%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM390+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 : n016.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 11.12s 1.95s
% Output : CNFRefutation 11.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 74 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 63 ( 21 ~; 20 |; 6 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 31 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [X0] :
( ordinal(X0)
=> ( 'epsilon$uconnected'(X0)
& 'epsilon$utransitive'(X0) ) ) ).
fof(d2_ordinal1,axiom,
! [X0] :
( 'epsilon$utransitive'(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ) ).
fof(d8_xboole_0,axiom,
! [X0,X1] :
( 'proper$usubset'(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ) ).
fof(t1_xboole_1,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ).
fof(t21_ordinal1,axiom,
! [X0] :
( 'epsilon$utransitive'(X0)
=> ! [X1] :
( ordinal(X1)
=> ( 'proper$usubset'(X0,X1)
=> in(X0,X1) ) ) ) ).
fof(t7_ordinal1,axiom,
! [X0,X1] :
~ ( subset(X1,X0)
& in(X0,X1) ) ).
fof(t22_ordinal1,conjecture,
! [X0] :
( 'epsilon$utransitive'(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( in(X1,X2)
& subset(X0,X1) )
=> in(X0,X2) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'epsilon$utransitive'(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( in(X1,X2)
& subset(X0,X1) )
=> in(X0,X2) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t22_ordinal1]) ).
cnf(c3,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(c15,plain,
( X0 = X1
| ~ subset(X0,X1)
| 'proper$usubset'(X0,X1) ),
inference(clausification,[status(esa)],[d8_xboole_0]) ).
cnf(c51,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t1_xboole_1]) ).
cnf(c52,plain,
( in(X0,X1)
| ~ 'proper$usubset'(X0,X1)
| ~ ordinal(X1)
| ~ 'epsilon$utransitive'(X0) ),
inference(clausification,[status(esa)],[t21_ordinal1]) ).
cnf(c60,plain,
( ~ subset(X1,X0)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t7_ordinal1]) ).
cnf(c62,plain,
'epsilon$utransitive'(sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c64,plain,
ordinal(sK57),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c65,plain,
subset(sK55,sK56),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
in(sK56,sK57),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c67,plain,
~ in(sK55,sK57),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(sK56,sK57)
| ~ 'epsilon$utransitive'(sK57) ),
inference(resolution,[status(thm)],[c10,c66]) ).
cnf(d1,plain,
'epsilon$utransitive'(sK57),
inference(resolution,[status(thm)],[c3,c64]) ).
cnf(d2,plain,
subset(sK56,sK57),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ subset(X0,sK56)
| subset(X0,sK57) ),
inference(resolution,[status(thm)],[c51,d2]) ).
cnf(d4,plain,
subset(sK55,sK57),
inference(resolution,[status(thm)],[d3,c65]) ).
cnf(d5,plain,
( 'proper$usubset'(sK55,sK57)
| sK55 = sK57 ),
inference(resolution,[status(thm)],[d4,c15]) ).
cnf(d6,plain,
( ~ 'epsilon$utransitive'(sK55)
| ~ ordinal(sK57)
| in(sK55,sK57)
| sK55 = sK57 ),
inference(resolution,[status(thm)],[d5,c52]) ).
cnf(d7,plain,
( ~ ordinal(sK57)
| in(sK55,sK57)
| sK55 = sK57 ),
inference(resolution,[status(thm)],[c62,d6]) ).
cnf(d8,plain,
( in(sK55,sK57)
| sK55 = sK57 ),
inference(resolution,[status(thm)],[c64,d7]) ).
cnf(d9,plain,
sK55 = sK57,
inference(resolution,[status(thm)],[c67,d8]) ).
cnf(d10,plain,
in(sK56,sK55),
inference(demodulation,[status(thm)],[c66,d9]) ).
cnf(d11,plain,
~ in(sK56,sK55),
inference(resolution,[status(thm)],[c60,c65]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 02:42:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.12/1.95 % SZS status Theorem for theBenchmark.p
% 11.12/1.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------