%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN082+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:18:57 AM UTC 2026
% Result : Theorem 31.05s 8.05s
% Output : CNFRefutation 31.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 20 unt; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 164 ( 77 ~; 60 |; 27 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 138 ( 9 sgn 22 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ) ).
fof(axiom_3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ id(X3,X2)
& ~ r3(X0,X1,X3) )
| ( r3(X0,X1,X3)
& id(X3,X2) ) ) ).
fof(axiom_4,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ id(X3,X2)
& ~ r4(X0,X1,X3) )
| ( r4(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_8,axiom,
! [X0,X1] :
( ( r1(X1)
& r1(X0) )
| ( ~ r1(X1)
& ~ r1(X0) )
| ~ id(X0,X1) ) ).
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_2a,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r4(X0,X1,X5)
& r3(X5,X0,X2) )
& ? [X3] :
( ? [X4] :
( r4(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(xtimesoneidzero,conjecture,
? [X0,X1] :
( ? [X4] :
( r1(X4)
& id(X1,X4) )
& ? [X2] :
( ? [X3] :
( r2(X3,X2)
& r1(X3) )
& r4(X0,X2,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] :
( ? [X4] :
( r1(X4)
& id(X1,X4) )
& ? [X2] :
( ? [X3] :
( r2(X3,X2)
& r1(X3) )
& r4(X0,X2,X1) ) ),
inference(negate_conjecture,[status(cth)],[xtimesoneidzero]) ).
cnf(c0,plain,
( ~ r1(X0)
| id(X0,sK0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c8,plain,
( ~ r3(X1,X2,X0)
| id(X0,sK7(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_3]) ).
cnf(c12,plain,
( ~ r4(X1,X2,X0)
| id(X0,sK11(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_4]) ).
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(c29,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(c40,plain,
id(sK46(X0,X1),sK45(X0,X1)),
inference(clausification,[status(esa)],[axiom_2a]) ).
cnf(c41,plain,
r2(X0,sK47(X1,X0)),
inference(clausification,[status(esa)],[axiom_2a]) ).
cnf(c42,plain,
r4(X0,sK47(X0,X1),sK46(X0,X1)),
inference(clausification,[status(esa)],[axiom_2a]) ).
cnf(c43,plain,
r3(sK48(X0,X1),X0,sK45(X0,X1)),
inference(clausification,[status(esa)],[axiom_2a]) ).
cnf(c44,plain,
r4(X0,X1,sK48(X0,X1)),
inference(clausification,[status(esa)],[axiom_2a]) ).
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(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,
( ~ r2(X2,X4)
| ~ r1(X1)
| ~ r4(X3,X4,X0)
| ~ r1(X2)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ r4(X0,X1,X2)
| ~ r1(X2)
| r1(sK11(X0,X1)) ),
inference(resolution,[status(thm)],[c20,c12]) ).
cnf(d1,plain,
( r1(sK11(X0,sK58(X0)))
| ~ r1(sK57(X0)) ),
inference(resolution,[status(thm)],[d0,c50]) ).
cnf(d2,plain,
( r1(sK57(X0))
| ~ r1(sK59(X0)) ),
inference(resolution,[status(thm)],[c51,c21]) ).
cnf(d3,plain,
r1(sK57(X0)),
inference(resolution,[status(thm)],[c52,d2]) ).
cnf(d4,plain,
r1(sK11(X0,sK58(X0))),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ r4(X0,X1,X2)
| r1(X2)
| ~ r1(sK11(X0,X1)) ),
inference(resolution,[status(thm)],[c21,c12]) ).
cnf(d6,plain,
( ~ r1(sK11(X0,X1))
| r1(sK48(X0,X1)) ),
inference(resolution,[status(thm)],[d5,c44]) ).
cnf(d7,plain,
r1(sK48(X0,sK58(X0))),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
id(X0,sK54(X0)),
inference(resolution,[status(thm)],[c17,c46]) ).
cnf(d9,plain,
( ~ r1(X0)
| r1(sK54(X0)) ),
inference(resolution,[status(thm)],[c20,d8]) ).
cnf(d10,plain,
( ~ r3(X0,X1,X2)
| ~ r1(X2)
| r1(sK7(X0,X1)) ),
inference(resolution,[status(thm)],[c20,c8]) ).
cnf(d11,plain,
( r1(sK7(X0,sK55(X0)))
| ~ r1(sK54(X0)) ),
inference(resolution,[status(thm)],[d10,c48]) ).
cnf(d12,plain,
( ~ r2(X1,sK47(X2,X3))
| ~ id(sK46(X2,X3),X0)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c42,c58]) ).
cnf(d13,plain,
( ~ id(sK46(X2,X0),X1)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d12,c41]) ).
cnf(d14,plain,
( ~ r3(X0,X1,sK46(X3,X2))
| ~ r1(X2)
| ~ r1(sK7(X0,X1)) ),
inference(resolution,[status(thm)],[d13,c8]) ).
cnf(d15,plain,
( r3(X0,X4,X3)
| ~ id(X4,X1)
| ~ id(X3,sK45(X1,X2))
| ~ id(X0,sK48(X1,X2)) ),
inference(resolution,[status(thm)],[c43,c29]) ).
cnf(d16,plain,
( r3(sK48(X1,X3),X0,X2)
| ~ id(X2,sK45(X1,X3))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d15,c16]) ).
cnf(d17,plain,
( ~ r1(sK7(sK48(X2,X3),X4))
| ~ r1(X1)
| ~ id(X4,X2)
| ~ id(sK46(X0,X1),sK45(X2,X3)) ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( ~ id(X2,X1)
| ~ r1(sK7(sK48(X1,X0),X2))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d17,c40]) ).
cnf(d19,plain,
( ~ r1(sK54(sK48(X1,X0)))
| ~ id(sK55(sK48(X1,X0)),X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d18,d11]) ).
cnf(d20,plain,
( ~ r1(sK55(sK48(sK0,X0)))
| ~ r1(sK54(sK48(sK0,X0)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
( ~ r1(sK54(sK48(sK0,X0)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c47,d20]) ).
cnf(d22,plain,
( ~ r1(sK48(sK0,X0))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d21,d9]) ).
cnf(d23,plain,
~ r1(sK58(sK0)),
inference(resolution,[status(thm)],[d22,d7]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[c49,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN082+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n019.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 04:31:48 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.05/8.05 % SZS status Theorem for theBenchmark.p
% 31.05/8.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------