%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV448+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 : n008.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 03:22:11 PM UTC 2026
% Result : Theorem 4.27s 1.19s
% Output : CNFRefutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 79 ( 26 unt; 0 def)
% Number of atoms : 684 ( 330 equ)
% Maximal formula atoms : 65 ( 8 avg)
% Number of connectives : 969 ( 364 ~; 309 |; 237 &)
% ( 2 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 19 con; 0-2 aty)
% Number of variables : 250 ( 2 sgn 229 !; 21 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] : leq(host(X0),nbr_proc),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_04) ).
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(f62,axiom,
! [X0,X1] :
( ( leq(X1,X0)
& leq(X0,X1) )
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_61) ).
fof(f67,conjecture,
! [X0,X1,X2,X3] :
( ( queue(host(X2)) = cons(m_Down(X3),X0)
& ! [X4,X6,X5] :
( ( index(status,host(X5)) = elec_1
& elem(m_Down(X6),queue(host(X5)))
& ~ leq(host(X5),host(X4))
& ! [X7] :
( ( leq(s(zero),X7)
& ~ leq(host(X5),X7) )
=> ( X7 = host(X6)
| setIn(X7,index(down,host(X5))) ) ) )
=> ~ ( index(status,host(X4)) = norm
& index(ldr,host(X4)) = host(X4)
& setIn(X4,alive) ) )
& ! [X4,X6,X5] :
( ( host(X6) = index(pendack,host(X5))
& index(status,host(X5)) = elec_2
& leq(nbr_proc,index(pendack,host(X5)))
& elem(m_Ack(X5,X6),queue(host(X5)))
& setIn(X5,alive) )
=> ~ ( index(status,host(X4)) = norm
& index(ldr,host(X4)) = host(X4)
& setIn(X4,alive) ) )
& ! [X4,X6,X5] :
( ( host(X6) = index(pendack,host(X5))
& index(status,host(X5)) = elec_2
& leq(nbr_proc,index(pendack,host(X5)))
& elem(m_Down(X6),queue(host(X5)))
& setIn(X5,alive) )
=> ~ ( index(status,host(X4)) = norm
& index(ldr,host(X4)) = host(X4)
& setIn(X4,alive) ) )
& ! [X4,X5] :
( ( index(ldr,host(X5)) = host(X5)
& index(status,host(X5)) = norm
& index(status,host(X4)) = norm
& index(ldr,host(X4)) = host(X4)
& setIn(X5,alive)
& setIn(X4,alive) )
=> X5 = X4 )
& ! [X4] :
( ( setIn(X4,alive)
& ( index(status,host(X4)) = elec_2
| index(status,host(X4)) = elec_1 ) )
=> index(elid,host(X4)) = X4 )
& ! [X4,X5] :
( ( host(X5) = host(X4)
& X5 != X4 )
=> ( ~ setIn(X5,alive)
| ~ setIn(X4,alive) ) )
& ! [X4,X5] :
( elem(m_Ldr(X5),queue(host(X4)))
=> ~ leq(host(X4),host(X5)) ) )
=> ( 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) ) )
=> ( ( index(status,host(X2)) = elec_1
& ! [X4] :
( ( leq(s(zero),X4)
& ~ leq(host(X2),X4) )
=> ( X4 = host(X3)
| setIn(X4,index(down,host(X2))) ) ) )
=> ( leq(nbr_proc,host(X2))
=> ! [X4] :
( ~ setIn(host(X4),setEmpty)
=> ! [X7] :
( host(X2) = host(X7)
=> ! [X8] :
( host(X2) != host(X8)
=> ( ( index(status,host(X8)) = norm
& index(ldr,host(X8)) = host(X8)
& host(X2) = host(X7)
& setIn(X8,alive)
& setIn(X7,alive) )
=> X8 = X7 ) ) ) ) ) ) ) ) ) ),
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,X6,X5] :
( ( index(status,host(X5)) = elec_1
& elem(m_Down(X6),queue(host(X5)))
& ~ leq(host(X5),host(X4))
& ! [X7] :
( ( leq(s(zero),X7)
& ~ leq(host(X5),X7) )
=> ( X7 = host(X6)
| setIn(X7,index(down,host(X5))) ) ) )
=> ~ ( index(status,host(X4)) = norm
& index(ldr,host(X4)) = host(X4)
& setIn(X4,alive) ) )
& ! [X4,X6,X5] :
( ( host(X6) = index(pendack,host(X5))
& index(status,host(X5)) = elec_2
& leq(nbr_proc,index(pendack,host(X5)))
& elem(m_Ack(X5,X6),queue(host(X5)))
& setIn(X5,alive) )
=> ~ ( index(status,host(X4)) = norm
& index(ldr,host(X4)) = host(X4)
& setIn(X4,alive) ) )
& ! [X4,X6,X5] :
( ( host(X6) = index(pendack,host(X5))
& index(status,host(X5)) = elec_2
& leq(nbr_proc,index(pendack,host(X5)))
& elem(m_Down(X6),queue(host(X5)))
& setIn(X5,alive) )
=> ~ ( index(status,host(X4)) = norm
& index(ldr,host(X4)) = host(X4)
& setIn(X4,alive) ) )
& ! [X4,X5] :
( ( index(ldr,host(X5)) = host(X5)
& index(status,host(X5)) = norm
& index(status,host(X4)) = norm
& index(ldr,host(X4)) = host(X4)
& setIn(X5,alive)
& setIn(X4,alive) )
=> X5 = X4 )
& ! [X4] :
( ( setIn(X4,alive)
& ( index(status,host(X4)) = elec_2
| index(status,host(X4)) = elec_1 ) )
=> index(elid,host(X4)) = X4 )
& ! [X4,X5] :
( ( host(X5) = host(X4)
& X5 != X4 )
=> ( ~ setIn(X5,alive)
| ~ setIn(X4,alive) ) )
& ! [X4,X5] :
( elem(m_Ldr(X5),queue(host(X4)))
=> ~ leq(host(X4),host(X5)) ) )
=> ( 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) ) )
=> ( ( index(status,host(X2)) = elec_1
& ! [X4] :
( ( leq(s(zero),X4)
& ~ leq(host(X2),X4) )
=> ( X4 = host(X3)
| setIn(X4,index(down,host(X2))) ) ) )
=> ( leq(nbr_proc,host(X2))
=> ! [X4] :
( ~ setIn(host(X4),setEmpty)
=> ! [X7] :
( host(X2) = host(X7)
=> ! [X8] :
( host(X2) != host(X8)
=> ( ( index(status,host(X8)) = norm
& index(ldr,host(X8)) = host(X8)
& host(X2) = host(X7)
& setIn(X8,alive)
& setIn(X7,alive) )
=> X8 = X7 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f69,plain,
~ ! [X0,X2,X3] :
( ( queue(host(X2)) = cons(m_Down(X3),X0)
& ! [X17,X18,X19] :
( ( elec_1 = index(status,host(X19))
& elem(m_Down(X18),queue(host(X19)))
& ~ leq(host(X19),host(X17))
& ! [X20] :
( ( leq(s(zero),X20)
& ~ leq(host(X19),X20) )
=> ( host(X18) = X20
| setIn(X20,index(down,host(X19))) ) ) )
=> ~ ( norm = index(status,host(X17))
& host(X17) = index(ldr,host(X17))
& setIn(X17,alive) ) )
& ! [X14,X15,X16] :
( ( index(pendack,host(X16)) = host(X15)
& elec_2 = index(status,host(X16))
& leq(nbr_proc,index(pendack,host(X16)))
& elem(m_Ack(X16,X15),queue(host(X16)))
& setIn(X16,alive) )
=> ~ ( norm = index(status,host(X14))
& host(X14) = index(ldr,host(X14))
& setIn(X14,alive) ) )
& ! [X11,X12,X13] :
( ( index(pendack,host(X13)) = host(X12)
& elec_2 = index(status,host(X13))
& leq(nbr_proc,index(pendack,host(X13)))
& elem(m_Down(X12),queue(host(X13)))
& setIn(X13,alive) )
=> ~ ( norm = index(status,host(X11))
& host(X11) = index(ldr,host(X11))
& setIn(X11,alive) ) )
& ! [X9,X10] :
( ( host(X10) = index(ldr,host(X10))
& norm = index(status,host(X10))
& norm = index(status,host(X9))
& host(X9) = index(ldr,host(X9))
& setIn(X10,alive)
& setIn(X9,alive) )
=> X9 = X10 )
& ! [X8] :
( ( setIn(X8,alive)
& ( elec_2 = index(status,host(X8))
| elec_1 = index(status,host(X8)) ) )
=> index(elid,host(X8)) = X8 )
& ! [X6,X7] :
( ( host(X6) = host(X7)
& X6 != X7 )
=> ( ~ setIn(X7,alive)
| ~ setIn(X6,alive) ) )
& ! [X4,X5] :
( elem(m_Ldr(X5),queue(host(X4)))
=> ~ leq(host(X4),host(X5)) ) )
=> ( 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) ) )
=> ( ( index(status,host(X2)) = elec_1
& ! [X21] :
( ( leq(s(zero),X21)
& ~ leq(host(X2),X21) )
=> ( host(X3) = X21
| setIn(X21,index(down,host(X2))) ) ) )
=> ( leq(nbr_proc,host(X2))
=> ! [X22] :
( ~ setIn(host(X22),setEmpty)
=> ! [X23] :
( host(X2) = host(X23)
=> ! [X24] :
( host(X2) != host(X24)
=> ( ( norm = index(status,host(X24))
& host(X24) = index(ldr,host(X24))
& host(X2) = host(X23)
& setIn(X24,alive)
& setIn(X23,alive) )
=> X23 = X24 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
? [X0,X2,X3] :
( queue(host(X2)) = cons(m_Down(X3),X0)
& ! [X17,X18,X19] :
( elec_1 != index(status,host(X19))
| ~ elem(m_Down(X18),queue(host(X19)))
| leq(host(X19),host(X17))
| ? [X20] :
( leq(s(zero),X20)
& ~ leq(host(X19),X20)
& host(X18) != X20
& ~ setIn(X20,index(down,host(X19))) )
| norm != index(status,host(X17))
| host(X17) != index(ldr,host(X17))
| ~ setIn(X17,alive) )
& ! [X14,X15,X16] :
( index(pendack,host(X16)) != host(X15)
| elec_2 != index(status,host(X16))
| ~ leq(nbr_proc,index(pendack,host(X16)))
| ~ elem(m_Ack(X16,X15),queue(host(X16)))
| ~ setIn(X16,alive)
| norm != index(status,host(X14))
| host(X14) != index(ldr,host(X14))
| ~ setIn(X14,alive) )
& ! [X11,X12,X13] :
( index(pendack,host(X13)) != host(X12)
| elec_2 != index(status,host(X13))
| ~ leq(nbr_proc,index(pendack,host(X13)))
| ~ elem(m_Down(X12),queue(host(X13)))
| ~ setIn(X13,alive)
| norm != index(status,host(X11))
| host(X11) != index(ldr,host(X11))
| ~ setIn(X11,alive) )
& ! [X9,X10] :
( host(X10) != index(ldr,host(X10))
| norm != index(status,host(X10))
| norm != index(status,host(X9))
| host(X9) != index(ldr,host(X9))
| ~ setIn(X10,alive)
| ~ setIn(X9,alive)
| X9 = X10 )
& ! [X8] :
( ~ setIn(X8,alive)
| ( elec_2 != index(status,host(X8))
& elec_1 != index(status,host(X8)) )
| index(elid,host(X8)) = X8 )
& ! [X6,X7] :
( host(X6) != host(X7)
| X6 = X7
| ~ setIn(X7,alive)
| ~ setIn(X6,alive) )
& ! [X4,X5] :
( ~ elem(m_Ldr(X5),queue(host(X4)))
| ~ leq(host(X4),host(X5)) )
& setIn(X2,alive)
& ~ leq(host(X2),host(X3))
& ( host(X3) != host(index(elid,host(X2)))
| wait != index(status,host(X2)) )
& ( norm != index(status,host(X2))
| host(X3) != index(ldr,host(X2)) )
& index(status,host(X2)) = elec_1
& ! [X21] :
( ~ leq(s(zero),X21)
| leq(host(X2),X21)
| host(X3) = X21
| setIn(X21,index(down,host(X2))) )
& leq(nbr_proc,host(X2))
& ? [X22] :
( ~ setIn(host(X22),setEmpty)
& ? [X23] :
( host(X2) = host(X23)
& ? [X24] :
( host(X2) != host(X24)
& norm = index(status,host(X24))
& host(X24) = index(ldr,host(X24))
& host(X2) = host(X23)
& setIn(X24,alive)
& setIn(X23,alive)
& X23 != X24 ) ) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f71,plain,
? [X0,X2,X3] :
( queue(host(X2)) = cons(m_Down(X3),X0)
& ! [X17,X18,X19] :
( elec_1 != index(status,host(X19))
| ~ elem(m_Down(X18),queue(host(X19)))
| leq(host(X19),host(X17))
| ? [X20] :
( leq(s(zero),X20)
& ~ leq(host(X19),X20)
& host(X18) != X20
& ~ setIn(X20,index(down,host(X19))) )
| norm != index(status,host(X17))
| host(X17) != index(ldr,host(X17))
| ~ setIn(X17,alive) )
& ! [X14,X15,X16] :
( index(pendack,host(X16)) != host(X15)
| elec_2 != index(status,host(X16))
| ~ leq(nbr_proc,index(pendack,host(X16)))
| ~ elem(m_Ack(X16,X15),queue(host(X16)))
| ~ setIn(X16,alive)
| norm != index(status,host(X14))
| host(X14) != index(ldr,host(X14))
| ~ setIn(X14,alive) )
& ! [X11,X12,X13] :
( index(pendack,host(X13)) != host(X12)
| elec_2 != index(status,host(X13))
| ~ leq(nbr_proc,index(pendack,host(X13)))
| ~ elem(m_Down(X12),queue(host(X13)))
| ~ setIn(X13,alive)
| norm != index(status,host(X11))
| host(X11) != index(ldr,host(X11))
| ~ setIn(X11,alive) )
& ! [X9,X10] :
( host(X10) != index(ldr,host(X10))
| norm != index(status,host(X10))
| norm != index(status,host(X9))
| host(X9) != index(ldr,host(X9))
| ~ setIn(X10,alive)
| ~ setIn(X9,alive)
| X9 = X10 )
& ! [X8] :
( ~ setIn(X8,alive)
| ( elec_2 != index(status,host(X8))
& elec_1 != index(status,host(X8)) )
| index(elid,host(X8)) = X8 )
& ! [X6,X7] :
( host(X6) != host(X7)
| X6 = X7
| ~ setIn(X7,alive)
| ~ setIn(X6,alive) )
& ! [X4,X5] :
( ~ elem(m_Ldr(X5),queue(host(X4)))
| ~ leq(host(X4),host(X5)) )
& setIn(X2,alive)
& ~ leq(host(X2),host(X3))
& ( host(X3) != host(index(elid,host(X2)))
| wait != index(status,host(X2)) )
& ( norm != index(status,host(X2))
| host(X3) != index(ldr,host(X2)) )
& index(status,host(X2)) = elec_1
& ! [X21] :
( ~ leq(s(zero),X21)
| leq(host(X2),X21)
| host(X3) = X21
| setIn(X21,index(down,host(X2))) )
& leq(nbr_proc,host(X2))
& ? [X22] :
( ~ setIn(host(X22),setEmpty)
& ? [X23] :
( host(X2) = host(X23)
& ? [X24] :
( host(X2) != host(X24)
& norm = index(status,host(X24))
& host(X24) = index(ldr,host(X24))
& host(X2) = host(X23)
& setIn(X24,alive)
& setIn(X23,alive)
& X23 != X24 ) ) ) ),
inference(flattening,[],[f70]) ).
fof(f82,plain,
? [X0,X1,X2] :
( queue(host(X1)) = cons(m_Down(X2),X0)
& ! [X20,X21,X22] :
( elec_1 != index(status,host(X22))
| ~ elem(m_Down(X21),queue(host(X22)))
| leq(host(X22),host(X20))
| ? [X23] :
( leq(s(zero),X23)
& ~ leq(host(X22),X23)
& host(X21) != X23
& ~ setIn(X23,index(down,host(X22))) )
| norm != index(status,host(X20))
| host(X20) != index(ldr,host(X20))
| ~ setIn(X20,alive) )
& ! [X17,X18,X19] :
( host(X18) != index(pendack,host(X19))
| elec_2 != index(status,host(X19))
| ~ leq(nbr_proc,index(pendack,host(X19)))
| ~ elem(m_Ack(X19,X18),queue(host(X19)))
| ~ setIn(X19,alive)
| norm != index(status,host(X17))
| host(X17) != index(ldr,host(X17))
| ~ setIn(X17,alive) )
& ! [X14,X15,X16] :
( index(pendack,host(X16)) != host(X15)
| elec_2 != index(status,host(X16))
| ~ leq(nbr_proc,index(pendack,host(X16)))
| ~ elem(m_Down(X15),queue(host(X16)))
| ~ setIn(X16,alive)
| norm != index(status,host(X14))
| host(X14) != index(ldr,host(X14))
| ~ setIn(X14,alive) )
& ! [X12,X13] :
( host(X13) != index(ldr,host(X13))
| norm != index(status,host(X13))
| norm != index(status,host(X12))
| host(X12) != index(ldr,host(X12))
| ~ setIn(X13,alive)
| ~ setIn(X12,alive)
| X12 = X13 )
& ! [X11] :
( ~ setIn(X11,alive)
| ( elec_2 != index(status,host(X11))
& elec_1 != index(status,host(X11)) )
| index(elid,host(X11)) = X11 )
& ! [X9,X10] :
( host(X9) != host(X10)
| X9 = X10
| ~ setIn(X10,alive)
| ~ setIn(X9,alive) )
& ! [X7,X8] :
( ~ elem(m_Ldr(X8),queue(host(X7)))
| ~ leq(host(X7),host(X8)) )
& setIn(X1,alive)
& ~ leq(host(X1),host(X2))
& ( host(X2) != host(index(elid,host(X1)))
| wait != index(status,host(X1)) )
& ( norm != index(status,host(X1))
| host(X2) != index(ldr,host(X1)) )
& elec_1 = index(status,host(X1))
& ! [X6] :
( ~ leq(s(zero),X6)
| leq(host(X1),X6)
| host(X2) = X6
| setIn(X6,index(down,host(X1))) )
& leq(nbr_proc,host(X1))
& ? [X3] :
( ~ setIn(host(X3),setEmpty)
& ? [X4] :
( host(X1) = host(X4)
& ? [X5] :
( host(X1) != host(X5)
& norm = index(status,host(X5))
& host(X5) = index(ldr,host(X5))
& host(X1) = host(X4)
& setIn(X5,alive)
& setIn(X4,alive)
& X4 != X5 ) ) ) ),
inference(rectify,[],[f71]) ).
fof(f83,plain,
( queue(host(sK1)) = cons(m_Down(sK2),sK0)
& ! [X20,X21,X22] :
( elec_1 != index(status,host(X22))
| ~ elem(m_Down(X21),queue(host(X22)))
| leq(host(X22),host(X20))
| ( leq(s(zero),sK6(X21,X22))
& ~ leq(host(X22),sK6(X21,X22))
& host(X21) != sK6(X21,X22)
& ~ setIn(sK6(X21,X22),index(down,host(X22))) )
| norm != index(status,host(X20))
| host(X20) != index(ldr,host(X20))
| ~ setIn(X20,alive) )
& ! [X17,X18,X19] :
( host(X18) != index(pendack,host(X19))
| elec_2 != index(status,host(X19))
| ~ leq(nbr_proc,index(pendack,host(X19)))
| ~ elem(m_Ack(X19,X18),queue(host(X19)))
| ~ setIn(X19,alive)
| norm != index(status,host(X17))
| host(X17) != index(ldr,host(X17))
| ~ setIn(X17,alive) )
& ! [X14,X15,X16] :
( index(pendack,host(X16)) != host(X15)
| elec_2 != index(status,host(X16))
| ~ leq(nbr_proc,index(pendack,host(X16)))
| ~ elem(m_Down(X15),queue(host(X16)))
| ~ setIn(X16,alive)
| norm != index(status,host(X14))
| host(X14) != index(ldr,host(X14))
| ~ setIn(X14,alive) )
& ! [X12,X13] :
( host(X13) != index(ldr,host(X13))
| norm != index(status,host(X13))
| norm != index(status,host(X12))
| host(X12) != index(ldr,host(X12))
| ~ setIn(X13,alive)
| ~ setIn(X12,alive)
| X12 = X13 )
& ! [X11] :
( ~ setIn(X11,alive)
| ( elec_2 != index(status,host(X11))
& elec_1 != index(status,host(X11)) )
| index(elid,host(X11)) = X11 )
& ! [X9,X10] :
( host(X9) != host(X10)
| X9 = X10
| ~ setIn(X10,alive)
| ~ setIn(X9,alive) )
& ! [X7,X8] :
( ~ elem(m_Ldr(X8),queue(host(X7)))
| ~ leq(host(X7),host(X8)) )
& setIn(sK1,alive)
& ~ leq(host(sK1),host(sK2))
& ( host(sK2) != host(index(elid,host(sK1)))
| wait != index(status,host(sK1)) )
& ( norm != index(status,host(sK1))
| host(sK2) != index(ldr,host(sK1)) )
& elec_1 = index(status,host(sK1))
& ! [X6] :
( ~ leq(s(zero),X6)
| leq(host(sK1),X6)
| host(sK2) = X6
| setIn(X6,index(down,host(sK1))) )
& leq(nbr_proc,host(sK1))
& ~ setIn(host(sK3),setEmpty)
& host(sK1) = host(sK4)
& host(sK1) != host(sK5)
& norm = index(status,host(sK5))
& host(sK5) = index(ldr,host(sK5))
& host(sK1) = host(sK4)
& setIn(sK5,alive)
& setIn(sK4,alive)
& sK4 != sK5 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X23,sK6(X21,X22))],[f82]) ).
fof(f86,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(f87,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,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ( ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ( leq(X1,X0)
& leq(X0,X1) ) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f89,plain,
! [X0,X1] :
( ( ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ( leq(X1,X0)
& leq(X0,X1) ) ) ),
inference(flattening,[],[f88]) ).
fof(f98,plain,
queue(host(sK1)) = cons(m_Down(sK2),sK0),
inference(cnf_transformation,[],[f83]) ).
fof(f99,plain,
! [X21,X22,X20] :
( elec_1 != index(status,host(X22))
| ~ elem(m_Down(X21),queue(host(X22)))
| leq(host(X22),host(X20))
| leq(s(zero),sK6(X21,X22))
| norm != index(status,host(X20))
| host(X20) != index(ldr,host(X20))
| ~ setIn(X20,alive) ),
inference(cnf_transformation,[],[f83]) ).
fof(f100,plain,
! [X21,X22,X20] :
( elec_1 != index(status,host(X22))
| ~ elem(m_Down(X21),queue(host(X22)))
| leq(host(X22),host(X20))
| ~ leq(host(X22),sK6(X21,X22))
| norm != index(status,host(X20))
| host(X20) != index(ldr,host(X20))
| ~ setIn(X20,alive) ),
inference(cnf_transformation,[],[f83]) ).
fof(f101,plain,
! [X21,X22,X20] :
( elec_1 != index(status,host(X22))
| ~ elem(m_Down(X21),queue(host(X22)))
| leq(host(X22),host(X20))
| host(X21) != sK6(X21,X22)
| norm != index(status,host(X20))
| host(X20) != index(ldr,host(X20))
| ~ setIn(X20,alive) ),
inference(cnf_transformation,[],[f83]) ).
fof(f102,plain,
! [X21,X22,X20] :
( elec_1 != index(status,host(X22))
| ~ elem(m_Down(X21),queue(host(X22)))
| leq(host(X22),host(X20))
| ~ setIn(sK6(X21,X22),index(down,host(X22)))
| norm != index(status,host(X20))
| host(X20) != index(ldr,host(X20))
| ~ setIn(X20,alive) ),
inference(cnf_transformation,[],[f83]) ).
fof(f114,plain,
elec_1 = index(status,host(sK1)),
inference(cnf_transformation,[],[f83]) ).
fof(f115,plain,
! [X6] :
( ~ leq(s(zero),X6)
| leq(host(sK1),X6)
| host(sK2) = X6
| setIn(X6,index(down,host(sK1))) ),
inference(cnf_transformation,[],[f83]) ).
fof(f116,plain,
leq(nbr_proc,host(sK1)),
inference(cnf_transformation,[],[f83]) ).
fof(f119,plain,
host(sK1) != host(sK5),
inference(cnf_transformation,[],[f83]) ).
fof(f120,plain,
norm = index(status,host(sK5)),
inference(cnf_transformation,[],[f83]) ).
fof(f121,plain,
host(sK5) = index(ldr,host(sK5)),
inference(cnf_transformation,[],[f83]) ).
fof(f123,plain,
setIn(sK5,alive),
inference(cnf_transformation,[],[f83]) ).
fof(f138,plain,
! [X2,X0,X1] :
( X0 != X1
| elem(X0,cons(X1,X2)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f143,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f156,plain,
! [X0] : leq(host(X0),nbr_proc),
inference(cnf_transformation,[],[f5]) ).
fof(f195,plain,
! [X2,X1] : elem(X1,cons(X1,X2)),
inference(equality_resolution,[],[f138]) ).
tcf(c_51,negated_conjecture,
setIn(sK5,alive),
inference(cnf_transformation,[],[f123]) ).
tcf(c_53,negated_conjecture,
index(ldr,host(sK5)) = host(sK5),
inference(cnf_transformation,[],[f121]) ).
tcf(c_54,negated_conjecture,
index(status,host(sK5)) = norm,
inference(cnf_transformation,[],[f120]) ).
tcf(c_55,negated_conjecture,
host(sK5) != host(sK1),
inference(cnf_transformation,[],[f119]) ).
tcf(c_58,negated_conjecture,
leq(nbr_proc,host(sK1)),
inference(cnf_transformation,[],[f116]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( leq(host(sK1),X0)
| setIn(X0,index(down,host(sK1)))
| ( host(sK2) = X0 )
| ~ leq(s(zero),X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_60,negated_conjecture,
index(status,host(sK1)) = elec_1,
inference(cnf_transformation,[],[f114]) ).
tcf(c_72,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( leq(host(X1),host(X0))
| ~ setIn(X0,alive)
| ~ elem(m_Down(X2),queue(host(X1)))
| ~ setIn(sK6(X2,X1),index(down,host(X1)))
| ( index(status,host(X1)) != elec_1 )
| ( index(status,host(X0)) != norm )
| ( index(ldr,host(X0)) != host(X0) ) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_73,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( leq(host(X2),host(X0))
| ~ setIn(X0,alive)
| ~ elem(m_Down(X1),queue(host(X2)))
| ( sK6(X1,X2) != host(X1) )
| ( index(status,host(X2)) != elec_1 )
| ( index(status,host(X0)) != norm )
| ( index(ldr,host(X0)) != host(X0) ) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_74,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( leq(host(X1),host(X0))
| ~ setIn(X0,alive)
| ~ elem(m_Down(X2),queue(host(X1)))
| ~ leq(host(X1),sK6(X2,X1))
| ( index(status,host(X1)) != elec_1 )
| ( index(status,host(X0)) != norm )
| ( index(ldr,host(X0)) != host(X0) ) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_75,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( leq(host(X1),host(X0))
| leq(s(zero),sK6(X2,X1))
| ~ setIn(X0,alive)
| ~ elem(m_Down(X2),queue(host(X1)))
| ( index(status,host(X1)) != elec_1 )
| ( index(status,host(X0)) != norm )
| ( index(ldr,host(X0)) != host(X0) ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_76,negated_conjecture,
cons(m_Down(sK2),sK0) = queue(host(sK1)),
inference(cnf_transformation,[],[f98]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : elem(X0,cons(X0,X1)),
inference(cnf_transformation,[],[f195]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_106,plain,
! [X0: $i] : leq(host(X0),nbr_proc),
inference(cnf_transformation,[],[f156]) ).
tcf(c_3103,plain,
elem(m_Down(sK2),queue(host(sK1))),
inference(superposition,[status(thm)],[c_76,c_87]) ).
tcf(c_3205,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| leq(s(zero),sK6(X1,X0))
| ~ setIn(sK5,alive)
| ~ elem(m_Down(X1),queue(host(X0)))
| ( index(status,host(sK5)) != norm )
| ( index(status,host(X0)) != elec_1 ) ),
inference(superposition,[status(thm)],[c_53,c_75]) ).
tcf(c_3207,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| leq(s(zero),sK6(X1,X0))
| ~ setIn(sK5,alive)
| ~ elem(m_Down(X1),queue(host(X0)))
| ( index(status,host(X0)) != elec_1 ) ),
inference(ground_joinability,[status(thm)],[c_3205,c_54]) ).
tcf(c_3208,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| leq(s(zero),sK6(X1,X0))
| ~ elem(m_Down(X1),queue(host(X0)))
| ( index(status,host(X0)) != elec_1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3207,c_51]) ).
tcf(c_3229,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| ~ setIn(sK5,alive)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ leq(host(X0),sK6(X1,X0))
| ( index(status,host(sK5)) != norm )
| ( index(status,host(X0)) != elec_1 ) ),
inference(superposition,[status(thm)],[c_53,c_74]) ).
tcf(c_3231,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| ~ setIn(sK5,alive)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ leq(host(X0),sK6(X1,X0))
| ( index(status,host(X0)) != elec_1 ) ),
inference(ground_joinability,[status(thm)],[c_3229,c_54]) ).
tcf(c_3232,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ leq(host(X0),sK6(X1,X0))
| ( index(status,host(X0)) != elec_1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3231,c_51]) ).
tcf(c_3268,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| ~ setIn(sK5,alive)
| ~ elem(m_Down(X1),queue(host(X0)))
| ( sK6(X1,X0) != host(X1) )
| ( index(status,host(sK5)) != norm )
| ( index(status,host(X0)) != elec_1 ) ),
inference(superposition,[status(thm)],[c_53,c_73]) ).
tcf(c_3269,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| ~ setIn(sK5,alive)
| ~ elem(m_Down(X1),queue(host(X0)))
| ( sK6(X1,X0) != host(X1) )
| ( index(status,host(X0)) != elec_1 ) ),
inference(ground_joinability,[status(thm)],[c_3268,c_54]) ).
tcf(c_3270,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| ~ elem(m_Down(X1),queue(host(X0)))
| ( sK6(X1,X0) != host(X1) )
| ( index(status,host(X0)) != elec_1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3269,c_51]) ).
tcf(c_3290,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| ~ setIn(sK5,alive)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(sK6(X1,X0),index(down,host(X0)))
| ( index(status,host(sK5)) != norm )
| ( index(status,host(X0)) != elec_1 ) ),
inference(superposition,[status(thm)],[c_53,c_72]) ).
tcf(c_3291,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| ~ setIn(sK5,alive)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(sK6(X1,X0),index(down,host(X0)))
| ( index(status,host(X0)) != elec_1 ) ),
inference(ground_joinability,[status(thm)],[c_3290,c_54]) ).
tcf(c_3292,plain,
! [X0: $i,X1: $i] :
( leq(host(X0),host(sK5))
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(sK6(X1,X0),index(down,host(X0)))
| ( index(status,host(X0)) != elec_1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3291,c_51]) ).
tcf(c_3327,plain,
! [X0: $i] :
( leq(host(sK1),host(sK5))
| leq(s(zero),sK6(X0,sK1))
| ~ elem(m_Down(X0),queue(host(sK1))) ),
inference(superposition,[status(thm)],[c_60,c_3208]) ).
tcf(c_3351,plain,
! [X0: $i] :
( leq(host(sK1),host(sK5))
| ~ elem(m_Down(X0),queue(host(sK1)))
| ~ leq(host(sK1),sK6(X0,sK1)) ),
inference(superposition,[status(thm)],[c_60,c_3232]) ).
tcf(c_3374,plain,
! [X0: $i] :
( leq(host(sK1),host(sK5))
| ~ elem(m_Down(X0),queue(host(sK1)))
| ( sK6(X0,sK1) != host(X0) ) ),
inference(superposition,[status(thm)],[c_60,c_3270]) ).
tcf(c_3394,plain,
! [X0: $i] :
( leq(host(sK1),host(sK5))
| ~ elem(m_Down(X0),queue(host(sK1)))
| ~ setIn(sK6(X0,sK1),index(down,host(sK1))) ),
inference(superposition,[status(thm)],[c_60,c_3292]) ).
tcf(c_3405,plain,
! [X0: $i] :
( leq(host(sK1),host(sK5))
| leq(host(sK1),sK6(X0,sK1))
| ( sK6(X0,sK1) = host(sK2) )
| ~ elem(m_Down(X0),queue(host(sK1)))
| ~ leq(s(zero),sK6(X0,sK1)) ),
inference(superposition,[status(thm)],[c_59,c_3394]) ).
tcf(c_3427,plain,
! [X0: $i] :
( leq(host(sK1),host(sK5))
| ~ elem(m_Down(X0),queue(host(sK1)))
| ( sK6(X0,sK1) = host(sK2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3405,c_3327,c_3351,c_3405]) ).
tcf(c_3428,plain,
! [X0: $i] :
( leq(host(sK1),host(sK5))
| ( sK6(X0,sK1) = host(sK2) )
| ~ elem(m_Down(X0),queue(host(sK1))) ),
inference(renaming,[status(thm)],[c_3427]) ).
tcf(c_3436,plain,
( leq(host(sK1),host(sK5))
| ( sK6(sK2,sK1) = host(sK2) ) ),
inference(superposition,[status(thm)],[c_3103,c_3428]) ).
tcf(c_3903,plain,
( ( host(sK1) = nbr_proc )
| ~ leq(host(sK1),nbr_proc) ),
inference(superposition,[status(thm)],[c_58,c_95]) ).
tcf(c_3918,plain,
( ( host(sK5) = host(sK1) )
| ( sK6(sK2,sK1) = host(sK2) )
| ~ leq(host(sK5),host(sK1)) ),
inference(superposition,[status(thm)],[c_3436,c_95]) ).
tcf(c_3942,plain,
host(sK1) = nbr_proc,
inference(forward_subsumption_resolution,[status(thm)],[c_3903,c_106]) ).
tcf(c_3980,plain,
( ( sK6(sK2,sK1) = host(sK2) )
| ~ leq(host(sK5),host(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3918,c_55]) ).
tcf(c_4012,plain,
! [X0: $i] :
( leq(nbr_proc,host(sK5))
| ~ elem(m_Down(X0),queue(nbr_proc))
| ( sK6(X0,sK1) != host(X0) ) ),
inference(demodulation,[status(thm)],[c_3374,c_3942]) ).
tcf(c_4017,plain,
elem(m_Down(sK2),queue(nbr_proc)),
inference(demodulation,[status(thm)],[c_3103,c_3942]) ).
tcf(c_4023,plain,
host(sK5) != nbr_proc,
inference(demodulation,[status(thm)],[c_55,c_3942]) ).
tcf(c_4173,plain,
( ( sK6(sK2,sK1) = host(sK2) )
| ~ leq(host(sK5),nbr_proc) ),
inference(light_normalisation,[status(thm)],[c_3980,c_3942]) ).
tcf(c_4174,plain,
sK6(sK2,sK1) = host(sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_4173,c_106]) ).
tcf(c_4547,plain,
( leq(nbr_proc,host(sK5))
| ~ elem(m_Down(sK2),queue(nbr_proc)) ),
inference(superposition,[status(thm)],[c_4174,c_4012]) ).
tcf(c_4548,plain,
leq(nbr_proc,host(sK5)),
inference(forward_subsumption_resolution,[status(thm)],[c_4547,c_4017]) ).
tcf(c_4551,plain,
( ( host(sK5) = nbr_proc )
| ~ leq(host(sK5),nbr_proc) ),
inference(superposition,[status(thm)],[c_4548,c_95]) ).
tcf(c_4556,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4551,c_4023,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV448+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 19:48:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 4.27/1.19 % SZS status Started for theBenchmark.p
% 4.27/1.19 % SZS status Theorem for theBenchmark.p
% 4.27/1.19
% 4.27/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.27/1.19
% 4.27/1.19 % ------ iProver source info
% 4.27/1.19
% 4.27/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 4.27/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.27/1.19 % git: non_committed_changes: false
% 4.27/1.19
% 4.27/1.19 % ------ Parsing...
% 4.27/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.27/1.19
% 4.27/1.19 % ------ Preprocessing... sup_sim: 4 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 %
% 4.27/1.19
% 4.27/1.19 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.27/1.19
% 4.27/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.27/1.19 % ------ Proving...
% 4.27/1.19 % ------ Problem Properties
% 4.27/1.19
% 4.27/1.19 %
% 4.27/1.19 % clauses 85
% 4.27/1.19 % conjectures 27
% 4.27/1.19 % EPR 19
% 4.27/1.19 % Horn 77
% 4.27/1.19 % unary 48
% 4.27/1.19 % binary 19
% 4.27/1.19 % lits 170
% 4.27/1.19 % lits eq 84
% 4.27/1.19 % fd_pure 0
% 4.27/1.19 % fd_pseudo 0
% 4.27/1.19 % fd_cond 1
% 4.27/1.19 % fd_pseudo_cond 13
% 4.27/1.19 % AC symbols 0
% 4.27/1.19
% 4.27/1.19 % ------ Schedule dynamic 5 is on
% 4.27/1.19
% 4.27/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.27/1.19
% 4.27/1.19
% 4.27/1.19 % ------
% 4.27/1.19 % Current options:
% 4.27/1.19 % ------
% 4.27/1.19
% 4.27/1.19
% 4.27/1.19 %
% 4.27/1.19
% 4.27/1.19 % ------ Proving...
% 4.27/1.19 %
% 4.27/1.19
% 4.27/1.19 % SZS status Theorem for theBenchmark.p
% 4.27/1.19
% 4.27/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.27/1.20
% 4.27/1.20
%------------------------------------------------------------------------------