%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:18:51 AM UTC 2026
% Result : Theorem 10.88s 2.94s
% Output : CNFRefutation 10.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 14 unt; 0 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 179 ( 84 ~; 67 |; 28 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 128 ( 2 sgn 21 !; 21 ?)
% 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_3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ id(X3,X2)
& ~ r3(X0,X1,X3) )
| ( r3(X0,X1,X3)
& id(X3,X2) ) ) ).
fof(axiom_5,axiom,
! [X0] : id(X0,X0) ).
fof(axiom_6,axiom,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ) ).
fof(axiom_7,axiom,
! [X0,X1,X2] :
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ) ).
fof(axiom_8,axiom,
! [X0,X1] :
( ( r1(X1)
& r1(X0) )
| ( ~ r1(X1)
& ~ r1(X0) )
| ~ id(X0,X1) ) ).
fof(axiom_9,axiom,
! [X0,X1,X2,X3] :
( ( r2(X2,X3)
& r2(X0,X1) )
| ( ~ r2(X2,X3)
& ~ r2(X0,X1) )
| ~ id(X1,X3)
| ~ id(X0,X2) ) ).
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(zeroplusoneidone,conjecture,
? [X0] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& id(X0,X4) )
& ? [X1] :
( ? [X3] :
( r2(X3,X1)
& r1(X3) )
& ? [X2] :
( r3(X2,X1,X0)
& r1(X2) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& id(X0,X4) )
& ? [X1] :
( ? [X3] :
( r2(X3,X1)
& r1(X3) )
& ? [X2] :
( r3(X2,X1,X0)
& r1(X2) ) ) ),
inference(negate_conjecture,[status(cth)],[zeroplusoneidone]) ).
cnf(c3,plain,
( ~ id(X0,sK0)
| r1(X0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c4,plain,
( ~ r2(X1,X0)
| id(X0,sK3(X1)) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c7,plain,
( ~ id(X1,sK3(X0))
| r2(X0,X1) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c8,plain,
( ~ r3(X1,X2,X0)
| id(X0,sK7(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_3]) ).
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(c18,plain,
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_7]) ).
cnf(c20,plain,
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_8]) ).
cnf(c24,plain,
( r2(X1,X3)
| ~ r2(X0,X2)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_9]) ).
cnf(c35,plain,
id(sK40(X0,X1),sK39(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c36,plain,
r2(X0,sK41(X1,X0)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c37,plain,
r3(X0,sK41(X0,X1),sK40(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c38,plain,
r2(sK42(X0,X1),sK39(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c39,plain,
r3(X0,X1,sK42(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c46,plain,
id(sK54(X0),X0),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c47,plain,
r1(sK55(X0)),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c48,plain,
r3(X0,sK55(X0),sK54(X0)),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c58,plain,
( ~ r3(X4,X1,X5)
| ~ id(X5,X3)
| ~ r1(X4)
| ~ r1(X0)
| ~ r2(X2,X3)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
r1(sK0),
inference(resolution,[status(thm)],[c3,c16]) ).
cnf(d1,plain,
id(X0,sK54(X0)),
inference(resolution,[status(thm)],[c17,c46]) ).
cnf(d2,plain,
( ~ r1(X0)
| r1(sK54(X0)) ),
inference(resolution,[status(thm)],[c20,d1]) ).
cnf(d3,plain,
( ~ r3(X0,X1,X2)
| ~ r1(X2)
| r1(sK7(X0,X1)) ),
inference(resolution,[status(thm)],[c20,c8]) ).
cnf(d4,plain,
( r1(sK7(X0,sK55(X0)))
| ~ r1(sK54(X0)) ),
inference(resolution,[status(thm)],[d3,c48]) ).
cnf(d5,plain,
( ~ r2(X1,sK41(X2,X3))
| ~ r2(X0,X4)
| ~ id(sK40(X2,X3),X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c37,c58]) ).
cnf(d6,plain,
( ~ r2(X2,X3)
| ~ id(sK40(X0,X1),X3)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d5,c36]) ).
cnf(d7,plain,
( ~ r2(X1,X2)
| ~ id(X0,X2)
| id(X0,sK3(X1)) ),
inference(resolution,[status(thm)],[c18,c4]) ).
cnf(d8,plain,
( id(X0,sK3(sK42(X1,X2)))
| ~ id(X0,sK39(X1,X2)) ),
inference(resolution,[status(thm)],[d7,c38]) ).
cnf(d9,plain,
( ~ r2(X4,sK3(sK42(X2,X3)))
| ~ r1(X0)
| ~ r1(X1)
| ~ r1(X4)
| ~ id(sK40(X0,X1),sK39(X2,X3)) ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( ~ r2(X0,sK3(sK42(X2,X1)))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d9,c35]) ).
cnf(d11,plain,
r2(X0,sK3(X0)),
inference(resolution,[status(thm)],[c7,c16]) ).
cnf(d12,plain,
( r2(X1,X2)
| ~ id(sK3(X0),X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[c24,d11]) ).
cnf(d13,plain,
( r2(X1,sK3(X0))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d12,c16]) ).
cnf(d14,plain,
( ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0)
| ~ id(sK42(X0,X1),X2) ),
inference(resolution,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
( ~ r3(X0,X1,sK42(X3,X2))
| ~ r1(X3)
| ~ r1(X2)
| ~ r1(sK7(X0,X1)) ),
inference(resolution,[status(thm)],[d14,c8]) ).
cnf(d16,plain,
( ~ r1(sK7(X0,X1))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d15,c39]) ).
cnf(d17,plain,
( ~ r1(sK54(X0))
| ~ r1(X0)
| ~ r1(sK55(X0)) ),
inference(resolution,[status(thm)],[d16,d4]) ).
cnf(d18,plain,
( ~ r1(sK54(X0))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c47,d17]) ).
cnf(d19,plain,
( ~ r1(X0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 04:27:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.88/2.94 % SZS status Theorem for theBenchmark.p
% 10.88/2.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------