%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET809+4 : 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 : n002.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 102.88s 22.55s
% Output : CNFRefutation 102.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 53 ( 20 ~; 12 |; 10 &)
% ( 4 <=>; 7 =>; 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 30 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(thV2,conjecture,
! [X0] :
( member(X0,on)
=> ~ member(X0,X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> ~ member(X0,X0) ),
inference(negate_conjecture,[status(cth)],[thV2]) ).
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(sK70,on),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c65,plain,
member(sK70,sK70),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'strict$uwell$uorder'('member$upredicate',sK70),
inference(resolution,[status(thm)],[c31,c64]) ).
cnf(d1,plain,
'strict$uorder'('member$upredicate',sK70),
inference(resolution,[status(thm)],[c34,d0]) ).
cnf(d2,plain,
( ~ apply(X1,X0,sK70)
| ~ apply(X1,sK70,X0)
| ~ 'strict$uorder'(X1,sK70)
| ~ member(X0,sK70) ),
inference(resolution,[status(thm)],[c46,c65]) ).
cnf(d3,plain,
( ~ apply(X0,sK70,sK70)
| ~ apply(X0,sK70,sK70)
| ~ 'strict$uorder'(X0,sK70) ),
inference(resolution,[status(thm)],[d2,c65]) ).
cnf(d4,plain,
~ apply('member$upredicate',sK70,sK70),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
apply('member$upredicate',sK70,sK70),
inference(resolution,[status(thm)],[c45,c65]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET809+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n002.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 08:20:12 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 102.88/22.55 % SZS status Theorem for theBenchmark.p
% 102.88/22.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------