%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN085+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 : n008.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 08:18:58 AM UTC 2026
% Result : Theorem 56.29s 20.29s
% Output : CNFRefutation 56.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 28 unt; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 223 ( 112 ~; 93 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 151 ( 15 sgn 40 !; 9 ?)
% 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_10,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( r3(X3,X4,X5)
& r3(X0,X1,X2) )
| ( ~ r3(X3,X4,X5)
& ~ r3(X0,X1,X2) )
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ) ).
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_7a,axiom,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( ~ r1(X2)
| ~ id(X2,X1) ) ) ).
fof(zeroplusoneidzero,conjecture,
! [X0] :
( ! [X4] :
( ~ r1(X4)
| ~ id(X0,X4) )
| ! [X1] :
( ! [X3] :
( ~ r2(X3,X1)
| ~ r1(X3) )
| ! [X2] :
( ~ r3(X2,X1,X0)
| ~ r1(X2) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ! [X4] :
( ~ r1(X4)
| ~ id(X0,X4) )
| ! [X1] :
( ! [X3] :
( ~ r2(X3,X1)
| ~ r1(X3) )
| ! [X2] :
( ~ r3(X2,X1,X0)
| ~ r1(X2) ) ) ),
inference(negate_conjecture,[status(cth)],[zeroplusoneidzero]) ).
cnf(c0,plain,
( ~ r1(X0)
| id(X0,sK0) ),
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(X0,X2)
| ~ id(X1,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,
( ~ id(X2,X3)
| r2(X1,X3)
| ~ r2(X0,X2)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_9]) ).
cnf(c28,plain,
( ~ r3(X1,X3,X5)
| r3(X0,X2,X4)
| ~ id(X4,X5)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_10]) ).
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(c46,plain,
id(sK54(X0),X0),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c57,plain,
( ~ r2(X2,X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_7a]) ).
cnf(c58,plain,
r1(sK69),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
r3(sK69,sK68,sK67),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c61,plain,
r2(sK70,sK68),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c62,plain,
id(sK67,sK71),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c63,plain,
r1(sK71),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ r2(X0,X1)
| id(sK3(X0),X1) ),
inference(resolution,[status(thm)],[c17,c4]) ).
cnf(d1,plain,
( ~ id(X2,sK3(X0))
| id(X2,X1)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[d0,c18]) ).
cnf(d2,plain,
( r2(X0,X1)
| ~ id(sK68,X1)
| ~ id(sK70,X0) ),
inference(resolution,[status(thm)],[c24,c61]) ).
cnf(d3,plain,
( r2(sK70,X0)
| ~ id(sK68,X0) ),
inference(resolution,[status(thm)],[d2,c16]) ).
cnf(d4,plain,
id(X0,sK54(X0)),
inference(resolution,[status(thm)],[c46,c17]) ).
cnf(d5,plain,
r2(sK70,sK54(sK68)),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ id(X0,sK54(X1))
| id(X0,X1) ),
inference(resolution,[status(thm)],[c46,c18]) ).
cnf(d7,plain,
( ~ r2(X0,sK54(X1))
| id(sK3(X0),X1) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
id(sK3(sK70),sK68),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
id(sK68,sK3(sK70)),
inference(resolution,[status(thm)],[d8,c17]) ).
cnf(d10,plain,
( ~ r2(sK70,X0)
| id(sK68,X0) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
id(sK68,sK41(X0,sK70)),
inference(resolution,[status(thm)],[d10,c36]) ).
cnf(d12,plain,
id(sK41(X0,sK70),sK68),
inference(resolution,[status(thm)],[d11,c17]) ).
cnf(d13,plain,
( ~ r3(X0,X1,X2)
| r1(X2)
| ~ r1(sK7(X0,X1)) ),
inference(resolution,[status(thm)],[c20,c8]) ).
cnf(d14,plain,
( ~ r1(sK7(X0,sK41(X0,X1)))
| r1(sK40(X0,X1)) ),
inference(resolution,[status(thm)],[d13,c37]) ).
cnf(d15,plain,
( ~ r1(sK40(X0,X1))
| r1(sK39(X0,X1)) ),
inference(resolution,[status(thm)],[c35,c21]) ).
cnf(d16,plain,
( ~ r2(X0,X1)
| ~ r1(X1)
| r1(sK3(X0)) ),
inference(resolution,[status(thm)],[c21,c4]) ).
cnf(d17,plain,
( ~ id(X0,sK67)
| id(X0,sK71) ),
inference(resolution,[status(thm)],[c18,c62]) ).
cnf(d18,plain,
( ~ r1(X0)
| id(sK0,X0) ),
inference(resolution,[status(thm)],[c17,c0]) ).
cnf(d19,plain,
( id(sK0,sK71)
| ~ r1(sK67) ),
inference(resolution,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
( r1(sK67)
| ~ r1(sK71) ),
inference(resolution,[status(thm)],[c20,c62]) ).
cnf(d21,plain,
r1(sK67),
inference(resolution,[status(thm)],[c63,d20]) ).
cnf(d22,plain,
id(sK0,sK71),
inference(resolution,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
( ~ id(X0,sK0)
| id(X0,sK71) ),
inference(resolution,[status(thm)],[d22,c18]) ).
cnf(d24,plain,
( ~ r1(X0)
| id(X0,sK71) ),
inference(resolution,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
( id(sK71,X0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d24,c17]) ).
cnf(d26,plain,
r2(X0,sK3(X0)),
inference(resolution,[status(thm)],[c16,c7]) ).
cnf(d27,plain,
( ~ id(X0,sK3(X1))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d26,c57]) ).
cnf(d28,plain,
( ~ r1(sK3(X0))
| ~ r1(sK71) ),
inference(resolution,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
~ r1(sK3(X0)),
inference(resolution,[status(thm)],[c63,d28]) ).
cnf(d30,plain,
( ~ r2(X1,X0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d29,d16]) ).
cnf(d31,plain,
~ r1(sK39(X0,X1)),
inference(resolution,[status(thm)],[d30,c38]) ).
cnf(d32,plain,
~ r1(sK40(X0,X1)),
inference(resolution,[status(thm)],[d31,d15]) ).
cnf(d33,plain,
~ r1(sK7(X0,sK41(X0,X1))),
inference(resolution,[status(thm)],[d32,d14]) ).
cnf(d34,plain,
( ~ r3(X0,X1,X2)
| ~ r1(X2)
| r1(sK7(X0,X1)) ),
inference(resolution,[status(thm)],[c21,c8]) ).
cnf(d35,plain,
( r3(X0,X2,X1)
| ~ id(X2,sK68)
| ~ id(X1,sK67)
| ~ id(X0,sK69) ),
inference(resolution,[status(thm)],[c28,c59]) ).
cnf(d36,plain,
( r1(sK7(X2,X0))
| ~ r1(X1)
| ~ id(X2,sK69)
| ~ id(X1,sK67)
| ~ id(X0,sK68) ),
inference(resolution,[status(thm)],[d35,d34]) ).
cnf(d37,plain,
id(sK71,sK67),
inference(resolution,[status(thm)],[c17,c62]) ).
cnf(d38,plain,
( ~ id(X0,sK71)
| id(X0,sK67) ),
inference(resolution,[status(thm)],[c18,d37]) ).
cnf(d39,plain,
( id(X0,sK67)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d24,d38]) ).
cnf(d40,plain,
( ~ id(X2,sK68)
| ~ id(X1,sK69)
| r1(sK7(X1,X2))
| ~ r1(X0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d39,d36]) ).
cnf(d41,plain,
( ~ r1(sK69)
| ~ id(X1,sK68)
| r1(sK7(sK0,X1))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d40,d18]) ).
cnf(d42,plain,
( ~ id(X0,sK68)
| r1(sK7(sK0,X0))
| ~ r1(sK69) ),
inference(factoring,[status(thm)],[d41]) ).
cnf(d43,plain,
( ~ id(X0,sK68)
| r1(sK7(sK0,X0)) ),
inference(resolution,[status(thm)],[c58,d42]) ).
cnf(d44,plain,
~ id(sK41(sK0,X0),sK68),
inference(resolution,[status(thm)],[d43,d33]) ).
cnf(d45,plain,
$false,
inference(resolution,[status(thm)],[d44,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN085+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n008.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 04:33:09 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.29/20.29 % SZS status Theorem for theBenchmark.p
% 56.29/20.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------