%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV456+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 : Fri Sep 25 03:22:12 PM UTC 2026
% Result : Theorem 6.05s 11.93s
% Output : CNFRefutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 115 ( 53 unt; 11 def)
% Number of atoms : 733 ( 316 equ)
% Maximal formula atoms : 56 ( 6 avg)
% Number of connectives : 867 ( 344 ~; 249 |; 216 &)
% ( 1 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 280 ( 0 sgn 256 !; 24 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f47,axiom,
! [X0,X1,X2] :
( elem(X0,cons(X1,X2))
<=> ( elem(X0,X2)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_46) ).
fof(f67,conjecture,
! [X0,X1,X2,X3] :
( ( queue(host(X2)) = cons(m_Down(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_Down(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_Down(X7),queue(host(X6)))
& elem(m_Down(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_Ack(X5,X4),queue(host(X6)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( elem(m_Halt(X5),queue(host(X4)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( elem(m_Down(X5),queue(host(X4)))
=> host(X5) != host(X4) )
& ! [X4,X5] :
( elem(m_Down(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_Down(X10),X0) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
fof(f68,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( queue(host(X2)) = cons(m_Down(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_Down(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_Down(X7),queue(host(X6)))
& elem(m_Down(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_Ack(X5,X4),queue(host(X6)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( elem(m_Halt(X5),queue(host(X4)))
=> ~ leq(host(X4),host(X5)) )
& ! [X4,X5] :
( elem(m_Down(X5),queue(host(X4)))
=> host(X5) != host(X4) )
& ! [X4,X5] :
( elem(m_Down(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_Down(X10),X0) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f69,plain,
~ ! [X0,X1,X2,X3] :
( ( queue(host(X2)) = cons(m_Down(X3),X0)
& ! [X21,X22,X23,X24] :
( ( host(X23) = host(X24)
& host(X21) = host(X22)
& setIn(X23,alive)
& setIn(X21,alive)
& host(X21) != host(X23) )
=> ~ ( setIn(host(X22),index(down,host(X23)))
& elem(m_Down(X24),queue(host(X21))) ) )
& ! [X17,X18,X19,X20] :
( ( host(X19) = host(X20)
& host(X17) = host(X18)
& setIn(X19,alive)
& setIn(X17,alive)
& host(X17) != host(X19) )
=> ~ ( elem(m_Down(X18),queue(host(X19)))
& elem(m_Down(X20),queue(host(X17))) ) )
& ! [X15,X16] :
( ( host(X15) = host(X16)
& X15 != X16 )
=> ( ~ setIn(X16,alive)
| ~ setIn(X15,alive) ) )
& ! [X13,X14] :
( ( host(X13) = host(X14)
& leq(X14,X13)
& ~ setIn(X13,alive) )
=> ~ setIn(X14,alive) )
& ! [X10,X11,X12] :
( elem(m_Ack(X12,X10),queue(host(X11)))
=> ~ leq(host(X10),host(X12)) )
& ! [X8,X9] :
( elem(m_Halt(X9),queue(host(X8)))
=> ~ leq(host(X8),host(X9)) )
& ! [X6,X7] :
( elem(m_Down(X7),queue(host(X6)))
=> host(X6) != host(X7) )
& ! [X4,X5] :
( elem(m_Down(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)
& ! [X25] :
( host(X2) = host(X25)
=> leq(X25,X1) ) )
=> ( host(X1) != s(zero)
=> ! [X26] :
( host(X2) = host(X26)
=> ! [X27,X28] :
( host(X1) != host(X28)
=> ( host(X2) != host(X28)
=> ! [X29] :
( ( host(X28) = host(X29)
& host(X26) = host(X27)
& host(X26) != host(X28)
& ( X1 = X28
| ( setIn(X28,alive)
& X2 != X28 ) )
& ( X1 = X26
| ( setIn(X26,alive)
& X2 != X26 ) ) )
=> ~ ( setIn(host(X27),index(down,host(X28)))
& elem(m_Down(X29),X0) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f68]) ).
fof(f85,plain,
? [X0,X1,X2,X3] :
( queue(host(X2)) = cons(m_Down(X3),X0)
& ! [X21,X22,X23,X24] :
( host(X23) != host(X24)
| host(X21) != host(X22)
| ~ setIn(X23,alive)
| ~ setIn(X21,alive)
| host(X21) = host(X23)
| ~ setIn(host(X22),index(down,host(X23)))
| ~ elem(m_Down(X24),queue(host(X21))) )
& ! [X17,X18,X19,X20] :
( host(X19) != host(X20)
| host(X17) != host(X18)
| ~ setIn(X19,alive)
| ~ setIn(X17,alive)
| host(X17) = host(X19)
| ~ elem(m_Down(X18),queue(host(X19)))
| ~ elem(m_Down(X20),queue(host(X17))) )
& ! [X15,X16] :
( host(X15) != host(X16)
| X15 = X16
| ~ setIn(X16,alive)
| ~ setIn(X15,alive) )
& ! [X13,X14] :
( host(X13) != host(X14)
| ~ leq(X14,X13)
| setIn(X13,alive)
| ~ setIn(X14,alive) )
& ! [X10,X11,X12] :
( ~ elem(m_Ack(X12,X10),queue(host(X11)))
| ~ leq(host(X10),host(X12)) )
& ! [X8,X9] :
( ~ elem(m_Halt(X9),queue(host(X8)))
| ~ leq(host(X8),host(X9)) )
& ! [X6,X7] :
( ~ elem(m_Down(X7),queue(host(X6)))
| host(X6) != host(X7) )
& ! [X4,X5] :
( ~ elem(m_Down(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)
& ! [X25] :
( host(X2) != host(X25)
| leq(X25,X1) )
& host(X1) != s(zero)
& ? [X26] :
( host(X2) = host(X26)
& ? [X27,X28] :
( host(X1) != host(X28)
& host(X2) != host(X28)
& ? [X29] :
( host(X28) = host(X29)
& host(X26) = host(X27)
& host(X26) != host(X28)
& ( X1 = X28
| ( setIn(X28,alive)
& X2 != X28 ) )
& ( X1 = X26
| ( setIn(X26,alive)
& X2 != X26 ) )
& setIn(host(X27),index(down,host(X28)))
& elem(m_Down(X29),X0) ) ) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f86,plain,
? [X0,X1,X2,X3] :
( queue(host(X2)) = cons(m_Down(X3),X0)
& ! [X21,X22,X23,X24] :
( host(X23) != host(X24)
| host(X21) != host(X22)
| ~ setIn(X23,alive)
| ~ setIn(X21,alive)
| host(X21) = host(X23)
| ~ setIn(host(X22),index(down,host(X23)))
| ~ elem(m_Down(X24),queue(host(X21))) )
& ! [X17,X18,X19,X20] :
( host(X19) != host(X20)
| host(X17) != host(X18)
| ~ setIn(X19,alive)
| ~ setIn(X17,alive)
| host(X17) = host(X19)
| ~ elem(m_Down(X18),queue(host(X19)))
| ~ elem(m_Down(X20),queue(host(X17))) )
& ! [X15,X16] :
( host(X15) != host(X16)
| X15 = X16
| ~ setIn(X16,alive)
| ~ setIn(X15,alive) )
& ! [X13,X14] :
( host(X13) != host(X14)
| ~ leq(X14,X13)
| setIn(X13,alive)
| ~ setIn(X14,alive) )
& ! [X10,X11,X12] :
( ~ elem(m_Ack(X12,X10),queue(host(X11)))
| ~ leq(host(X10),host(X12)) )
& ! [X8,X9] :
( ~ elem(m_Halt(X9),queue(host(X8)))
| ~ leq(host(X8),host(X9)) )
& ! [X6,X7] :
( ~ elem(m_Down(X7),queue(host(X6)))
| host(X6) != host(X7) )
& ! [X4,X5] :
( ~ elem(m_Down(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)
& ! [X25] :
( host(X2) != host(X25)
| leq(X25,X1) )
& host(X1) != s(zero)
& ? [X26] :
( host(X2) = host(X26)
& ? [X27,X28] :
( host(X1) != host(X28)
& host(X2) != host(X28)
& ? [X29] :
( host(X28) = host(X29)
& host(X26) = host(X27)
& host(X26) != host(X28)
& ( X1 = X28
| ( setIn(X28,alive)
& X2 != X28 ) )
& ( X1 = X26
| ( setIn(X26,alive)
& X2 != X26 ) )
& setIn(host(X27),index(down,host(X28)))
& elem(m_Down(X29),X0) ) ) ) ),
inference(flattening,[],[f85]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( ~ elem(X0,cons(X1,X2))
| elem(X0,X2)
| X0 = X1 )
& ( ( ~ elem(X0,X2)
& X0 != X1 )
| elem(X0,cons(X1,X2)) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( ~ elem(X0,cons(X1,X2))
| elem(X0,X2)
| X0 = X1 )
& ( ( ~ elem(X0,X2)
& X0 != X1 )
| elem(X0,cons(X1,X2)) ) ),
inference(flattening,[],[f92]) ).
fof(f112,plain,
? [X0,X1,X2,X3] :
( queue(host(X2)) = cons(m_Down(X3),X0)
& ! [X26,X27,X28,X29] :
( host(X28) != host(X29)
| host(X26) != host(X27)
| ~ setIn(X28,alive)
| ~ setIn(X26,alive)
| host(X26) = host(X28)
| ~ setIn(host(X27),index(down,host(X28)))
| ~ elem(m_Down(X29),queue(host(X26))) )
& ! [X22,X23,X24,X25] :
( host(X24) != host(X25)
| host(X23) != host(X22)
| ~ setIn(X24,alive)
| ~ setIn(X22,alive)
| host(X22) = host(X24)
| ~ elem(m_Down(X23),queue(host(X24)))
| ~ elem(m_Down(X25),queue(host(X22))) )
& ! [X20,X21] :
( host(X20) != host(X21)
| X20 = X21
| ~ setIn(X21,alive)
| ~ setIn(X20,alive) )
& ! [X18,X19] :
( host(X19) != host(X18)
| ~ leq(X19,X18)
| setIn(X18,alive)
| ~ setIn(X19,alive) )
& ! [X15,X16,X17] :
( ~ elem(m_Ack(X17,X15),queue(host(X16)))
| ~ leq(host(X15),host(X17)) )
& ! [X13,X14] :
( ~ elem(m_Halt(X14),queue(host(X13)))
| ~ leq(host(X13),host(X14)) )
& ! [X11,X12] :
( ~ elem(m_Down(X12),queue(host(X11)))
| host(X11) != host(X12) )
& ! [X9,X10] :
( ~ elem(m_Down(X10),queue(host(X9)))
| ~ setIn(X10,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)
& ! [X8] :
( host(X2) != host(X8)
| leq(X8,X1) )
& host(X1) != s(zero)
& ? [X4] :
( host(X2) = host(X4)
& ? [X5,X6] :
( host(X1) != host(X6)
& host(X2) != host(X6)
& ? [X7] :
( host(X6) = host(X7)
& host(X4) = host(X5)
& host(X4) != host(X6)
& ( X1 = X6
| ( setIn(X6,alive)
& X2 != X6 ) )
& ( X1 = X4
| ( setIn(X4,alive)
& X2 != X4 ) )
& setIn(host(X5),index(down,host(X6)))
& elem(m_Down(X7),X0) ) ) ) ),
inference(rectify,[],[f86]) ).
fof(f113,plain,
( queue(host(sK5)) = cons(m_Down(sK6),sK3)
& ! [X26,X27,X28,X29] :
( host(X28) != host(X29)
| host(X26) != host(X27)
| ~ setIn(X28,alive)
| ~ setIn(X26,alive)
| host(X26) = host(X28)
| ~ setIn(host(X27),index(down,host(X28)))
| ~ elem(m_Down(X29),queue(host(X26))) )
& ! [X22,X23,X24,X25] :
( host(X24) != host(X25)
| host(X23) != host(X22)
| ~ setIn(X24,alive)
| ~ setIn(X22,alive)
| host(X22) = host(X24)
| ~ elem(m_Down(X23),queue(host(X24)))
| ~ elem(m_Down(X25),queue(host(X22))) )
& ! [X20,X21] :
( host(X20) != host(X21)
| X20 = X21
| ~ setIn(X21,alive)
| ~ setIn(X20,alive) )
& ! [X18,X19] :
( host(X19) != host(X18)
| ~ leq(X19,X18)
| setIn(X18,alive)
| ~ setIn(X19,alive) )
& ! [X15,X16,X17] :
( ~ elem(m_Ack(X17,X15),queue(host(X16)))
| ~ leq(host(X15),host(X17)) )
& ! [X13,X14] :
( ~ elem(m_Halt(X14),queue(host(X13)))
| ~ leq(host(X13),host(X14)) )
& ! [X11,X12] :
( ~ elem(m_Down(X12),queue(host(X11)))
| host(X11) != host(X12) )
& ! [X9,X10] :
( ~ elem(m_Down(X10),queue(host(X9)))
| ~ setIn(X10,alive) )
& setIn(sK5,alive)
& ~ leq(host(sK5),host(sK6))
& ( ( host(sK6) = host(index(elid,host(sK5)))
& wait = index(status,host(sK5)) )
| ( norm = index(status,host(sK5))
& host(sK6) = index(ldr,host(sK5)) ) )
& host(sK5) = host(sK4)
& ~ setIn(sK4,pids)
& ! [X8] :
( host(X8) != host(sK5)
| leq(X8,sK4) )
& s(zero) != host(sK4)
& host(sK7) = host(sK5)
& host(sK9) != host(sK4)
& host(sK9) != host(sK5)
& host(sK9) = host(sK10)
& host(sK8) = host(sK7)
& host(sK9) != host(sK7)
& ( sK4 = sK9
| ( setIn(sK9,alive)
& sK5 != sK9 ) )
& ( sK4 = sK7
| ( setIn(sK7,alive)
& sK5 != sK7 ) )
& setIn(host(sK8),index(down,host(sK9)))
& elem(m_Down(sK10),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8),skolemize(X6,sK9),skolemize(X7,sK10)],[f112]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ elem(X0,X2)
| elem(X0,cons(X1,X2)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f210,plain,
queue(host(sK5)) = cons(m_Down(sK6),sK3),
inference(cnf_transformation,[],[f113]) ).
fof(f211,plain,
! [X28,X29,X26,X27] :
( host(X28) != host(X29)
| host(X26) != host(X27)
| ~ setIn(X28,alive)
| ~ setIn(X26,alive)
| host(X26) = host(X28)
| ~ setIn(host(X27),index(down,host(X28)))
| ~ elem(m_Down(X29),queue(host(X26))) ),
inference(cnf_transformation,[],[f113]) ).
fof(f213,plain,
! [X21,X20] :
( host(X20) != host(X21)
| X20 = X21
| ~ setIn(X21,alive)
| ~ setIn(X20,alive) ),
inference(cnf_transformation,[],[f113]) ).
fof(f214,plain,
! [X18,X19] :
( host(X19) != host(X18)
| ~ leq(X19,X18)
| setIn(X18,alive)
| ~ setIn(X19,alive) ),
inference(cnf_transformation,[],[f113]) ).
fof(f217,plain,
! [X11,X12] :
( ~ elem(m_Down(X12),queue(host(X11)))
| host(X11) != host(X12) ),
inference(cnf_transformation,[],[f113]) ).
fof(f219,plain,
setIn(sK5,alive),
inference(cnf_transformation,[],[f113]) ).
fof(f225,plain,
host(sK5) = host(sK4),
inference(cnf_transformation,[],[f113]) ).
fof(f227,plain,
! [X8] :
( host(X8) != host(sK5)
| leq(X8,sK4) ),
inference(cnf_transformation,[],[f113]) ).
fof(f229,plain,
host(sK7) = host(sK5),
inference(cnf_transformation,[],[f113]) ).
fof(f232,plain,
host(sK9) = host(sK10),
inference(cnf_transformation,[],[f113]) ).
fof(f233,plain,
host(sK8) = host(sK7),
inference(cnf_transformation,[],[f113]) ).
fof(f235,plain,
( sK4 = sK9
| setIn(sK9,alive) ),
inference(cnf_transformation,[],[f113]) ).
fof(f237,plain,
( sK4 = sK7
| setIn(sK7,alive) ),
inference(cnf_transformation,[],[f113]) ).
fof(f239,plain,
setIn(host(sK8),index(down,host(sK9))),
inference(cnf_transformation,[],[f113]) ).
fof(f240,plain,
elem(m_Down(sK10),sK3),
inference(cnf_transformation,[],[f113]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( elem(X0,cons(X2,X1))
| ~ elem(X0,X1) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_139,negated_conjecture,
elem(m_Down(sK10),sK3),
inference(cnf_transformation,[],[f240]) ).
tcf(c_140,negated_conjecture,
setIn(host(sK8),index(down,host(sK9))),
inference(cnf_transformation,[],[f239]) ).
tcf(c_142,negated_conjecture,
( setIn(sK7,alive)
| ( sK7 = sK4 ) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_144,negated_conjecture,
( setIn(sK9,alive)
| ( sK9 = sK4 ) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_146,negated_conjecture,
host(sK8) = host(sK7),
inference(cnf_transformation,[],[f233]) ).
tcf(c_147,negated_conjecture,
host(sK10) = host(sK9),
inference(cnf_transformation,[],[f232]) ).
tcf(c_150,negated_conjecture,
host(sK5) = host(sK7),
inference(cnf_transformation,[],[f229]) ).
tcf(c_152,negated_conjecture,
! [X0: $i] :
( leq(X0,sK4)
| ( host(X0) != host(sK5) ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_154,negated_conjecture,
host(sK5) = host(sK4),
inference(cnf_transformation,[],[f225]) ).
tcf(c_160,negated_conjecture,
setIn(sK5,alive),
inference(cnf_transformation,[],[f219]) ).
tcf(c_162,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ elem(m_Down(X1),queue(host(X0)))
| ( host(X0) != host(X1) ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_165,negated_conjecture,
! [X0: $i,X1: $i] :
( setIn(X1,alive)
| ~ setIn(X0,alive)
| ~ leq(X0,X1)
| ( host(X0) != host(X1) ) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_166,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ setIn(X1,alive)
| ~ setIn(X0,alive)
| ( host(X0) != host(X1) ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_168,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( host(X0) = host(X2) )
| ~ setIn(X2,alive)
| ~ setIn(X0,alive)
| ~ elem(m_Down(X3),queue(host(X0)))
| ~ setIn(host(X1),index(down,host(X2)))
| ( host(X2) != host(X3) )
| ( host(X0) != host(X1) ) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_169,negated_conjecture,
cons(m_Down(sK6),sK3) = queue(host(sK5)),
inference(cnf_transformation,[],[f210]) ).
tcf(c_972,plain,
host(sK8) = host(sK5),
inference(light_normalisation,[status(thm)],[c_146,c_150]) ).
tcf(c_986,plain,
setIn(host(sK5),index(down,host(sK9))),
inference(light_normalisation,[status(thm)],[c_140,c_972]) ).
tcf(c_2357,definition,
iPr_def_10 = host(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2358,definition,
iPr_def_11 = host(sK9),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2359,definition,
iPr_def_12 = index(down,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2361,definition,
iPr_def_14 = host(sK8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2362,definition,
iPr_def_15 = m_Down(sK6),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2363,definition,
iPr_def_16 = cons(iPr_def_15,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2364,definition,
iPr_def_17 = queue(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_2370,definition,
iPr_def_23 = host(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_2371,definition,
iPr_def_24 = host(sK7),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_2372,definition,
iPr_def_25 = host(sK10),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_2373,definition,
iPr_def_26 = m_Down(sK10),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_2374,plain,
setIn(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_986,c_2358,c_2359,c_2357]) ).
tcf(c_2376,plain,
iPr_def_14 = iPr_def_10,
inference(demodulation,[status(thm)],[c_972,c_2361]) ).
tcf(c_2377,negated_conjecture,
iPr_def_16 = iPr_def_17,
inference(demodulation,[status(thm)],[c_169,c_2364,c_2362,c_2363]) ).
tcf(c_2378,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( host(X0) = host(X2) )
| ~ setIn(X2,alive)
| ~ setIn(X0,alive)
| ~ elem(m_Down(X3),queue(host(X0)))
| ~ setIn(host(X1),index(down,host(X2)))
| ( host(X2) != host(X3) )
| ( host(X0) != host(X1) ) ),
inference(demodulation,[status(thm)],[c_168]) ).
tcf(c_2380,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ setIn(X1,alive)
| ~ setIn(X0,alive)
| ( host(X0) != host(X1) ) ),
inference(demodulation,[status(thm)],[c_166]) ).
tcf(c_2381,negated_conjecture,
! [X0: $i,X1: $i] :
( setIn(X1,alive)
| ~ setIn(X0,alive)
| ~ leq(X0,X1)
| ( host(X0) != host(X1) ) ),
inference(demodulation,[status(thm)],[c_165]) ).
tcf(c_2384,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ elem(m_Down(X1),queue(host(X0)))
| ( host(X0) != host(X1) ) ),
inference(demodulation,[status(thm)],[c_162]) ).
tcf(c_2386,negated_conjecture,
setIn(sK5,alive),
inference(demodulation,[status(thm)],[c_160]) ).
tcf(c_2392,negated_conjecture,
iPr_def_10 = iPr_def_23,
inference(demodulation,[status(thm)],[c_154,c_2370]) ).
tcf(c_2394,negated_conjecture,
! [X0: $i] :
( leq(X0,sK4)
| ( host(X0) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_152]) ).
tcf(c_2395,negated_conjecture,
iPr_def_10 = iPr_def_24,
inference(demodulation,[status(thm)],[c_150,c_2371]) ).
tcf(c_2397,negated_conjecture,
iPr_def_25 = iPr_def_11,
inference(demodulation,[status(thm)],[c_147,c_2372]) ).
tcf(c_2398,negated_conjecture,
( setIn(sK9,alive)
| ( sK9 = sK4 ) ),
inference(demodulation,[status(thm)],[c_144]) ).
tcf(c_2400,negated_conjecture,
( setIn(sK7,alive)
| ( sK7 = sK4 ) ),
inference(demodulation,[status(thm)],[c_142]) ).
tcf(c_2402,negated_conjecture,
elem(iPr_def_26,sK3),
inference(demodulation,[status(thm)],[c_139,c_2373]) ).
tcf(c_4329,plain,
leq(sK5,sK4),
inference(superposition,[status(thm)],[c_2357,c_2394]) ).
tcf(c_4390,plain,
! [X0: $i] :
( ~ elem(m_Down(X0),queue(host(sK5)))
| ( host(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2357,c_2384]) ).
tcf(c_4398,plain,
! [X0: $i] :
( ~ elem(m_Down(X0),iPr_def_16)
| ( host(X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_4390,c_2357,c_2364,c_2377]) ).
tcf(c_4417,plain,
! [X0: $i] :
( setIn(X0,alive)
| ~ setIn(sK5,alive)
| ~ leq(sK5,X0)
| ( host(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2357,c_2381]) ).
tcf(c_4425,plain,
! [X0: $i] :
( setIn(X0,alive)
| ~ leq(sK5,X0)
| ( host(X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4417,c_2386]) ).
tcf(c_4444,plain,
! [X0: $i] :
( ( X0 = sK9 )
| ~ setIn(sK9,alive)
| ~ setIn(X0,alive)
| ( host(X0) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_2358,c_2380]) ).
tcf(c_4445,plain,
! [X0: $i] :
( ( X0 = sK5 )
| ~ setIn(sK5,alive)
| ~ setIn(X0,alive)
| ( host(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2357,c_2380]) ).
tcf(c_4447,plain,
! [X0: $i] :
( ( X0 = sK5 )
| ~ setIn(X0,alive)
| ( host(X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4445,c_2386]) ).
tcf(c_4530,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( host(X0) = host(sK5) )
| ~ setIn(sK5,alive)
| ~ setIn(X0,alive)
| ~ elem(m_Down(X1),queue(host(sK5)))
| ~ setIn(host(X2),index(down,host(X0)))
| ( host(X2) != iPr_def_10 )
| ( host(X0) != host(X1) ) ),
inference(superposition,[status(thm)],[c_2357,c_2378]) ).
tcf(c_4556,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( host(X0) = iPr_def_10 )
| ~ setIn(sK5,alive)
| ~ setIn(X0,alive)
| ~ elem(m_Down(X1),iPr_def_16)
| ~ setIn(host(X2),index(down,host(X0)))
| ( host(X2) != iPr_def_10 )
| ( host(X0) != host(X1) ) ),
inference(light_normalisation,[status(thm)],[c_4530,c_2357,c_2364,c_2377]) ).
tcf(c_4557,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( host(X0) = iPr_def_10 )
| ~ setIn(X0,alive)
| ~ elem(m_Down(X1),iPr_def_16)
| ~ setIn(host(X2),index(down,host(X0)))
| ( host(X2) != iPr_def_10 )
| ( host(X0) != host(X1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4556,c_2386]) ).
tcf(c_4595,plain,
host(sK8) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2361,c_2376]) ).
tcf(c_4939,plain,
host(sK4) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2370,c_2392]) ).
tcf(c_5057,plain,
( setIn(sK4,alive)
| ~ leq(sK5,sK4) ),
inference(superposition,[status(thm)],[c_4939,c_4425]) ).
tcf(c_5060,plain,
setIn(sK4,alive),
inference(forward_subsumption_resolution,[status(thm)],[c_5057,c_4329]) ).
tcf(c_5092,plain,
host(sK7) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2371,c_2395]) ).
tcf(c_5173,plain,
host(sK10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_2372,c_2397]) ).
tcf(c_5179,plain,
( ~ elem(m_Down(sK10),iPr_def_16)
| ( iPr_def_10 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_5173,c_4398]) ).
tcf(c_5203,plain,
( ~ elem(iPr_def_26,iPr_def_16)
| ( iPr_def_10 != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_5179,c_2373]) ).
tcf(c_5402,plain,
( ( sK5 = sK7 )
| ~ setIn(sK7,alive) ),
inference(superposition,[status(thm)],[c_5092,c_4447]) ).
tcf(c_5405,plain,
( ( sK5 = sK4 )
| ~ setIn(sK4,alive) ),
inference(superposition,[status(thm)],[c_4939,c_4447]) ).
tcf(c_5408,plain,
sK5 = sK4,
inference(forward_subsumption_resolution,[status(thm)],[c_5405,c_5060]) ).
tcf(c_5434,plain,
( setIn(sK7,alive)
| ( sK5 = sK7 ) ),
inference(demodulation,[status(thm)],[c_2400,c_5408]) ).
tcf(c_5435,plain,
( setIn(sK9,alive)
| ( sK9 = sK5 ) ),
inference(demodulation,[status(thm)],[c_2398,c_5408]) ).
tcf(c_5444,plain,
sK5 = sK7,
inference(backward_subsumption_resolution,[status(thm)],[c_5402,c_5434]) ).
tcf(c_5446,plain,
host(sK5) = iPr_def_10,
inference(demodulation,[status(thm)],[c_5092,c_5444]) ).
tcf(c_5765,plain,
( ( sK8 = sK9 )
| ~ setIn(sK9,alive)
| ~ setIn(sK8,alive)
| ( iPr_def_10 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_4595,c_4444]) ).
tcf(c_6006,plain,
! [X0: $i,X1: $i] :
( ( host(X0) = iPr_def_10 )
| ~ setIn(X0,alive)
| ~ elem(m_Down(sK9),iPr_def_16)
| ~ setIn(host(X1),index(down,host(X0)))
| ( host(X1) != iPr_def_10 )
| ( host(X0) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_2358,c_4557]) ).
tcf(c_6007,plain,
! [X0: $i,X1: $i] :
( ( host(X0) = iPr_def_10 )
| ~ setIn(X0,alive)
| ~ elem(m_Down(sK10),iPr_def_16)
| ~ setIn(host(X1),index(down,host(X0)))
| ( host(X1) != iPr_def_10 )
| ( host(X0) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_5173,c_4557]) ).
tcf(c_6031,plain,
! [X0: $i,X1: $i] :
( ( host(X0) = iPr_def_10 )
| ~ elem(iPr_def_26,iPr_def_16)
| ~ setIn(X0,alive)
| ~ setIn(host(X1),index(down,host(X0)))
| ( host(X1) != iPr_def_10 )
| ( host(X0) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_6007,c_2373]) ).
tcf(c_6766,plain,
! [X0: $i] :
( elem(X0,iPr_def_16)
| ~ elem(X0,sK3) ),
inference(superposition,[status(thm)],[c_2363,c_96]) ).
tcf(c_6931,plain,
elem(iPr_def_26,iPr_def_16),
inference(superposition,[status(thm)],[c_2402,c_6766]) ).
tcf(c_6962,plain,
iPr_def_10 != iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_5765,c_5203,c_6931]) ).
tcf(c_9268,plain,
! [X0: $i,X1: $i] :
( ( host(X0) = iPr_def_10 )
| ~ setIn(X0,alive)
| ( host(X0) != iPr_def_11 )
| ( host(X1) != iPr_def_10 )
| ~ setIn(host(X1),index(down,host(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_6006,c_6031,c_6931]) ).
tcf(c_9269,plain,
! [X0: $i,X1: $i] :
( ( host(X0) = iPr_def_10 )
| ~ setIn(X0,alive)
| ~ setIn(host(X1),index(down,host(X0)))
| ( host(X1) != iPr_def_10 )
| ( host(X0) != iPr_def_11 ) ),
inference(renaming,[status(thm)],[c_9268]) ).
tcf(c_9281,plain,
! [X0: $i] :
( ( host(sK9) = iPr_def_10 )
| ~ setIn(sK9,alive)
| ~ setIn(host(X0),index(down,host(sK9)))
| ( host(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2358,c_9269]) ).
tcf(c_9287,plain,
! [X0: $i] :
( ( iPr_def_10 = iPr_def_11 )
| ~ setIn(sK9,alive)
| ~ setIn(host(X0),iPr_def_12)
| ( host(X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_9281,c_2358,c_2359]) ).
tcf(c_9288,plain,
! [X0: $i] :
( ~ setIn(sK9,alive)
| ~ setIn(host(X0),iPr_def_12)
| ( host(X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9287,c_6962]) ).
tcf(c_16674,plain,
( ~ setIn(sK9,alive)
| ~ setIn(host(sK5),iPr_def_12) ),
inference(superposition,[status(thm)],[c_5446,c_9288]) ).
tcf(c_16678,plain,
( ~ setIn(iPr_def_10,iPr_def_12)
| ~ setIn(sK9,alive) ),
inference(light_normalisation,[status(thm)],[c_16674,c_5446]) ).
tcf(c_16679,plain,
~ setIn(sK9,alive),
inference(forward_subsumption_resolution,[status(thm)],[c_16678,c_2374]) ).
tcf(c_16681,plain,
sK9 = sK5,
inference(backward_subsumption_resolution,[status(thm)],[c_5435,c_16679]) ).
tcf(c_16703,plain,
host(sK5) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2358,c_16681]) ).
tcf(c_16704,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_16703,c_5446]) ).
tcf(c_16705,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16704,c_6962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV456+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.61 % Computer : n010.cluster.edu
% 0.12/10.61 % Model : x86_64 x86_64
% 0.12/10.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.61 % Memory : 8046.5625MB
% 0.12/10.61 % OS : Linux 6.8.0-71-generic
% 0.12/10.61 % CPULimit : 300
% 0.12/10.61 % WCLimit : 300
% 0.12/10.61 % DateTime : Thu Sep 24 19:49:20 UTC 2026
% 0.12/10.62 % CPUTime :
% 0.12/10.62 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.67 Running first-order theorem proving
% 0.12/10.67 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.69
% 0.12/10.69 % ======== iProver multi-core TPTP/SMT =========
% 0.12/10.69
% 0.12/10.69 % Detected problem language: tptp
% 0.17/10.71 % Proving...
% 6.05/11.93 % SZS status Started for theBenchmark.p
% 6.05/11.93 % SZS status Theorem for theBenchmark.p
% 6.05/11.93
% 6.05/11.93 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.05/11.93
% 6.05/11.93 % ------ iProver source info
% 6.05/11.93
% 6.05/11.93 % git: date: 2026-07-19 20:42:38 +0200
% 6.05/11.93 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.05/11.93 % git: non_committed_changes: false
% 6.05/11.93
% 6.05/11.93 % ------ Parsing...
% 6.05/11.93 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.05/11.93
% 6.05/11.93 % ------ Preprocessing... sup_sim: 8 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 6.05/11.93
% 6.05/11.93 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.05/11.93
% 6.05/11.93 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.05/11.93 % ------ Proving...
% 6.05/11.93 % ------ Problem Properties
% 6.05/11.93
% 6.05/11.93 %
% 6.05/11.93 % clauses 132
% 6.05/11.93 % conjectures 26
% 6.05/11.93 % EPR 34
% 6.05/11.93 % Horn 111
% 6.05/11.93 % unary 74
% 6.05/11.93 % binary 35
% 6.05/11.93 % lits 230
% 6.05/11.93 % lits eq 111
% 6.05/11.93 % fd_pure 0
% 6.05/11.93 % fd_pseudo 0
% 6.05/11.93 % fd_cond 0
% 6.05/11.93 % fd_pseudo_cond 12
% 6.05/11.93 % AC symbols 0
% 6.05/11.93
% 6.05/11.93 % ------ Schedule dynamic 5 is on
% 6.05/11.93
% 6.05/11.93 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.05/11.93
% 6.05/11.93
% 6.05/11.93 % ------
% 6.05/11.93 % Current options:
% 6.05/11.93 % ------
% 6.05/11.93
% 6.05/11.93
% 6.05/11.93 %
% 6.05/11.93
% 6.05/11.93 % ------ Proving...
% 6.05/11.93 %
% 6.05/11.93
% 6.05/11.93 % SZS status Theorem for theBenchmark.p
% 6.05/11.93
% 6.05/11.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.05/11.93
% 6.05/11.93
%------------------------------------------------------------------------------