%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU178+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 : 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 08:41:10 AM UTC 2026
% Result : Theorem 12.50s 8.92s
% Output : CNFRefutation 12.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 78 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 87 ( 40 ~; 33 |; 2 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 51 ( 4 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relat_1,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : X1 != 'ordered$upair'(X2,X3)
& in(X1,X0) ) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(d4_relat_1,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = 'relation$udom'(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in('ordered$upair'(X2,X3),X0) ) ) ) ).
fof(d5_relat_1,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = 'relation$urng'(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in('ordered$upair'(X3,X2),X0) ) ) ) ).
fof(t106_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ) ).
fof(t21_relat_1,conjecture,
! [X0] :
( relation(X0)
=> subset(X0,'cartesian$uproduct2'('relation$udom'(X0),'relation$urng'(X0))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> subset(X0,'cartesian$uproduct2'('relation$udom'(X0),'relation$urng'(X0))) ),
inference(negate_conjecture,[status(cth)],[t21_relat_1]) ).
cnf(c2,plain,
( X1 = 'ordered$upair'(sK6(X1),sK7(X1))
| ~ in(X1,X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d1_relat_1]) ).
cnf(c6,plain,
( in(sK14(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c7,plain,
( ~ in(sK14(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c9,plain,
( ~ in('ordered$upair'(X2,X3),X0)
| in(X2,X1)
| X1 != 'relation$udom'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d4_relat_1]) ).
cnf(c15,plain,
( ~ in('ordered$upair'(X3,X2),X0)
| in(X2,X1)
| X1 != 'relation$urng'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d5_relat_1]) ).
cnf(c39,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[t106_zfmisc_1]) ).
cnf(c49,plain,
relation(sK73),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c50,plain,
~ subset(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ relation(X1)
| ~ in('ordered$upair'(X0,X2),X1)
| in(X0,'relation$udom'(X1)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d1,plain,
( ~ relation(X0)
| sK14(X0,X1) = 'ordered$upair'(sK6(sK14(X0,X1)),sK7(sK14(X0,X1)))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d2,plain,
( ~ relation(sK73)
| sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))) = 'ordered$upair'(sK6(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),sK7(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))))) ),
inference(resolution,[status(thm)],[d1,c50]) ).
cnf(d3,plain,
sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))) = 'ordered$upair'(sK6(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),sK7(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))))),
inference(resolution,[status(thm)],[c49,d2]) ).
cnf(d4,plain,
( ~ relation(X0)
| in(sK6(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),'relation$udom'(X0))
| ~ in(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),X0) ),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ relation(X1)
| ~ in('ordered$upair'(X2,X0),X1)
| in(X0,'relation$urng'(X1)) ),
inference(equality_resolution,[status(thm)],[c15]) ).
cnf(d6,plain,
( ~ relation(X0)
| in(sK7(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),'relation$urng'(X0))
| ~ in(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),X0) ),
inference(superposition,[status(thm)],[d3,d5]) ).
cnf(d7,plain,
( ~ in(sK7(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),X1)
| ~ in(sK6(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),X0)
| in(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),'cartesian$uproduct2'(X0,X1)) ),
inference(superposition,[status(thm)],[d3,c39]) ).
cnf(d8,plain,
( subset(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))
| ~ in(sK7(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),'relation$urng'(sK73))
| ~ in(sK6(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),'relation$udom'(sK73)) ),
inference(resolution,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
( ~ in(sK7(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),'relation$urng'(sK73))
| ~ in(sK6(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),'relation$udom'(sK73)) ),
inference(resolution,[status(thm)],[c50,d8]) ).
cnf(d10,plain,
( ~ relation(sK73)
| ~ in(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),sK73)
| ~ in(sK6(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),'relation$udom'(sK73)) ),
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ in(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),sK73)
| ~ in(sK6(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73)))),'relation$udom'(sK73)) ),
inference(resolution,[status(thm)],[c49,d10]) ).
cnf(d12,plain,
( ~ relation(sK73)
| ~ in(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),sK73)
| ~ in(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),sK73) ),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
~ in(sK14(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),sK73),
inference(resolution,[status(thm)],[c49,d12]) ).
cnf(d14,plain,
subset(sK73,'cartesian$uproduct2'('relation$udom'(sK73),'relation$urng'(sK73))),
inference(resolution,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[c50,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU178+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.40 % Computer : n016.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Sat Sep 26 08:49:52 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.50/8.92 % SZS status Theorem for theBenchmark.p
% 12.50/8.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------