%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN055+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 : n006.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 31.24s 4.23s
% Output : CNFRefutation 31.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 14 unt; 0 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 280 ( 135 ~; 113 |; 32 &)
% ( 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 : 194 ( 2 sgn 21 !; 25 ?)
% 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(zeroplustwoidtwo,conjecture,
? [X0] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r2(X6,X5) )
& id(X0,X5) )
& ? [X1] :
( ? [X4] :
( r3(X4,X1,X0)
& r1(X4) )
& ? [X2] :
( ? [X3] :
( r2(X3,X2)
& r1(X3) )
& r2(X2,X1) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r2(X6,X5) )
& id(X0,X5) )
& ? [X1] :
( ? [X4] :
( r3(X4,X1,X0)
& r1(X4) )
& ? [X2] :
( ? [X3] :
( r2(X3,X2)
& r1(X3) )
& r2(X2,X1) ) ) ),
inference(negate_conjecture,[status(cth)],[zeroplustwoidtwo]) ).
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(c21,plain,
( r1(X0)
| ~ r1(X1)
| ~ 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(c25,plain,
( r2(X0,X2)
| ~ r2(X1,X3)
| ~ 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,
( ~ r2(X4,X7)
| ~ r1(X0)
| ~ r2(X6,X3)
| ~ r1(X5)
| ~ r2(X7,X1)
| ~ r2(X5,X6)
| ~ r1(X4)
| ~ id(X2,X3)
| ~ r3(X0,X1,X2) ),
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)
| id(sK7(X0,X1),X2) ),
inference(resolution,[status(thm)],[c17,c8]) ).
cnf(d4,plain,
( ~ id(X0,sK40(X1,X2))
| id(X0,sK39(X1,X2)) ),
inference(resolution,[status(thm)],[c35,c18]) ).
cnf(d5,plain,
( ~ r3(X0,X1,sK40(X2,X3))
| id(sK7(X0,X1),sK39(X2,X3)) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ r2(X2,X6)
| ~ r2(X6,sK41(X1,X3))
| ~ r2(X5,X4)
| ~ r2(X0,X5)
| ~ id(sK40(X1,X3),X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c37,c58]) ).
cnf(d7,plain,
( ~ r2(X2,X5)
| ~ r2(X0,X3)
| ~ r2(X5,X4)
| ~ id(sK40(X1,X3),X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d6,c36]) ).
cnf(d8,plain,
( ~ r2(X1,X2)
| ~ id(X0,X2)
| id(X0,sK3(X1)) ),
inference(resolution,[status(thm)],[c18,c4]) ).
cnf(d9,plain,
( id(X0,sK3(sK42(X1,X2)))
| ~ id(X0,sK39(X1,X2)) ),
inference(resolution,[status(thm)],[d8,c38]) ).
cnf(d10,plain,
( ~ r2(X5,X1)
| ~ r2(X4,X6)
| ~ r2(X6,sK3(sK42(X2,X3)))
| ~ r1(X5)
| ~ r1(X0)
| ~ r1(X4)
| ~ id(sK40(X0,X1),sK39(X2,X3)) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ r2(X1,X3)
| ~ r2(X0,X4)
| ~ r2(X3,sK3(sK42(X2,X4)))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d10,c35]) ).
cnf(d12,plain,
r2(X0,sK3(X0)),
inference(resolution,[status(thm)],[c7,c16]) ).
cnf(d13,plain,
( r2(X1,X2)
| ~ id(sK3(X0),X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[c24,d12]) ).
cnf(d14,plain,
( r2(X1,sK3(X0))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d13,c16]) ).
cnf(d15,plain,
( ~ r2(X4,X1)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r1(X3)
| ~ r1(X0)
| ~ id(sK42(X0,X1),X2) ),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( ~ r3(X4,X5,sK42(X2,X3))
| ~ r2(X1,sK7(X4,X5))
| ~ r2(X0,X3)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d15,c8]) ).
cnf(d17,plain,
( ~ r2(X2,X3)
| ~ r2(X1,sK7(X0,X3))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d16,c39]) ).
cnf(d18,plain,
( r2(X0,X3)
| ~ id(X3,sK39(X1,X2))
| ~ id(X0,sK42(X1,X2)) ),
inference(resolution,[status(thm)],[c38,c25]) ).
cnf(d19,plain,
( r2(sK54(sK42(X1,X2)),X0)
| ~ id(X0,sK39(X1,X2)) ),
inference(resolution,[status(thm)],[d18,c46]) ).
cnf(d20,plain,
( ~ r2(X4,X1)
| ~ r1(X0)
| ~ r1(sK54(sK42(X2,X3)))
| ~ r1(X4)
| ~ id(sK7(X0,X1),sK39(X2,X3)) ),
inference(resolution,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
( ~ r3(X1,X4,sK40(X2,X3))
| ~ r2(X0,X4)
| ~ r1(sK54(sK42(X2,X3)))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d20,d5]) ).
cnf(d22,plain,
( ~ r2(X1,sK41(X0,X2))
| ~ r1(sK54(sK42(X0,X2)))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d21,c37]) ).
cnf(d23,plain,
( ~ r1(sK54(sK42(X1,X0)))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d22,c36]) ).
cnf(d24,plain,
( ~ r1(sK42(X0,X1))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d23,d2]) ).
cnf(d25,plain,
( ~ r3(X0,X1,X2)
| ~ r1(X2)
| r1(sK7(X0,X1)) ),
inference(resolution,[status(thm)],[c20,c8]) ).
cnf(d26,plain,
( r1(sK7(X0,sK55(X0)))
| ~ r1(sK54(X0)) ),
inference(resolution,[status(thm)],[d25,c48]) ).
cnf(d27,plain,
( ~ r3(X0,X1,X2)
| r1(X2)
| ~ r1(sK7(X0,X1)) ),
inference(resolution,[status(thm)],[c21,c8]) ).
cnf(d28,plain,
( ~ r1(sK7(X0,X1))
| r1(sK42(X0,X1)) ),
inference(resolution,[status(thm)],[d27,c39]) ).
cnf(d29,plain,
( ~ r1(sK54(X0))
| r1(sK42(X0,sK55(X0))) ),
inference(resolution,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
( ~ r1(X0)
| ~ r1(sK55(X0))
| ~ r1(sK54(X0)) ),
inference(resolution,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
( ~ r1(sK54(X0))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c47,d30]) ).
cnf(d32,plain,
( ~ r1(X0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d31,d2]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN055+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n006.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 04:27:40 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.24/4.23 % SZS status Theorem for theBenchmark.p
% 31.24/4.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------