%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU391+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 08:41:51 AM UTC 2026
% Result : Theorem 30.48s 4.56s
% Output : CNFRefutation 30.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 4
% Syntax : Number of formulae : 67 ( 9 unt; 0 def)
% Number of atoms : 248 ( 26 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 294 ( 113 ~; 157 |; 13 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_yellow19,axiom,
! [X0] :
( ( 'one$usorted$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( ( 'net$ustr'(X1,X0)
& ~ 'empty$ucarrier'(X1) )
=> 'filter$uof$unet$ustr'(X0,X1) = 'a$u2$u1$uyellow19'(X0,X1) ) ) ).
fof(fraenkel_a_2_1_yellow19,axiom,
! [X0,X1,X2] :
( ( 'net$ustr'(X2,X1)
& ~ 'empty$ucarrier'(X2)
& 'one$usorted$ustr'(X1)
& ~ 'empty$ucarrier'(X1) )
=> ( in(X0,'a$u2$u1$uyellow19'(X1,X2))
<=> ? [X3] :
( 'is$ueventually$uin'(X1,X2,X3)
& X0 = X3
& element(X3,powerset('the$ucarrier'(X1))) ) ) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ) ).
fof(t11_yellow19,conjecture,
! [X0] :
( ( 'one$usorted$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( ( 'net$ustr'(X1,X0)
& ~ 'empty$ucarrier'(X1) )
=> ! [X2] :
( in(X2,'filter$uof$unet$ustr'(X0,X1))
<=> ( element(X2,powerset('the$ucarrier'(X0)))
& 'is$ueventually$uin'(X0,X1,X2) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'one$usorted$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( ( 'net$ustr'(X1,X0)
& ~ 'empty$ucarrier'(X1) )
=> ! [X2] :
( in(X2,'filter$uof$unet$ustr'(X0,X1))
<=> ( element(X2,powerset('the$ucarrier'(X0)))
& 'is$ueventually$uin'(X0,X1,X2) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t11_yellow19]) ).
cnf(c57,plain,
( ~ 'one$usorted$ustr'(X0)
| 'empty$ucarrier'(X0)
| 'empty$ucarrier'(X1)
| ~ 'net$ustr'(X1,X0)
| 'filter$uof$unet$ustr'(X0,X1) = 'a$u2$u1$uyellow19'(X0,X1) ),
inference(clausification,[status(esa)],[d3_yellow19]) ).
cnf(c165,plain,
( 'empty$ucarrier'(X2)
| element(sK76(X1,X0,X2),powerset('the$ucarrier'(X0)))
| 'empty$ucarrier'(X0)
| ~ 'net$ustr'(X2,X0)
| ~ in(X1,'a$u2$u1$uyellow19'(X0,X2))
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[fraenkel_a_2_1_yellow19]) ).
cnf(c166,plain,
( 'empty$ucarrier'(X2)
| X1 = sK76(X1,X0,X2)
| 'empty$ucarrier'(X0)
| ~ 'net$ustr'(X2,X0)
| ~ in(X1,'a$u2$u1$uyellow19'(X0,X2))
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[fraenkel_a_2_1_yellow19]) ).
cnf(c167,plain,
( 'empty$ucarrier'(X1)
| 'empty$ucarrier'(X0)
| ~ 'net$ustr'(X1,X0)
| ~ in(X2,'a$u2$u1$uyellow19'(X0,X1))
| 'is$ueventually$uin'(X0,X1,sK76(X2,X0,X1))
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[fraenkel_a_2_1_yellow19]) ).
cnf(c168,plain,
( X2 != X3
| ~ 'is$ueventually$uin'(X0,X1,X3)
| 'empty$ucarrier'(X1)
| ~ element(X3,powerset('the$ucarrier'(X0)))
| in(X2,'a$u2$u1$uyellow19'(X0,X1))
| 'empty$ucarrier'(X0)
| ~ 'net$ustr'(X1,X0)
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[fraenkel_a_2_1_yellow19]) ).
cnf(c318,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c319,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c325,plain,
~ 'empty$ucarrier'(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c326,plain,
'one$usorted$ustr'(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c327,plain,
~ 'empty$ucarrier'(sK151),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c328,plain,
'net$ustr'(sK151,sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c330,plain,
( 'is$ueventually$uin'(sK150,sK151,sK152)
| in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c331,plain,
( element(sK152,powerset('the$ucarrier'(sK150)))
| in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c332,plain,
( ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151))
| ~ element(sK152,powerset('the$ucarrier'(sK150)))
| ~ 'is$ueventually$uin'(sK150,sK151,sK152) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'is$ueventually$uin'(X1,X2,X0)
| ~ 'one$usorted$ustr'(X1)
| ~ 'net$ustr'(X2,X1)
| ~ element(X0,powerset('the$ucarrier'(X1)))
| 'empty$ucarrier'(X2)
| 'empty$ucarrier'(X1)
| in(X0,'a$u2$u1$uyellow19'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c168]) ).
cnf(d1,plain,
( ~ 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151))
| ~ subset(sK152,'the$ucarrier'(sK150)) ),
inference(resolution,[status(thm)],[c319,c332]) ).
cnf(d2,plain,
( ~ 'one$usorted$ustr'(sK150)
| 'empty$ucarrier'(sK151)
| 'empty$ucarrier'(sK150)
| 'filter$uof$unet$ustr'(sK150,sK151) = 'a$u2$u1$uyellow19'(sK150,sK151) ),
inference(resolution,[status(thm)],[c57,c328]) ).
cnf(d3,plain,
( ~ 'one$usorted$ustr'(sK150)
| 'empty$ucarrier'(sK151)
| 'filter$uof$unet$ustr'(sK150,sK151) = 'a$u2$u1$uyellow19'(sK150,sK151) ),
inference(resolution,[status(thm)],[c325,d2]) ).
cnf(d4,plain,
( 'empty$ucarrier'(sK151)
| 'filter$uof$unet$ustr'(sK150,sK151) = 'a$u2$u1$uyellow19'(sK150,sK151) ),
inference(resolution,[status(thm)],[c326,d3]) ).
cnf(d5,plain,
'filter$uof$unet$ustr'(sK150,sK151) = 'a$u2$u1$uyellow19'(sK150,sK151),
inference(resolution,[status(thm)],[c327,d4]) ).
cnf(d6,plain,
( ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| 'empty$ucarrier'(sK150)
| X0 = sK76(X0,sK150,sK151)
| ~ in(X0,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(superposition,[status(thm)],[d5,c166]) ).
cnf(d7,plain,
( ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| ~ in(X0,'filter$uof$unet$ustr'(sK150,sK151))
| X0 = sK76(X0,sK150,sK151) ),
inference(resolution,[status(thm)],[c325,d6]) ).
cnf(d8,plain,
( ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| ~ in(X0,'filter$uof$unet$ustr'(sK150,sK151))
| X0 = sK76(X0,sK150,sK151) ),
inference(resolution,[status(thm)],[c326,d7]) ).
cnf(d9,plain,
( ~ 'net$ustr'(sK151,sK150)
| ~ in(X0,'filter$uof$unet$ustr'(sK150,sK151))
| X0 = sK76(X0,sK150,sK151) ),
inference(resolution,[status(thm)],[c327,d8]) ).
cnf(d10,plain,
( ~ in(X0,'filter$uof$unet$ustr'(sK150,sK151))
| X0 = sK76(X0,sK150,sK151) ),
inference(resolution,[status(thm)],[c328,d9]) ).
cnf(d11,plain,
( 'is$ueventually$uin'(sK150,sK151,sK152)
| sK152 = sK76(sK152,sK150,sK151) ),
inference(resolution,[status(thm)],[d10,c330]) ).
cnf(d12,plain,
( element(sK152,powerset('the$ucarrier'(sK150)))
| sK152 = sK76(sK152,sK150,sK151) ),
inference(resolution,[status(thm)],[d10,c331]) ).
cnf(d13,plain,
( sK152 = sK76(sK152,sK150,sK151)
| ~ 'is$ueventually$uin'(sK150,X0,sK152)
| ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(X0,sK150)
| 'empty$ucarrier'(sK150)
| 'empty$ucarrier'(X0)
| in(sK152,'a$u2$u1$uyellow19'(sK150,X0)) ),
inference(resolution,[status(thm)],[d0,d12]) ).
cnf(d14,plain,
( ~ 'is$ueventually$uin'(sK150,X0,sK152)
| ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(X0,sK150)
| 'empty$ucarrier'(X0)
| in(sK152,'a$u2$u1$uyellow19'(sK150,X0))
| sK152 = sK76(sK152,sK150,sK151) ),
inference(resolution,[status(thm)],[c325,d13]) ).
cnf(d15,plain,
( ~ 'is$ueventually$uin'(sK150,X0,sK152)
| ~ 'net$ustr'(X0,sK150)
| 'empty$ucarrier'(X0)
| in(sK152,'a$u2$u1$uyellow19'(sK150,X0))
| sK152 = sK76(sK152,sK150,sK151) ),
inference(resolution,[status(thm)],[c326,d14]) ).
cnf(d16,plain,
( ~ 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| sK152 = sK76(sK152,sK150,sK151)
| in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(superposition,[status(thm)],[d5,d15]) ).
cnf(d17,plain,
( ~ 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ 'net$ustr'(sK151,sK150)
| in(sK152,'filter$uof$unet$ustr'(sK150,sK151))
| sK152 = sK76(sK152,sK150,sK151) ),
inference(resolution,[status(thm)],[c327,d16]) ).
cnf(d18,plain,
( ~ 'is$ueventually$uin'(sK150,sK151,sK152)
| in(sK152,'filter$uof$unet$ustr'(sK150,sK151))
| sK152 = sK76(sK152,sK150,sK151) ),
inference(resolution,[status(thm)],[c328,d17]) ).
cnf(d19,plain,
( sK152 = sK76(sK152,sK150,sK151)
| ~ 'is$ueventually$uin'(sK150,sK151,sK152)
| sK152 = sK76(sK152,sK150,sK151) ),
inference(resolution,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
( sK152 = sK76(sK152,sK150,sK151)
| sK152 = sK76(sK152,sK150,sK151) ),
inference(resolution,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
( ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| 'empty$ucarrier'(sK150)
| ~ in(sK152,'a$u2$u1$uyellow19'(sK150,sK151))
| 'is$ueventually$uin'(sK150,sK151,sK152) ),
inference(superposition,[status(thm)],[d20,c167]) ).
cnf(d22,plain,
( 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| 'empty$ucarrier'(sK150)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(demodulation,[status(thm)],[d21,d5]) ).
cnf(d23,plain,
( 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c325,d22]) ).
cnf(d24,plain,
( 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c326,d23]) ).
cnf(d25,plain,
( 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ 'net$ustr'(sK151,sK150)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c327,d24]) ).
cnf(d26,plain,
( 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c328,d25]) ).
cnf(d27,plain,
( 'is$ueventually$uin'(sK150,sK151,sK152)
| 'is$ueventually$uin'(sK150,sK151,sK152) ),
inference(resolution,[status(thm)],[d26,c330]) ).
cnf(d28,plain,
( ~ subset(sK152,'the$ucarrier'(sK150))
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[d27,d1]) ).
cnf(d29,plain,
( ~ 'one$usorted$ustr'(X1)
| ~ 'net$ustr'(X2,X1)
| 'empty$ucarrier'(X2)
| 'empty$ucarrier'(X1)
| ~ in(X0,'a$u2$u1$uyellow19'(X1,X2))
| subset(sK76(X0,X1,X2),'the$ucarrier'(X1)) ),
inference(resolution,[status(thm)],[c318,c165]) ).
cnf(d30,plain,
( ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK150)
| 'empty$ucarrier'(sK151)
| ~ in(sK152,'a$u2$u1$uyellow19'(sK150,sK151))
| subset(sK152,'the$ucarrier'(sK150)) ),
inference(superposition,[status(thm)],[d20,d29]) ).
cnf(d31,plain,
( subset(sK152,'the$ucarrier'(sK150))
| ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| 'empty$ucarrier'(sK150)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(demodulation,[status(thm)],[d30,d5]) ).
cnf(d32,plain,
( subset(sK152,'the$ucarrier'(sK150))
| ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c325,d31]) ).
cnf(d33,plain,
( subset(sK152,'the$ucarrier'(sK150))
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c326,d32]) ).
cnf(d34,plain,
( subset(sK152,'the$ucarrier'(sK150))
| ~ 'net$ustr'(sK151,sK150)
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c327,d33]) ).
cnf(d35,plain,
( subset(sK152,'the$ucarrier'(sK150))
| ~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c328,d34]) ).
cnf(d36,plain,
( element(sK152,powerset('the$ucarrier'(sK150)))
| subset(sK152,'the$ucarrier'(sK150)) ),
inference(resolution,[status(thm)],[d35,c331]) ).
cnf(d37,plain,
( subset(sK152,'the$ucarrier'(sK150))
| subset(sK152,'the$ucarrier'(sK150)) ),
inference(resolution,[status(thm)],[d36,c318]) ).
cnf(d38,plain,
~ in(sK152,'filter$uof$unet$ustr'(sK150,sK151)),
inference(resolution,[status(thm)],[d37,d28]) ).
cnf(d39,plain,
element(sK152,powerset('the$ucarrier'(sK150))),
inference(resolution,[status(thm)],[d38,c331]) ).
cnf(d40,plain,
( ~ 'is$ueventually$uin'(sK150,X0,sK152)
| ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(X0,sK150)
| 'empty$ucarrier'(sK150)
| 'empty$ucarrier'(X0)
| in(sK152,'a$u2$u1$uyellow19'(sK150,X0)) ),
inference(resolution,[status(thm)],[d39,d0]) ).
cnf(d41,plain,
( ~ 'is$ueventually$uin'(sK150,X0,sK152)
| ~ 'one$usorted$ustr'(sK150)
| ~ 'net$ustr'(X0,sK150)
| 'empty$ucarrier'(X0)
| in(sK152,'a$u2$u1$uyellow19'(sK150,X0)) ),
inference(resolution,[status(thm)],[c325,d40]) ).
cnf(d42,plain,
( ~ 'is$ueventually$uin'(sK150,X0,sK152)
| ~ 'net$ustr'(X0,sK150)
| 'empty$ucarrier'(X0)
| in(sK152,'a$u2$u1$uyellow19'(sK150,X0)) ),
inference(resolution,[status(thm)],[c326,d41]) ).
cnf(d43,plain,
( ~ 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ 'net$ustr'(sK151,sK150)
| 'empty$ucarrier'(sK151)
| in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(superposition,[status(thm)],[d5,d42]) ).
cnf(d44,plain,
( ~ 'is$ueventually$uin'(sK150,sK151,sK152)
| ~ 'net$ustr'(sK151,sK150)
| in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c327,d43]) ).
cnf(d45,plain,
( ~ 'is$ueventually$uin'(sK150,sK151,sK152)
| in(sK152,'filter$uof$unet$ustr'(sK150,sK151)) ),
inference(resolution,[status(thm)],[c328,d44]) ).
cnf(d46,plain,
in(sK152,'filter$uof$unet$ustr'(sK150,sK151)),
inference(resolution,[status(thm)],[d27,d45]) ).
cnf(d47,plain,
$false,
inference(resolution,[status(thm)],[d38,d46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU391+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n011.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 09:24:44 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.48/4.56 % SZS status Theorem for theBenchmark.p
% 30.48/4.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------