TSTP Solution File: SEV428^1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEV428^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 17:36:40 EDT 2022
% Result : Theorem 0.19s 0.54s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 94 ( 40 unt; 8 typ; 2 def)
% Number of atoms : 689 ( 155 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 1489 ( 523 ~; 227 |; 4 &; 735 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 173 ( 173 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 187 ( 135 ^ 47 !; 5 ?; 187 :)
% 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/sandbox/benchmark/theBenchmark.p',choosenonempty) ).
thf(setunion,definition,
( setunion
= ( ^ [C: ( $i > $o ) > $o,X: $i] :
? [Y: $i > $o] :
( ( C @ Y )
& ( Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion) ).
thf(1,axiom,
setunion @ c @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ca) ).
thf(4,conjecture,
( ( c @ ( choosenonempty @ c ) )
& ? [X: $i] : ( choosenonempty @ c @ X ) ),
file('/export/starexec/sandbox/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 @ ( choosenonempty @ c ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(7,plain,
( ( ? [X: $i] : ( choosenonempty @ c @ X ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(8,plain,
( ( ~ ( c @ ( choosenonempty @ c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ? [X: $i] : ( choosenonempty @ c @ X ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i] :
~ ( choosenonempty @ c @ X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(15,plain,
( ( setunion @ c @ a )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(16,plain,
( ( ~ ( c @ ( choosenonempty @ c ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(17,plain,
( ( ~ ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,choosenonempty,setunion]) ).
thf(18,plain,
( ( ~ ! [SX0: $i > $o] :
~ ~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,choosenonempty,setunion]) ).
thf(21,plain,
( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
( ( ! [SX0: $i > $o] :
~ ~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(25,plain,
( ( ~ ~ ( ~ ( c @ sK1_SX0 )
| ~ ( sK1_SX0 @ a ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(28,plain,
( ( ~ ( ~ ( c @ sK1_SX0 )
| ~ ( sK1_SX0 @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( c @ sK1_SX0 )
| ~ ( sK1_SX0 @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ( c @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(33,plain,
( ( ~ ( sK1_SX0 @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(34,plain,
( ( c @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(35,plain,
( ( sK1_SX0 @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ~ ! [SY2: $i > $o] :
~ ~ ( ~ ( c @ SY2 )
| ~ ( SY2 @ ( eps @ SY2 ) ) )
| ~ ( ~ ( 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)],[21]) ).
thf(37,plain,
( ( ( ~ ~ ! [SY2: $i > $o] :
~ ~ ( ~ ( c @ SY2 )
| ~ ( SY2 @ ( eps @ SY2 ) ) ) )
= $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)],[36]) ).
thf(38,plain,
( ( ( ~ ! [SY2: $i > $o] :
~ ~ ( ~ ( c @ SY2 )
| ~ ( SY2 @ ( eps @ SY2 ) ) ) )
= $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)],[37]) ).
thf(39,plain,
( ( ( ! [SY2: $i > $o] :
~ ~ ( ~ ( c @ SY2 )
| ~ ( SY2 @ ( eps @ SY2 ) ) ) )
= $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)],[38]) ).
thf(40,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)],[39]) ).
thf(41,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)],[40]) ).
thf(42,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)],[41]) ).
thf(43,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)],[42]) ).
thf(44,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)],[43]) ).
thf(45,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)],[44]) ).
thf(46,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)],[45]) ).
thf(47,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)],[46]) ).
thf(48,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)],[46]) ).
thf(49,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)],[47]) ).
thf(50,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)],[48]) ).
thf(51,plain,
( ( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] : $true )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[49:[bind(SV6,$thf( ^ [SV10: $i] : $true ))]]) ).
thf(53,plain,
! [SV8: $i > $o] :
( ( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( ~ ( SV8
@ ( eps
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[49:[bind(SV6,$thf( ^ [SV7: $i] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(55,plain,
( ( ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] : $true )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[50:[bind(SV6,$thf( ^ [SV10: $i] : $true ))]]) ).
thf(57,plain,
! [SV8: $i > $o] :
( ( ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( ~ ( SV8
@ ( eps
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[50:[bind(SV6,$thf( ^ [SV7: $i] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(59,plain,
! [SV8: $i > $o] :
( ( ( SV8
@ ( eps
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
! [SV8: $i > $o] :
( ( ( SV8
@ ( eps
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( 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)],[57]) ).
thf(61,plain,
( ( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] : $true )
= $false ) ),
inference(sim,[status(thm)],[51]) ).
thf(62,plain,
( ( ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] : $true )
= $false ) ),
inference(sim,[status(thm)],[55]) ).
thf(63,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,62,61,60,59,50,49,35,34]) ).
thf(66,plain,
( ( setunion @ c @ a )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(67,plain,
( ( ! [X: $i] :
~ ( choosenonempty @ c @ X ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(68,plain,
( ( ~ ! [SX0: $i > $o] :
~ ~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66,choosenonempty,setunion]) ).
thf(69,plain,
( ( ! [SX0: $i] :
~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[67,choosenonempty,setunion]) ).
thf(72,plain,
( ( ! [SX0: $i > $o] :
~ ~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV14: $i] :
( ( ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(76,plain,
( ( ~ ~ ( ~ ( c @ sK2_SX0 )
| ~ ( sK2_SX0 @ a ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(77,plain,
! [SV14: $i] :
( ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ SV14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(80,plain,
( ( ~ ( ~ ( c @ sK2_SX0 )
| ~ ( sK2_SX0 @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(83,plain,
( ( ~ ( c @ sK2_SX0 )
| ~ ( sK2_SX0 @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
( ( ~ ( c @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(85,plain,
( ( ~ ( sK2_SX0 @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(86,plain,
( ( c @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(87,plain,
( ( sK2_SX0 @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(88,plain,
( ( ~ ~ ! [SY10: $i > $o] :
~ ~ ( ~ ( c @ SY10 )
| ~ ( SY10 @ ( eps @ SY10 ) ) )
| ~ ( ~ ( 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)],[77]) ).
thf(89,plain,
( ( ( ~ ~ ! [SY10: $i > $o] :
~ ~ ( ~ ( c @ SY10 )
| ~ ( SY10 @ ( eps @ SY10 ) ) ) )
= $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)],[88]) ).
thf(90,plain,
( ( ( ~ ! [SY10: $i > $o] :
~ ~ ( ~ ( c @ SY10 )
| ~ ( SY10 @ ( eps @ SY10 ) ) ) )
= $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)],[89]) ).
thf(91,plain,
( ( ( ! [SY10: $i > $o] :
~ ~ ( ~ ( c @ SY10 )
| ~ ( SY10 @ ( eps @ SY10 ) ) ) )
= $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)],[90]) ).
thf(92,plain,
! [SV18: $i > $o] :
( ( ( ~ ~ ( ~ ( c @ SV18 )
| ~ ( SV18 @ ( eps @ SV18 ) ) ) )
= $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)],[91]) ).
thf(93,plain,
! [SV18: $i > $o] :
( ( ( ~ ( ~ ( c @ SV18 )
| ~ ( SV18 @ ( eps @ SV18 ) ) ) )
= $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,
! [SV18: $i > $o] :
( ( ( ~ ( c @ SV18 )
| ~ ( SV18 @ ( eps @ SV18 ) ) )
= $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,
! [SV18: $i > $o] :
( ( ( ~ ( c @ SV18 ) )
= $true )
| ( ( ~ ( SV18 @ ( eps @ SV18 ) ) )
= $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)],[94]) ).
thf(96,plain,
! [SV18: $i > $o] :
( ( ( c @ SV18 )
= $false )
| ( ( ~ ( SV18 @ ( eps @ SV18 ) ) )
= $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)],[95]) ).
thf(97,plain,
! [SV18: $i > $o] :
( ( ( SV18 @ ( eps @ SV18 ) )
= $false )
| ( ( c @ SV18 )
= $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)],[96]) ).
thf(98,plain,
! [SV18: $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 @ SV18 )
= $false )
| ( ( SV18 @ ( eps @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(99,plain,
! [SV18: $i > $o] :
( ( ( ~ ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) )
= $false )
| ( ( c @ SV18 )
= $false )
| ( ( SV18 @ ( eps @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(100,plain,
! [SV18: $i > $o] :
( ( ( ~ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) ) )
= $false )
| ( ( c @ SV18 )
= $false )
| ( ( SV18 @ ( eps @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(101,plain,
! [SV18: $i > $o] :
( ( ( c
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) )
= $true )
| ( ( c @ SV18 )
= $false )
| ( ( SV18 @ ( eps @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(102,plain,
! [SV18: $i > $o] :
( ( ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX1: $i > $o] :
~ ( ~ ( c @ SX1 )
| ~ ( SX1 @ ( eps @ SX1 ) ) ) ) ) )
= $true )
| ( ( c @ SV18 )
= $false )
| ( ( SV18 @ ( eps @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(103,plain,
( ( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] : $true )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[101:[bind(SV18,$thf( ^ [SV22: $i] : $true ))]]) ).
thf(105,plain,
! [SV20: $i > $o] :
( ( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) )
= $false )
| ( ( ~ ( SV20
@ ( eps
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[101:[bind(SV18,$thf( ^ [SV19: $i] : ~ ( SV20 @ SV19 ) ))]]) ).
thf(107,plain,
( ( ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] : $true )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[102:[bind(SV18,$thf( ^ [SV22: $i] : $true ))]]) ).
thf(109,plain,
! [SV20: $i > $o] :
( ( ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) )
= $false )
| ( ( ~ ( SV20
@ ( eps
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[102:[bind(SV18,$thf( ^ [SV19: $i] : ~ ( SV20 @ SV19 ) ))]]) ).
thf(111,plain,
! [SV20: $i > $o] :
( ( ( SV20
@ ( eps
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) )
= $false )
| ( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV20: $i > $o] :
( ( ( SV20
@ ( eps
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) )
= $false )
| ( ( 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)],[109]) ).
thf(113,plain,
( ( ( c
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] : $true )
= $false ) ),
inference(sim,[status(thm)],[103]) ).
thf(114,plain,
( ( ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) )
@ ( eps
@ ( epsio
@ ^ [SX0: $i > $o] :
~ ( ~ ( c @ SX0 )
| ~ ( SX0 @ ( eps @ SX0 ) ) ) ) ) )
= $true )
| ( ( c
@ ^ [SX0: $i] : $true )
= $false ) ),
inference(sim,[status(thm)],[107]) ).
thf(115,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[77,114,113,112,111,102,101,87,86]) ).
thf(116,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[115,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV428^1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 28 01:54:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 3
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 357
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: true
% 0.13/0.35 (rf:0,axioms:3,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.38
% 0.13/0.38 *** Modified list of choice operators: eps ***
% 0.13/0.38
% 0.13/0.38 *** Modified list of choice operators: epsio, eps ***
% 0.13/0.40 .
% 0.19/0.47
% 0.19/0.47 *** Modified list of choice operators: eps ***
% 0.19/0.47
% 0.19/0.47 *** Modified list of choice operators: epsio, eps ***
% 0.19/0.48 .
% 0.19/0.54
% 0.19/0.54 ********************************
% 0.19/0.54 * All subproblems solved! *
% 0.19/0.54 ********************************
% 0.19/0.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:115,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.19/0.54
% 0.19/0.54 %**** Beginning of derivation protocol ****
% 0.19/0.54 % SZS output start CNFRefutation
% See solution above
% 0.19/0.54
% 0.19/0.54 %**** End of derivation protocol ****
% 0.19/0.54 %**** no. of clauses in derivation: 84 ****
% 0.19/0.54 %**** clause counter: 115 ****
% 0.19/0.54
% 0.19/0.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:115,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------