%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:18:53 AM UTC 2026
% Result : Theorem 9.17s 18.04s
% Output : CNFRefutation 9.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 35 ~; 25 |; 14 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 13 sgn 17 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ) ).
fof(axiom_2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,X1) ) ) ).
fof(axiom_5,axiom,
! [X0] : id(X0,X0) ).
fof(axiom_6,axiom,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ) ).
fof(axiom_8,axiom,
! [X0,X1] :
( ( r1(X1)
& r1(X0) )
| ( ~ r1(X1)
& ~ r1(X0) )
| ~ id(X0,X1) ) ).
fof(axiom_1a,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r3(X0,X1,X5)
& r2(X5,X2) )
& ? [X3] :
( ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) )
& id(X3,X2) ) ) ).
fof(axiom_7a,axiom,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( ~ r1(X2)
| ~ id(X2,X1) ) ) ).
fof(infiniteNumbersid,conjecture,
! [X0] :
? [X1,X2] :
( ? [X4] :
( r3(X0,X2,X4)
& id(X4,X1) )
& ! [X3] :
( ~ r1(X3)
| ~ id(X2,X3) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ? [X4] :
( r3(X0,X2,X4)
& id(X4,X1) )
& ! [X3] :
( ~ r1(X3)
| ~ id(X2,X3) ) ),
inference(negate_conjecture,[status(cth)],[infiniteNumbersid]) ).
cnf(c0,plain,
( ~ r1(X0)
| id(X0,sK0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c7,plain,
( ~ id(X1,sK3(X0))
| r2(X0,X1) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c16,plain,
id(X0,X0),
inference(clausification,[status(esa)],[axiom_5]) ).
cnf(c17,plain,
( id(X1,X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_6]) ).
cnf(c21,plain,
( r1(X0)
| ~ r1(X1)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_8]) ).
cnf(c39,plain,
r3(X0,X1,sK42(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c57,plain,
( ~ r2(X2,X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_7a]) ).
cnf(c58,plain,
( ~ r3(sK67,X0,X1)
| ~ id(X1,X2)
| id(X0,sK70(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
( ~ r3(sK67,X0,X1)
| ~ id(X1,X2)
| r1(sK70(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ r1(X0)
| id(sK0,X0) ),
inference(resolution,[status(thm)],[c17,c0]) ).
cnf(d1,plain,
( id(X0,sK70(X0))
| ~ id(sK42(sK67,X0),X1) ),
inference(resolution,[status(thm)],[c39,c58]) ).
cnf(d2,plain,
id(X0,sK70(X0)),
inference(resolution,[status(thm)],[d1,c16]) ).
cnf(d3,plain,
( r1(X0)
| ~ r1(sK70(X0)) ),
inference(resolution,[status(thm)],[d2,c21]) ).
cnf(d4,plain,
( ~ id(sK42(sK67,X0),X1)
| r1(sK70(X0)) ),
inference(resolution,[status(thm)],[c39,c59]) ).
cnf(d5,plain,
r1(sK70(X0)),
inference(resolution,[status(thm)],[d4,c16]) ).
cnf(d6,plain,
r1(X0),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
id(sK0,X0),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
r2(X0,sK0),
inference(resolution,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
( ~ r2(X2,X1)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d6,c57]) ).
cnf(d10,plain,
~ id(X0,sK0),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
id(X0,sK0),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/15.32 % Computer : n012.cluster.edu
% 0.05/15.32 % Model : x86_64 x86_64
% 0.05/15.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/15.32 % Memory : 8046.5625MB
% 0.05/15.32 % OS : Linux 6.8.0-71-generic
% 0.05/15.33 % CPULimit : 300
% 0.05/15.33 % WCLimit : 300
% 0.05/15.33 % DateTime : Sat Sep 26 04:29:05 UTC 2026
% 0.05/15.33 % CPUTime :
% 0.05/15.33 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.17/18.04 % SZS status Theorem for theBenchmark.p
% 9.17/18.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------