%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV456+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 : Tue Sep 29 01:15:51 PM UTC 2026
% Result : Theorem 2.34s 0.89s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 25 unt; 6 def)
% Number of atoms : 520 ( 227 equ)
% Maximal formula atoms : 56 ( 7 avg)
% Number of connectives : 727 ( 275 ~; 174 |; 216 &)
% ( 5 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 233 ( 0 sgn 209 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,axiom,
! [X0,X1,X2] :
( elem(X0,cons(X1,X2))
<=> ( X0 = X1
| elem(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).
fof(f67,conjecture,
! [X0,X1,X2,X3] :
( ( ! [X4,X5] :
( elem(m_Down(X5),queue(host(X4)))
=> ~ setIn(X5,alive) )
& ! [X4,X5] :
( elem(m_Down(X5),queue(host(X4)))
=> host(X5) != host(X4) )
& ! [X4,X5] :
( elem(m_Halt(X5),queue(host(X4)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X6,X5] :
( elem(m_Ack(X5,X4),queue(host(X6)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( ( ~ setIn(X4,alive)
& leq(X5,X4)
& host(X5) = host(X4) )
=> ~ setIn(X5,alive) )
& ! [X4,X5] :
( ( X5 != X4
& host(X5) = host(X4) )
=> ( ~ setIn(X4,alive)
| ~ setIn(X5,alive) ) )
& ! [X4,X7,X6,X5] :
( ( host(X6) != host(X4)
& setIn(X4,alive)
& setIn(X6,alive)
& host(X7) = host(X4)
& host(X5) = host(X6) )
=> ~ ( elem(m_Down(X5),queue(host(X4)))
& elem(m_Down(X7),queue(host(X6))) ) )
& ! [X4,X7,X6,X5] :
( ( host(X6) != host(X4)
& setIn(X4,alive)
& setIn(X6,alive)
& host(X7) = host(X4)
& host(X5) = host(X6) )
=> ~ ( elem(m_Down(X5),queue(host(X4)))
& setIn(host(X7),index(down,host(X6))) ) )
& queue(host(X2)) = cons(m_Down(X3),X0) )
=> ( setIn(X2,alive)
=> ( ~ leq(host(X2),host(X3))
=> ( ( ( index(ldr,host(X2)) = host(X3)
& index(status,host(X2)) = norm )
| ( index(status,host(X2)) = wait
& host(X3) = host(index(elid,host(X2))) ) )
=> ( ( ! [X4] :
( host(X2) = host(X4)
=> leq(X4,X1) )
& ~ setIn(X1,pids)
& host(X2) = host(X1) )
=> ( host(X1) != s(zero)
=> ! [X4] :
( host(X2) = host(X4)
=> ! [X8,X9] :
( host(X1) != host(X9)
=> ( host(X2) != host(X9)
=> ! [X10] :
( ( ( ( X4 != X2
& setIn(X4,alive) )
| X4 = X1 )
& ( ( X9 != X2
& setIn(X9,alive) )
| X9 = X1 )
& host(X9) != host(X4)
& host(X8) = host(X4)
& host(X10) = host(X9) )
=> ~ ( elem(m_Down(X10),X0)
& setIn(host(X8),index(down,host(X9))) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
fof(f68,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ! [X4,X5] :
( elem(m_Down(X5),queue(host(X4)))
=> ~ setIn(X5,alive) )
& ! [X4,X5] :
( elem(m_Down(X5),queue(host(X4)))
=> host(X5) != host(X4) )
& ! [X4,X5] :
( elem(m_Halt(X5),queue(host(X4)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X6,X5] :
( elem(m_Ack(X5,X4),queue(host(X6)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( ( ~ setIn(X4,alive)
& leq(X5,X4)
& host(X5) = host(X4) )
=> ~ setIn(X5,alive) )
& ! [X4,X5] :
( ( X5 != X4
& host(X5) = host(X4) )
=> ( ~ setIn(X4,alive)
| ~ setIn(X5,alive) ) )
& ! [X4,X7,X6,X5] :
( ( host(X6) != host(X4)
& setIn(X4,alive)
& setIn(X6,alive)
& host(X7) = host(X4)
& host(X5) = host(X6) )
=> ~ ( elem(m_Down(X5),queue(host(X4)))
& elem(m_Down(X7),queue(host(X6))) ) )
& ! [X4,X7,X6,X5] :
( ( host(X6) != host(X4)
& setIn(X4,alive)
& setIn(X6,alive)
& host(X7) = host(X4)
& host(X5) = host(X6) )
=> ~ ( elem(m_Down(X5),queue(host(X4)))
& setIn(host(X7),index(down,host(X6))) ) )
& queue(host(X2)) = cons(m_Down(X3),X0) )
=> ( setIn(X2,alive)
=> ( ~ leq(host(X2),host(X3))
=> ( ( ( index(ldr,host(X2)) = host(X3)
& index(status,host(X2)) = norm )
| ( index(status,host(X2)) = wait
& host(X3) = host(index(elid,host(X2))) ) )
=> ( ( ! [X4] :
( host(X2) = host(X4)
=> leq(X4,X1) )
& ~ setIn(X1,pids)
& host(X2) = host(X1) )
=> ( host(X1) != s(zero)
=> ! [X4] :
( host(X2) = host(X4)
=> ! [X8,X9] :
( host(X1) != host(X9)
=> ( host(X2) != host(X9)
=> ! [X10] :
( ( ( ( X4 != X2
& setIn(X4,alive) )
| X4 = X1 )
& ( ( X9 != X2
& setIn(X9,alive) )
| X9 = X1 )
& host(X9) != host(X4)
& host(X8) = host(X4)
& host(X10) = host(X9) )
=> ~ ( elem(m_Down(X10),X0)
& setIn(host(X8),index(down,host(X9))) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f69,plain,
~ ! [X0,X1,X2,X3] :
( ( ! [X4,X5] :
( elem(m_Down(X5),queue(host(X4)))
=> ~ setIn(X5,alive) )
& ! [X6,X7] :
( elem(m_Down(X7),queue(host(X6)))
=> host(X6) != host(X7) )
& ! [X8,X9] :
( elem(m_Halt(X9),queue(host(X8)))
=> ~ leq(host(X8),host(X9)) )
& ! [X10,X11,X12] :
( elem(m_Ack(X12,X10),queue(host(X11)))
=> ~ leq(host(X10),host(X12)) )
& ! [X13,X14] :
( ( ~ setIn(X13,alive)
& leq(X14,X13)
& host(X13) = host(X14) )
=> ~ setIn(X14,alive) )
& ! [X15,X16] :
( ( X15 != X16
& host(X15) = host(X16) )
=> ( ~ setIn(X15,alive)
| ~ setIn(X16,alive) ) )
& ! [X17,X18,X19,X20] :
( ( host(X17) != host(X19)
& setIn(X17,alive)
& setIn(X19,alive)
& host(X17) = host(X18)
& host(X19) = host(X20) )
=> ~ ( elem(m_Down(X20),queue(host(X17)))
& elem(m_Down(X18),queue(host(X19))) ) )
& ! [X21,X22,X23,X24] :
( ( host(X21) != host(X23)
& setIn(X21,alive)
& setIn(X23,alive)
& host(X21) = host(X22)
& host(X23) = host(X24) )
=> ~ ( elem(m_Down(X24),queue(host(X21)))
& setIn(host(X22),index(down,host(X23))) ) )
& queue(host(X2)) = cons(m_Down(X3),X0) )
=> ( setIn(X2,alive)
=> ( ~ leq(host(X2),host(X3))
=> ( ( ( index(ldr,host(X2)) = host(X3)
& index(status,host(X2)) = norm )
| ( index(status,host(X2)) = wait
& host(X3) = host(index(elid,host(X2))) ) )
=> ( ( ! [X25] :
( host(X2) = host(X25)
=> leq(X25,X1) )
& ~ setIn(X1,pids)
& host(X2) = host(X1) )
=> ( host(X1) != s(zero)
=> ! [X26] :
( host(X2) = host(X26)
=> ! [X27,X28] :
( host(X1) != host(X28)
=> ( host(X2) != host(X28)
=> ! [X29] :
( ( ( ( X2 != X26
& setIn(X26,alive) )
| X1 = X26 )
& ( ( X2 != X28
& setIn(X28,alive) )
| X1 = X28 )
& host(X26) != host(X28)
& host(X26) = host(X27)
& host(X28) = host(X29) )
=> ~ ( elem(m_Down(X29),X0)
& setIn(host(X27),index(down,host(X28))) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
? [X0,X1,X2,X3] :
( ? [X26] :
( ? [X27,X28] :
( ? [X29] :
( elem(m_Down(X29),X0)
& setIn(host(X27),index(down,host(X28)))
& ( ( X2 != X26
& setIn(X26,alive) )
| X1 = X26 )
& ( ( X2 != X28
& setIn(X28,alive) )
| X1 = X28 )
& host(X26) != host(X28)
& host(X26) = host(X27)
& host(X28) = host(X29) )
& host(X2) != host(X28)
& host(X1) != host(X28) )
& host(X2) = host(X26) )
& host(X1) != s(zero)
& ! [X25] :
( leq(X25,X1)
| host(X2) != host(X25) )
& ~ setIn(X1,pids)
& host(X2) = host(X1)
& ( ( index(ldr,host(X2)) = host(X3)
& index(status,host(X2)) = norm )
| ( index(status,host(X2)) = wait
& host(X3) = host(index(elid,host(X2))) ) )
& ~ leq(host(X2),host(X3))
& setIn(X2,alive)
& ! [X4,X5] :
( ~ setIn(X5,alive)
| ~ elem(m_Down(X5),queue(host(X4))) )
& ! [X6,X7] :
( host(X6) != host(X7)
| ~ elem(m_Down(X7),queue(host(X6))) )
& ! [X8,X9] :
( ~ leq(host(X8),host(X9))
| ~ elem(m_Halt(X9),queue(host(X8))) )
& ! [X10,X11,X12] :
( ~ leq(host(X10),host(X12))
| ~ elem(m_Ack(X12,X10),queue(host(X11))) )
& ! [X13,X14] :
( ~ setIn(X14,alive)
| setIn(X13,alive)
| ~ leq(X14,X13)
| host(X13) != host(X14) )
& ! [X15,X16] :
( ~ setIn(X15,alive)
| ~ setIn(X16,alive)
| X15 = X16
| host(X15) != host(X16) )
& ! [X17,X18,X19,X20] :
( ~ elem(m_Down(X20),queue(host(X17)))
| ~ elem(m_Down(X18),queue(host(X19)))
| host(X17) = host(X19)
| ~ setIn(X17,alive)
| ~ setIn(X19,alive)
| host(X17) != host(X18)
| host(X19) != host(X20) )
& ! [X21,X22,X23,X24] :
( ~ elem(m_Down(X24),queue(host(X21)))
| ~ setIn(host(X22),index(down,host(X23)))
| host(X21) = host(X23)
| ~ setIn(X21,alive)
| ~ setIn(X23,alive)
| host(X21) != host(X22)
| host(X23) != host(X24) )
& queue(host(X2)) = cons(m_Down(X3),X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f71,plain,
? [X0,X1,X2,X3] :
( ? [X26] :
( ? [X27,X28] :
( ? [X29] :
( elem(m_Down(X29),X0)
& setIn(host(X27),index(down,host(X28)))
& ( ( X2 != X26
& setIn(X26,alive) )
| X1 = X26 )
& ( ( X2 != X28
& setIn(X28,alive) )
| X1 = X28 )
& host(X26) != host(X28)
& host(X26) = host(X27)
& host(X28) = host(X29) )
& host(X2) != host(X28)
& host(X1) != host(X28) )
& host(X2) = host(X26) )
& host(X1) != s(zero)
& ! [X25] :
( leq(X25,X1)
| host(X2) != host(X25) )
& ~ setIn(X1,pids)
& host(X2) = host(X1)
& ( ( index(ldr,host(X2)) = host(X3)
& index(status,host(X2)) = norm )
| ( index(status,host(X2)) = wait
& host(X3) = host(index(elid,host(X2))) ) )
& ~ leq(host(X2),host(X3))
& setIn(X2,alive)
& ! [X4,X5] :
( ~ setIn(X5,alive)
| ~ elem(m_Down(X5),queue(host(X4))) )
& ! [X6,X7] :
( host(X6) != host(X7)
| ~ elem(m_Down(X7),queue(host(X6))) )
& ! [X8,X9] :
( ~ leq(host(X8),host(X9))
| ~ elem(m_Halt(X9),queue(host(X8))) )
& ! [X10,X11,X12] :
( ~ leq(host(X10),host(X12))
| ~ elem(m_Ack(X12,X10),queue(host(X11))) )
& ! [X13,X14] :
( ~ setIn(X14,alive)
| setIn(X13,alive)
| ~ leq(X14,X13)
| host(X13) != host(X14) )
& ! [X15,X16] :
( ~ setIn(X15,alive)
| ~ setIn(X16,alive)
| X15 = X16
| host(X15) != host(X16) )
& ! [X17,X18,X19,X20] :
( ~ elem(m_Down(X20),queue(host(X17)))
| ~ elem(m_Down(X18),queue(host(X19)))
| host(X17) = host(X19)
| ~ setIn(X17,alive)
| ~ setIn(X19,alive)
| host(X17) != host(X18)
| host(X19) != host(X20) )
& ! [X21,X22,X23,X24] :
( ~ elem(m_Down(X24),queue(host(X21)))
| ~ setIn(host(X22),index(down,host(X23)))
| host(X21) = host(X23)
| ~ setIn(X21,alive)
| ~ setIn(X23,alive)
| host(X21) != host(X22)
| host(X23) != host(X24) )
& queue(host(X2)) = cons(m_Down(X3),X0) ),
inference(flattening,[],[f70]) ).
fof(f79,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ? [X5,X6] :
( ? [X7] :
( elem(m_Down(X7),X0)
& setIn(host(X5),index(down,host(X6)))
& ( ( X2 != X4
& setIn(X4,alive) )
| X1 = X4 )
& ( ( X2 != X6
& setIn(X6,alive) )
| X1 = X6 )
& host(X4) != host(X6)
& host(X4) = host(X5)
& host(X6) = host(X7) )
& host(X2) != host(X6)
& host(X1) != host(X6) )
& host(X2) = host(X4) )
& host(X1) != s(zero)
& ! [X8] :
( leq(X8,X1)
| host(X2) != host(X8) )
& ~ setIn(X1,pids)
& host(X2) = host(X1)
& ( ( index(ldr,host(X2)) = host(X3)
& index(status,host(X2)) = norm )
| ( index(status,host(X2)) = wait
& host(X3) = host(index(elid,host(X2))) ) )
& ~ leq(host(X2),host(X3))
& setIn(X2,alive)
& ! [X9,X10] :
( ~ setIn(X10,alive)
| ~ elem(m_Down(X10),queue(host(X9))) )
& ! [X11,X12] :
( host(X11) != host(X12)
| ~ elem(m_Down(X12),queue(host(X11))) )
& ! [X13,X14] :
( ~ leq(host(X13),host(X14))
| ~ elem(m_Halt(X14),queue(host(X13))) )
& ! [X15,X16,X17] :
( ~ leq(host(X15),host(X17))
| ~ elem(m_Ack(X17,X15),queue(host(X16))) )
& ! [X18,X19] :
( ~ setIn(X19,alive)
| setIn(X18,alive)
| ~ leq(X19,X18)
| host(X19) != host(X18) )
& ! [X20,X21] :
( ~ setIn(X20,alive)
| ~ setIn(X21,alive)
| X20 = X21
| host(X20) != host(X21) )
& ! [X22,X23,X24,X25] :
( ~ elem(m_Down(X25),queue(host(X22)))
| ~ elem(m_Down(X23),queue(host(X24)))
| host(X22) = host(X24)
| ~ setIn(X22,alive)
| ~ setIn(X24,alive)
| host(X23) != host(X22)
| host(X24) != host(X25) )
& ! [X26,X27,X28,X29] :
( ~ elem(m_Down(X29),queue(host(X26)))
| ~ setIn(host(X27),index(down,host(X28)))
| host(X26) = host(X28)
| ~ setIn(X26,alive)
| ~ setIn(X28,alive)
| host(X26) != host(X27)
| host(X28) != host(X29) )
& queue(host(X2)) = cons(m_Down(X3),X0) ),
inference(rectify,[],[f71]) ).
fof(f80,plain,
( elem(m_Down(sK7),sK0)
& setIn(host(sK5),index(down,host(sK6)))
& ( ( sK2 != sK4
& setIn(sK4,alive) )
| sK1 = sK4 )
& ( ( sK2 != sK6
& setIn(sK6,alive) )
| sK1 = sK6 )
& host(sK6) != host(sK4)
& host(sK5) = host(sK4)
& host(sK6) = host(sK7)
& host(sK6) != host(sK2)
& host(sK6) != host(sK1)
& host(sK4) = host(sK2)
& s(zero) != host(sK1)
& ! [X8] :
( leq(X8,sK1)
| host(X8) != host(sK2) )
& ~ setIn(sK1,pids)
& host(sK2) = host(sK1)
& ( ( host(sK3) = index(ldr,host(sK2))
& norm = index(status,host(sK2)) )
| ( wait = index(status,host(sK2))
& host(sK3) = host(index(elid,host(sK2))) ) )
& ~ leq(host(sK2),host(sK3))
& setIn(sK2,alive)
& ! [X9,X10] :
( ~ setIn(X10,alive)
| ~ elem(m_Down(X10),queue(host(X9))) )
& ! [X11,X12] :
( host(X11) != host(X12)
| ~ elem(m_Down(X12),queue(host(X11))) )
& ! [X13,X14] :
( ~ leq(host(X13),host(X14))
| ~ elem(m_Halt(X14),queue(host(X13))) )
& ! [X15,X16,X17] :
( ~ leq(host(X15),host(X17))
| ~ elem(m_Ack(X17,X15),queue(host(X16))) )
& ! [X18,X19] :
( ~ setIn(X19,alive)
| setIn(X18,alive)
| ~ leq(X19,X18)
| host(X19) != host(X18) )
& ! [X20,X21] :
( ~ setIn(X20,alive)
| ~ setIn(X21,alive)
| X20 = X21
| host(X20) != host(X21) )
& ! [X22,X23,X24,X25] :
( ~ elem(m_Down(X25),queue(host(X22)))
| ~ elem(m_Down(X23),queue(host(X24)))
| host(X22) = host(X24)
| ~ setIn(X22,alive)
| ~ setIn(X24,alive)
| host(X23) != host(X22)
| host(X24) != host(X25) )
& ! [X26,X27,X28,X29] :
( ~ elem(m_Down(X29),queue(host(X26)))
| ~ setIn(host(X27),index(down,host(X28)))
| host(X26) = host(X28)
| ~ setIn(X26,alive)
| ~ setIn(X28,alive)
| host(X26) != host(X27)
| host(X28) != host(X29) )
& queue(host(sK2)) = cons(m_Down(sK3),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f79]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( elem(X0,cons(X1,X2))
| ( X0 != X1
& ~ elem(X0,X2) ) )
& ( X0 = X1
| elem(X0,X2)
| ~ elem(X0,cons(X1,X2)) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( elem(X0,cons(X1,X2))
| ( X0 != X1
& ~ elem(X0,X2) ) )
& ( X0 = X1
| elem(X0,X2)
| ~ elem(X0,cons(X1,X2)) ) ),
inference(flattening,[],[f83]) ).
fof(f92,plain,
queue(host(sK2)) = cons(m_Down(sK3),sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f93,plain,
! [X28,X29,X26,X27] :
( ~ elem(m_Down(X29),queue(host(X26)))
| ~ setIn(host(X27),index(down,host(X28)))
| host(X26) = host(X28)
| ~ setIn(X26,alive)
| ~ setIn(X28,alive)
| host(X26) != host(X27)
| host(X28) != host(X29) ),
inference(cnf_transformation,[],[f80]) ).
fof(f101,plain,
setIn(sK2,alive),
inference(cnf_transformation,[],[f80]) ).
fof(f107,plain,
host(sK2) = host(sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f111,plain,
host(sK4) = host(sK2),
inference(cnf_transformation,[],[f80]) ).
fof(f112,plain,
host(sK6) != host(sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f114,plain,
host(sK6) = host(sK7),
inference(cnf_transformation,[],[f80]) ).
fof(f115,plain,
host(sK5) = host(sK4),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
host(sK6) != host(sK4),
inference(cnf_transformation,[],[f80]) ).
fof(f117,plain,
( setIn(sK6,alive)
| sK1 = sK6 ),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
setIn(host(sK5),index(down,host(sK6))),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
elem(m_Down(sK7),sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f131,plain,
! [X2,X0,X1] :
( elem(X0,cons(X1,X2))
| ~ elem(X0,X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f162,definition,
~ sP10(host(sK6)),
introduced(definition,[new_symbols(definition,[sP10])],[inequality_splitting_name_introduction]) ).
fof(f163,plain,
sP10(host(sK4)),
inference(inequality_splitting,[],[f116,f162]) ).
fof(f166,definition,
~ sP12(host(sK6)),
introduced(definition,[new_symbols(definition,[sP12])],[inequality_splitting_name_introduction]) ).
fof(f167,plain,
sP12(host(sK1)),
inference(inequality_splitting,[],[f112,f166]) ).
fof(f184,plain,
! [X28,X29,X26] :
( host(X28) != host(X29)
| ~ elem(m_Down(X29),queue(host(X26)))
| sP17(X28,X26) ),
inference(cnf_transformation,[],[f184_D]) ).
fof(f184_D,definition,
! [X26,X28] :
( ! [X29] :
( host(X28) != host(X29)
| ~ elem(m_Down(X29),queue(host(X26))) )
<=> ~ sP17(X28,X26) ),
introduced(definition,[new_symbols(definition,[sP17])],[general_splitting_component_introduction]) ).
fof(f185,plain,
! [X28,X26,X27] :
( host(X26) != host(X27)
| host(X26) = host(X28)
| ~ setIn(X26,alive)
| ~ setIn(X28,alive)
| ~ setIn(host(X27),index(down,host(X28)))
| ~ sP17(X28,X26) ),
inference(general_splitting,[],[f93,f184_D]) ).
fof(f207,plain,
sP12(host(sK2)),
inference(forward_demodulation,[],[f167,f107]) ).
fof(f208,plain,
host(sK5) = host(sK2),
inference(forward_demodulation,[],[f115,f111]) ).
fof(f209,plain,
sP10(host(sK2)),
inference(forward_demodulation,[],[f163,f111]) ).
fof(f211,definition,
( spl18_5
<=> sK1 = sK6 ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
fof(f213,plain,
( sK1 = sK6
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f215,definition,
( spl18_6
<=> setIn(sK6,alive) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f217,plain,
( setIn(sK6,alive)
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,plain,
( spl18_5
| spl18_6 ),
inference(avatar_split_clause,[],[f117,f215,f211]) ).
fof(f238,plain,
( ~ sP12(host(sK1))
| ~ spl18_5 ),
inference(superposition,[],[f166,f213]) ).
fof(f243,plain,
( ~ sP12(host(sK2))
| ~ spl18_5 ),
inference(forward_demodulation,[],[f238,f107]) ).
fof(f248,plain,
( $false
| ~ spl18_5 ),
inference(forward_subsumption_resolution,[],[f243,f207]) ).
fof(f249,plain,
~ spl18_5,
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f321,plain,
setIn(host(sK2),index(down,host(sK6))),
inference(superposition,[],[f121,f208]) ).
fof(f376,plain,
! [X0] :
( elem(X0,queue(host(sK2)))
| ~ elem(X0,sK0) ),
inference(superposition,[],[f131,f92]) ).
fof(f546,plain,
! [X0,X1] :
( host(X0) != host(sK6)
| ~ elem(m_Down(sK7),queue(host(X1)))
| sP17(X0,X1) ),
inference(superposition,[],[f184,f114]) ).
fof(f581,plain,
! [X0,X1] :
( ~ setIn(host(X0),index(down,host(X1)))
| ~ setIn(X0,alive)
| ~ setIn(X1,alive)
| host(X0) = host(X1)
| ~ sP17(X1,X0) ),
inference(equality_resolution,[],[f185]) ).
fof(f856,definition,
( spl18_47
<=> host(sK6) = host(sK2) ),
introduced(definition,[new_symbols(definition,[spl18_47])],[avatar_definition]) ).
fof(f857,plain,
( host(sK6) = host(sK2)
| ~ spl18_47 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f858,plain,
( host(sK6) != host(sK2)
| spl18_47 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f1045,plain,
! [X0] :
( ~ elem(m_Down(sK7),queue(host(X0)))
| sP17(sK6,X0) ),
inference(equality_resolution,[],[f546]) ).
fof(f1094,plain,
( ~ setIn(sK2,alive)
| ~ setIn(sK6,alive)
| host(sK6) = host(sK2)
| ~ sP17(sK6,sK2) ),
inference(resolution,[],[f581,f321]) ).
fof(f1109,plain,
( ~ setIn(sK6,alive)
| host(sK6) = host(sK2)
| ~ sP17(sK6,sK2) ),
inference(forward_subsumption_resolution,[],[f1094,f101]) ).
fof(f1114,plain,
( host(sK6) = host(sK2)
| ~ sP17(sK6,sK2)
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f1109,f217]) ).
fof(f1117,plain,
( ~ sP17(sK6,sK2)
| ~ spl18_6
| spl18_47 ),
inference(forward_subsumption_resolution,[],[f1114,f858]) ).
fof(f1351,plain,
( sP17(sK6,sK2)
| ~ elem(m_Down(sK7),sK0) ),
inference(resolution,[],[f1045,f376]) ).
fof(f1360,plain,
( ~ elem(m_Down(sK7),sK0)
| ~ spl18_6
| spl18_47 ),
inference(forward_subsumption_resolution,[],[f1351,f1117]) ).
fof(f1365,plain,
( $false
| ~ spl18_6
| spl18_47 ),
inference(forward_subsumption_resolution,[],[f1360,f122]) ).
fof(f1366,plain,
( ~ spl18_6
| spl18_47 ),
inference(avatar_contradiction_clause,[],[f1365]) ).
fof(f1405,plain,
( ~ sP10(host(sK2))
| ~ spl18_47 ),
inference(superposition,[],[f162,f857]) ).
fof(f1571,plain,
( $false
| ~ spl18_47 ),
inference(forward_subsumption_resolution,[],[f1405,f209]) ).
fof(f1572,plain,
~ spl18_47,
inference(avatar_contradiction_clause,[],[f1571]) ).
cnf(s5,plain,
( spl18_5
| spl18_6 ),
inference(sat_conversion,[],[f218]) ).
cnf(s11,plain,
~ spl18_5,
inference(sat_conversion,[],[f249]) ).
cnf(s52,plain,
( ~ spl18_6
| spl18_47 ),
inference(sat_conversion,[],[f1366]) ).
cnf(s63,plain,
~ spl18_47,
inference(sat_conversion,[],[f1572]) ).
cnf(s67,plain,
~ spl18_6,
inference(rat,[],[s52,s63]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s5,s67,s11]) ).
fof(f1581,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV456+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n017.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 11:04:21 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.34/0.89 % (3478785)Detected formulas, will run a generic FOF schedule.
% 2.34/0.89 % (3478816)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2103393762:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.34/0.89 % (3478811)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=891214387:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.34/0.89 % (3478815)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1747112406:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.34/0.89 % (3478813)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=396644064:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.34/0.89 % (3478817)dis-21_1_sil=8000:lcm=predicate:random_seed=3074017705:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.34/0.89 % (3478814)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2902807390:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.34/0.89 % (3478812)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2528559529:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.34/0.89 % (3478814)First to succeed.
% 2.34/0.89 % (3478814)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3478785"
% 2.34/0.89 % (3478816)Instruction limit reached!
% 2.34/0.89 % (3478816)------------------------------
% 2.34/0.89 % (3478816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.89 % (3478816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.89 % (3478816)CaDiCaL version: 2.1.3
% 2.34/0.89 % (3478816)Termination reason: Instruction limit
% 2.34/0.89 % (3478816)Termination phase: Saturation
% 2.34/0.89 % (3478816)Time elapsed: 0.061 s
% 2.34/0.89 % (3478816)Peak memory usage: 90 MB
% 2.34/0.89 % (3478816)Instructions burned: 140 (million)
% 2.34/0.89 % (3478817)Instruction limit reached!
% 2.34/0.89 % (3478817)------------------------------
% 2.34/0.89 % (3478817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.89 % (3478817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.89 % (3478817)CaDiCaL version: 2.1.3
% 2.34/0.89 % (3478817)Termination reason: Instruction limit
% 2.34/0.89 % (3478817)Termination phase: Saturation
% 2.34/0.89 % (3478817)Time elapsed: 0.064 s
% 2.34/0.89 % (3478817)Peak memory usage: 90 MB
% 2.34/0.89 % (3478817)Instructions burned: 129 (million)
% 2.34/0.89 % (3478815)Instruction limit reached!
% 2.34/0.89 % (3478815)------------------------------
% 2.34/0.89 % (3478815)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.89 % (3478815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.89 % (3478815)CaDiCaL version: 2.1.3
% 2.34/0.89 % (3478815)Termination reason: Instruction limit
% 2.34/0.89 % (3478815)Termination phase: Saturation
% 2.34/0.89 % (3478815)Time elapsed: 0.065 s
% 2.34/0.89 % (3478815)Peak memory usage: 88 MB
% 2.34/0.89 % (3478815)Instructions burned: 120 (million)
% 2.34/0.89 % (3478887)lrs+10_1_sil=8000:sp=occurrence:random_seed=4168030938:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.34/0.89 % (3478889)lrs+1011_1_sil=32000:sp=occurrence:random_seed=382690496:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.34/0.89 % (3478887)Also succeeded, but the first one will report.
% 2.34/0.89 % (3478888)lrs+10_1_sil=32000:urr=on:br=off:random_seed=528521478:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.34/0.89 % (3478888)Also succeeded, but the first one will report.
% 2.34/0.89 % (3478814)Refutation found. Thanks to Tanya!
% 2.34/0.89 % SZS status Theorem for theBenchmark
% 2.34/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.09 % (3478814)------------------------------
% 3.53/1.09 % (3478814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.09 % (3478814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.09 % (3478814)CaDiCaL version: 2.1.3
% 3.53/1.09 % (3478814)Termination reason: Refutation
% 3.53/1.09 % (3478814)Time elapsed: 0.029 s
% 3.53/1.09 % (3478814)Peak memory usage: 90 MB
% 3.53/1.09 % (3478814)Instructions burned: 45 (million)
% 3.53/1.09 % (3478814)------------------------------
% 3.53/1.09 % (3478814)------------------------------
% 3.53/1.09 % (3478785)Success in time 0.45 s
% 3.53/1.09 % Vampire exiting
%------------------------------------------------------------------------------