%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:18:56 AM UTC 2026
% Result : Theorem 9.46s 3.22s
% Output : CNFRefutation 9.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 135 ( 61 ~; 47 |; 27 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 99 ( 9 sgn 12 !; 27 ?)
% 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_4a,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) ) ).
fof(axiom_5a,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( r1(X3)
& id(X1,X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ) ).
fof(thereexistsanevennumberid,conjecture,
? [X0,X1,X2] :
( ? [X7] :
( r3(X1,X2,X7)
& id(X7,X0) )
& ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r4(X4,X1,X3) )
& id(X3,X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X7] :
( r3(X1,X2,X7)
& id(X7,X0) )
& ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r4(X4,X1,X3) )
& id(X3,X0) ) ),
inference(negate_conjecture,[status(cth)],[thereexistsanevennumberid]) ).
cnf(c0,plain,
( ~ r1(X0)
| id(X0,sK0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c3,plain,
( ~ id(X0,sK0)
| r1(X0) ),
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(c20,plain,
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_8]) ).
cnf(c21,plain,
( r1(X0)
| ~ r1(X1)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_8]) ).
cnf(c36,plain,
r2(X0,sK41(X1,X0)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c46,plain,
id(sK54(X0),X0),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c48,plain,
r3(X0,sK55(X0),sK54(X0)),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c49,plain,
r1(sK58(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c50,plain,
r4(X0,sK58(X0),sK57(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c51,plain,
id(sK57(X0),sK59(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c52,plain,
r1(sK59(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c58,plain,
( ~ r4(X5,X6,X3)
| ~ r3(X6,X7,X1)
| ~ r2(X0,X4)
| ~ r2(X4,X5)
| ~ id(X3,X2)
| ~ id(X1,X2)
| ~ r1(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
r1(sK0),
inference(resolution,[status(thm)],[c3,c16]) ).
cnf(d1,plain,
r2(X0,sK3(X0)),
inference(resolution,[status(thm)],[c7,c16]) ).
cnf(d2,plain,
id(X0,sK54(X0)),
inference(resolution,[status(thm)],[c17,c46]) ).
cnf(d3,plain,
( ~ r1(X0)
| r1(sK54(X0)) ),
inference(resolution,[status(thm)],[c20,d2]) ).
cnf(d4,plain,
( ~ r3(sK58(X1),X5,X3)
| ~ r2(X4,X1)
| ~ r2(X0,X4)
| ~ id(X3,X2)
| ~ id(sK57(X1),X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c50,c58]) ).
cnf(d5,plain,
( ~ r2(X0,X3)
| ~ r2(X3,X1)
| ~ id(sK57(X1),X2)
| ~ id(sK54(sK58(X1)),X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d4,c48]) ).
cnf(d6,plain,
( ~ r1(sK54(sK58(X1)))
| ~ r2(X0,X2)
| ~ r2(X2,X1)
| ~ id(sK57(X1),sK0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
( ~ r1(sK57(X1))
| ~ r2(X0,X2)
| ~ r2(X2,X1)
| ~ r1(sK54(sK58(X1)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
( r1(sK57(X0))
| ~ r1(sK59(X0)) ),
inference(resolution,[status(thm)],[c51,c21]) ).
cnf(d9,plain,
r1(sK57(X0)),
inference(resolution,[status(thm)],[c52,d8]) ).
cnf(d10,plain,
( ~ r2(X0,X2)
| ~ r2(X2,X1)
| ~ r1(sK54(sK58(X1)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ r1(sK58(X2))
| ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
( ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c49,d11]) ).
cnf(d13,plain,
( ~ r2(sK3(X0),X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
~ r1(X0),
inference(resolution,[status(thm)],[d13,c36]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n003.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 04:32:09 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.46/3.22 % SZS status Theorem for theBenchmark.p
% 9.46/3.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------