%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Wed Oct 7 10:50:05 AM UTC 2026
% Result : Theorem 0.48s 0.31s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 73 ( 43 unt; 0 typ; 2 def)
% Number of atoms : 529 ( 114 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 1239 ( 441 ~; 177 |; 16 &; 605 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 146 ( 97 ^; 39 !; 10 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_c,type,
c: ( $i > $o ) > $o ).
thf(tp_choosenonempty,type,
choosenonempty: ( ( $i > $o ) > $o ) > $i > $o ).
thf(tp_eps,type,
eps: ( $i > $o ) > $i ).
thf(tp_epsio,type,
epsio: ( ( $i > $o ) > $o ) > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i > $o ).
thf(tp_setunion,type,
setunion: ( ( $i > $o ) > $o ) > $i > $o ).
thf(choosenonempty,definition,
( choosenonempty
= ( ^ [C: ( $i > $o ) > $o] :
( epsio
@ ^ [Y: $i > $o] :
( ( C @ Y )
& ( Y @ ( eps @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choosenonemptyd) ).
thf(setunion,definition,
( setunion
= ( ^ [C: ( $i > $o ) > $o,X: $i] :
? [Y: $i > $o] :
( ( C @ Y )
& ( Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setuniond) ).
thf(1,axiom,
setunion @ c @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca) ).
thf(4,conjecture,
( ( c @ ( choosenonempty @ c ) )
& ? [X: $i] : ( choosenonempty @ c @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(5,negated_conjecture,
( ( ( c @ ( choosenonempty @ c ) )
& ? [X: $i] : ( choosenonempty @ c @ X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ( c
@ ( epsio
@ ^ [SY0: $i > $o] :
( ( c @ SY0 )
& ( SY0 @ ( eps @ SY0 ) ) ) ) )
& ? [SY1: $i] :
( epsio
@ ^ [SY2: $i > $o] :
( ( c @ SY2 )
& ( SY2 @ ( eps @ SY2 ) ) )
@ SY1 ) )
= $false ),
inference(unfold_def,[status(thm)],[5,choosenonempty,setunion]) ).
thf(7,plain,
( ( ? [SY8: $i > $o] :
( ( c @ SY8 )
& ( SY8 @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,choosenonempty,setunion]) ).
thf(10,plain,
( ( c
@ ( epsio
@ ^ [SY0: $i > $o] :
( ( c @ SY0 )
& ( SY0 @ ( eps @ SY0 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(11,plain,
( ( ? [SY1: $i] :
( epsio
@ ^ [SY2: $i > $o] :
( ( c @ SY2 )
& ( SY2 @ ( eps @ SY2 ) ) )
@ SY1 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(12,plain,
( ( ~ ( c
@ ( epsio
@ ^ [SY0: $i > $o] :
( ( c @ SY0 )
& ( SY0 @ ( eps @ SY0 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ? [SY1: $i] :
( epsio
@ ^ [SY2: $i > $o] :
( ( c @ SY2 )
& ( SY2 @ ( eps @ SY2 ) ) )
@ SY1 ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(16,plain,
( ( ? [SY8: $i > $o] :
( ( c @ SY8 )
& ( SY8 @ a ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(17,plain,
( ( ~ ( c
@ ( epsio
@ ^ [SY0: $i > $o] :
( ( c @ SY0 )
& ( SY0 @ ( eps @ SY0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
( ( ~ ! [SX0: $i > $o] :
~ ~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,choosenonempty,setunion]) ).
thf(21,plain,
( ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,choosenonempty,setunion]) ).
thf(24,plain,
( ( ! [SX0: $i > $o] :
~ ~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(28,plain,
( ( ~ ~ ( ~ ( c @ sK1_SX0 )
| ~ ( sK1_SX0 @ a ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(31,plain,
( ( ~ ( ~ ( c @ sK1_SX0 )
| ~ ( sK1_SX0 @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ( c @ sK1_SX0 )
| ~ ( sK1_SX0 @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(37,plain,
( ( ~ ( c @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
( ( ~ ( sK1_SX0 @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( c @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
( ( sK1_SX0 @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
( ( ~ ~ ! [SY16: $i > $o] :
~ ~ ( ~ ( c @ SY16 )
| ~ ( SY16 @ ( eps @ SY16 ) ) )
| ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(choice,[status(thm)],[25]) ).
thf(44,plain,
( ( ( ~ ~ ! [SY16: $i > $o] :
~ ~ ( ~ ( c @ SY16 )
| ~ ( SY16 @ ( eps @ SY16 ) ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(45,plain,
( ( ( ~ ! [SY16: $i > $o] :
~ ~ ( ~ ( c @ SY16 )
| ~ ( SY16 @ ( eps @ SY16 ) ) ) )
= $false )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(46,plain,
( ( ( ! [SY16: $i > $o] :
~ ~ ( ~ ( c @ SY16 )
| ~ ( SY16 @ ( eps @ SY16 ) ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(47,plain,
! [SV6: $i > $o] :
( ( ( ~ ~ ( ~ ( c @ SV6 )
| ~ ( SV6 @ ( eps @ SV6 ) ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV6: $i > $o] :
( ( ( ~ ( ~ ( c @ SV6 )
| ~ ( SV6 @ ( eps @ SV6 ) ) ) )
= $false )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV6: $i > $o] :
( ( ( ~ ( c @ SV6 )
| ~ ( SV6 @ ( eps @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(50,plain,
! [SV6: $i > $o] :
( ( ( ~ ( c @ SV6 ) )
= $true )
| ( ( ~ ( SV6 @ ( eps @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(51,plain,
! [SV6: $i > $o] :
( ( ( c @ SV6 )
= $false )
| ( ( ~ ( SV6 @ ( eps @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(52,plain,
! [SV6: $i > $o] :
( ( ( SV6 @ ( eps @ SV6 ) )
= $false )
| ( ( c @ SV6 )
= $false )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(53,plain,
! [SV6: $i > $o] :
( ( ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
| ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) )
= $false )
| ( ( c @ SV6 )
= $false )
| ( ( SV6 @ ( eps @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(54,plain,
! [SV6: $i > $o] :
( ( ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $false )
| ( ( c @ SV6 )
= $false )
| ( ( SV6 @ ( eps @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(55,plain,
! [SV6: $i > $o] :
( ( ( ~ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) ) )
= $false )
| ( ( c @ SV6 )
= $false )
| ( ( SV6 @ ( eps @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV6: $i > $o] :
( ( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $true )
| ( ( c @ SV6 )
= $false )
| ( ( SV6 @ ( eps @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(57,plain,
! [SV6: $i > $o] :
( ( ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $true )
| ( ( c @ SV6 )
= $false )
| ( ( SV6 @ ( eps @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(58,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,57,56,42,41]) ).
thf(61,plain,
( ( ? [SY8: $i > $o] :
( ( c @ SY8 )
& ( SY8 @ a ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(62,plain,
( ( ~ ? [SY1: $i] :
( epsio
@ ^ [SY2: $i > $o] :
( ( c @ SY2 )
& ( SY2 @ ( eps @ SY2 ) ) )
@ SY1 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(63,plain,
( ( ~ ! [SX0: $i > $o] :
~ ~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61,choosenonempty,setunion]) ).
thf(66,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[62,choosenonempty,setunion]) ).
thf(67,plain,
( ( ! [SX0: $i > $o] :
~ ~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(70,plain,
( ( ~ ! [SX0: $i] :
~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
( ( ~ ~ ( ~ ( c @ sK2_SX0 )
| ~ ( sK2_SX0 @ a ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(74,plain,
( ( ! [SX0: $i] :
~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
( ( ~ ( ~ ( c @ sK2_SX0 )
| ~ ( sK2_SX0 @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(78,plain,
! [SV9: $i] :
( ( ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(79,plain,
( ( ~ ( c @ sK2_SX0 )
| ~ ( sK2_SX0 @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV9: $i] :
( ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ SV9 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(83,plain,
( ( ~ ( c @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(84,plain,
( ( ~ ( sK2_SX0 @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(87,plain,
( ( c @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(88,plain,
( ( sK2_SX0 @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(91,plain,
( ( ~ ~ ! [SY21: $i > $o] :
~ ~ ( ~ ( c @ SY21 )
| ~ ( SY21 @ ( eps @ SY21 ) ) )
| ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(choice,[status(thm)],[82]) ).
thf(92,plain,
( ( ( ~ ~ ! [SY21: $i > $o] :
~ ~ ( ~ ( c @ SY21 )
| ~ ( SY21 @ ( eps @ SY21 ) ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(93,plain,
( ( ( ~ ! [SY21: $i > $o] :
~ ~ ( ~ ( c @ SY21 )
| ~ ( SY21 @ ( eps @ SY21 ) ) ) )
= $false )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(94,plain,
( ( ( ! [SY21: $i > $o] :
~ ~ ( ~ ( c @ SY21 )
| ~ ( SY21 @ ( eps @ SY21 ) ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(95,plain,
! [SV13: $i > $o] :
( ( ( ~ ~ ( ~ ( c @ SV13 )
| ~ ( SV13 @ ( eps @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(96,plain,
! [SV13: $i > $o] :
( ( ( ~ ( ~ ( c @ SV13 )
| ~ ( SV13 @ ( eps @ SV13 ) ) ) )
= $false )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(97,plain,
! [SV13: $i > $o] :
( ( ( ~ ( c @ SV13 )
| ~ ( SV13 @ ( eps @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(98,plain,
! [SV13: $i > $o] :
( ( ( ~ ( c @ SV13 ) )
= $true )
| ( ( ~ ( SV13 @ ( eps @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(99,plain,
! [SV13: $i > $o] :
( ( ( c @ SV13 )
= $false )
| ( ( ~ ( SV13 @ ( eps @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(100,plain,
! [SV13: $i > $o] :
( ( ( SV13 @ ( eps @ SV13 ) )
= $false )
| ( ( c @ SV13 )
= $false )
| ( ( ~ ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(101,plain,
! [SV13: $i > $o] :
( ( ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
| ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) )
= $false )
| ( ( c @ SV13 )
= $false )
| ( ( SV13 @ ( eps @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(102,plain,
! [SV13: $i > $o] :
( ( ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) )
= $false )
| ( ( c @ SV13 )
= $false )
| ( ( SV13 @ ( eps @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(103,plain,
! [SV13: $i > $o] :
( ( ( ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) )
= $false )
| ( ( c @ SV13 )
= $false )
| ( ( SV13 @ ( eps @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(104,plain,
! [SV13: $i > $o] :
( ( ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
= $true )
| ( ( c @ SV13 )
= $false )
| ( ( SV13 @ ( eps @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(105,plain,
! [SV13: $i > $o] :
( ( ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) )
= $true )
| ( ( c @ SV13 )
= $false )
| ( ( SV13 @ ( eps @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(106,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[82,105,104,88,87]) ).
thf(107,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[106,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:46:36 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.31
% 0.48/0.31 No.of.Axioms: 3
% 0.48/0.31
% 0.48/0.31 Length.of.Defs: 361
% 0.48/0.31
% 0.48/0.31 Contains.Choice.Funs: true
% 0.48/0.31
% 0.48/0.31 *** Modified list of choice operators: epsio ***
% 0.48/0.31
% 0.48/0.31 *** Modified list of choice operators: eps, epsio ***
% 0.48/0.31 .
% 0.48/0.31
% 0.48/0.31 *** Modified list of choice operators: eps ***
% 0.48/0.31
% 0.48/0.31 *** Modified list of choice operators: epsio, eps ***
% 0.48/0.31 .
% 0.48/0.31
% 0.48/0.31 ********************************
% 0.48/0.31 * All subproblems solved! *
% 0.48/0.31 ********************************
% 0.48/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:106,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.48/0.31
% 0.48/0.31 %**** Beginning of derivation protocol ****
% 0.48/0.31 % SZS output start CNFRefutation
% See solution above
% 0.48/0.32
% 0.48/0.32 %**** End of derivation protocol ****
% 0.48/0.32 %**** no. of clauses in derivation: 71 ****
% 0.48/0.32 %**** clause counter: 106 ****
% 0.48/0.32
% 0.48/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:106,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------