%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU210+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 08:41:16 AM UTC 2026
% Result : Theorem 14.01s 2.46s
% Output : CNFRefutation 14.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 15 unt; 0 def)
% Number of atoms : 106 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 111 ( 50 ~; 40 |; 9 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 10 sgn 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(d5_relat_1,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = 'relation$urng'(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in('ordered$upair'(X3,X2),X0) ) ) ) ).
fof(existence_m1_subset_1,axiom,
! [X0] :
? [X1] : element(X1,X0) ).
fof(fc1_xboole_0,axiom,
empty('empty$uset') ).
fof(rc2_subset_1,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ) ).
fof(t166_relat_1,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,'relation$uinverse$uimage'(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in('ordered$upair'(X0,X3),X2)
& in(X3,'relation$urng'(X2)) ) ) ) ).
fof(t2_subset,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ) ).
fof(t5_subset,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ) ).
fof(t6_boole,axiom,
! [X0] :
( empty(X0)
=> X0 = 'empty$uset' ) ).
fof(t174_relat_1,conjecture,
! [X0,X1] :
( relation(X1)
=> ~ ( 'relation$uinverse$uimage'(X1,X0) = 'empty$uset'
& subset(X0,'relation$urng'(X1))
& X0 != 'empty$uset' ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ~ ( 'relation$uinverse$uimage'(X1,X0) = 'empty$uset'
& subset(X0,'relation$urng'(X1))
& X0 != 'empty$uset' ) ),
inference(negate_conjecture,[status(cth)],[t174_relat_1]) ).
cnf(c3,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c6,plain,
( in('ordered$upair'(sK12(X0,X2),X2),X0)
| ~ in(X2,X1)
| X1 != 'relation$urng'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d5_relat_1]) ).
cnf(c13,plain,
element(sK20(X0),X0),
inference(clausification,[status(esa)],[existence_m1_subset_1]) ).
cnf(c15,plain,
empty('empty$uset'),
inference(clausification,[status(esa)],[fc1_xboole_0]) ).
cnf(c31,plain,
element(sK35(X0),powerset(X0)),
inference(clausification,[status(esa)],[rc2_subset_1]) ).
cnf(c32,plain,
empty(sK35(X0)),
inference(clausification,[status(esa)],[rc2_subset_1]) ).
cnf(c38,plain,
( ~ in(X1,'relation$urng'(X2))
| ~ in(X1,X3)
| ~ relation(X2)
| in(X0,'relation$uinverse$uimage'(X2,X3))
| ~ in('ordered$upair'(X0,X1),X2) ),
inference(clausification,[status(esa)],[t166_relat_1]) ).
cnf(c40,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c41,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c42,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c44,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t5_subset]) ).
cnf(c45,plain,
( X0 = 'empty$uset'
| ~ empty(X0) ),
inference(clausification,[status(esa)],[t6_boole]) ).
cnf(c48,plain,
relation(sK62),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c49,plain,
sK61 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c50,plain,
subset(sK61,'relation$urng'(sK62)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c51,plain,
'relation$uinverse$uimage'(sK62,sK61) = 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( empty(X0)
| in(sK20(X0),X0) ),
inference(resolution,[status(thm)],[c40,c13]) ).
cnf(d1,plain,
( ~ in(X0,sK61)
| in(X0,'relation$urng'(sK62)) ),
inference(resolution,[status(thm)],[c3,c50]) ).
cnf(d2,plain,
sK35(X0) = 'empty$uset',
inference(resolution,[status(thm)],[c45,c32]) ).
cnf(d3,plain,
subset(sK35(X0),X0),
inference(resolution,[status(thm)],[c41,c31]) ).
cnf(d4,plain,
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c44,c42]) ).
cnf(d5,plain,
( ~ empty(X1)
| ~ in(X0,sK35(X1)) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ empty(X0)
| ~ in(X1,'empty$uset') ),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( ~ relation(X1)
| in('ordered$upair'(sK12(X1,X0),X0),X1)
| ~ in(X0,'relation$urng'(X1)) ),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(d8,plain,
( ~ relation(X1)
| in(sK12(X1,X0),'relation$uinverse$uimage'(X1,X2))
| ~ in(X0,'relation$urng'(X1))
| ~ in(X0,X2)
| ~ relation(X1)
| ~ in(X0,'relation$urng'(X1)) ),
inference(resolution,[status(thm)],[d7,c38]) ).
cnf(d9,plain,
( ~ relation(sK62)
| ~ in(X0,'relation$urng'(sK62))
| ~ in(X0,sK61)
| in(sK12(sK62,X0),'empty$uset') ),
inference(superposition,[status(thm)],[c51,d8]) ).
cnf(d10,plain,
( in(sK12(sK62,X0),'empty$uset')
| ~ in(X0,sK61)
| ~ in(X0,'relation$urng'(sK62)) ),
inference(resolution,[status(thm)],[c48,d9]) ).
cnf(d11,plain,
( ~ empty(X1)
| ~ in(X0,sK61)
| ~ in(X0,'relation$urng'(sK62)) ),
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( ~ in(X0,sK61)
| ~ empty(X1)
| ~ in(X0,sK61) ),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( empty(sK61)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
empty(sK61),
inference(resolution,[status(thm)],[d13,c15]) ).
cnf(d15,plain,
sK61 = 'empty$uset',
inference(resolution,[status(thm)],[d14,c45]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[c49,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU210+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 08:50:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.01/2.46 % SZS status Theorem for theBenchmark.p
% 14.01/2.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------