%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU235+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 08:41:23 AM UTC 2026
% Result : Theorem 98.50s 19.99s
% Output : CNFRefutation 98.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 8 unt; 0 def)
% Number of atoms : 205 ( 21 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 234 ( 97 ~; 98 |; 17 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 93 ( 10 sgn 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [X0] :
( ordinal(X0)
=> ( 'epsilon$uconnected'(X0)
& 'epsilon$utransitive'(X0) ) ) ).
fof(d2_ordinal1,axiom,
! [X0] :
( 'epsilon$utransitive'(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ) ).
fof(existence_m1_subset_1,axiom,
! [X0] :
? [X1] : element(X1,X0) ).
fof(redefinition_r1_ordinal1,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( 'ordinal$usubset'(X0,X1)
<=> subset(X0,X1) ) ) ).
fof(reflexivity_r1_ordinal1,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> 'ordinal$usubset'(X0,X0) ) ).
fof(t23_ordinal1,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ) ).
fof(t24_ordinal1,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ) ).
fof(t2_subset,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ) ).
fof(t4_subset,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ) ).
fof(t5_subset,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ) ).
fof(t6_boole,axiom,
! [X0] :
( empty(X0)
=> X0 = 'empty$uset' ) ).
fof(t7_tarski,axiom,
! [X0,X1] :
~ ( ! [X2] :
~ ( ! [X3] :
~ ( in(X3,X2)
& in(X3,X1) )
& in(X2,X1) )
& in(X0,X1) ) ).
fof(t32_ordinal1,conjecture,
! [X0,X1] :
( ordinal(X1)
=> ~ ( ! [X2] :
( ordinal(X2)
=> ~ ( ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> 'ordinal$usubset'(X2,X3) ) )
& in(X2,X0) ) )
& X0 != 'empty$uset'
& subset(X0,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ordinal(X1)
=> ~ ( ! [X2] :
( ordinal(X2)
=> ~ ( ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> 'ordinal$usubset'(X2,X3) ) )
& in(X2,X0) ) )
& X0 != 'empty$uset'
& subset(X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[t32_ordinal1]) ).
cnf(c2,plain,
( 'epsilon$utransitive'(X0)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[cc1_ordinal1]) ).
cnf(c13,plain,
( subset(X1,X0)
| ~ in(X1,X0)
| ~ 'epsilon$utransitive'(X0) ),
inference(clausification,[status(esa)],[d2_ordinal1]) ).
cnf(c16,plain,
element(sK14(X0),X0),
inference(clausification,[status(esa)],[existence_m1_subset_1]) ).
cnf(c68,plain,
( ~ subset(X1,X0)
| 'ordinal$usubset'(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[redefinition_r1_ordinal1]) ).
cnf(c69,plain,
( 'ordinal$usubset'(X1,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[reflexivity_r1_ordinal1]) ).
cnf(c72,plain,
( ~ in(X1,X0)
| ordinal(X1)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[t23_ordinal1]) ).
cnf(c73,plain,
( X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| in(X1,X0)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[t24_ordinal1]) ).
cnf(c74,plain,
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c76,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c77,plain,
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t4_subset]) ).
cnf(c78,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t5_subset]) ).
cnf(c79,plain,
( X0 = 'empty$uset'
| ~ empty(X0) ),
inference(clausification,[status(esa)],[t6_boole]) ).
cnf(c81,plain,
( in(sK55(X1),X1)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t7_tarski]) ).
cnf(c82,plain,
( ~ in(X2,sK55(X1))
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t7_tarski]) ).
cnf(c84,plain,
ordinal(sK60),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c85,plain,
sK59 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c86,plain,
( ~ in(X0,sK59)
| ordinal(sK62(X0))
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c87,plain,
( ~ in(X0,sK59)
| ~ 'ordinal$usubset'(X0,sK62(X0))
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c88,plain,
( ~ in(X0,sK59)
| in(sK62(X0),sK59)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c89,plain,
subset(sK59,sK60),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( empty(X0)
| in(sK14(X0),X0) ),
inference(resolution,[status(thm)],[c74,c16]) ).
cnf(d1,plain,
( ~ subset(X1,X2)
| element(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c77,c76]) ).
cnf(d2,plain,
( element(X0,sK60)
| ~ in(X0,sK59) ),
inference(resolution,[status(thm)],[d1,c89]) ).
cnf(d3,plain,
( in(sK55(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[d0,c81]) ).
cnf(d4,plain,
( element(sK55(sK59),sK60)
| empty(sK59) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( empty(sK60)
| in(sK55(sK59),sK60)
| empty(sK59) ),
inference(resolution,[status(thm)],[d4,c74]) ).
cnf(d6,plain,
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c78,c76]) ).
cnf(d7,plain,
( ~ empty(sK60)
| ~ in(X0,sK59) ),
inference(resolution,[status(thm)],[d6,c89]) ).
cnf(d8,plain,
( empty(sK59)
| ~ empty(sK60) ),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( empty(sK59)
| in(sK55(sK59),sK60)
| empty(sK59) ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( ordinal(sK55(sK59))
| ~ ordinal(sK60)
| empty(sK59) ),
inference(resolution,[status(thm)],[d9,c72]) ).
cnf(d11,plain,
( ordinal(sK55(sK59))
| empty(sK59) ),
inference(resolution,[status(thm)],[c84,d10]) ).
cnf(d12,plain,
( ~ in(X0,sK55(X1))
| ~ in(X0,X1) ),
inference(factoring,[status(thm)],[c82]) ).
cnf(d13,plain,
( subset(X1,X0)
| ~ 'epsilon$utransitive'(X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| in(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c73,c13]) ).
cnf(d14,plain,
( subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c2,d13]) ).
cnf(d15,plain,
( 'ordinal$usubset'(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| in(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[d14,c68]) ).
cnf(d16,plain,
( ~ ordinal(X0)
| ~ in(X0,sK59)
| ~ ordinal(sK62(X0))
| ~ ordinal(X0)
| in(sK62(X0),X0)
| sK62(X0) = X0 ),
inference(resolution,[status(thm)],[d15,c87]) ).
cnf(d17,plain,
( ~ ordinal(X0)
| in(sK62(X0),X0)
| ~ in(X0,sK59)
| sK62(X0) = X0
| ~ ordinal(X0)
| ~ in(X0,sK59) ),
inference(resolution,[status(thm)],[c86,d16]) ).
cnf(d18,plain,
( ~ in(sK62(sK55(X0)),X0)
| ~ ordinal(sK55(X0))
| ~ in(sK55(X0),sK59)
| sK62(sK55(X0)) = sK55(X0) ),
inference(resolution,[status(thm)],[d17,d12]) ).
cnf(d19,plain,
( ~ ordinal(sK55(sK59))
| ~ in(sK55(sK59),sK59)
| ~ ordinal(sK55(sK59))
| ~ in(sK55(sK59),sK59)
| sK62(sK55(sK59)) = sK55(sK59) ),
inference(resolution,[status(thm)],[d18,c88]) ).
cnf(d20,plain,
( ~ ordinal(sK55(sK59))
| sK62(sK55(sK59)) = sK55(sK59)
| ~ in(X0,sK59) ),
inference(resolution,[status(thm)],[c81,d19]) ).
cnf(d21,plain,
( empty(sK59)
| ~ in(X0,sK59)
| sK62(sK55(sK59)) = sK55(sK59) ),
inference(resolution,[status(thm)],[d20,d11]) ).
cnf(d22,plain,
( empty(sK59)
| empty(sK59)
| sK62(sK55(sK59)) = sK55(sK59) ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
( sK59 = 'empty$uset'
| sK62(sK55(sK59)) = sK55(sK59) ),
inference(resolution,[status(thm)],[d22,c79]) ).
cnf(d24,plain,
sK62(sK55(sK59)) = sK55(sK59),
inference(resolution,[status(thm)],[c85,d23]) ).
cnf(d25,plain,
( ~ ordinal(sK55(sK59))
| ~ in(sK55(sK59),sK59)
| ~ 'ordinal$usubset'(sK55(sK59),sK55(sK59)) ),
inference(superposition,[status(thm)],[d24,c87]) ).
cnf(d26,plain,
( 'ordinal$usubset'(X0,X0)
| ~ ordinal(X0) ),
inference(factoring,[status(thm)],[c69]) ).
cnf(d27,plain,
( ~ ordinal(sK55(sK59))
| ~ in(sK55(sK59),sK59)
| ~ ordinal(sK55(sK59)) ),
inference(resolution,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
( ~ ordinal(sK55(sK59))
| ~ in(X0,sK59) ),
inference(resolution,[status(thm)],[c81,d27]) ).
cnf(d29,plain,
( empty(sK59)
| ~ in(X0,sK59) ),
inference(resolution,[status(thm)],[d28,d11]) ).
cnf(d30,plain,
( empty(sK59)
| empty(sK59) ),
inference(resolution,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
sK59 = 'empty$uset',
inference(resolution,[status(thm)],[d30,c79]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[c85,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU235+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 08:58:51 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.50/19.99 % SZS status Theorem for theBenchmark.p
% 98.50/19.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------