%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV451+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 09:02:26 AM UTC 2026
% Result : Theorem 15.81s 8.00s
% Output : CNFRefutation 15.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 23 unt; 0 def)
% Number of atoms : 222 ( 98 equ)
% Maximal formula atoms : 51 ( 4 avg)
% Number of connectives : 272 ( 105 ~; 71 |; 54 &)
% ( 2 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 16 con; 0-2 aty)
% Number of variables : 92 ( 3 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_17,axiom,
! [X0,X1] : 'm$uDown'(X0) != 'm$uHalt'(X1) ).
fof(axiom_46,axiom,
! [X0,X1,X2] :
( elem(X0,cons(X1,X2))
<=> ( elem(X0,X2)
| X0 = X1 ) ) ).
fof(axiom_47,axiom,
! [X0,X1,X2] :
( elem(X0,snoc(X2,X1))
<=> ( elem(X0,X2)
| X0 = X1 ) ) ).
fof(conj,conjecture,
! [X0,X1,X2,X3] :
( ( queue(host(X3)) = cons('m$uNotNorm'(X2),X0)
& ! [X4,X7,X6,X5] :
( ( host(X5) = host(X6)
& host(X7) = host(X4)
& setIn(X6,alive)
& setIn(X4,alive)
& host(X6) != host(X4) )
=> ~ ( elem('m$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$uDown'(X5),queue(host(X4)))
=> ~ setIn(X5,alive) )
& ! [X4,X5] :
( setIn(X5,alive)
=> ~ elem('m$uDown'(X5),queue(host(X4))) ) )
=> ( setIn(X3,alive)
=> ( ( index(elid,host(X3)) = X2
& index(status,host(X3)) = norm
& index(ldr,host(X3)) = host(X3) )
=> ( ( host(X3) = host(X1)
& ~ setIn(X1,pids)
& ! [X4] :
( host(X3) = host(X4)
=> leq(X4,X1) ) )
=> ( host(X1) = s(zero)
=> ( ~ leq('nbr$uproc',host(X1))
=> ! [X4] :
( s(host(X1)) = host(X4)
=> ( host(X3) != host(X4)
=> ! [X8,X9] :
( s(host(X1)) != host(X9)
=> ( host(X3) = host(X9)
=> ! [X10] :
( ( host(X10) = host(X9)
& host(X8) = host(X4)
& host(X9) != host(X4)
& ( X9 = X1
| ( setIn(X9,alive)
& X9 != X3 ) )
& ( X4 = X1
| ( setIn(X4,alive)
& X4 != X3 ) ) )
=> ~ ( elem('m$uDown'(X10),snoc(queue(host(X4)),'m$uHalt'(X1)))
& elem('m$uDown'(X8),X0) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( queue(host(X3)) = cons('m$uNotNorm'(X2),X0)
& ! [X4,X7,X6,X5] :
( ( host(X5) = host(X6)
& host(X7) = host(X4)
& setIn(X6,alive)
& setIn(X4,alive)
& host(X6) != host(X4) )
=> ~ ( elem('m$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$uDown'(X5),queue(host(X4)))
=> ~ setIn(X5,alive) )
& ! [X4,X5] :
( setIn(X5,alive)
=> ~ elem('m$uDown'(X5),queue(host(X4))) ) )
=> ( setIn(X3,alive)
=> ( ( index(elid,host(X3)) = X2
& index(status,host(X3)) = norm
& index(ldr,host(X3)) = host(X3) )
=> ( ( host(X3) = host(X1)
& ~ setIn(X1,pids)
& ! [X4] :
( host(X3) = host(X4)
=> leq(X4,X1) ) )
=> ( host(X1) = s(zero)
=> ( ~ leq('nbr$uproc',host(X1))
=> ! [X4] :
( s(host(X1)) = host(X4)
=> ( host(X3) != host(X4)
=> ! [X8,X9] :
( s(host(X1)) != host(X9)
=> ( host(X3) = host(X9)
=> ! [X10] :
( ( host(X10) = host(X9)
& host(X8) = host(X4)
& host(X9) != host(X4)
& ( X9 = X1
| ( setIn(X9,alive)
& X9 != X3 ) )
& ( X4 = X1
| ( setIn(X4,alive)
& X4 != X3 ) ) )
=> ~ ( elem('m$uDown'(X10),snoc(queue(host(X4)),'m$uHalt'(X1)))
& elem('m$uDown'(X8),X0) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[conj]) ).
cnf(c18,plain,
'm$uDown'(X0) != 'm$uHalt'(X1),
inference(clausification,[status(esa)],[axiom_17]) ).
cnf(c54,plain,
( ~ elem(X0,X2)
| elem(X0,cons(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_46]) ).
cnf(c55,plain,
( elem(X0,X1)
| X0 = X2
| ~ elem(X0,snoc(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_47]) ).
cnf(c105,plain,
( ~ setIn(X1,alive)
| host(X1) != host(X0)
| ~ leq(X1,X0)
| setIn(X0,alive) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c106,plain,
( ~ setIn(X0,alive)
| ~ setIn(X1,alive)
| host(X0) != host(X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c107,plain,
( host(X1) = host(X2)
| ~ setIn(X2,alive)
| host(X3) != host(X2)
| ~ setIn(X1,alive)
| ~ elem('m$uDown'(X3),queue(host(X1)))
| ~ elem('m$uDown'(X0),queue(host(X2)))
| host(X0) != host(X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c108,plain,
queue(host(sK127)) = cons('m$uNotNorm'(sK126),sK124),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c109,plain,
setIn(sK127,alive),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c113,plain,
( leq(X0,sK125)
| host(sK127) != host(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c115,plain,
host(sK127) = host(sK125),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c119,plain,
host(sK127) != host(sK148),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c121,plain,
host(sK127) = host(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c123,plain,
( sK148 = sK125
| setIn(sK148,alive) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c124,plain,
( sK150 = sK125
| sK150 != sK127 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c125,plain,
( sK150 = sK125
| setIn(sK150,alive) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c127,plain,
host(sK149) = host(sK148),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c128,plain,
host(sK151) = host(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c129,plain,
elem('m$uDown'(sK149),sK124),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c130,plain,
elem('m$uDown'(sK151),snoc(queue(host(sK148)),'m$uHalt'(sK125))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ setIn(sK150,alive)
| ~ setIn(X0,alive)
| sK150 = X0
| host(sK127) != host(X0) ),
inference(superposition,[status(thm)],[c121,c106]) ).
cnf(d1,plain,
( ~ setIn(sK150,alive)
| ~ setIn(sK127,alive)
| sK150 = sK127 ),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
( ~ setIn(sK150,alive)
| sK150 = sK127 ),
inference(resolution,[status(thm)],[c109,d1]) ).
cnf(d3,plain,
( sK150 = sK125
| sK150 = sK127 ),
inference(resolution,[status(thm)],[d2,c125]) ).
cnf(d4,plain,
( sK150 = sK127
| sK150 = sK127
| ~ setIn(sK125,alive) ),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ leq(X0,sK125)
| ~ setIn(X0,alive)
| setIn(sK125,alive)
| host(X0) != host(sK127) ),
inference(superposition,[status(thm)],[c115,c105]) ).
cnf(d6,plain,
( ~ leq(sK127,sK125)
| setIn(sK125,alive)
| ~ setIn(sK127,alive) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ~ leq(sK127,sK125)
| setIn(sK125,alive) ),
inference(resolution,[status(thm)],[c109,d6]) ).
cnf(d8,plain,
leq(sK127,sK125),
inference(equality_resolution,[status(thm)],[c113]) ).
cnf(d9,plain,
setIn(sK125,alive),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
sK150 = sK127,
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
sK150 = sK125,
inference(resolution,[status(thm)],[d10,c124]) ).
cnf(d12,plain,
sK127 = sK125,
inference(demodulation,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( setIn(sK148,alive)
| sK148 = sK127 ),
inference(demodulation,[status(thm)],[c123,d12]) ).
cnf(d14,plain,
( ~ elem(X0,sK124)
| elem(X0,queue(host(sK127))) ),
inference(superposition,[status(thm)],[c108,c54]) ).
cnf(d15,plain,
host(sK151) = host(sK127),
inference(demodulation,[status(thm)],[c128,c121]) ).
cnf(d16,plain,
( ~ setIn(X0,alive)
| ~ setIn(X2,alive)
| ~ elem('m$uDown'(sK151),queue(host(X2)))
| ~ elem('m$uDown'(X1),queue(host(X0)))
| host(X0) = host(X2)
| host(X1) != host(X2)
| host(sK127) != host(X0) ),
inference(superposition,[status(thm)],[d15,c107]) ).
cnf(d17,plain,
( ~ setIn(sK127,alive)
| ~ setIn(X1,alive)
| ~ elem('m$uDown'(sK151),queue(host(X1)))
| ~ elem('m$uDown'(X0),queue(host(sK127)))
| host(sK127) = host(X1)
| host(X0) != host(X1) ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( ~ setIn(X1,alive)
| ~ elem('m$uDown'(sK151),queue(host(X1)))
| ~ elem('m$uDown'(X0),queue(host(sK127)))
| host(sK127) = host(X1)
| host(X0) != host(X1) ),
inference(resolution,[status(thm)],[c109,d17]) ).
cnf(d19,plain,
( ~ setIn(X0,alive)
| ~ elem('m$uDown'(sK151),queue(host(X0)))
| ~ elem('m$uDown'(sK149),queue(host(sK127)))
| host(sK127) = host(X0)
| host(sK148) != host(X0) ),
inference(superposition,[status(thm)],[c127,d18]) ).
cnf(d20,plain,
( ~ setIn(sK148,alive)
| ~ elem('m$uDown'(sK151),queue(host(sK148)))
| ~ elem('m$uDown'(sK149),queue(host(sK127)))
| host(sK127) = host(sK148) ),
inference(equality_resolution,[status(thm)],[d19]) ).
cnf(d21,plain,
( ~ setIn(sK148,alive)
| ~ elem('m$uDown'(sK151),queue(host(sK148)))
| ~ elem('m$uDown'(sK149),queue(host(sK127))) ),
inference(resolution,[status(thm)],[c119,d20]) ).
cnf(d22,plain,
elem('m$uDown'(sK151),snoc(queue(host(sK148)),'m$uHalt'(sK127))),
inference(demodulation,[status(thm)],[c130,d12]) ).
cnf(d23,plain,
( elem('m$uDown'(sK151),queue(host(sK148)))
| 'm$uDown'(sK151) = 'm$uHalt'(sK127) ),
inference(resolution,[status(thm)],[c55,d22]) ).
cnf(d24,plain,
elem('m$uDown'(sK151),queue(host(sK148))),
inference(resolution,[status(thm)],[c18,d23]) ).
cnf(d25,plain,
( ~ setIn(sK148,alive)
| ~ elem('m$uDown'(sK149),queue(host(sK127))) ),
inference(resolution,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
( ~ elem('m$uDown'(sK149),sK124)
| ~ setIn(sK148,alive) ),
inference(resolution,[status(thm)],[d25,d14]) ).
cnf(d27,plain,
~ setIn(sK148,alive),
inference(resolution,[status(thm)],[c129,d26]) ).
cnf(d28,plain,
sK148 = sK127,
inference(resolution,[status(thm)],[d27,d13]) ).
cnf(d29,plain,
~ setIn(sK127,alive),
inference(demodulation,[status(thm)],[d27,d28]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[c109,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV451+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/5.90 % Computer : n012.cluster.edu
% 0.03/5.90 % Model : x86_64 x86_64
% 0.03/5.90 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.90 % Memory : 8046.5625MB
% 0.03/5.90 % OS : Linux 6.8.0-71-generic
% 0.03/5.90 % CPULimit : 300
% 0.03/5.90 % WCLimit : 300
% 0.03/5.90 % DateTime : Sat Sep 26 13:54:19 UTC 2026
% 0.03/5.90 % CPUTime :
% 0.03/5.90 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.81/8.00 % SZS status Theorem for theBenchmark.p
% 15.81/8.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------