~ ordinal(succ(sK77))
| in(sK77,sK78)
| in(sK77,sK78) ),
inference(resolution,[status(thm)],[d3,c91]) ).
cnf(d5,plain,
( ~ ordinal(sK77)
| in(sK77,sK78) ),
inference(resolution,[status(thm)],[d4,c46]) ).
cnf(d6,plain,
in(sK77,sK78),
inference(resolution,[status(thm)],[c103,d5]) ).
cnf(d7,plain,
~ 'ordinal$usubset'(succ(sK77),sK78),
inference(resolution,[status(thm)],[d6,c107]) ).
cnf(d8,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c15]) ).
cnf(d9,plain,
( subset(singleton(X0),X1)
| sK23(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[d8,c25]) ).
cnf(d10,plain,
( 'ordinal$usubset'('set$uunion2'(X0,X2),X1)
| ~ ordinal(X1)
| ~ ordinal('set$uunion2'(X0,X2))
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[c102,c88]) ).
cnf(d11,plain,
( ~ subset(X0,X1)
| ~ subset(singleton(X0),X1)
| ~ ordinal('set$uunion2'(X0,singleton(X0)))
| ~ ordinal(X1)
| 'ordinal$usubset'(succ(X0),X1) ),
inference(superposition,[status(thm)],[c14,d10]) ).
cnf(d12,plain,
( ~ subset(singleton(X0),X1)
| ~ subset(X0,X1)
| 'ordinal$usubset'(succ(X0),X1)
| ~ ordinal(succ(X0))
| ~ ordinal(X1) ),
inference(demodulation,[status(thm)],[d11,c14]) ).
cnf(d13,plain,
( sK23(singleton(X1),X0) = X1
| ~ subset(X1,X0)
| 'ordinal$usubset'(succ(X1),X0)
| ~ ordinal(succ(X1))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
( ~ subset(sK77,sK78)
| ~ ordinal(succ(sK77))
| ~ ordinal(sK78)
| sK23(singleton(sK77),sK78) = sK77 ),
inference(resolution,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
( ~ subset(sK77,sK78)
| ~ ordinal(succ(sK77))
| sK23(singleton(sK77),sK78) = sK77 ),
inference(resolution,[status(thm)],[c104,d14]) ).
cnf(d16,plain,
( subset(sK77,sK78)
| ~ 'epsilon$utransitive'(sK78) ),
inference(resolution,[status(thm)],[d6,c21]) ).
cnf(d17,plain,
'epsilon$utransitive'(sK78),
inference(resolution,[status(thm)],[c2,c104]) ).
cnf(d18,plain,
subset(sK77,sK78),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
( ~ ordinal(succ(sK77))
| sK23(singleton(sK77),sK78) = sK77 ),
inference(resolution,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
( ~ ordinal(sK77)
| sK23(singleton(sK77),sK78) = sK77 ),
inference(resolution,[status(thm)],[d19,c46]) ).
cnf(d21,plain,
sK23(singleton(sK77),sK78) = sK77,
inference(resolution,[status(thm)],[c103,d20]) ).
cnf(d22,plain,
( subset(singleton(sK77),sK78)
| ~ in(sK77,sK78) ),
inference(superposition,[status(thm)],[d21,c26]) ).
cnf(d23,plain,
subset(singleton(sK77),sK78),
inference(resolution,[status(thm)],[d6,d22]) ).
cnf(d24,plain,
( subset(succ(sK77),sK78)
| ~ subset(sK77,sK78) ),
inference(resolution,[status(thm)],[d23,d0]) ).
cnf(d25,plain,
subset(succ(sK77),sK78),
inference(resolution,[status(thm)],[d18,d24]) ).
cnf(d26,plain,
( 'ordinal$usubset'(succ(sK77),sK78)
| ~ ordinal(sK78)
| ~ ordinal(succ(sK77)) ),
inference(resolution,[status(thm)],[d25,c88]) ).
cnf(d27,plain,
( 'ordinal$usubset'(succ(sK77),sK78)
| ~ ordinal(succ(sK77)) ),
inference(resolution,[status(thm)],[c104,d26]) ).
cnf(d28,plain,
~ ordinal(succ(sK77)),
inference(resolution,[status(thm)],[d7,d27]) ).
cnf(d29,plain,
~ ordinal(sK77),
inference(resolution,[status(thm)],[d28,c46]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[c103,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU236+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n018.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 08:59:21 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.67/10.50 % SZS status Theorem for theBenchmark.p
% 11.67/10.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------