%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 06:55:42 AM UTC 2026
% Result : Theorem 8.90s 8.62s
% Output : CNFRefutation 8.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 66 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 31 ~; 26 |; 5 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : 'r1$utarski'(X0,X0) ).
fof(fc5_ens_1,axiom,
! [X0] :
( ( 'l1$ucat$u1'(X0)
& 'v2$ucat$u1'(X0) )
=> ~ 'v1$uxboole$u0'('k17$uens$u1'(X0)) ) ).
fof(d1_yoneda_1,axiom,
! [X0] :
( ( 'l1$ucat$u1'(X0)
& 'v2$ucat$u1'(X0) )
=> 'k1$uyoneda$u1'(X0) = 'k12$uens$u1'('k17$uens$u1'(X0)) ) ).
fof(t49_ens_1,axiom,
! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( ( 'l1$ucat$u1'(X1)
& 'v2$ucat$u1'(X1) )
=> ! [X2] :
( 'm1$usubset$u1'(X2,'u1$ucat$u1'(X1))
=> ( 'r1$utarski'('k17$uens$u1'(X1),X0)
=> 'm2$ucat$u1'('k20$uens$u1'(X1,X2),X1,'k12$uens$u1'(X0)) ) ) ) ) ).
fof(t2_yoneda_1,conjecture,
! [X0] :
( ( 'l1$ucat$u1'(X0)
& 'v2$ucat$u1'(X0) )
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ucat$u1'(X0))
=> 'm2$ucat$u1'('k20$uens$u1'(X0,X1),X0,'k1$uyoneda$u1'(X0)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l1$ucat$u1'(X0)
& 'v2$ucat$u1'(X0) )
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ucat$u1'(X0))
=> 'm2$ucat$u1'('k20$uens$u1'(X0,X1),X0,'k1$uyoneda$u1'(X0)) ) ),
inference(negate_conjecture,[status(cth)],[t2_yoneda_1]) ).
cnf(c46,plain,
'r1$utarski'(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c63,plain,
( ~ 'v1$uxboole$u0'('k17$uens$u1'(X0))
| ~ 'l1$ucat$u1'(X0)
| ~ 'v2$ucat$u1'(X0) ),
inference(clausification,[status(esa)],[fc5_ens_1]) ).
cnf(c71,plain,
( 'k1$uyoneda$u1'(X0) = 'k12$uens$u1'('k17$uens$u1'(X0))
| ~ 'l1$ucat$u1'(X0)
| ~ 'v2$ucat$u1'(X0) ),
inference(clausification,[status(esa)],[d1_yoneda_1]) ).
cnf(c72,plain,
( ~ 'v2$ucat$u1'(X1)
| ~ 'l1$ucat$u1'(X1)
| ~ 'm1$usubset$u1'(X2,'u1$ucat$u1'(X1))
| ~ 'r1$utarski'('k17$uens$u1'(X1),X0)
| 'm2$ucat$u1'('k20$uens$u1'(X1,X2),X1,'k12$uens$u1'(X0))
| 'v1$uxboole$u0'(X0) ),
inference(clausification,[status(esa)],[t49_ens_1]) ).
cnf(c73,plain,
'v2$ucat$u1'(sK89),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c74,plain,
'l1$ucat$u1'(sK89),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c75,plain,
'm1$usubset$u1'(sK90,'u1$ucat$u1'(sK89)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c76,plain,
~ 'm2$ucat$u1'('k20$uens$u1'(sK89,sK90),sK89,'k1$uyoneda$u1'(sK89)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'l1$ucat$u1'(sK89)
| 'k1$uyoneda$u1'(sK89) = 'k12$uens$u1'('k17$uens$u1'(sK89)) ),
inference(resolution,[status(thm)],[c71,c73]) ).
cnf(d1,plain,
'k1$uyoneda$u1'(sK89) = 'k12$uens$u1'('k17$uens$u1'(sK89)),
inference(resolution,[status(thm)],[c74,d0]) ).
cnf(d2,plain,
( ~ 'v2$ucat$u1'(X0)
| ~ 'r1$utarski'('k17$uens$u1'(X0),'k17$uens$u1'(sK89))
| ~ 'm1$usubset$u1'(X1,'u1$ucat$u1'(X0))
| ~ 'l1$ucat$u1'(X0)
| 'v1$uxboole$u0'('k17$uens$u1'(sK89))
| 'm2$ucat$u1'('k20$uens$u1'(X0,X1),X0,'k1$uyoneda$u1'(sK89)) ),
inference(superposition,[status(thm)],[d1,c72]) ).
cnf(d3,plain,
( ~ 'v2$ucat$u1'(sK89)
| ~ 'r1$utarski'('k17$uens$u1'(sK89),'k17$uens$u1'(sK89))
| ~ 'm1$usubset$u1'(sK90,'u1$ucat$u1'(sK89))
| ~ 'l1$ucat$u1'(sK89)
| 'v1$uxboole$u0'('k17$uens$u1'(sK89)) ),
inference(resolution,[status(thm)],[d2,c76]) ).
cnf(d4,plain,
( ~ 'r1$utarski'('k17$uens$u1'(sK89),'k17$uens$u1'(sK89))
| ~ 'm1$usubset$u1'(sK90,'u1$ucat$u1'(sK89))
| ~ 'l1$ucat$u1'(sK89)
| 'v1$uxboole$u0'('k17$uens$u1'(sK89)) ),
inference(resolution,[status(thm)],[c73,d3]) ).
cnf(d5,plain,
( ~ 'r1$utarski'('k17$uens$u1'(sK89),'k17$uens$u1'(sK89))
| ~ 'm1$usubset$u1'(sK90,'u1$ucat$u1'(sK89))
| 'v1$uxboole$u0'('k17$uens$u1'(sK89)) ),
inference(resolution,[status(thm)],[c74,d4]) ).
cnf(d6,plain,
( ~ 'r1$utarski'('k17$uens$u1'(sK89),'k17$uens$u1'(sK89))
| 'v1$uxboole$u0'('k17$uens$u1'(sK89)) ),
inference(resolution,[status(thm)],[c75,d5]) ).
cnf(d7,plain,
'v1$uxboole$u0'('k17$uens$u1'(sK89)),
inference(resolution,[status(thm)],[c46,d6]) ).
cnf(d8,plain,
( ~ 'v2$ucat$u1'(sK89)
| ~ 'l1$ucat$u1'(sK89) ),
inference(resolution,[status(thm)],[d7,c63]) ).
cnf(d9,plain,
~ 'l1$ucat$u1'(sK89),
inference(resolution,[status(thm)],[c73,d8]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c74,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.42 % Computer : n026.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Sat Sep 26 23:01:31 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.90/8.62 % SZS status Theorem for theBenchmark.p
% 8.90/8.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------