%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV456+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 09:02:27 AM UTC 2026
% Result : Theorem 28.47s 10.02s
% Output : CNFRefutation 28.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 49 ( 21 unt; 0 def)
% Number of atoms : 217 ( 98 equ)
% Maximal formula atoms : 56 ( 4 avg)
% Number of connectives : 270 ( 102 ~; 65 |; 64 &)
% ( 1 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 84 ( 1 sgn 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_46,axiom,
! [X0,X1,X2] :
( elem(X0,cons(X1,X2))
<=> ( elem(X0,X2)
| X0 = X1 ) ) ).
fof(conj,conjecture,
! [X0,X1,X2,X3] :
( ( queue(host(X2)) = cons('m$uDown'(X3),X0)
& ! [X4,X7,X6,X5] :
( ( host(X5) = host(X6)
& host(X7) = host(X4)
& setIn(X6,alive)
& setIn(X4,alive)
& host(X6) != host(X4) )
=> ~ ( setIn(host(X7),index(down,host(X6)))
& elem('m$uDown'(X5),queue(host(X4))) ) )
& ! [X4,X7,X6,X5] :
( ( host(X5) = host(X6)
& host(X7) = host(X4)
& setIn(X6,alive)
& setIn(X4,alive)
& host(X6) != host(X4) )
=> ~ ( elem('m$uDown'(X7),queue(host(X6)))
& elem('m$uDown'(X5),queue(host(X4))) ) )
& ! [X4,X5] :
( ( host(X5) = host(X4)
& X5 != X4 )
=> ( ~ setIn(X5,alive)
| ~ setIn(X4,alive) ) )
& ! [X4,X5] :
( ( host(X5) = host(X4)
& leq(X5,X4)
& ~ setIn(X4,alive) )
=> ~ setIn(X5,alive) )
& ! [X4,X6,X5] :
( elem('m$uAck'(X5,X4),queue(host(X6)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( elem('m$uHalt'(X5),queue(host(X4)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( elem('m$uDown'(X5),queue(host(X4)))
=> host(X5) != host(X4) )
& ! [X4,X5] :
( elem('m$uDown'(X5),queue(host(X4)))
=> ~ setIn(X5,alive) ) )
=> ( setIn(X2,alive)
=> ( ~ leq(host(X2),host(X3))
=> ( ( ( host(X3) = host(index(elid,host(X2)))
& index(status,host(X2)) = wait )
| ( index(status,host(X2)) = norm
& index(ldr,host(X2)) = host(X3) ) )
=> ( ( host(X2) = host(X1)
& ~ setIn(X1,pids)
& ! [X4] :
( host(X2) = host(X4)
=> leq(X4,X1) ) )
=> ( host(X1) != s(zero)
=> ! [X4] :
( host(X2) = host(X4)
=> ! [X8,X9] :
( host(X1) != host(X9)
=> ( host(X2) != host(X9)
=> ! [X10] :
( ( host(X10) = host(X9)
& host(X8) = host(X4)
& host(X9) != host(X4)
& ( X9 = X1
| ( setIn(X9,alive)
& X9 != X2 ) )
& ( X4 = X1
| ( setIn(X4,alive)
& X4 != X2 ) ) )
=> ~ ( setIn(host(X8),index(down,host(X9)))
& elem('m$uDown'(X10),X0) ) ) ) ) ) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( queue(host(X2)) = cons('m$uDown'(X3),X0)
& ! [X4,X7,X6,X5] :
( ( host(X5) = host(X6)
& host(X7) = host(X4)
& setIn(X6,alive)
& setIn(X4,alive)
& host(X6) != host(X4) )
=> ~ ( setIn(host(X7),index(down,host(X6)))
& elem('m$uDown'(X5),queue(host(X4))) ) )
& ! [X4,X7,X6,X5] :
( ( host(X5) = host(X6)
& host(X7) = host(X4)
& setIn(X6,alive)
& setIn(X4,alive)
& host(X6) != host(X4) )
=> ~ ( elem('m$uDown'(X7),queue(host(X6)))
& elem('m$uDown'(X5),queue(host(X4))) ) )
& ! [X4,X5] :
( ( host(X5) = host(X4)
& X5 != X4 )
=> ( ~ setIn(X5,alive)
| ~ setIn(X4,alive) ) )
& ! [X4,X5] :
( ( host(X5) = host(X4)
& leq(X5,X4)
& ~ setIn(X4,alive) )
=> ~ setIn(X5,alive) )
& ! [X4,X6,X5] :
( elem('m$uAck'(X5,X4),queue(host(X6)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( elem('m$uHalt'(X5),queue(host(X4)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( elem('m$uDown'(X5),queue(host(X4)))
=> host(X5) != host(X4) )
& ! [X4,X5] :
( elem('m$uDown'(X5),queue(host(X4)))
=> ~ setIn(X5,alive) ) )
=> ( setIn(X2,alive)
=> ( ~ leq(host(X2),host(X3))
=> ( ( ( host(X3) = host(index(elid,host(X2)))
& index(status,host(X2)) = wait )
| ( index(status,host(X2)) = norm
& index(ldr,host(X2)) = host(X3) ) )
=> ( ( host(X2) = host(X1)
& ~ setIn(X1,pids)
& ! [X4] :
( host(X2) = host(X4)
=> leq(X4,X1) ) )
=> ( host(X1) != s(zero)
=> ! [X4] :
( host(X2) = host(X4)
=> ! [X8,X9] :
( host(X1) != host(X9)
=> ( host(X2) != host(X9)
=> ! [X10] :
( ( host(X10) = host(X9)
& host(X8) = host(X4)
& host(X9) != host(X4)
& ( X9 = X1
| ( setIn(X9,alive)
& X9 != X2 ) )
& ( X4 = X1
| ( setIn(X4,alive)
& X4 != X2 ) ) )
=> ~ ( setIn(host(X8),index(down,host(X9)))
& elem('m$uDown'(X10),X0) ) ) ) ) ) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[conj]) ).
cnf(c54,plain,
( ~ elem(X0,X2)
| elem(X0,cons(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_46]) ).
cnf(c104,plain,
( ~ setIn(X1,alive)
| host(X1) != host(X0)
| ~ leq(X1,X0)
| setIn(X0,alive) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c105,plain,
( ~ setIn(X0,alive)
| ~ setIn(X1,alive)
| host(X0) != host(X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c107,plain,
( ~ setIn(X1,alive)
| ~ setIn(host(X0),index(down,host(X3)))
| host(X2) != host(X3)
| host(X3) = host(X1)
| ~ setIn(X3,alive)
| ~ elem('m$uDown'(X2),queue(host(X1)))
| host(X0) != host(X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c108,plain,
queue(host(sK126)) = cons('m$uDown'(sK127),sK124),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c109,plain,
setIn(sK126,alive),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c115,plain,
( leq(X0,sK125)
| host(sK126) != host(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c117,plain,
host(sK126) = host(sK125),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c119,plain,
host(sK126) = host(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c122,plain,
( sK150 = sK125
| sK150 != sK126 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c123,plain,
( sK150 = sK125
| setIn(sK150,alive) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c125,plain,
( sK152 = sK125
| setIn(sK152,alive) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c126,plain,
host(sK152) != host(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c127,plain,
host(sK151) = host(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c128,plain,
host(sK153) = host(sK152),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c129,plain,
elem('m$uDown'(sK153),sK124),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c130,plain,
setIn(host(sK151),index(down,host(sK152))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ setIn(X0,alive)
| ~ setIn(sK150,alive)
| sK150 = X0
| host(sK126) != host(X0) ),
inference(superposition,[status(thm)],[c119,c105]) ).
cnf(d1,plain,
( ~ setIn(sK150,alive)
| ~ setIn(sK126,alive)
| sK150 = sK126 ),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
( ~ setIn(sK150,alive)
| sK150 = sK126 ),
inference(resolution,[status(thm)],[c109,d1]) ).
cnf(d3,plain,
( sK150 = sK125
| sK150 = sK126 ),
inference(resolution,[status(thm)],[d2,c123]) ).
cnf(d4,plain,
( sK150 = sK126
| sK150 = sK126
| ~ setIn(sK125,alive) ),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ leq(X0,sK125)
| ~ setIn(X0,alive)
| setIn(sK125,alive)
| host(X0) != host(sK126) ),
inference(superposition,[status(thm)],[c117,c104]) ).
cnf(d6,plain,
( ~ leq(sK126,sK125)
| setIn(sK125,alive)
| ~ setIn(sK126,alive) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ~ leq(sK126,sK125)
| setIn(sK125,alive) ),
inference(resolution,[status(thm)],[c109,d6]) ).
cnf(d8,plain,
leq(sK126,sK125),
inference(equality_resolution,[status(thm)],[c115]) ).
cnf(d9,plain,
setIn(sK125,alive),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
sK150 = sK126,
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
sK150 = sK125,
inference(resolution,[status(thm)],[d10,c122]) ).
cnf(d12,plain,
sK126 = sK125,
inference(demodulation,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( setIn(sK152,alive)
| sK152 = sK126 ),
inference(demodulation,[status(thm)],[c125,d12]) ).
cnf(d14,plain,
host(sK151) = host(sK126),
inference(demodulation,[status(thm)],[c127,c119]) ).
cnf(d15,plain,
setIn(host(sK126),index(down,host(sK152))),
inference(demodulation,[status(thm)],[c130,d14]) ).
cnf(d16,plain,
( ~ setIn(host(X2),index(down,host(X0)))
| ~ setIn(X1,alive)
| ~ setIn(X0,alive)
| ~ elem('m$uDown'(sK153),queue(host(X1)))
| host(X2) != host(X1)
| host(X0) = host(X1)
| host(sK152) != host(X0) ),
inference(superposition,[status(thm)],[c128,c107]) ).
cnf(d17,plain,
( ~ setIn(host(X0),index(down,host(sK152)))
| ~ setIn(sK152,alive)
| ~ setIn(X1,alive)
| ~ elem('m$uDown'(sK153),queue(host(X1)))
| host(sK152) = host(X1)
| host(X0) != host(X1) ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( ~ setIn(sK152,alive)
| ~ setIn(host(X0),index(down,host(sK152)))
| ~ setIn(X0,alive)
| ~ elem('m$uDown'(sK153),queue(host(X0)))
| host(sK152) = host(X0) ),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( ~ setIn(sK152,alive)
| ~ setIn(sK126,alive)
| ~ elem('m$uDown'(sK153),queue(host(sK126)))
| host(sK152) = host(sK126) ),
inference(resolution,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
( ~ setIn(sK152,alive)
| ~ elem('m$uDown'(sK153),queue(host(sK126)))
| host(sK152) = host(sK126) ),
inference(resolution,[status(thm)],[c109,d19]) ).
cnf(d21,plain,
host(sK152) != host(sK126),
inference(demodulation,[status(thm)],[c126,c119]) ).
cnf(d22,plain,
( ~ setIn(sK152,alive)
| ~ elem('m$uDown'(sK153),queue(host(sK126))) ),
inference(resolution,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
( ~ elem(X0,sK124)
| elem(X0,queue(host(sK126))) ),
inference(superposition,[status(thm)],[c108,c54]) ).
cnf(d24,plain,
( ~ setIn(sK152,alive)
| ~ elem('m$uDown'(sK153),sK124) ),
inference(resolution,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
~ setIn(sK152,alive),
inference(resolution,[status(thm)],[c129,d24]) ).
cnf(d26,plain,
sK152 = sK126,
inference(resolution,[status(thm)],[d25,d13]) ).
cnf(d27,plain,
~ setIn(sK126,alive),
inference(demodulation,[status(thm)],[d25,d26]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[c109,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV456+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n002.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 13:57:28 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.47/10.02 % SZS status Theorem for theBenchmark.p
% 28.47/10.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------