%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM414+1 : 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 : n007.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 08:12:40 AM UTC 2026
% Result : Theorem 13.48s 2.30s
% Output : CNFRefutation 10.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 8 unt; 0 def)
% Number of atoms : 77 ( 18 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 88 ( 35 ~; 38 |; 7 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(connectedness_r1_ordinal1,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( 'ordinal$usubset'(X1,X0)
| 'ordinal$usubset'(X0,X1) ) ) ).
fof(d8_xboole_0,axiom,
! [X0,X1] :
( 'proper$usubset'(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ) ).
fof(redefinition_r1_ordinal1,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( 'ordinal$usubset'(X0,X1)
<=> subset(X0,X1) ) ) ).
fof(t50_ordinal1,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ 'proper$usubset'(X1,X0)
& X0 != X1
& ~ 'proper$usubset'(X0,X1) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ 'proper$usubset'(X1,X0)
& X0 != X1
& ~ 'proper$usubset'(X0,X1) ) ) ),
inference(negate_conjecture,[status(cth)],[t50_ordinal1]) ).
cnf(c13,plain,
( 'ordinal$usubset'(X1,X0)
| 'ordinal$usubset'(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[connectedness_r1_ordinal1]) ).
cnf(c16,plain,
( X0 = X1
| ~ subset(X0,X1)
| 'proper$usubset'(X0,X1) ),
inference(clausification,[status(esa)],[d8_xboole_0]) ).
cnf(c72,plain,
( subset(X0,X1)
| ~ 'ordinal$usubset'(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(clausification,[status(esa)],[redefinition_r1_ordinal1]) ).
cnf(c85,plain,
ordinal(sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c86,plain,
ordinal(sK56),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c87,plain,
~ 'proper$usubset'(sK55,sK56),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c88,plain,
sK55 != sK56,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c89,plain,
~ 'proper$usubset'(sK56,sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'ordinal$usubset'(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c72,c13]) ).
cnf(d1,plain,
( subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[d0,c72]) ).
cnf(d2,plain,
( 'proper$usubset'(X0,X1)
| X0 = X1
| subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[d1,c16]) ).
cnf(d3,plain,
( 'proper$usubset'(X1,X0)
| X1 = X0
| ~ ordinal(X0)
| ~ ordinal(X1)
| 'proper$usubset'(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[d2,c16]) ).
cnf(d4,plain,
( ~ ordinal(sK55)
| ~ ordinal(sK56)
| 'proper$usubset'(sK55,sK56)
| sK55 = sK56
| sK56 = sK55 ),
inference(resolution,[status(thm)],[d3,c89]) ).
cnf(d5,plain,
( ~ ordinal(sK56)
| 'proper$usubset'(sK55,sK56)
| sK56 = sK55
| sK55 = sK56 ),
inference(resolution,[status(thm)],[c85,d4]) ).
cnf(d6,plain,
( 'proper$usubset'(sK55,sK56)
| sK56 = sK55
| sK55 = sK56 ),
inference(resolution,[status(thm)],[c86,d5]) ).
cnf(d7,plain,
( sK56 = sK55
| sK55 = sK56 ),
inference(resolution,[status(thm)],[c87,d6]) ).
cnf(d8,plain,
sK56 = sK55,
inference(resolution,[status(thm)],[c88,d7]) ).
cnf(d9,plain,
sK55 != sK55,
inference(demodulation,[status(thm)],[c88,d8]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 02:37:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.48/2.30 % SZS status Theorem for theBenchmark.p
% 13.48/2.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------