%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET810+4 : 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 : 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 08:33:16 AM UTC 2026
% Result : Theorem 33.25s 15.26s
% Output : CNFRefutation 33.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 71 ( 26 ~; 18 |; 14 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(ordinal_number,axiom,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( member(X1,X0)
=> subset(X1,X0) )
& 'strict$uwell$uorder'('member$upredicate',X0)
& set(X0) ) ) ).
fof(strict_well_order,axiom,
! [X0,X1] :
( 'strict$uwell$uorder'(X0,X1)
<=> ( ! [X2] :
( ( ? [X3] : member(X3,X2)
& subset(X2,X1) )
=> ? [X4] : least(X4,X0,X2) )
& 'strict$uorder'(X0,X1) ) ) ).
fof(rel_member,axiom,
! [X0,X1] :
( apply('member$upredicate',X0,X1)
<=> member(X0,X1) ) ).
fof(strict_order,axiom,
! [X0,X1] :
( 'strict$uorder'(X0,X1)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X2,X3] :
( ( member(X3,X1)
& member(X2,X1) )
=> ~ ( apply(X0,X3,X2)
& apply(X0,X2,X3) ) ) ) ) ).
fof(thV3,conjecture,
! [X0,X1] :
( ( member(X1,on)
& member(X0,on) )
=> ~ ( member(X1,X0)
& member(X0,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( member(X1,on)
& member(X0,on) )
=> ~ ( member(X1,X0)
& member(X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[thV3]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c30,plain,
( subset(X1,X0)
| ~ member(X1,X0)
| ~ member(X0,on) ),
inference(clausification,[status(esa)],[ordinal_number]) ).
cnf(c31,plain,
( 'strict$uwell$uorder'('member$upredicate',X0)
| ~ member(X0,on) ),
inference(clausification,[status(esa)],[ordinal_number]) ).
cnf(c34,plain,
( 'strict$uorder'(X0,X1)
| ~ 'strict$uwell$uorder'(X0,X1) ),
inference(clausification,[status(esa)],[strict_well_order]) ).
cnf(c45,plain,
( ~ member(X0,X1)
| apply('member$upredicate',X0,X1) ),
inference(clausification,[status(esa)],[rel_member]) ).
cnf(c46,plain,
( ~ member(X3,X1)
| ~ apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ apply(X0,X2,X3)
| ~ 'strict$uorder'(X0,X1) ),
inference(clausification,[status(esa)],[strict_order]) ).
cnf(c64,plain,
member(sK71,on),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c65,plain,
member(sK70,on),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
member(sK71,sK70),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c67,plain,
member(sK70,sK71),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'strict$uwell$uorder'('member$upredicate',sK71),
inference(resolution,[status(thm)],[c31,c64]) ).
cnf(d1,plain,
'strict$uorder'('member$upredicate',sK71),
inference(resolution,[status(thm)],[c34,d0]) ).
cnf(d2,plain,
( ~ apply(X1,X0,sK70)
| ~ apply(X1,sK70,X0)
| ~ 'strict$uorder'(X1,sK71)
| ~ member(X0,sK71) ),
inference(resolution,[status(thm)],[c46,c67]) ).
cnf(d3,plain,
( ~ apply(X0,sK70,sK70)
| ~ apply(X0,sK70,sK70)
| ~ 'strict$uorder'(X0,sK71) ),
inference(resolution,[status(thm)],[d2,c67]) ).
cnf(d4,plain,
~ apply('member$upredicate',sK70,sK70),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ member(sK70,on)
| subset(sK71,sK70) ),
inference(resolution,[status(thm)],[c30,c66]) ).
cnf(d6,plain,
subset(sK71,sK70),
inference(resolution,[status(thm)],[c65,d5]) ).
cnf(d7,plain,
( ~ member(X0,sK71)
| member(X0,sK70) ),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
member(sK70,sK70),
inference(resolution,[status(thm)],[d7,c67]) ).
cnf(d9,plain,
apply('member$upredicate',sK70,sK70),
inference(resolution,[status(thm)],[d8,c45]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET810+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n006.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sat Sep 26 08:17:28 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.08/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.25/15.26 % SZS status Theorem for theBenchmark.p
% 33.25/15.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------